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Low-Light Performance Calculator

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Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: October/06/2008 at 17:35
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For anyone interested, I've created a Low-Light Performance Calculator with interactive graphical comparisons at http://scopecalc.com

I hope for this to grow into a community-based project that can help to make scope selection easier for everyone, but much work will need to be done gathering data to make accurate comparisons among different scope brands and lines. See the site for details.

...example usage with pre-filled values comparing five Zeiss Diavari Victory rifle scopes:

http://scopecalc.com/?EyePupilDiameter=7&NumScopes=5&ChangeScopeNum=0&ScopeTitle1=Zeiss+Diavari+Victory+1.5-6x42T*&LightTransmissionPercent1=90.2&MinMagnification1=&MinObjectiveLensDiameter1=22.6&MinExitPupilDiameter1=15&MaxMagnification1=&MaxObjectiveLensDiameter1=42&MaxExitPupilDiameter1=7&ScopeTitle2=Zeiss+Diavari+Victory+2.5-10x50T*&LightTransmissionPercent2=90.2&MinMagnification2=&MinObjectiveLensDiameter2=37.7&MinExitPupilDiameter2=15&MaxMagnification2=&MaxObjectiveLensDiameter2=50&MaxExitPupilDiameter2=5&ScopeTitle3=Zeiss+Diavari+Victory+6-24x56T*&LightTransmissionPercent3=90.2&MinMagnification3=6&MinObjectiveLensDiameter3=56&MinExitPupilDiameter3=&MaxMagnification3=24&MaxObjectiveLensDiameter3=56&MaxExitPupilDiameter3=&ScopeTitle4=Zeiss+Diavari+Victory+3-12x56T*&LightTransmissionPercent4=90.2&MinMagnification4=3&MinObjectiveLensDiameter4=44&MinExitPupilDiameter4=&MaxMagnification4=12&MaxObjectiveLensDiameter4=56&MaxExitPupilDiameter4=&ScopeTitle5=Zeiss+Diavari+Victory+6-24x72T*&LightTransmissionPercent5=90.2&MinMagnification5=6&MinObjectiveLensDiameter5=72&MinExitPupilDiameter5=&MaxMagnification5=24&MaxObjectiveLensDiameter5=72&MaxExitPupilDiameter5=&BrightnessCalcType=Stevens+Power+Law
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: October/06/2008 at 18:27
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Looks like a nice winter project, thanks and good luck with it.
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: October/06/2008 at 18:36
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How will this help a layman like myself determine which scope will outperform another based on punching in fixed number values for different scopes.
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: October/06/2008 at 20:08
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Until resolution and light transmission are known with a single standard across all scope brands and lines, this will only be useful when comparing scopes of comparable quality optics. This is perfect for when you are considering several scopes from among the same scope line or among different lines that are known to be about equivalent in optical quality and want to know how much more effective one will be over another for low light. Then you can consider that effectiveness with other considerations such as size, weight, durability, features, reticle selection, and cost etc.
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: October/06/2008 at 20:17
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Thank you. I have no formal education in this area, however, I am wondering how this will differ from using what is known as Twilight Factor to make comparisons between scopes, bino's and spotters of like quality. I think TF and Relative Brightness calculations are useful to those who are in the market for new optics for rough comparisons only.

Edited by Roy Finn - October/06/2008 at 20:18
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: October/06/2008 at 22:29
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The explanation from the site outlines the improvement over Twilight factor...
 
 
Apparent Brightness Factor:
The Apparent Brightness Factor is the perception of the amount of target light through the scope relative to the perception of the amount of target light with the single unscoped eye. Apparent brightness is calculated as the cube root of the total light factor, which is the basis for modern computer color space brightness scaling and is also the apparent brightness of a 5-degree target in the dark with a uniformly dark background and surround. If the unscoped eye pupil luminous flux is 1 lumen and the scoped eye pupil luminous flux is 50 lumen, then the Eye Pupil Luminous Flux Factor is 50x, and 50 times the amount of light from the objects within the field of view of the scope is reaching the eye pupil through the scope than without the scope, although the light from the objects through the scope will appear 3.6 times as bright than with one eye without the scope. If you consider that one eye is closed when looking through the scope, then only 25 times the light is reaching the one eye through the scope than with both eyes open without the scope, and the objects through the scope will appear 2.9 times as bright as with both eyes open without the scope. Both the unscoped eye pupil luminous flux and the scoped eye pupil luminous flux are the amounts of light reaching the eye pupil from only the objects that are within the field of view of the scope.

Apparent Brightness Factor = (Practical Eye Pupil Luminous Flux Factor)^(1/3)

Low Light Performance:
This calculation derives Low Light Performance as the average of light gain and resolution gain through magnification, similar to Twilight Performance specified by scope manufacturers. Low Light Performance calculated here is much more useful than Twilight Performance, as Twilight performance is the average of the just the objective lens diameter times magnification, while Low Light Performance is the average of the actual Apparent Brightness times magnification, which also includes the exit pupil/eye pupil relation, light transmission, approximated diffraction, as well as the perception of relative light gain. Just as with Twilight Performance, this Low Light Performance calculation does not yet include lens resolution and contrast as factors. Therefore lower quality optics will yield relatively less gains at higher magnifications.

Low Light Performance = (Apparent Brightness Factor x Magnification)^(1/2)

Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: October/07/2008 at 12:12
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Ok, I've replaced all of the technical jargon with words that are easier to relate to. I hope this helps. An update of the definitions from my previous post here is on the site now.
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: October/07/2008 at 15:27
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opticsmike, at first I didn't realize that you could plug in your own eye pupil diameter, although I'm sure the calculator is using a standard number for comparisons between scopes. Now that I plugged in the eye pupil diameter and exit pupil diameter, I can see where you are able to make more accurate comparisons between scopes than you could by just using TF data. I will say that most of the folks who visit here are looking for the kind of information that the calculator will not be able to capture such as glass and coating differences, stray light efficiency and overall design differences that will set one scope apart from the next. In other words, usually someone will come here and state that they are shopping for a new 3-9x40, and they want to know what differences exist from same. Now if there was a way to capture say, contrast and image resolution, that would be interesting. Frankly, I have no ides how a consumer would be able to determine those factors.

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Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: October/07/2008 at 15:56
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Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: October/07/2008 at 16:04
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Roy, my hope is that a measuring standard could be developed for light transmission, resolution , and contrastp; and people that do have the means to take measurements could contribute the data. Maybe I'd consider buying the tools needed to take the measurements and send them out to people that I could trust. Just a thought at this point.
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I have had long conversations with folks here and also some industry folks that I've gotten to know over the years and a standard of light transmission sounds like it would be a challenge to say the least. I don't know of any two companies that test their products the same as others do. In a very competitive market, manufactures want to be able to claim high light transmission figures and I believe that we as the consumers are only getting partial data at best. Take Bushnell for example, claiming, "world's brightest riflescopes". They claim 95% light transmission at 550nm. You know as well as I do that figures for the middle of the color spectrum are not necessarily going to provide the kind of data that would indicate what would work best for light (color) transmission toward the lower end of the color spectrum, say 400nm or so. Zeiss claims their transmission numbers are averaged across the visible color spectrum which, IMO, is much more accurate and realistic. Leupold makes claims of nearly "98%" light transmission, but God himself can't figure out how they are arriving at their claimed figures. When you consider then number of lenses in a variable riflescope, that figure would be practically impossible to obtain. I know Steiner also measures across the entire visible spectrum as well. As I stated before, I have no formal education in this field, but it is something that interests me. I started to gain interest in this by accident so to speak as a family member suffers from macular degeneration. Having a special interest in sporting optics was just a natural progression into vision concepts.
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: October/07/2008 at 16:47
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We can devise an impartial standard for light transmission in low-light conditions to measure by.
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: October/07/2008 at 17:04
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The standard would be the easy part. I'm just not sure how an instrument could be used to capture what the human eye actually sees in real life conditions. An instrument will collect data at a standard rate. What you see through a riflescope and what I see could be very different depending on age, health, weather conditions etc. etc. And yes, I realize that even though our vision differs, the relationship between scope A and scope B should be the same regardless.
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: October/07/2008 at 17:44
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To be usable as a factor, light transmission only needs to be measured as a percentage of the amount of visible light through the scope, not the perception of it.
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: October/07/2008 at 17:50
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For those who are interested, the following is how the calculation is performed. To help make this easier to understand here, I'll substitute "Luminous Intensity" with "Light Intensity" and "Luminous Flux" with "Light", and "Factor" with "Gain"...

EyePupilDiameter = 7 mm
LightTransmission = 90%

Given two of the following properties: Magnification, ObjectiveLensDiameter, ExitPupilDiameter

Objective = 56 mm
Magnification = 7
ExitPupilDiameter = ?

The third can be deduced by...
ObjectiveLensDiameter = ExitPupilDiameter x Magnification
ExitPupilDiameter = 56 mm / 7 = 8 mm

ObjectiveLensArea = 3.14159265358979323846 x (ObjectiveLensDiameter/2)^2
ObjectiveLensArea = 2463.00864041439789895264 mm2

...To calculate final caluclation as a factor of initial LightIntensity:
LightIntensity = 1 lumen/mm^2 (millilux)

ObjectiveLensLight = ObjectiveLensArea x LightIntensity
ObjectiveLensLight = 2463.00864041439789895264 mm2 x 1 lumen/mm^2
ObjectiveLensLight = 2463.00864041439789895264 lumen

EyePupilArea = 3.14159265358979323846 x (EyePupilDiameter/2)^2
EyePupilArea = 38.484510006474967171135 mm2

UscopedEyePupilLight = EyePupilArea x LightIntensity
UscopedEyePupilLight = 38.484510006474967171135 mm2 x 1 lumen/mm^2
UscopedEyePupilLight = 38.484510006474967171135 lumen

ExitPupilArea = 3.14159265358979323846 x (ExitPupilDiameter/2)^2
ExitPupilArea = 50.26548245743669181536 mm2

ExitPupilLightIntensity = (ObjectiveLensLight / ExitPupilArea) x (LightTransmission/100) x LightDiffractionFactor
ExitPupilLightIntensity = (2463.00864041439789895264 lumen / 50.26548245743669181536 mm2) x (90/100) x 0.9768
ExitPupilLightIntensity = 43.07688 lumen/mm2

if (ExitPupilArea <= EyePupilArea){
     EyePupilIlluminanceArea = ExitPupilArea
} else {
     EyePupilIlluminanceArea = EyePupilArea
}
EyePupilIlluminanceArea = 38.484510006474967171135 mm2

ScopedEyePupilLight = EyePupilIlluminanceArea x ExitPupilLightIntensity
ScopedEyePupilLight = 38.484510006474967171135 mm2 x 43.07688 lumen/mm2
ScopedEyePupilLight = 1657.7926194077213838349218588 lumen

EyePupilLightGain = ScopedEyePupilLight / UscopedEyePupilLight
EyePupilLightGain = 1657.7926194077213838349218588 lumen / 38.484510006474967171135 lumen
EyePupilLightGain = 43.07688

PerceivedBrightnessGain = EyePupilLightGain^(1/3)
PerceivedBrightnessGain = 43.07688^(1/3)
PerceivedBrightnessGain = 3.5054847338991602325977612730388

LowLightPerformance = (PerceivedBrightnessGain x Magnification)^(1/2)
LowLightPerformance = (3.51 x 7)^(1/2)
LowLightPerformance = 4.95

This is reflected in the following calculation with pre-entered values...
http://scopecalc.com/?EyePupilDiameter=7&NumScopes=1&ChangeScopeNum=0&ScopeTitle1=&LightTransmissionPercent1=90&MinMagnification1=7&MinObjectiveLensDiameter1=56&MinExitPupilDiameter1=&MaxMagnification1=&MaxObjectiveLensDiameter1=&MaxExitPupilDiameter1=&BrightnessCalcType=Stevens+Power+Law

Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: October/07/2008 at 18:16
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Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: October/07/2008 at 19:12
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Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: October/07/2008 at 19:12
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What can I do for you CT?

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Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: October/08/2008 at 04:57
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Originally posted by koshkin koshkin wrote:

What can I do for you CT?

ILya
 
I'm getting dizzy just reading about this guys low light calculator.
(You know how I get sometimes.) Wink  Bucky
 
I'd like to see what your take on this instrument is.   
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: October/08/2008 at 06:20
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Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: October/08/2008 at 10:57
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Originally posted by cheaptrick cheaptrick wrote:

Originally posted by koshkin koshkin wrote:

What can I do for you CT?

ILya
 
I'm getting dizzy just reading about this guys low light calculator.
(You know how I get sometimes.) Wink  Bucky
 
I'd like to see what your take on this instrument is.   


His calculations seem to be fairly accurate.  How useful this is going to be is a little questionable, but time will tell.  I have only looked at the calculations briefly, but it seems to be an improvement on the existing measures that some people use ("twilight factor", etc) by taking the size of your eye pupil into account.

It seems to have the same weaknesses as the "twilight factor" though:  there is no easy way to take into account optical quality or specifics of optical design that differ from scope to scope.  Also, even with the same product line, apparent optical quality is not the same for all models.  For example, for many moderately priced scope lines, a higher magnification model will have appreciably worse optical quality simply because it is harder to build high magnification optics at a lower price point.  Same for large objective lenses.

Another consideration is that the calculations seem to treat a scope as a non-imaging optic: it is mostly about light transfer.  However, the type of an image (which is very difficult to take into account) is very important since a scope is not just transferring light to your eye, it is transferring an image.

Anyhow, we'll see how it works out.  When I have a little more time I'll look into it in more detail.

ILya
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: October/08/2008 at 11:17
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What koshkin explained is dead on. There's a whole new summit to be reached to make it any more useful than just an improvement over twilight factor for generalized use, although the improvement is significant. To be any more useful, a standard for measuring resolution, contrast, and light transmission needs to be developed and that data has to be collected and utilized in the calculation.
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: October/11/2008 at 08:32
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In a prior thread, I said I would not respond further, but I changed my mind. Opticsmike appears to be into computer graphics. The following link will offer you insight into his model, and the problems with it:

http://www.cg.tuwien.ac.at/research/theses/matkovic/node17.html

Originally posted by koshkin koshkin wrote:

His calculations seem to be fairly accurate (but) I have only looked at the calculations briefly .....()it seems to be an improvement on the existing measures that some people use ("twilight factor", etc) by taking the size of your eye pupil into account. ..... When I have a little more time I'll look into it in more detail.ILya

While my wife was having eye surgery yesterday, I had time to look at a couple of examples of the calculations. The first problem that caught my eye was that Opticsmike has optical gain (and therefore perceived brightness) increasing as magnification increases, which is not correct.

Increasing magnification makes the image get dimmer, not brighter.    Depending upon your experience with zoom lenses, it is an easy mistake to make. I, too, sometimes make it.

As an aside, zoom lenses can be used as beam expanders for lasers. If you use the largest diameter as a reference, when the laser beam is made smaller, its intensity increases. It is why I sometimes make the mistake, and I will guess it is why Koshkin did not catch it.

Opticsmike defines the variables in his equations as follows:

Theoretical Exit Pupil Intensity Gain = square of the Obj lens diameter divided by the square of the exit pupil diameter. TG = (Od^2/EP^2)

Realistic Exit Pupil Gain = Theoretical Gain X Transmission Factor. RG = (TG x T fct)

Perceived Brightness = cube root of Realistic Gain. PB =(RG)^1/3

Low Light Performance = the square root of the product of Perceived Brightness and Magnification.

LLP = [(RG)^1/3 x Mag]^1/2

The cube root (1/3 power) he uses appears to come from the Stevens work that relates to computer graphics that I don't accept to be true or appropriate for our application. But it is like talking to a liberal; you sometimes have to accept half-truths to discuss something.

I have purposefully omitted the definitons of Theoertical Light Gain and Realistic Light Gain because we cannot measure Luminance with our eyes. In any event, (more half-truth stuff) in those cases where the exit pupil is larger than our eye pupil, he has Light Gain as identical to Exit Pupil Gain.

When we substitute for the variables in his equation and expand it into terms we can readily identify with, we find that

LLP Index = [{(Od/EP)^2 X Trans factor}^1/3 x Mag]^1/2

Remember that the ratio of the obj lens diam to the exit pupil diam is one way to express magnification. While not technically true, it is either identical or often very close. If we substitue magnification for the ratio (Od/EP), we get:

LLP Index = [{Mag^2 x Trans Fact}^1/3 x Mag]^1/2

You can get his LLP index by using this simple formula when the exit pupil is larger than the eye pupil. In other words, Opticsmike would have you believe that the low light performance of a scope is all about magnification. It is easy to prove that isn't true.

For all its faults, the twilight factor is much more reasonable.

Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: October/11/2008 at 17:05
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I hope your wife's surgery went well. The link you provided illustrates why I use the Steven's Power law. Every scene is different and the parameters for complex scenes always differ. The very fact that it's completely infeasible for everyone using the calculator to know those parameters is the very reason why I utilize the brightness perception of the target on a uniformly dark background and surround. Modern brightness scaling calculations begin with that basic function and increase in complexity as more parameters are considered. So while the link you provided is correct in stating that complex scenes require more parameters, it is incorrect in stating that the Steven's Power function fails because the link fails to recognize the use of parameters for complex scenes applied to the Stevens' Power law. The calculations for complex scenes become quite complex with the Stevens' Power law, but using the basic function is very effective alone. By utilizing the basis of the Steven's Power law for a target on a uniformly dark background and surround, brightness comparisons can be made very effectively on an accurate linear perception scale without having to rely on parameters that are infeasible for everyone to obtain.

My calculation does not does not increase light gain according to magnification as you suggest. Look at the first graph for Theoretical Light Gain on the following link and you will see that once all of the light from the objective can reach the pupil there is no further light gain...

http://scopecalc.com/?EyePupilDiameter=7&NumScopes=1&ChangeScopeNum=0&ScopeTitle1=&LightTransmissionPercent1=&MinMagnification1=3&MinObjectiveLensDiameter1=56&MinExitPupilDiameter1=&MaxMagnification1=12&MaxObjectiveLensDiameter1=56&MaxExitPupilDiameter1=&BrightnessCalcType=Stevens+Power+Law

In fact, light gain becomes reduced as the exit pupil diameter is reduced and light diffraction increases. That is exactly what the second graph for Realistic Light Gain illustrates. Incidental, you've outlined this relation to show that the calculation does not work before you even noticed that how easily the calculation graphically presents this relation for you.

The third graph, Perceived Brightness is then calculated based upon Realistic Light Gain, which does not increase do to magnification, but due to exit pupil/eye pupil relation.

The fourth graph is Low Light Performance. Under conditions with ample light, visual acuity is in relation to resolution (and of course optical quality). Under low light conditions, visual acuity is a combination of brightness and resolution. As magnification increases, target image resolution increases to assist visual acuity in combination with image brightness in the form of diminishing returns because of increasing light loss due light diffraction at smaller exit pupil diameters.

Twilight Factor is also a measure of visual acuity as the relation of light gain and magnification, but Twilight Factor does not calculate that relation in nearly a realistic nor helpful manner as it does not consider exit pupil/eye pupil relation, nor does it provide any form of real usable light gain, nor does is include light gain as we perceive it. Those three reasons are why my calculation is a significant improvement over the Twilight Factor. My calculation determines real light gain, brightness perception, as well as a measure of comparative visual acuity under low light conditions.

As I've said before, I encourage open discussion. I do not expect you to accept anything as a half-truth to discuss this. Definitely the opposite of a liberal. I do however expect that you be more open minded and be more considerate before making incorrect assumptions. To claim that I would have anyone believe that low light performance of a scope is all about magnification is complete BS and I'm just not sure how much more clearly I can graphically illustrate and explicitly state that low light visual acuity is about brightness and resolution. Do you even know how Twilight Factor is determined? I think your whimsical quest to prove me wrong is blinding you Whacker

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Thank you. My wife is doing well.

Originally posted by opticsmike opticsmike wrote:

My calculation does not does not increase light gain according to magnification as you suggest. ... As magnification increases, target image resolution increases ....

When the exit pupil is larger than the eye pupil, all of us can see that your values for perceived brightness and LLP increase as magnificataion increases. That is not realistic.

My use of a scope is primarily for hunting. As such, I'm looking at light reflected off extended objects in a terrestrial environment, not at a growling bear on a computer screen. The image we see gets dimmer and dimmer as magnification increases. And there is a good reason why.

Yes, I know how to calculate Twilight Factor, Geometric Brightness and the Adler Index.

I don't have a quest to prove you wrong, but I won't accept things that I know to be incorrect. In beginning, I wished you well and I meant it. I also warned you about trying to use brightness in a quantitative manner; my intent was to be helpful. The Stevens work dates to 1963 when I was a student. I have been down this road several time before.

I would be happy for you to come up with something that improves what we now have, something based on our real observations. From what I can see, you aren't close.
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