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Re: [bigdob] Telescopic Limiting Magnitude calculator

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  • Event Horizon
    Ok, I ll bite.... For what it s worth.   I ve not had luck with these calculators matching my observations.  I tend to see about 2 magnitudes fainter stars
    Message 1 of 26 , Jul 1, 2009
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      Ok, I'll bite.... For what it's worth.
       
      I've not had luck with these calculators matching my observations.  I tend to see about 2 magnitudes fainter stars and 1 magnitude fainter galaxies than what the calcs show when plugging in each box the numbers asked for.  I just assumed I'm at the upper end of the bell curve of vision.
       
      However, I've noticed some things about the calcs....  If I change the magnification the calc says fainter can be seen, I agree with that direction, but, still the numbers don't come close to my observations.  Now, if I change the Fully Dilated Eye Pupil Diameter box to match the exit pupil derived as a function of magnification/eyepiece/telescope I plugged in earlier, the numbers get closer, much closer, to what I currently experience for the 20" scope.  See below.
       
      20" Telescope, 511x, .99mm exit pupil at 511x yields:
       
      Telescope 




      Telescope Aperture:
      mminch

      Power:


      Telescope Type:





      Reflector
          

      Refractor
          

      Schmidt-Cassegrain

      Mirror Coatings:





      Standard 88% reflectivity    

      Enhanced 95% reflectivity

      Optics Cleanliness:





      Dirty    

      Normal    

      Clean

       Observer 



      Fully dilated Eye Pupil Diameter:

      mm
          OR    
      Your Age:

      years



      Experience:  




      Novice





      Expert

       Sky Conditions 



      Naked Eye Limiting Magnitude near the Zenith:

          OR    
      SQM Reading:

      mag/sec²



      Seeing Disk Diameter:

      arc seconds
            
      Color Index of Star:


      Zenith Distance:

      degrees

      Extinction:

      mag/atm






        
      The estimated Telescopic Limiting Magnitude is 20.1
       
      I now agree with the calc numbers for the 20" to a first order.  But I had to screw around with it to get there.
       
      Based upon my observations with the 20" I had estimated what limit I'd get to in my 36".  My estimate was low 21st magnitude.  The calc does not work in its current fashion, if using it by filling in all the numbers as requested, it says I'd see what I see in the 20" currently.
       
      However, if I apply this new Fully Dilated Eye Pupil Diameter box to match the Exit Pupil Derived as a function of magnification/eyepiece/telescope and making the appropriate changes in exit pupil along with its associated magnification with that combination, it once again comes close to increasing the aperture by 3.24x by having gone from a 20 to 36".  See below.
       
      Telescope 



      Telescope Aperture:
      mminch

      Power:


      Telescope Type:





      Reflector
          

      Refractor
          

      Schmidt-Cassegrain

      Mirror Coatings:





      Standard 88% reflectivity    

      Enhanced 95% reflectivity

      Optics Cleanliness:





      Dirty    

      Normal    

      Clean
       Observer 



      Fully dilated Eye Pupil Diameter:

      mm
          OR    
      Your Age:

      years



      Experience:  




      Novice





      Expert

       Sky Conditions 



      Naked Eye Limiting Magnitude near the Zenith:

          OR    
      SQM Reading:

      mag/sec²



      Seeing Disk Diameter:

      arc seconds
            
      Color Index of Star:


      Zenith Distance:

      degrees

      Extinction:

      mag/atm






        
      The estimated Telescopic Limiting Magnitude is 21.4
       
      It would seem that not just one but two mag limits are needed, low power and high power.  Low power associated with the fully dilated pupil, and the High Power calc associated with the exit puil of having used high power.  The new 'Low Power Telescopic Limiting Magnitude box' is needed linked to the Fully dilated Eye Pupil Diameter.  And, change the current Telescopic Limiting Magnitude box to 'High Power Telescopic Limiting Magnitude, linking it to the smaller exit pupil and associated higher power.
       
      It would seem that making the change to use of the exit pupil does not break any rules since I don't think it requires my iris to be an aperture stop in the system when the exit pupil of an eyepiece is just as defined an area.
       
      At a minimum, I've found a way of getting the calc to match me.
      Best regards,
      Steven
      http://darkskyobserving.com/




      [Non-text portions of this message have been removed]
    • Event Horizon
      Well, the copied formatting from the mag cac site did not transfer like it looked when I pasted it in my email, but, the two conditions are:   20 Telescope,
      Message 2 of 26 , Jul 1, 2009
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        Well, the copied formatting from the mag cac site did not transfer like it looked when I pasted it in my email, but, the two conditions are:
         
        20" Telescope, 511x, .99mm exit pupil at 511x yields a 20.1 mag limit
        And, 36" Telescope 985x, 0.93mm exit pupil at 985x yields a 21.4 mag limit
         
        Basically keeping the exit pupil linked to the calc matches the observations.
        Regards, Steven

        --- On Wed, 7/1/09, Event Horizon <eventhorizon2112@...> wrote:


        From: Event Horizon <eventhorizon2112@...>
        Subject: Re: [bigdob] Telescopic Limiting Magnitude calculator
        To: bigdob@yahoogroups.com
        Date: Wednesday, July 1, 2009, 9:09 AM








        Ok, I'll bite.... For what it's worth.
         
        I've not had luck with these calculators matching my observations.  I tend to see about 2 magnitudes fainter stars and 1 magnitude fainter galaxies than what the calcs show when plugging in each box the numbers asked for.  I just assumed I'm at the upper end of the bell curve of vision.
         
        However, I've noticed some things about the calcs....  If I change the magnification the calc says fainter can be seen, I agree with that direction, but, still the numbers don't come close to my observations.  Now, if I change the Fully Dilated Eye Pupil Diameter box to match the exit pupil derived as a function of magnification/ eyepiece/ telescope I plugged in earlier, the numbers get closer, much closer, to what I currently experience for the 20" scope.  See below.
         
        20" Telescope, 511x, .99mm exit pupil at 511x yields:
         The estimated Telescopic Limiting Magnitude is 20.1
         
        I now agree with the calc numbers for the 20" to a first order.  But I had to screw around with it to get there.
         
        Based upon my observations with the 20" I had estimated what limit I'd get to in my 36".  My estimate was low 21st magnitude.  The calc does not work in its current fashion, if using it by filling in all the numbers as requested, it says I'd see what I see in the 20" currently.
         
        However, if I apply this new Fully Dilated Eye Pupil Diameter box to match the Exit Pupil Derived as a function of magnification/ eyepiece/ telescope  and making the appropriate changes in exit pupil along with its associated magnification with that combination, it once again comes close to increasing the aperture by 3.24x by having gone from a 20 to 36".  See below.
         
        36" Telescope 985x, 0.93mm exit pupil at 985x yields
        The estimated Telescopic Limiting Magnitude is 21.4
         
        It would seem that not just one but two mag limits are needed, low power and high power.  Low power associated with the fully dilated pupil, and the High Power calc associated with the exit puil of having used high power.  The new 'Low Power Telescopic Limiting Magnitude box'  is needed linked to the Fully dilated Eye Pupil Diameter.  And, change the current Telescopic Limiting Magnitude box to 'High Power Telescopic Limiting Magnitude, linking it to the smaller exit pupil and associated higher power.
         
        It would seem that making the change to use of the exit pupil does not break any rules since I don't think it requires my iris to be an aperture stop in the system when the exit pupil of an eyepiece is just as defined an area.
         
        At a minimum, I've found a way of getting the calc to match me.
        Best regards,
        Steven
        http://darkskyobser ving.com/

        [Non-text portions of this message have been removed]



















        [Non-text portions of this message have been removed]
      • Robert Houdart
        Steven, You must be very experienced observer with excellent eyesight at a pristine location. Very few people reach magnitude 20 with a 20 scope. Your numbers
        Message 3 of 26 , Jul 1, 2009
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          Steven,

          You must be very experienced observer with excellent eyesight at a pristine
          location. Very few people reach magnitude 20 with a 20" scope.

          Your numbers are at the extreme end of the scale, about as impressive than
          O'Meara's famous visually recovery of Halley's comet in 1985, at the time a
          mag 19.1 object, with a 24" scope. He was breathing bottled pure oxygen on
          the top of Mauna Kea.

          Your using the Pupil Diameter of the telescopic observations changes the
          rules, because it's supposed to be the Pupil corresponding to the NELM
          estimate. It makes more sense to modify the NELM to take into account the
          outstanding nature of your observations. Using a NELM of 9.0 (!!) appears to
          produce the correct results for your case.

          For the 20", 511X, Enhanced coatings, Clean Optics, 6 mm pupil, Expert, NELM
          9.0, Extinction 0.15 mag/atm, the result is mag 20.1. For the 36" at 985X
          the result is mag 21.4.

          I doubt that somebody else on this list comes even close...

          Robert



          -----Oorspronkelijk bericht-----
          Van: bigdob@yahoogroups.com [mailto:bigdob@yahoogroups.com] Namens Event
          Horizon
          Verzonden: woensdag 1 juli 2009 18:24
          Aan: bigdob@yahoogroups.com
          Onderwerp: Re: [bigdob] Telescopic Limiting Magnitude calculator

          Well, the copied formatting from the mag cac site did not transfer like it
          looked when I pasted it in my email, but, the two conditions are:
           
          20" Telescope, 511x, .99mm exit pupil at 511x yields a 20.1 mag limit
          And, 36" Telescope 985x, 0.93mm exit pupil at 985x yields a 21.4 mag limit
           
          Basically keeping the exit pupil linked to the calc matches the
          observations.
          Regards, Steven
        • Nils Olof Carlin
          Steven You will find Schaefer s original article at:
          Message 4 of 26 , Jul 1, 2009
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            Steven

            You will find Schaefer's original article at:

            http://adsbit.harvard.edu/cgi-bin/nph-iarticle_query?bibcode=1990PASP..102..212S&db_key=AST&page_ind=0&plate_select=NO&data_type=GIF&type=SCREEN_GIF

            or

            http://tinyurl.com/3nc8y9

            You will find (apart from a piece of not so easy reading ;-) that Schaefer
            corrects for the light loss by comparing the exit pupil to the eye pupil and
            adjust for light losses if the former is greater - which it usually isn't,
            unless you deliberately go for the widest possible field and waste aperture
            in the process. See p. 213, eq. (6). So there should be no need for you to
            do any other adjustment for pupil size.

            >>>Now, if I change the Fully Dilated Eye Pupil Diameter box to match the
            >>>exit pupil derived as a function of magnification/ eyepiece/ telescope I
            >>>plugged in earlier, the numbers get closer, much closer, to what I
            >>>currently experience for the 20" scope.>>>

            Changing the fully dilated eye pupil diameter can have unexpected
            consequences due to a quirk in Schaefer's model - the sensitivity according
            to the equation (2) does not allow for the pupil diameter (as it reasonably
            should - as it stands, the sensitivity of the retina would appear to
            increase as the fully dilated eye pupil size decreases with age - hardly
            reasonable (if anything, due to the yellowing of the eye pupil with age,
            particularly the blue sensitivity would fall). Entering a smaller value than
            the true eye pupil would thus make the eye sensitivity appear much higher.
            This is not negligible - a 5 mm eye pupil will have appr. half the light
            collecting area, and thus 0.75 mags loss of sensitivity compared to a 7 mm
            pupil in front of an equally sensitive retina. In reality, the difference
            will be less, since the background appears darker, as well as the star.

            This is one of the points I discuss in
            http://web.telia.com/~u41105032/visual/Schaefer.htm


            Nils Olof



















            [Non-text portions of this message have been removed]



            ------------------------------------

            Yahoo! Groups Links
          • Event Horizon
            Hi Robert, I have been at this observing thing for a while.  With the things I ve seen I d say, given my vision, scopes, nights of exceptional seeing, that I
            Message 5 of 26 , Jul 1, 2009
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              Hi Robert, I have been at this observing thing for a while.  With the things I've seen I'd say, given my vision, scopes, nights of exceptional seeing, that I am/have been fortunate as Stephen O'Meara's been.
               
              These calc's are not accurate the way they're currently set up but should be theoretical, "best case" with regard to seeing, and therefore I've not 'seen' 20.1mag in the 20" but I've seen galaxies and globulars at 18+, in other words non-stellar to 18+.  Stellar, much more point-source than non-stellar to 18.5 to 19.  Though considered neither of these, the detail in the spokes on Saturn's rings in the 20" was astounding one night. 
               
              The generally published (and accepted) magnitudes of the five galaxies in Hickson 50 (from brightest to dimmest) are 18.7, 18.9, 19.5, 19.6 and 20.0. According to some online accounts, some astronomers have claimed to have viewed the two brightest ones through the eyepiece using telescopes of at least 20-inches in aperture (not me).  With the 36" I see five galaxies in Hickson 50.  These are non-stellar, therefore the stellar limit should be fainter as point-sources.  My previous ecperience with non-stellar and stellar is roughly one magnitude.  Adding one magnitude to the faintest Hickson 50 galaxy gets to 21, which is still below the modified calc value and inline with observations of the 20" and then scaling up for the increased reflecting surface area of the 36".
               
              For both scopes I'm not above the atmosphere, just 6000' in a high elevation desert.  Either case my observations are much fainter than plugging in the asked-for values and brighter than theoretical.  Darn that atmosphere anyhow....
               
              I've only suggested a modification to include a parameter related to exit pupil at high power, which seems reasonable to me, which puts my observations inline with a parameter not included; 'seeing'.  I think if the seeing of those nights had been better then fainter was still possible.
               
              Steven

              --- On Wed, 7/1/09, Robert Houdart <robert.houdart@...> wrote:


              From: Robert Houdart <robert.houdart@...>
              Subject: RE: [bigdob] Telescopic Limiting Magnitude calculator
              To: bigdob@yahoogroups.com
              Date: Wednesday, July 1, 2009, 10:23 AM








              Steven,

              You must be very experienced observer with excellent eyesight at a pristine
              location. Very few people reach magnitude 20 with a 20" scope.

              Your numbers are at the extreme end of the scale, about as impressive than
              O'Meara's famous visually recovery of Halley's comet in 1985, at the time a
              mag 19.1 object, with a 24" scope. He was breathing bottled pure oxygen on
              the top of Mauna Kea.

              Your using the Pupil Diameter of the telescopic observations changes the
              rules, because it's supposed to be the Pupil corresponding to the NELM
              estimate. It makes more sense to modify the NELM to take into account the
              outstanding nature of your observations. Using a NELM of 9.0 (!!) appears to
              produce the correct results for your case.

              For the 20", 511X, Enhanced coatings, Clean Optics, 6 mm pupil, Expert, NELM
              9.0, Extinction 0.15 mag/atm, the result is mag 20.1. For the 36" at 985X
              the result is mag 21.4.

              I doubt that somebody else on this list comes even close...

              Robert

              -----Oorspronkelijk bericht-----
              Van: bigdob@yahoogroups. com [mailto:bigdob@yahoogroups. com] Namens Event
              Horizon
              Verzonden: woensdag 1 juli 2009 18:24
              Aan: bigdob@yahoogroups. com
              Onderwerp: Re: [bigdob] Telescopic Limiting Magnitude calculator

              Well, the copied formatting from the mag cac site did not transfer like it
              looked when I pasted it in my email, but, the two conditions are:
               
              20" Telescope, 511x, .99mm exit pupil at 511x yields a 20.1 mag limit
              And, 36" Telescope 985x, 0.93mm exit pupil at 985x yields a 21.4 mag limit
               
              Basically keeping the exit pupil linked to the calc matches the
              observations.
              Regards, Steven



















              [Non-text portions of this message have been removed]
            • Event Horizon
              Thanks, if there are adverse effects by altering the exit pupil for having used high power, though the result comes closer to my observations and puts the
              Message 6 of 26 , Jul 1, 2009
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                Thanks, if there are adverse effects by altering the exit pupil for having used high power, though the result comes closer to my observations and puts the limit only slightly beyond the observations, that leaves me with my original premise; the calc's don't work for me.  I'm still ok with that.  As with any night it's: Let's see what I see tonight....
                 
                Steven

                --- On Wed, 7/1/09, Nils Olof Carlin <nilsolof.carlin@...> wrote:


                From: Nils Olof Carlin <nilsolof.carlin@...>
                Subject: Re: [bigdob] Telescopic Limiting Magnitude calculator
                To: bigdob@yahoogroups.com
                Date: Wednesday, July 1, 2009, 10:49 AM








                Steven

                You will find Schaefer's original article at:

                http://adsbit. harvard.edu/ cgi-bin/nph- iarticle_ query?bibcode= 1990PASP. .102..212S& db_key=AST& page_ind= 0&plate_select= NO&data_type= GIF&type= SCREEN_GIF

                or

                http://tinyurl. com/3nc8y9

                You will find (apart from a piece of not so easy reading ;-) that Schaefer
                corrects for the light loss by comparing the exit pupil to the eye pupil and
                adjust for light losses if the former is greater - which it usually isn't,
                unless you deliberately go for the widest possible field and waste aperture
                in the process. See p. 213, eq. (6). So there should be no need for you to
                do any other adjustment for pupil size.

                >>>Now, if I change the Fully Dilated Eye Pupil Diameter box to match the
                >>>exit pupil derived as a function of magnification/ eyepiece/ telescope I
                >>>plugged in earlier, the numbers get closer, much closer, to what I
                >>>currently experience for the 20" scope.>>>

                Changing the fully dilated eye pupil diameter can have unexpected
                consequences due to a quirk in Schaefer's model - the sensitivity according
                to the equation (2) does not allow for the pupil diameter (as it reasonably
                should - as it stands, the sensitivity of the retina would appear to
                increase as the fully dilated eye pupil size decreases with age - hardly
                reasonable (if anything, due to the yellowing of the eye pupil with age,
                particularly the blue sensitivity would fall). Entering a smaller value than
                the true eye pupil would thus make the eye sensitivity appear much higher.
                This is not negligible - a 5 mm eye pupil will have appr. half the light
                collecting area, and thus 0.75 mags loss of sensitivity compared to a 7 mm
                pupil in front of an equally sensitive retina. In reality, the difference
                will be less, since the background appears darker, as well as the star.

                This is one of the points I discuss in
                http://web.telia. com/~u41105032/ visual/Schaefer. htm

                Nils Olof

                [Non-text portions of this message have been removed]

                ------------ --------- --------- ------

                Yahoo! Groups Links



















                [Non-text portions of this message have been removed]
              • pensack1
                By modifying the html for Bogen s Schaefer-derived to correspond to the correct reflectivity of my telescope s mirrors, and also modifying the pupil diameter
                Message 7 of 26 , Jul 1, 2009
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                  By modifying the html for Bogen's Schaefer-derived to correspond to the correct reflectivity of my telescope's mirrors, and also modifying the pupil diameter calculator to correspond with my own reality, I have tested the calculator using 5" and 8" cats and a 12.5" newtonian. Using the parameter of a stellar source, visible at least 10% of the time, I have reached the limits predicted in each of those scopes to around 0.1 magnitude. Kudos to the predictability of Schaefer's work.

                  For me, that says the limit calculated is just about right for my 8350' site, with SQM limits of about 21.5mpsas.
                  [By the way, NELM is a visual-acuity-related figure, and varies so widely with observers at the same site and on the same night, that I no longer feel it is a relevant figure for a group of people or for describing the darkness of a site. It IS relevant for a single individual keeping records over time, but I have done "group finds" on the same night and gotten figures from 5.5 to past 8 in a group of 10 people. In contrast, all the people could see approximately the same limit in the scope with a 1mm exit pupil.]
                  I have been observing 46 years, so my age and yellowness of the lenses in my eyes must have a deleterious effect. So it is easy for me to believe a younger person may reach a different limit at a more pristine site. Indeed, when I adjust for the site and sky conditions, I should have reached to past 17.5 in the 12.5" instead of the "just past 17" that I have reached a few separate times.

                  Sadly, nearly every limiting magnitude chart I've seen published is about what one would expect for a rank beginner using dirty optics.
                  Perhaps that's just so the beginner won't be discouraged?

                  But as all the readers of this site know, there is a wide variation from observer to observer.

                  Don Pensack
                  Los Angeles

                  Extended objects are entirely different, however. And I do not believe the Schaefer-derived calculators can be predictive of limits for them. There are simply too many variables not taken into account for these calculators to work there.



                  --- In bigdob@yahoogroups.com, Event Horizon <eventhorizon2112@...> wrote:
                  >
                  > Thanks, if there are adverse effects by altering the exit pupil for having used high power, though the result comes closer to my observations and puts the limit only slightly beyond the observations, that leaves me with my original premise; the calc's don't work for me.  I'm still ok with that.  As with any night it's: Let's see what I see tonight....
                  >  
                  > Steven
                  >
                  > --- On Wed, 7/1/09, Nils Olof Carlin <nilsolof.carlin@...> wrote:
                  >
                  >
                  > From: Nils Olof Carlin <nilsolof.carlin@...>
                  > Subject: Re: [bigdob] Telescopic Limiting Magnitude calculator
                  > To: bigdob@yahoogroups.com
                  > Date: Wednesday, July 1, 2009, 10:49 AM
                  >
                  >
                  >
                  >
                  >
                  >
                  >
                  >
                  > Steven
                  >
                  > You will find Schaefer's original article at:
                  >
                  > http://adsbit. harvard.edu/ cgi-bin/nph- iarticle_ query?bibcode= 1990PASP. .102..212S& db_key=AST& page_ind= 0&plate_select= NO&data_type= GIF&type= SCREEN_GIF
                  >
                  > or
                  >
                  > http://tinyurl. com/3nc8y9
                  >
                  > You will find (apart from a piece of not so easy reading ;-) that Schaefer
                  > corrects for the light loss by comparing the exit pupil to the eye pupil and
                  > adjust for light losses if the former is greater - which it usually isn't,
                  > unless you deliberately go for the widest possible field and waste aperture
                  > in the process. See p. 213, eq. (6). So there should be no need for you to
                  > do any other adjustment for pupil size.
                  >
                  > >>>Now, if I change the Fully Dilated Eye Pupil Diameter box to match the
                  > >>>exit pupil derived as a function of magnification/ eyepiece/ telescope I
                  > >>>plugged in earlier, the numbers get closer, much closer, to what I
                  > >>>currently experience for the 20" scope.>>>
                  >
                  > Changing the fully dilated eye pupil diameter can have unexpected
                  > consequences due to a quirk in Schaefer's model - the sensitivity according
                  > to the equation (2) does not allow for the pupil diameter (as it reasonably
                  > should - as it stands, the sensitivity of the retina would appear to
                  > increase as the fully dilated eye pupil size decreases with age - hardly
                  > reasonable (if anything, due to the yellowing of the eye pupil with age,
                  > particularly the blue sensitivity would fall). Entering a smaller value than
                  > the true eye pupil would thus make the eye sensitivity appear much higher.
                  > This is not negligible - a 5 mm eye pupil will have appr. half the light
                  > collecting area, and thus 0.75 mags loss of sensitivity compared to a 7 mm
                  > pupil in front of an equally sensitive retina. In reality, the difference
                  > will be less, since the background appears darker, as well as the star.
                  >
                  > This is one of the points I discuss in
                  > http://web.telia. com/~u41105032/ visual/Schaefer. htm
                  >
                  > Nils Olof
                  >
                  > [Non-text portions of this message have been removed]
                  >
                  > ------------ --------- --------- ------
                  >
                  > Yahoo! Groups Links
                  >
                  >
                  >
                  >
                  >
                  >
                  >
                  >
                  >
                  >
                  >
                  >
                  >
                  >
                  >
                  >
                  >
                  >
                  >
                  > [Non-text portions of this message have been removed]
                  >
                • eventhorizon2112@yahoo.com
                  Well, I don t know if I m NELM of 9.0.  It s high for sure as I can still use an eyepiece combo that produces 8.7mm exit pupil and my iris does not
                  Message 8 of 26 , Jul 1, 2009
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                    Well, I don't know if I'm NELM of 9.0.  It's high for sure as I can still use an eyepiece combo that produces 8.7mm exit pupil and my iris does not vignette, given that naked-eye limiting factors are retinal accuity, eye aperture, plus that nasty atmosphere.  I'm still holding out hope for a 41mm Nagler while I can still use one.
                     
                    I do know that when others are stumbling around the observing area stating how "...black things are tonight, this is a great site!", I see the extension cord they trip on and can pick up my dropped pen clearly visible in the grass or dirt.
                     
                    So is there a calc with other, better adjustment boxes?
                     
                    Thanks, Steven
                     

                    --- On Wed, 7/1/09, Robert Houdart <robert.houdart@...> wrote:


                    From: Robert Houdart <robert.houdart@...>
                    Subject: RE: [bigdob] Telescopic Limiting Magnitude calculator
                    To: bigdob@yahoogroups.com
                    Date: Wednesday, July 1, 2009, 10:23 AM








                    Steven,

                    You must be very experienced observer with excellent eyesight at a pristine
                    location. Very few people reach magnitude 20 with a 20" scope.

                    Your numbers are at the extreme end of the scale, about as impressive than
                    O'Meara's famous visually recovery of Halley's comet in 1985, at the time a
                    mag 19.1 object, with a 24" scope. He was breathing bottled pure oxygen on
                    the top of Mauna Kea.

                    Your using the Pupil Diameter of the telescopic observations changes the
                    rules, because it's supposed to be the Pupil corresponding to the NELM
                    estimate. It makes more sense to modify the NELM to take into account the
                    outstanding nature of your observations. Using a NELM of 9.0 (!!) appears to
                    produce the correct results for your case.

                    For the 20", 511X, Enhanced coatings, Clean Optics, 6 mm pupil, Expert, NELM
                    9.0, Extinction 0.15 mag/atm, the result is mag 20.1. For the 36" at 985X
                    the result is mag 21.4.

                    I doubt that somebody else on this list comes even close...

                    Robert

                    -----Oorspronkelijk bericht-----
                    Van: bigdob@yahoogroups. com [mailto:bigdob@yahoogroups. com] Namens Event
                    Horizon
                    Verzonden: woensdag 1 juli 2009 18:24
                    Aan: bigdob@yahoogroups. com
                    Onderwerp: Re: [bigdob] Telescopic Limiting Magnitude calculator

                    Well, the copied formatting from the mag cac site did not transfer like it
                    looked when I pasted it in my email, but, the two conditions are:
                     
                    20" Telescope, 511x, .99mm exit pupil at 511x yields a 20.1 mag limit
                    And, 36" Telescope 985x, 0.93mm exit pupil at 985x yields a 21.4 mag limit
                     
                    Basically keeping the exit pupil linked to the calc matches the
                    observations.
                    Regards, Steven



















                    [Non-text portions of this message have been removed]
                  • Nils Olof Carlin
                    Don, While I m well familiar with Schaefer s 1990 paper, the 1998 article in S&T seems to be missing from my collection, and I don t know the details of
                    Message 9 of 26 , Jul 2, 2009
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                      Don,

                      While I'm well familiar with Schaefer's 1990 paper, the 1998 article in S&T
                      seems to be missing from my collection, and I don't know the details of
                      neither Bogen's nor Robert's calculators and their algorithms. So,
                      considering the quirk (or worse) in Schaefer's application of the
                      sensitivity equation (of Knoll et al) that I described, I wonder how your
                      "modifying the pupil diameter calculator to correspond with my own reality"
                      was done. Perhaps like what Steven just described, artificially adjusting
                      the retinal sensitivity by entering a downsized eye pupil value?

                      I don't know the details of how the Knoll data were obtained (or even how
                      his equation fits the experimental data), but Blackwell defines his
                      threshold as "corresponding to a probability of 50 percent, due allowance
                      having been made for chance success ". If Knoll's data are comparable in
                      this respect, the limiting magnitude for careful star observation with no
                      time limit, where the object is seen only intermittently, should be
                      (numerically) significantly higher. In the 1990 article, this can be
                      adjusted for by an "experience" term, awarding about 0.5 mag. advantage over
                      the average for a very experienced observer trained in such a technique -
                      this term is included in Bogen's but not in Houdart's calculator, I believe.

                      As for common magnitude limiting charts, I suspect they just re-calculate to
                      correspond to a naked-eye limit of mag 6 or so (by direct vision) - thus
                      playing it safe by disregarding the effects of high magnification and
                      training in using averted vision.

                      As for extended objects, Blackwell's data will give some guidance, but the
                      light distribution within deep-sky objects seldom correspond well to the
                      disc-shaped test objects used - the Owl nebula may, but then again the line
                      spectra of gaseous nebulae make their apparent brightness to averted vision
                      difficult (but not impossible) to estimate.

                      Nils Olof

                      >>>By modifying the html for Bogen's Schaefer-derived to correspond to the
                      >>>correct reflectivity of my telescope's mirrors, and also modifying the
                      >>>pupil diameter calculator to correspond with my own reality, I have
                      >>>tested the calculator using 5" and 8" cats and a 12.5" newtonian. Using
                      >>>the parameter of a stellar source, visible at least 10% of the time, I
                      >>>have reached the limits predicted in each of those scopes to around 0.1
                      >>>magnitude. Kudos to the predictability of Schaefer's work.

                      For me, that says the limit calculated is just about right for my 8350'
                      site, with SQM limits of about 21.5mpsas.
                      [By the way, NELM is a visual-acuity-related figure, and varies so widely
                      with observers at the same site and on the same night, that I no longer feel
                      it is a relevant figure for a group of people or for describing the darkness
                      of a site. It IS relevant for a single individual keeping records over
                      time, but I have done "group finds" on the same night and gotten figures
                      from 5.5 to past 8 in a group of 10 people. In contrast, all the people
                      could see approximately the same limit in the scope with a 1mm exit pupil.]
                      I have been observing 46 years, so my age and yellowness of the lenses in my
                      eyes must have a deleterious effect. So it is easy for me to believe a
                      younger person may reach a different limit at a more pristine site. Indeed,
                      when I adjust for the site and sky conditions, I should have reached to past
                      17.5 in the 12.5" instead of the "just past 17" that I have reached a few
                      separate times.

                      Sadly, nearly every limiting magnitude chart I've seen published is about
                      what one would expect for a rank beginner using dirty optics.
                      Perhaps that's just so the beginner won't be discouraged?

                      But as all the readers of this site know, there is a wide variation from
                      observer to observer.

                      Don Pensack
                      Los Angeles

                      Extended objects are entirely different, however. And I do not believe the
                      Schaefer-derived calculators can be predictive of limits for them. There
                      are simply too many variables not taken into account for these calculators
                      to work there.



                      --- In bigdob@yahoogroups.com, Event Horizon <eventhorizon2112@...> wrote:
                      >
                      > Thanks, if there are adverse effects by altering the exit pupil for having
                      > used high power, though the result comes closer to my observations and
                      > puts the limit only slightly beyond the observations, that leaves me with
                      > my original premise; the calc's don't work for me. I'm still ok with that.
                      > As with any night it's: Let's see what I see tonight....
                      >
                      > Steven
                      >
                      > --- On Wed, 7/1/09, Nils Olof Carlin <nilsolof.carlin@...> wrote:
                      >
                      >
                      > From: Nils Olof Carlin <nilsolof.carlin@...>
                      > Subject: Re: [bigdob] Telescopic Limiting Magnitude calculator
                      > To: bigdob@yahoogroups.com
                      > Date: Wednesday, July 1, 2009, 10:49 AM
                      >
                      >
                      >
                      >
                      >
                      >
                      >
                      >
                      > Steven
                      >
                      > You will find Schaefer's original article at:
                      >
                      > http://adsbit. harvard.edu/ cgi-bin/nph- iarticle_ query?bibcode=
                      > 1990PASP. .102..212S& db_key=AST& page_ind= 0&plate_select= NO&data_type=
                      > GIF&type= SCREEN_GIF
                      >
                      > or
                      >
                      > http://tinyurl. com/3nc8y9
                      >
                      > You will find (apart from a piece of not so easy reading ;-) that Schaefer
                      > corrects for the light loss by comparing the exit pupil to the eye pupil
                      > and
                      > adjust for light losses if the former is greater - which it usually isn't,
                      > unless you deliberately go for the widest possible field and waste
                      > aperture
                      > in the process. See p. 213, eq. (6). So there should be no need for you to
                      > do any other adjustment for pupil size.
                      >
                      > >>>Now, if I change the Fully Dilated Eye Pupil Diameter box to match the
                      > >>>exit pupil derived as a function of magnification/ eyepiece/ telescope
                      > >>>I
                      > >>>plugged in earlier, the numbers get closer, much closer, to what I
                      > >>>currently experience for the 20" scope.>>>
                      >
                      > Changing the fully dilated eye pupil diameter can have unexpected
                      > consequences due to a quirk in Schaefer's model - the sensitivity
                      > according
                      > to the equation (2) does not allow for the pupil diameter (as it
                      > reasonably
                      > should - as it stands, the sensitivity of the retina would appear to
                      > increase as the fully dilated eye pupil size decreases with age - hardly
                      > reasonable (if anything, due to the yellowing of the eye pupil with age,
                      > particularly the blue sensitivity would fall). Entering a smaller value
                      > than
                      > the true eye pupil would thus make the eye sensitivity appear much higher.
                      > This is not negligible - a 5 mm eye pupil will have appr. half the light
                      > collecting area, and thus 0.75 mags loss of sensitivity compared to a 7 mm
                      > pupil in front of an equally sensitive retina. In reality, the difference
                      > will be less, since the background appears darker, as well as the star.
                      >
                      > This is one of the points I discuss in
                      > http://web.telia. com/~u41105032/ visual/Schaefer. htm
                      >
                      > Nils Olof
                      >
                      > [Non-text portions of this message have been removed]
                      >
                      > ------------ --------- --------- ------
                      >
                      > Yahoo! Groups Links
                      >
                      >
                      >
                      >
                      >
                      >
                      >
                      >
                      >
                      >
                      >
                      >
                      >
                      >
                      >
                      >
                      >
                      >
                      >
                      > [Non-text portions of this message have been removed]
                      >




                      ------------------------------------

                      Yahoo! Groups Links
                    • Nils Olof Carlin
                      Don, While I m well familiar with Schaefer s 1990 paper, the 1998 article in S&T seems to be missing from my collection, and I don t know the details of
                      Message 10 of 26 , Jul 2, 2009
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                        Don,

                        While I'm well familiar with Schaefer's 1990 paper, the 1998 article in S&T
                        seems to be missing from my collection, and I don't know the details of
                        neither Bogen's nor Robert's calculators and their algorithms. So,
                        considering the quirk (or worse) in Schaefer's application of the
                        sensitivity equation (of Knoll et al) that I described, I wonder how your
                        "modifying the pupil diameter calculator to correspond with my own reality"
                        was done. Perhaps like what Steven just described, artificially adjusting
                        the retinal sensitivity by entering a downsized eye pupil value?

                        I don't know the details of how the Knoll data were obtained (or even how
                        his equation fits the experimental data), but Blackwell defines his
                        threshold as "corresponding to a probability of 50 percent, due allowance
                        having been made for chance success ". If Knoll's data are comparable in
                        this respect, the limiting magnitude for careful star observation with no
                        time limit, where the object is seen only intermittently, should be
                        (numerically) significantly higher. In the 1990 article, this can be
                        adjusted for by an "experience" term, awarding about 0.5 mag. advantage over
                        the average for a very experienced observer trained in such a technique -
                        this term is included in Bogen's and Houdart's calculators and seems to give
                        about 0.6 mag advantage from "mid-position" to "expert".

                        As for common magnitude limiting charts, I suspect they just re-calculate to
                        correspond to a naked-eye limit of mag 6 or so (by direct vision) - thus
                        playing it safe by disregarding the effects of high magnification and
                        training in using averted vision.

                        As for extended objects, Blackwell's data will give some guidance, but the
                        light distribution within deep-sky objects seldom correspond well to the
                        disc-shaped test objects used - the Owl nebula may, but then again the line
                        spectra of gaseous nebulae make their apparent brightness to averted vision
                        difficult (but not impossible) to estimate.

                        Nils Olof

                        >>>By modifying the html for Bogen's Schaefer-derived to correspond to the
                        >>>correct reflectivity of my telescope's mirrors, and also modifying the
                        >>>pupil diameter calculator to correspond with my own reality, I have
                        >>>tested the calculator using 5" and 8" cats and a 12.5" newtonian. Using
                        >>>the parameter of a stellar source, visible at least 10% of the time, I
                        >>>have reached the limits predicted in each of those scopes to around 0.1
                        >>>magnitude. Kudos to the predictability of Schaefer's work.

                        For me, that says the limit calculated is just about right for my 8350'
                        site, with SQM limits of about 21.5mpsas.
                        [By the way, NELM is a visual-acuity-related figure, and varies so widely
                        with observers at the same site and on the same night, that I no longer feel
                        it is a relevant figure for a group of people or for describing the darkness
                        of a site. It IS relevant for a single individual keeping records over
                        time, but I have done "group finds" on the same night and gotten figures
                        from 5.5 to past 8 in a group of 10 people. In contrast, all the people
                        could see approximately the same limit in the scope with a 1mm exit pupil.]
                        I have been observing 46 years, so my age and yellowness of the lenses in my
                        eyes must have a deleterious effect. So it is easy for me to believe a
                        younger person may reach a different limit at a more pristine site. Indeed,
                        when I adjust for the site and sky conditions, I should have reached to past
                        17.5 in the 12.5" instead of the "just past 17" that I have reached a few
                        separate times.

                        Sadly, nearly every limiting magnitude chart I've seen published is about
                        what one would expect for a rank beginner using dirty optics.
                        Perhaps that's just so the beginner won't be discouraged?

                        But as all the readers of this site know, there is a wide variation from
                        observer to observer.

                        Don Pensack
                        Los Angeles

                        Extended objects are entirely different, however. And I do not believe the
                        Schaefer-derived calculators can be predictive of limits for them. There
                        are simply too many variables not taken into account for these calculators
                        to work there.

                        > Changing the fully dilated eye pupil diameter can have unexpected
                        > consequences due to a quirk in Schaefer's model - the sensitivity
                        > according
                        > to the equation (2) does not allow for the pupil diameter (as it
                        > reasonably
                        > should - as it stands, the sensitivity of the retina would appear to
                        > increase as the fully dilated eye pupil size decreases with age - hardly
                        > reasonable (if anything, due to the yellowing of the eye pupil with age,
                        > particularly the blue sensitivity would fall). Entering a smaller value
                        > than
                        > the true eye pupil would thus make the eye sensitivity appear much higher.
                        > This is not negligible - a 5 mm eye pupil will have appr. half the light
                        > collecting area, and thus 0.75 mags loss of sensitivity compared to a 7 mm
                        > pupil in front of an equally sensitive retina. In reality, the difference
                        > will be less, since the background appears darker, as well as the star.
                        >
                        > This is one of the points I discuss in
                        > http://web.telia com/~u41105032/ visual/Schaefer. htm
                        >
                        > Nils Olof
                      • Nils Olof Carlin
                        Sorry about the double messages - the difference was that in the first version, I incorrectly stated that the experience factor was not included in Robert
                        Message 11 of 26 , Jul 2, 2009
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                          Sorry about the double messages - the difference was that in the first
                          version, I incorrectly stated that the experience factor was not included in
                          Robert Houdart's calculator - my apologies

                          Nils Olof

                          > In the 1990 article, this can be
                          > adjusted for by an "experience" term, awarding about 0.5 mag. advantage
                          > over
                          > the average for a very experienced observer trained in such a technique -
                          > this term is included in Bogen's and Houdart's calculators and seems to
                          > give
                          > about 0.6 mag advantage from "mid-position" to "expert".
                        • bob_hill12000
                          Hi Robert, Steven s experience with his 20 matches mine with my 20. When going after some of the very dim targets that I do, I have seen that I can detect
                          Message 12 of 26 , Jul 2, 2009
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                            Hi Robert,

                            Steven's experience with his 20 matches mine with my 20. When going after some of the very dim targets that I do, I have seen that I can detect stars close to or at the limits of the POSS 1 plates used by RealSky when I use powers in the 400x - 600x range. I have detected galaxies in the mid to high 17s range with this scope. The observing location we normally use has unlensed SQM readings in the 21.6 - 21.7 area, and the Milky Way in the summertime will cast a shadow on a regular basis.

                            I do feel that I am lucky that my visual acuity does not seem to have decreased with age (61), but maybe that is counterbalanced by almost 5 decades of experience as an amateur. On another forum it was stated that objects in the mag 12 - 13 range were "dim", I feel that that is where the universe starts getting interesting.

                            Bob

                            -- In bigdob@yahoogroups.com, "Robert Houdart" <robert.houdart@...> wrote:
                            >
                            > Steven,
                            >
                            > You must be very experienced observer with excellent eyesight at a pristine
                            > location. Very few people reach magnitude 20 with a 20" scope.
                            >
                            > Your numbers are at the extreme end of the scale, about as impressive than
                            > O'Meara's famous visually recovery of Halley's comet in 1985, at the time a
                            > mag 19.1 object, with a 24" scope. He was breathing bottled pure oxygen on
                            > the top of Mauna Kea.
                            >
                            > Your using the Pupil Diameter of the telescopic observations changes the
                            > rules, because it's supposed to be the Pupil corresponding to the NELM
                            > estimate. It makes more sense to modify the NELM to take into account the
                            > outstanding nature of your observations. Using a NELM of 9.0 (!!) appears to
                            > produce the correct results for your case.
                            >
                            > For the 20", 511X, Enhanced coatings, Clean Optics, 6 mm pupil, Expert, NELM
                            > 9.0, Extinction 0.15 mag/atm, the result is mag 20.1. For the 36" at 985X
                            > the result is mag 21.4.
                            >
                            > I doubt that somebody else on this list comes even close...
                            >
                            > Robert
                            >
                            >
                            >
                            > -----Oorspronkelijk bericht-----
                            > Van: bigdob@yahoogroups.com [mailto:bigdob@yahoogroups.com] Namens Event
                            > Horizon
                            > Verzonden: woensdag 1 juli 2009 18:24
                            > Aan: bigdob@yahoogroups.com
                            > Onderwerp: Re: [bigdob] Telescopic Limiting Magnitude calculator
                            >
                            > Well, the copied formatting from the mag cac site did not transfer like it
                            > looked when I pasted it in my email, but, the two conditions are:
                            >  
                            > 20" Telescope, 511x, .99mm exit pupil at 511x yields a 20.1 mag limit
                            > And, 36" Telescope 985x, 0.93mm exit pupil at 985x yields a 21.4 mag limit
                            >  
                            > Basically keeping the exit pupil linked to the calc matches the
                            > observations.
                            > Regards, Steven
                            >
                          • Event Horizon
                            It s interesting that the visual recovery of Halley was brought up.  I too remember reading about that observation and just a few weeks ago I looked up the
                            Message 13 of 26 , Jul 2, 2009
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                              It's interesting that the visual recovery of Halley was brought up.  I too remember reading about that observation and just a few weeks ago I looked up the magnitude of 1P/Halley just to see what it was.  JPL Horizons put it at +25.08 total mag, and +28 nuclear magnitude, so it's still several magnitudes away from visual observers :o) , and, still out-bound....
                               
                              Steven

                              --- On Wed, 7/1/09, Robert Houdart <robert.houdart@...> wrote:


                              From: Robert Houdart <robert.houdart@...>
                              Subject: RE: [bigdob] Telescopic Limiting Magnitude calculator
                              To: bigdob@yahoogroups.com
                              Date: Wednesday, July 1, 2009, 10:23 AM








                              Steven,

                              You must be very experienced observer with excellent eyesight at a pristine
                              location. Very few people reach magnitude 20 with a 20" scope.

                              Your numbers are at the extreme end of the scale, about as impressive than
                              O'Meara's famous visually recovery of Halley's comet in 1985, at the time a
                              mag 19.1 object, with a 24" scope. He was breathing bottled pure oxygen on
                              the top of Mauna Kea.

                              Your using the Pupil Diameter of the telescopic observations changes the
                              rules, because it's supposed to be the Pupil corresponding to the NELM
                              estimate. It makes more sense to modify the NELM to take into account the
                              outstanding nature of your observations. Using a NELM of 9.0 (!!) appears to
                              produce the correct results for your case.

                              For the 20", 511X, Enhanced coatings, Clean Optics, 6 mm pupil, Expert, NELM
                              9.0, Extinction 0.15 mag/atm, the result is mag 20.1. For the 36" at 985X
                              the result is mag 21.4.

                              I doubt that somebody else on this list comes even close...

                              Robert

                              -----Oorspronkelijk bericht-----
                              Van: bigdob@yahoogroups. com [mailto:bigdob@yahoogroups. com] Namens Event
                              Horizon
                              Verzonden: woensdag 1 juli 2009 18:24
                              Aan: bigdob@yahoogroups. com
                              Onderwerp: Re: [bigdob] Telescopic Limiting Magnitude calculator

                              Well, the copied formatting from the mag cac site did not transfer like it
                              looked when I pasted it in my email, but, the two conditions are:
                               
                              20" Telescope, 511x, .99mm exit pupil at 511x yields a 20.1 mag limit
                              And, 36" Telescope 985x, 0.93mm exit pupil at 985x yields a 21.4 mag limit
                               
                              Basically keeping the exit pupil linked to the calc matches the
                              observations.
                              Regards, Steven



















                              [Non-text portions of this message have been removed]
                            • Nils Olof Carlin
                              looking again art Schaerfer s article (it must have been over 10 years since last time I perused it), I find these comments, that might be very relevant
                              Message 14 of 26 , Jul 3, 2009
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                                looking again art Schaerfer's article (it must have been over 10 years since
                                last time I perused it), I find these comments, that might be very relevant
                                (p.215) ;
                                "One final correction may be needed if the observer has high or low
                                sensitivity for the detection of point sources compared to the average
                                observer."
                                and
                                "...and this paper ... reports on observations with [limiting magnitude at
                                zenith] as faint as 8.9 ... it is known that the observers had much greater
                                than average acuity." The estimated factor 0.12 would mean a 2.2 magnitude
                                advantage over the norm - I guess an observer who has good data to estimate
                                the sensitivity must also be ranked with high experience.

                                So, Robert, maybe there should be an extra box for entering a factor (or
                                term, as I prefer) for the individual sensitivity. Enter the difference
                                between observed and estimated (uncorrected) limiting magnitudes - as an
                                average over several observations.

                                So, Steven, your visual acuity may be well above average, but not
                                inconsistent with reports in the scientific literature ;-)

                                Nils Olof
                                --------------------
                                Well, I don't know if I'm NELM of 9.0. It's high for sure as I can still use
                                an eyepiece combo that produces 8.7mm exit pupil and my iris does not
                                vignette, given that naked-eye limiting factors are retinal accuity, eye
                                aperture, plus that nasty atmosphere. I'm still holding out hope for a 41mm
                                Nagler while I can still use one.

                                I do know that when others are stumbling around the observing area stating
                                how "...black things are tonight, this is a great site!", I see the
                                extension cord they trip on and can pick up my dropped pen clearly visible
                                in the grass or dirt.

                                So is there a calc with other, better adjustment boxes?
                              • Robert Houdart
                                Nils Olof, ... In the calculator the NELM deals with that, any value larger than 7.0 is interpreted by the Javascript as a perfect sky plus a sensitivity
                                Message 15 of 26 , Jul 3, 2009
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                                  Nils Olof,

                                  > So, Robert, maybe there should be an extra box for entering
                                  > a factor (or term, as I prefer) for the individual
                                  > sensitivity. Enter the difference between observed and
                                  > estimated (uncorrected) limiting magnitudes - as an
                                  > average over several observations.

                                  In the calculator the NELM deals with that, any value larger than 7.0 is
                                  interpreted by the Javascript as a perfect sky plus a sensitivity correction
                                  for the observer.

                                  In Steven's case entering a NELM of 9.0 gives him a sensitivity gain of 2
                                  magnitudes.

                                  Robert
                                • pensack1
                                  Nils, Replies below. Don ... Wasn t that a 1989 article? ... Look at the html code behind this page: http://www.go.ednet.ns.ca/~larry/astro/maglimit.html In IE
                                  Message 16 of 26 , Jul 3, 2009
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                                    Nils,
                                    Replies below.
                                    Don

                                    --- In bigdob@yahoogroups.com, "Nils Olof Carlin" <nilsolof.carlin@...> wrote:
                                    >
                                    > Don,
                                    >
                                    > While I'm well familiar with Schaefer's 1990 paper, the 1998 article in S&T
                                    > seems to be missing from my collection,

                                    Wasn't that a 1989 article?

                                    >and I don't know the details of
                                    > either Bogen's or Robert's calculators and their algorithms.

                                    Look at the html code behind this page:
                                    http://www.go.ednet.ns.ca/~larry/astro/maglimit.html
                                    In IE or Opera, Click View, then Source.


                                    >So,
                                    > considering the quirk (or worse) in Schaefer's application of the
                                    > sensitivity equation (of Knoll et al) that I described, I wonder how your
                                    > "modifying the pupil diameter calculator to correspond with my own reality"
                                    > was done.

                                    It is a simple matter to modify the html code and then see the resultant pupil diameter. This definitely adjusts the results. I experimented to find the correct results for pupil diameter and sensitivity.

                                    >Perhaps like what Steven just described, artificially adjusting
                                    >the retinal sensitivity by entering a downsized eye pupil value?

                                    Actually, sensitivity can be adjusted separately in the code.


                                    > I don't know the details of how the Knoll data were obtained (or even how
                                    > his equation fits the experimental data), but Blackwell defines his
                                    > threshold as "corresponding to a probability of 50 percent, due allowance
                                    > having been made for chance success ". If Knoll's data are comparable in
                                    > this respect, the limiting magnitude for careful star observation with no
                                    > time limit, where the object is seen only intermittently, should be
                                    > (numerically) significantly higher.

                                    A reviewer in CN cited Schaefer's results dependent on a "visible 10% of the time" as a "threshold" observation. I'm not certain whether that is true or not.

                                    >In the 1990 article, this can be
                                    > adjusted for by an "experience" term, awarding about 0.5 mag. advantage over
                                    > the average for a very experienced observer trained in such a technique -
                                    > this term is included in Bogen's but not in Houdart's calculator, I believe.

                                    Correct. But the "fudge" factor can be adjusted in the html code.


                                    > As for common magnitude limiting charts, I suspect they just re-calculate to
                                    > correspond to a naked-eye limit of mag 6 or so (by direct vision) - thus
                                    > playing it safe by disregarding the effects of high magnification and
                                    > training in using averted vision.

                                    You may be right. I suspect it has more to do with the undesirable effects of discouraging a beginning observer when he can't see what he's supposed to see.
                                    Don Pensack
                                    Los Angeles.

                                    > As for extended objects, Blackwell's data will give some guidance, but the
                                    > light distribution within deep-sky objects seldom correspond well to the
                                    > disc-shaped test objects used - the Owl nebula may, but then again the line
                                    > spectra of gaseous nebulae make their apparent brightness to averted vision
                                    > difficult (but not impossible) to estimate.
                                    >
                                    > Nils Olof
                                  • pensack1
                                    Robert, There is dark adaptation and there is dark adaptation. To wit: in the old days, serious observers doing threshold observations would often cover their
                                    Message 17 of 26 , Jul 3, 2009
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                                      Robert,
                                      There is dark adaptation and there is dark adaptation.
                                      To wit: in the old days, serious observers doing threshold observations would often cover their heads with black cloths that blocked out all peripheral light.

                                      I find this technique can often gain several tenths of a magnitude for the same reason that looking at the sky seems to damage night vision.

                                      Even while observing under 21.5mpsas skies, I find that, by staring at the ground, I can soon make out pebbles, cord details, and even page numbers in my U2000 atlas without any light other than that from the clear sky. If I go from staring at the ground to looking through the eyepiece, I definitely see fainter details than if I first glance up at the sky for a few seconds and then look in the eyepiece. In fact, at that point I have lost the ability to see small details on the ground.

                                      So it's obvious to me that there is a range of dark adaptation that occurs depending on the brightness of the surroundings and the brightness of the last target viewed (who has not lost night vision by looking at a bright star or planet in the eyepiece?).

                                      Reaching the very limit of one's telescope's stellar observation not only requires high power, but it requires keeping one's eyes off the sky for a period of several minutes, I think.

                                      Don Pensack
                                      Los Angeles


                                      --- In bigdob@yahoogroups.com, "Robert Houdart" <robert.houdart@...> wrote:
                                      >
                                      > Nils Olof,
                                      >
                                      > > So, Robert, maybe there should be an extra box for entering
                                      > > a factor (or term, as I prefer) for the individual
                                      > > sensitivity. Enter the difference between observed and
                                      > > estimated (uncorrected) limiting magnitudes - as an
                                      > > average over several observations.
                                      >
                                      > In the calculator the NELM deals with that, any value larger than 7.0 is
                                      > interpreted by the Javascript as a perfect sky plus a sensitivity correction
                                      > for the observer.
                                      >
                                      > In Steven's case entering a NELM of 9.0 gives him a sensitivity gain of 2
                                      > magnitudes.
                                      >
                                      > Robert
                                      >
                                    • Robert Houdart
                                      Don, ... In the new calculator you can enter your true pupil diameter instead of relying on the automatically calculated age-dependent value. Other changes
                                      Message 18 of 26 , Jul 3, 2009
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                                        Don,

                                        > It is a simple matter to modify the html code and then see
                                        > the resultant pupil diameter. This definitely adjusts the
                                        > results. I experimented to find the correct results for
                                        > pupil diameter and sensitivity.

                                        In the new calculator you can enter your true pupil diameter instead of
                                        relying on the automatically calculated age-dependent value.

                                        Other changes I've implemented compared to Larry Bogan's code:
                                        - Correction for the inversion of refractor and reflector.
                                        - Choice between standard or enhanced coatings (88% v. 95% reflectivity).
                                        - More realistic difference between "dirty" and "clean" optics (Larry
                                        Bogan's value was to small)
                                        - You can enter SQM value instead of NELM
                                        - Use of seeing disk diameter instead of radius

                                        Overall I hope that the calculator has become easier to use and more
                                        accurate than before.

                                        Robert

                                        http://www.cruxis.com
                                      • Nils Olof Carlin
                                        Don, ... You re right - I copied the wrong year from somewhere I can t recall now. ... While this is possible, I just don t think it s fair to the user to
                                        Message 19 of 26 , Jul 4, 2009
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                                          Don,

                                          >
                                          > Wasn't that a 1989 article?

                                          You're right - I copied the wrong year from somewhere I can't recall now.
                                          >
                                          >>and I don't know the details of
                                          >> either Bogen's or Robert's calculators and their algorithms.
                                          >
                                          > Look at the html code behind this page:
                                          > http://www.go.ednet.ns.ca/~larry/astro/maglimit.html
                                          > In IE or Opera, Click View, then Source.

                                          While this is possible, I just don't think it's fair to the user to force
                                          her to dissect the Javascript code to find out what the calculator actually
                                          does. This criticism applies equally well to Robert's version - including
                                          the undocumented sensitivity adjustment mentioned in a recent message.
                                          I'd much prefer to read about the algorithms used, in order to understand
                                          what factors are considered (or left out).
                                          >
                                          >
                                          >>So,
                                          >> considering the quirk (or worse) in Schaefer's application of the
                                          >> sensitivity equation (of Knoll et al) that I described, I wonder how your
                                          >> "modifying the pupil diameter calculator to correspond with my own
                                          >> reality"
                                          >> was done.
                                          >
                                          > It is a simple matter to modify the html code and then see the resultant
                                          > pupil diameter. This definitely adjusts the results. I experimented to
                                          > find the correct results for pupil diameter and sensitivity.

                                          Simple or not, I had hoped you would have answered my question and told us
                                          what modifications you did.
                                          >
                                          >>Perhaps like what Steven just described, artificially adjusting
                                          >>the retinal sensitivity by entering a downsized eye pupil value?
                                          >
                                          > Actually, sensitivity can be adjusted separately in the code.

                                          Of course you could do any modification to please yourself, but undocumented
                                          modifications puts any other potential user at a serious disadvantage - and
                                          yourself, if you (like Steven) don't understand the true consequences. In
                                          the 1990 paper, Schaefer uses established scientific practice in giving a
                                          detailed account of the model he uses, and I have done my best to do the
                                          same, but by not giving away the details, meaningful discussion is
                                          essentially made impossible. (With reservations for possible discussion in
                                          the S&T article (BTW could anyone scan it for me? if so, please reply off
                                          list), which is not readily available (the 1990 paper is available on the
                                          net!).
                                          >
                                          >> I don't know the details of how the Knoll data were obtained (or even how
                                          >> his equation fits the experimental data), but Blackwell defines his
                                          >> threshold as "corresponding to a probability of 50 percent, due allowance
                                          >> having been made for chance success ". If Knoll's data are comparable in
                                          >> this respect, the limiting magnitude for careful star observation with no
                                          >> time limit, where the object is seen only intermittently, should be
                                          >> (numerically) significantly higher.
                                          >
                                          > A reviewer in CN cited Schaefer's results dependent on a "visible 10% of
                                          > the time" as a "threshold" observation. I'm not certain whether that is
                                          > true or not.

                                          I think you refer to a discussion that you initiated 2 years ago in the
                                          reflectors forum - but it is not so. I think it should be clearly understood
                                          that for basic light sensitivity, Schaefer uses the equation by Knoll et al,
                                          based on experimental sensitivity data - *not* data from actual star
                                          observations. The sensitivity of the eye (including binocular vision, a
                                          feature that the calculators have left out) of an individual observer will
                                          differ to some extent, and if allowance is desirable for this (which it is),
                                          it should be done explicitly.

                                          http://www.sciencecartoonsplus.com/pages/gallery.php
                                          I think Robert should be more explicit in step 2 <grin>

                                          Nils Olof
                                        • Nils Olof Carlin
                                          ... Seems many observers are not aware of this, but you will notice that after looking at a dark branch against the dark sky, moving your gaze shows there is a
                                          Message 20 of 26 , Jul 4, 2009
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                                            > Reaching the very limit of one's telescope's stellar observation not only
                                            > requires high power, but it requires keeping one's eyes off the sky for a
                                            > period of several minutes, I think.

                                            Seems many observers are not aware of this, but you will notice that after
                                            looking at a dark branch against the dark sky, moving your gaze shows there
                                            is a distinct after-image, showing that the sky will very significantly
                                            affect your dark adaptation. Or keep one eye closed for a minute or two,
                                            looking at the sky with the other. Then change - for a moment before dark
                                            adaption is lost again in the newly opened eye, you may find the sky
                                            abnormally bright.

                                            The mechanisms of dark adaptation are complex indeed, but luckily, the time
                                            constant of recovery from low light exposure appears to be less than for
                                            exposure to bright daylight. Thus, during obsevation for several minutes to
                                            confirm a star near the limit, your vision would essentially fully recover.

                                            Nils Olof
                                          • pensack1
                                            Nils, Regarding the html code, here are some changes to make to adjust for your experience: 1) if (form1.Teletype[0].checked) { var DS=0.21*D; var
                                            Message 21 of 26 , Jul 4, 2009
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                                              Nils,
                                              Regarding the html code, here are some changes to make to adjust for your experience:

                                              1) if (form1.Teletype[0].checked) {
                                              var DS=0.21*D;
                                              var FL=Math.pow(0.96,2);
                                              }
                                              if (form1.Teletype[1].checked) {
                                              var DS=0.00;
                                              var FL=Math.pow(0.99,2);
                                              }
                                              if (form1.Teletype[2].checked) {
                                              var DS=0.35*D;
                                              var FL=Math.pow(0.98*0.96,2);

                                              First is reflector. I changed to enhanced coatings for my own scope, and the obstruction % on personal scope.
                                              Second is refractor. Changed to best multi-coatings.
                                              Third is contemporary SCT. Changed to typical current coatings.
                                              These were all inaccurate in the on-line calculators.


                                              2) FO = Math.pow(0.99,6); // EYEPIECE (4 COATED AIR-GLASS SURFACES)

                                              Changed to 6 air-to-glass surfaces for more typical widefield. This could be changed for a specific eyepiece if desired by changing the number after the comma.

                                              3) DE = 7*Math.exp(-AG*AG/20000); // DIAM EYE PUPIL IN MM

                                              This is the age-dependent diameter decrease in pupil diameter that predicts a certain pupil diameter at a particular age. Adjusting the starting point (7mm) may result in a more realistic level IF you know your exact pupil diameter. My own dark-adapted pupil was never as large as 7, and currently stands at 4.5mm. Altering this changes an assumption and changes limiting magnitude calculations. I experimented to find a realisting starting point for my pupil diamter than works in the calculator. I was NOT adjusting the age asumption, which might nt be a valid one.

                                              4) FS=1.0; // OBSERVER'S SENSITIVITY

                                              This figure can be adjusted for the individual. I recommend playing with the figure if you consistently reach deeper or not as deep as the predictions in a variety of scopes.

                                              5) // CALCULATE SKY BRIGHTNESS
                                              if (MZ>=(7-K)) {
                                              BS=54; // BEST POSS. SKY BRIGHTNESS
                                              FS=Math.pow(10,0.4*(7-K-MZ)); // & GOOD EYESIGHT
                                              }
                                              else {
                                              XX=0.2*(8.68-K-MZ); // FS ASSUMED = 1

                                              Here, pupil diameter and observer sensitivity are assumed. These figures can be adjusted as well.

                                              6) M=M+(EX-6)*0.16; // EMPIRICAL EXPERIENCE CORRECTION

                                              Here an adjustment can be made for experience in the end factor if you think the difference is too great or too little.


                                              I think the purpose for a limiting magnitude calculator is to predict the limit for a particular observer on a particular scope on a particular night.

                                              There is no harm in playing around with the assumptions IF it leads to a more accurate prediction. I have a fair amount of experience using a 5" Maksutov, 8" SCT and 12.5" newtonian, and know the average darkness of the site where I observe. I find that I can predict my limit +/-0.2 magnitudes on all three scopes (as verified using limiting magnitude charts from Roger Clark and Brian Skiff and photomeric charts of M14, NGC206 and a few others), which means to me that the adjustments I made in the code made the calculator more accurate for me in my circumstances.

                                              Robert's calculator cleans up some of the errors in the Bogen one and is a little friendlier.

                                              Here is a chart for people on this site to use for a limit determination:
                                              http://www.geocities.com/SiliconValley/Garage/9531/lim_mag.htm

                                              Don Pensack
                                              Los Angeles








                                              --- In bigdob@yahoogroups.com, "Nils Olof Carlin" <nilsolof.carlin@...> wrote:
                                              >
                                              > Don,
                                              >
                                              > >
                                              > > Wasn't that a 1989 article?
                                              >
                                              > You're right - I copied the wrong year from somewhere I can't recall now.
                                              > >
                                              > >>and I don't know the details of
                                              > >> either Bogen's or Robert's calculators and their algorithms.
                                              > >
                                              > > Look at the html code behind this page:
                                              > > http://www.go.ednet.ns.ca/~larry/astro/maglimit.html
                                              > > In IE or Opera, Click View, then Source.
                                              >
                                              > While this is possible, I just don't think it's fair to the user to force
                                              > her to dissect the Javascript code to find out what the calculator actually
                                              > does. This criticism applies equally well to Robert's version - including
                                              > the undocumented sensitivity adjustment mentioned in a recent message.
                                              > I'd much prefer to read about the algorithms used, in order to understand
                                              > what factors are considered (or left out).
                                              > >
                                              > >
                                              > >>So,
                                              > >> considering the quirk (or worse) in Schaefer's application of the
                                              > >> sensitivity equation (of Knoll et al) that I described, I wonder how your
                                              > >> "modifying the pupil diameter calculator to correspond with my own
                                              > >> reality"
                                              > >> was done.
                                              > >
                                              > > It is a simple matter to modify the html code and then see the resultant
                                              > > pupil diameter. This definitely adjusts the results. I experimented to
                                              > > find the correct results for pupil diameter and sensitivity.
                                              >
                                              > Simple or not, I had hoped you would have answered my question and told us
                                              > what modifications you did.
                                              > >
                                              > >>Perhaps like what Steven just described, artificially adjusting
                                              > >>the retinal sensitivity by entering a downsized eye pupil value?
                                              > >
                                              > > Actually, sensitivity can be adjusted separately in the code.
                                              >
                                              > Of course you could do any modification to please yourself, but undocumented
                                              > modifications puts any other potential user at a serious disadvantage - and
                                              > yourself, if you (like Steven) don't understand the true consequences. In
                                              > the 1990 paper, Schaefer uses established scientific practice in giving a
                                              > detailed account of the model he uses, and I have done my best to do the
                                              > same, but by not giving away the details, meaningful discussion is
                                              > essentially made impossible. (With reservations for possible discussion in
                                              > the S&T article (BTW could anyone scan it for me? if so, please reply off
                                              > list), which is not readily available (the 1990 paper is available on the
                                              > net!).
                                              > >
                                              > >> I don't know the details of how the Knoll data were obtained (or even how
                                              > >> his equation fits the experimental data), but Blackwell defines his
                                              > >> threshold as "corresponding to a probability of 50 percent, due allowance
                                              > >> having been made for chance success ". If Knoll's data are comparable in
                                              > >> this respect, the limiting magnitude for careful star observation with no
                                              > >> time limit, where the object is seen only intermittently, should be
                                              > >> (numerically) significantly higher.
                                              > >
                                              > > A reviewer in CN cited Schaefer's results dependent on a "visible 10% of
                                              > > the time" as a "threshold" observation. I'm not certain whether that is
                                              > > true or not.
                                              >
                                              > I think you refer to a discussion that you initiated 2 years ago in the
                                              > reflectors forum - but it is not so. I think it should be clearly understood
                                              > that for basic light sensitivity, Schaefer uses the equation by Knoll et al,
                                              > based on experimental sensitivity data - *not* data from actual star
                                              > observations. The sensitivity of the eye (including binocular vision, a
                                              > feature that the calculators have left out) of an individual observer will
                                              > differ to some extent, and if allowance is desirable for this (which it is),
                                              > it should be done explicitly.
                                              >
                                              > http://www.sciencecartoonsplus.com/pages/gallery.php
                                              > I think Robert should be more explicit in step 2 <grin>
                                              >
                                              > Nils Olof
                                              >
                                            • Nils Olof Carlin
                                              Don, thanks a lot for this - it helps to have something substantial to discuss. ... It would be nice to choose from standard valuer or calulate the recipe for
                                              Message 22 of 26 , Jul 4, 2009
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                                                Don, thanks a lot for this - it helps to have something substantial to
                                                discuss.

                                                > First is reflector. I changed to enhanced coatings for my own scope, and
                                                > the obstruction % on personal scope.
                                                > Second is refractor. Changed to best multi-coatings.
                                                > Third is contemporary SCT. Changed to typical current coatings.
                                                > These were all inaccurate in the on-line calculators.

                                                It would be nice to choose from standard valuer or calulate the recipe for
                                                your own personal telescope - and in either case, display the estimated
                                                total loss.

                                                > 2) FO = Math.pow(0.99,6); // EYEPIECE (4 COATED AIR-GLASS SURFACES)
                                                >
                                                > Changed to 6 air-to-glass surfaces for more typical widefield. This could
                                                > be changed for a specific eyepiece if desired by changing the number after
                                                > the comma.

                                                same here - but for modern EPs with good coatings, I would think the total
                                                light loss is so small that the difference between 4 and 6 coatings should
                                                be negligible in the big context.

                                                >
                                                > 3) DE = 7*Math.exp(-AG*AG/20000); // DIAM EYE PUPIL IN MM
                                                >
                                                > This is the age-dependent diameter decrease in pupil diameter that
                                                > predicts a certain pupil diameter at a particular age. Adjusting the
                                                > starting point (7mm) may result in a more realistic level IF you know your
                                                > exact pupil diameter. My own dark-adapted pupil was never as large as 7,
                                                > and currently stands at 4.5mm. Altering this changes an assumption and
                                                > changes limiting magnitude calculations. I experimented to find a
                                                > realisting starting point for my pupil diamter than works in the
                                                > calculator. I was NOT adjusting the age asumption, which might nt be a
                                                > valid one.

                                                Yes, Schaefer uses some age-dependent estimate of the average pupil
                                                diameter. Robert does the right thing by letting you enter your actual
                                                pupil, if you know it, as any serious deep sky observer will know from
                                                measuring. If so, there is no reason for an age correction, of course. Enter
                                                your age, and Robert's routine will calculate an estimated width - if you
                                                know it doesn't apply to you, you can enter a true value.


                                                >
                                                > 4) FS=1.0; // OBSERVER'S SENSITIVITY
                                                >
                                                > This figure can be adjusted for the individual. I recommend playing with
                                                > the figure if you consistently reach deeper or not as deep as the
                                                > predictions in a variety of scopes.

                                                Yes, this is a factor that should be brought up explicitly. However, I see
                                                no good reason to separate this from the experience factor - they might as
                                                well be combined to one individual sensitivity factor (equivalent to the
                                                experience factor if you have no observations yet for a given observer, but
                                                a factor that you could modify once you have some good data). I really doubt
                                                the suggestion in Schaeffer's paper about individual(s) having a factor of 8
                                                more sensitive retina than the average - the physiologic sensitivity would
                                                vary some, surely, but I doubt by anything as much upward (neither the
                                                number of rods nor their dark-adapted charge of rhodopsin would increase
                                                substantially - skill in using them to best advantage can!). I think it is a
                                                matter of training your averted vision, and the patience and time needed to
                                                catch those 10%. This skill could be factored into the individual
                                                sensitivity factor.
                                                >
                                                > 5) // CALCULATE SKY BRIGHTNESS
                                                > if (MZ>=(7-K)) {
                                                > BS=54; // BEST POSS. SKY BRIGHTNESS
                                                > FS=Math.pow(10,0.4*(7-K-MZ)); // & GOOD EYESIGHT
                                                > }
                                                > else {
                                                > XX=0.2*(8.68-K-MZ); // FS ASSUMED = 1
                                                >
                                                > Here, pupil diameter and observer sensitivity are assumed. These figures
                                                > can be adjusted as well.

                                                Yes, and perhaps the color correction for the limit star should be applied
                                                as well, if known (I guess it is known for all naked-eye stars!) Perhaps you
                                                could display the calculated bacground brightness.

                                                >
                                                > 6) M=M+(EX-6)*0.16; // EMPIRICAL EXPERIENCE CORRECTION
                                                >
                                                > Here an adjustment can be made for experience in the end factor if you
                                                > think the difference is too great or too little.

                                                see above - any individual should need only one factor (to be adjusted as
                                                needed for changes in age, experience and wisdom in general ;-)

                                                > I think the purpose for a limiting magnitude calculator is to predict the
                                                > limit for a particular observer on a particular scope on a particular
                                                > night.

                                                The purpose of such a calculator can well be discussed - I believe your
                                                definition is as good as any, but others are possible. You the observer and
                                                your scope would be fairly constant - the background and seeing may vary
                                                from night to night, and if you have any idea of the parameters for a
                                                particular observing night, you may know if you should expect more or less
                                                than your "norm" limit.
                                                For a beginner, it might show if an intended object ought to be easy,
                                                difficult or plain impossible - but there is nothing to prevent you from
                                                trying, and doing so will give you yet another data point for your
                                                individual sensitivity factor. (The inverse of Schaefer's, to get a higher
                                                value for higher sensitivity)
                                                For me, a didactic purpose is important, and that's why I am asking you
                                                again as I did, and why I wish for a "transparent" algorithm - teaching what
                                                factors are important (be it the object itself, the sky conditions, the
                                                telescope you use, or your individual factors such as pupil size, retinal
                                                sensitivity and more importantly, skill in using your averted vision to best
                                                advantage) and potentially improvable.
                                                >
                                                > There is no harm in playing around with the assumptions IF it leads to a
                                                > more accurate prediction. I have a fair amount of experience using a 5"
                                                > Maksutov, 8" SCT and 12.5" newtonian, and know the average darkness of the
                                                > site where I observe. I find that I can predict my limit +/-0.2
                                                > magnitudes on all three scopes (as verified using limiting magnitude
                                                > charts from Roger Clark and Brian Skiff and photomeric charts of M14,
                                                > NGC206 and a few others), which means to me that the adjustments I made in
                                                > the code made the calculator more accurate for me in my circumstances.

                                                Very true! Only I think you should not need to actually modify the code, but
                                                enter your own individual factor explicitly. If you can beat the average
                                                test subject of Knoll's by 2 full magnitudes, it isn't unreasonable - but if
                                                so, I would believe it is mainly a matter of acquired skill in observing by
                                                averted vision, and giving time to let those 10% observations add to
                                                certainty.

                                                > Robert's calculator cleans up some of the errors in the Bogen one and is a
                                                > little friendlier.

                                                It is indeed, but even so, I could think of possible improvements - I have
                                                suggested one or two like adjusting the Knoll limit for pupil size, a
                                                binocular option, the background estimate from the NELM shown, and perhaps
                                                even color correction for the star of your NELM estimate.

                                                Nils Olof
                                              • pensack1
                                                Nils, I think that an experienced observer will always see more through a scope than an inexperienced observer--in all conditions. So experience is important.
                                                Message 23 of 26 , Jul 5, 2009
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                                                  Nils,

                                                  I think that an experienced observer will always see more through a scope than an inexperienced observer--in all conditions.

                                                  So experience is important.

                                                  But I think sky darkness trumps experience, so that factor has to have more weight.

                                                  But aperture trumps experience. A novice, looking through 60", will see more than an experienced observer in an 8" scope.
                                                  [I mean actually see, not observe. I find that rank amateurs can actually SEE more than they OBSERVE if you ask them pointed questions about what they're looking at. The experienced observer more or less automatically observes what he sees.]

                                                  So, ranked:
                                                  Aperture
                                                  Sky darkness
                                                  Experience

                                                  I consider pupil diameter, star color, distance from zenith, telescope type, cleanliness and coating type, and seeing conditions all as lesser factors.

                                                  Upon reflection, aperture and sky darkness are close to equal in importance. My home is about mag.17mpsas, while my observing site is magnitude 21.5mpsas. That difference radically overcomes the difference between my 5" and 12.5" scopes. At the dark site, the 5" sees more than the 12.5" at my home.
                                                  If the difference in sky darkness is larger than the difference in the apertures, sky darkness is the more important factor.
                                                  But, since amateurs are unlikely to be able to experience 40:1 aperture differences at their observing sites, sky darkness is really the most critical factor for determinining what can be seen.

                                                  At a given site, though, aperture is the most important factor of all.
                                                • jpcannavo
                                                  While enjoying the discussion, I had to comment... Glad to see reference to this classic cartoon by Sidney Harris. I first saw it a few decades ago in American
                                                  Message 24 of 26 , Jul 7, 2009
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                                                    While enjoying the discussion, I had to comment...
                                                    Glad to see reference to this classic cartoon by Sidney Harris. I first saw it a few decades ago in American Scientist. It crosses my path every now and then, and still gets a chuckle out of me!
                                                    Joe


                                                    > http://www.sciencecartoonsplus.com/pages/gallery.php
                                                    > I think Robert should be more explicit in step 2 <grin>
                                                    >
                                                    > Nils Olof
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