Home Forums Hunting & Shooting Hunting Optics Light transfer formula for optics

I know that I should know this but can't remember for sure. Do you take the objective lenses of the optic and divide by magnifying power to come up with a number to compare with your pupil size? Something like this? And then what does it all mean when trying to find out how much light an optic allows you to see? I am looking for good numbers at dusk and dark. Thanks and hope you understand what I am trying to ask. Gary

I think you are correct 7mm is optimal but I also read that two scopes with the same exit pupil, the higher magnification will be brighter ??

Read Mule Deers, aka John Barnesness, book on optics, Modern Sporting Optics, very informative and well written.

The exit pupil number means little if you have a crappy glass with bad lens coatings, also the light spectrum being measured or seen has a big effect on real world transmission of light.

Spence

The exit pupil doesn't seem to mean much. When I compared my Bushnell 6500 4 1/2-30X50 set on 13x with my minox 13x56 binoculars which cost 600 bucks, the scope lasted 2 minutes longer in low light.

Everybody seems to make to much noise over low light. I used a fixed 2 3/4x scope for years and never ran out of light to shoot in legal hours. People make it sound like the only time your gonna see game is 2 minutes before quitting time, bunch of garbage!

Maaax,

You may be thinking of twilight factor, which is the square root of the magnification x objective lens diameter in millimeters. This formula was primarily developed in Europe, for figuring the potential brightness of scopes in dim-light shooting.

But it only indicates the potential of a particular scope, because light transmission/brightness also depends on the quality of lenses and their coatings, along with effectiveness of "baffling" or inside coating of scope tubes to reduce reflection.

With all due respect, your post is almost laughable. Most of the hogs and coyotes I have killed have either been in low light or moonlight. Thinking back over the past 4-5 years, I can count on one hand the times I've seen hogs here in decent daylight.

Hogs like the one below don't reach that size by being dumb -- or by prancing around in daylight. And under the conditions I killed him in, your 2 3/4x scope wouldn't have worked at all.

I am happy for you that all your game has been taken in good lighting. Not all of us are quite that fortunate.

Bobby,

Yep, and as I mentioned legal European shooting hours are often "dimmer" than in the U.S., often an hour after sunset and before sunrise--yet most don't allow the use of artificial lights, much less night-vision or thermal optics. It varies from country to country.

It can also vary with species and country. When I hunted in the Czech Republic in 1993, the regulations for various kinds of deer were one hour after sunset and before sunrise--but pigs were legal all night long.

I think I have to agree with Don Fisher. From deer in the forests of northern MN and WI to coyotes in the coastal forest of WA to the deserts of the Southwest I find that if I can see a deer or coyote at any distance with my bare eyes 1-1.5x and a 20mm objective works.

I will say that I don't hunt over feeders or bait so I have to see them at a distance so more natural light might be the factor that makes these small scopes work for me.

Another problem with the twilight factor/index is it gives false performance numbers. For example, 10x40 binoculars have a higher twilight index than 7x42s, yet Zeiss advertised the 7x42 Dialyts as having "high twilight performance" not the 10x40s.




It also doesn't take into account pupil diameter as we age. According to a paper several years ago, 10x50 binoculars would perform better in twilight and night than 8x56s for the average elder observer around 60.





http://www.holgermerlitz.de/bino_performance/bino_performance.pdf

I have done a little optics and I think the biggest factor that you may be overlooking is the quality of the optics, primarily the surface finish of the glass and the anti-reflection coatings. In the low light regime every photon (chunk of light) is crucial to form an image on your eye so any that are lost to reflection or scattered by imperfections on the optical surface are noticed by poorer low light performance.

I think the best way to evaluate low light performance is to go to a vendor that will allow you to take multiple scopes out at dusk and see which one you can see fine branches on a tree last. I choose branches on a tree as I always wanted to be able to evaluate rack size and fine branches were not far off. You may find your variable scopes have a sweet spot, a point where they low light performance is best, if you find that mark it with a fine tip sharpie and put your scope on that power as dusk approaches. I find the sweet spot is usually on the low end of the power.

When I hunted deer in the UP of Michigan I spent a lot of time in cedar and alder swamps. It gets dark in the swamp early so I felt low light performance was crucial to be able to determine if that deer was a trophy during the last 30 minutes of legal shooting time.

Just my two cents,
wade

Brightness is one thing resolving power is another. You can have a 7x42 that is brighter than a 10x42 but you will be able to see better detail with the higher magnification even though the image is dimmer. For example reading a news paper at arms length with the light from a 60 watt bulb as opposed to reading the same from 1 foot away with a 40 watt bulb. You will be able to see better detail because it closer.

Resolution during twilight was addressed in the Merlitz paper.

In real life,target detection under low light is rarely resolution, but
rather contrast limited. Wild animals, which are ac-
tive under twilight conditions, are often well adapted to
their environment (camouflaged) and represent targets
of particularly low contrast. They remain hidden to the
observer’s eye, even when their apparent angular sizes by
far exceed the resolution limits of high contrast targets.

Experienced observers would agree that, under
twilight conditions, it is not just fine-detail that deter-
mines visibility, but a recognition of patterns, contours,
directions or movements, and how these visual cues are
connecting to individual objects in the context of the
background motives. The 8x56 offers a brighter im-
age than the over-magnifying 12x42 [15], and the def-
inition of binocular performance through the threshold
contrast seems to reproduce the combined factors that
grant recognition of a target more accurately than a
purely resolution-based model.

Two more comments:


Yep! The twilight factor formula works because more magnification essentially gets our eye closer to the target--which in dim light works whether through magnification or simply walking closer. Another example is walking down a dimly-lit street at night.

Will also comment that it's rare for a store to allow us to take various optics home and test them side-by-side in dim light. Which is why the easiest test in most stores is to look into its dimmest corners, which are often above us. But I often see customers looking through scopes and binoculars out the nearest window....

I have never asked to take optics home but have usually been able to take the optics out to the parking lot, leave my wallet behind as security or have someone from the store come out to make sure I don't run off with highend optics. When dropping over a $1,000 on an optics purchase the stores are usually happy to help make that sale.

Lots here to digest. Two leupold scopes; FX11 in fixed 3x20 and a 1.5-5x20 VX111. Pretty similar glass I am guessing. All things being what they are, will the VX111 set at 1.5x be brighter than the fixed 3x at dusk/dawn conditions? I was using the 3x on my 375 trying to see a buffalo at dusk and could only see his outline. My guide could see the buffalo clearly thru his Swarovski 10x42 binos. Sooo, FX11=6.7 twilight and the Swaros=4.2. Glass quality?

Taking optics outside the store isn't the best test, especially during the day but even at night because most parking lots have plenty of lighting. Which is why I advised to look into the dimmest parts of the store--which are usually higher up in the remote corners.

FXII=7.7 Swaros=20.5

Ohhhh. Thank you for the formula.

The biggest mistake you made in your analysis is comparing a riflescope to a binoculars. The riflescope will only present one image to one eye, whereas the binoculars will present two slightly different images, one to each eye. Unless you're a pirate.

Leaving aside the difference in the quality of the glass inherent when comparing Leupold to Swarovski (or anything halfway decent), the fact the brain is receiving double the input with a binoculars makes a huge difference in how it perceives the target.

The TF formula is pretty much laughable as it only really measures the theoretical outcome, without paying attention to critical things such as quality and type of glass, coatings and overall light transmission. Instead, it heavily favors the size of the objective, which we already know is the main factor. This is also why many manufacturers don't even bother to list the TF. If you don't know that a larger objective is critical in how much light will go through the riflescope, you should take up Bingo or knitting. In a variable riflescope, when it gets dark, you can wind down the magnification to compensate for the loss of light, up to a point, of course. If you want high magnification, get the bigger objective lens.

When you want to compare similar optics for suitability in low light conditions, you need to find out the overall light transmission of the optics. Some manufacturers will list it, others make vague claims, and some ignore it. An old-time trick is to have a large objective lens and a relatively low magnification and then make claims about a wonderful TF, totally ognoring the fact the optics are minimally coated and 40% of the light is lost in the optics. When you lose 5% of your light at every air/glass surface, it doesn't take long to lose the plot, so to speak. It's all in the coatings.