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Low-Light Performance Calculator

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opticsmike View Drop Down
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Post Options Post Options   Thanks (0) Thanks(0)   Quote opticsmike Quote  Post ReplyReply Direct Link To This Post Topic: Low-Light Performance Calculator
    Posted: October/06/2008 at 17:35

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
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Post Options Post Options   Thanks (0) Thanks(0)   Quote lucytuma Quote  Post ReplyReply Direct Link To This Post Posted: October/06/2008 at 18:27
Looks like a nice winter project, thanks and good luck with it.
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Post Options Post Options   Thanks (0) Thanks(0)   Quote Roy Finn Quote  Post ReplyReply Direct Link To This Post Posted: October/06/2008 at 18:36
How will this help a layman like myself determine which scope will outperform another based on punching in fixed number values for different scopes.
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Post Options Post Options   Thanks (0) Thanks(0)   Quote opticsmike Quote  Post ReplyReply Direct Link To This Post Posted: October/06/2008 at 20:08
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.
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Post Options Post Options   Thanks (0) Thanks(0)   Quote Roy Finn Quote  Post ReplyReply Direct Link To This Post Posted: October/06/2008 at 20:17
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
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opticsmike View Drop Down
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Post Options Post Options   Thanks (0) Thanks(0)   Quote opticsmike Quote  Post ReplyReply Direct Link To This Post Posted: October/06/2008 at 22:29
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)

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Post Options Post Options   Thanks (0) Thanks(0)   Quote opticsmike Quote  Post ReplyReply Direct Link To This Post Posted: October/07/2008 at 12:12
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.
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Post Options Post Options   Thanks (0) Thanks(0)   Quote Roy Finn Quote  Post ReplyReply Direct Link To This Post Posted: October/07/2008 at 15:27
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)   Quote cheaptrick Quote  Post ReplyReply Direct Link To This Post Posted: October/07/2008 at 15:56
Tagged.
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Post Options Post Options   Thanks (0) Thanks(0)   Quote opticsmike Quote  Post ReplyReply Direct Link To This Post Posted: October/07/2008 at 16:04
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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Post Options Post Options   Thanks (0) Thanks(0)   Quote Roy Finn Quote  Post ReplyReply Direct Link To This Post Posted: October/07/2008 at 16:27
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.
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Post Options Post Options   Thanks (0) Thanks(0)   Quote opticsmike Quote  Post ReplyReply Direct Link To This Post Posted: October/07/2008 at 16:47
We can devise an impartial standard for light transmission in low-light conditions to measure by.
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Post Options Post Options   Thanks (0) Thanks(0)   Quote Roy Finn Quote  Post ReplyReply Direct Link To This Post Posted: October/07/2008 at 17:04
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.
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Post Options Post Options   Thanks (0) Thanks(0)   Quote opticsmike Quote  Post ReplyReply Direct Link To This Post Posted: October/07/2008 at 17:44
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.
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Post Options Post Options   Thanks (0) Thanks(0)   Quote opticsmike Quote  Post ReplyReply Direct Link To This Post Posted: October/07/2008 at 17:50

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

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Post Options Post Options   Thanks (0) Thanks(0)   Quote cheaptrick Quote  Post ReplyReply Direct Link To This Post Posted: October/07/2008 at 18:16
 
"Mr. Koshkin....Mr. Koshkin...please pick up the red courtesy phone."  
 
 
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Post Options Post Options   Thanks (0) Thanks(0)   Quote koshkin Quote  Post ReplyReply Direct Link To This Post Posted: October/07/2008 at 19:12
Did someone call?
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Post Options Post Options   Thanks (0) Thanks(0)   Quote koshkin Quote  Post ReplyReply Direct Link To This Post Posted: October/07/2008 at 19:12
What can I do for you CT?

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Post Options Post Options   Thanks (0) Thanks(0)   Quote cheaptrick Quote  Post ReplyReply Direct Link To This Post Posted: October/08/2008 at 04:57
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.   
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Post Options Post Options   Thanks (0) Thanks(0)   Quote Ed Connelly Quote  Post ReplyReply Direct Link To This Post Posted: October/08/2008 at 06:20
( " But, Ollie, I didn't understand a word of what that man said...I'm in the dark and he's feeding me mushrooms....." )
 
 
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