Entering the Dark Zone - Part II
In this post I explain why very large exit pupils (more than 5mm) and very high light transmission (say more than 85% ) have very minimal affect on the performance of binoculars in twilight. Again, I emphasize that my analysis is confined to viewing nature scenes as encountered during hunting or bird watching. This analysis is not related to viewing high-contrast self-luminous point-source objects such as those encountered in astronomy.
Fact I - Human eye does not perceive brightness proportional to the area of the eye pupil. This is due to an effect known as
Stiles–
Crawford effect of the first kind. The graph below shows the relative sensitivity of the cone receptors of human eye as the pencil of light entering the pupil gets larger. As you can see, the light that enters near the edges of eye pupil is much less effective in creating "perceived brightness".
Fact - II: Human eye is not designed to respond to brightness. Brightness is not a characteristic of objects that we encounter in nature. Oranges, flowers and snakes don't have a characteristic brightness. They have a characteristic reflectance that defines their apparent color and texture. Our eye automatically perceives this reflectance and ignores brightness changes. According to Weber's law, human perceptual threshold for detecting a change in brightness is about 8%. This means, on average, people can not perceive a change in brightness less than 8% of a base level. This law implies that an increase of less than 8% in light transmission would be barely perceptible to most people, even those with young healthy eyes. Again, this is not the eye's fault. It is exactly what human eye is designed to do: ignore brightness (a highly variable quantity) and perceive reflectance (a stable feature of objects and environment).
Fact III: Even if your eye pupil enlarge to 7mm or more, this may not help with resolving details in twilight. A wide open pupil increases the eye's intrinsic aberrations so visual acuity decreases. Human eye achieves maximum visual acuity at pupil dimeters about 2-4mm (Campbell and Gregory, Nature, Sept. 24, 1960, page 1122). At low light, the eye's acuity is very poor and it is independent of pupil dimeter (if artificially constricted).
Fact -IV: Magnification can help the eye see better in twilight by enlarging the object such that it's spatial frequencies fall within the mid-level range of frequencies where the eye can still perceive and resolve details. That's why a 10X50 could be better than a 7X50 in some cases. Picture below shows how the eye's contrast sensitivity changes with spatial frequency. Spatial frequency is measured as number of black and white stripes (cycles) per visual angle (degree). Looking at a low contrast target, the eye can best discriminate spatial detail in the range of about 1 to 5 cycles per degree. Looking at high-contrast targets, the eye can resolve up to 60 cycles/degree.
Finally, the most serious obstacle in using binoculars under low light is "focusing":
Fact -V: As luminance fades, so does contrast of objects (animals, birds, etc.) against their background. Under these conditions, human eye loses a significant portion of its accommodation power. At very low luminance, the eye simply ceases to accommodate and stays at a constant focus state known as "dark focus" state. At the same time, the retina does not provide sufficient blur feedback to allow manual focusing of the binoculars by turning the focus wheel. Lack of precise focus causes more blur in the image which in turn causes lower perceived contrast, a vicious cycle.
Fact - VI: The response time of the retina slows down (signals are sent to brain with more delay) when luminance decreases. The delay in providing visual response to the brain causes the hunter's fingers to overshoot or undershoot the binocular's focus adjustment. (In technical terms, the feedback loop oscillates instead of settling on a fixed value. This is similar to our experience when taking a shower: It is difficult to adjust the hot/cold mixing valve due to the time lag between the time you adjust the valve and the time water pours down from the shower head) .
As a result of factors V and VI mentioned above, a hunter or bird watcher will find it nearly impossible to focus his binoculars in twilight.