If you compare ANY two binoculars of the same magnification you will see virtually the same size disc. I say virtually because the actual magnifications may not be exactly the same between two bins labeled with the same magnification. I place one binocular to one eye and the other binocular to the other eye and center the disc in both side by side which allows a very accurate comparison. If you compare bins of different magnifications the difference in the disc sizes is not subtle. The disc through a 6x bin is about half as large as an 8x bin and a 10x is 60-70% larger than an 8x.
Well, I composed a response yesterday, but deleted it because I thought it might be interpreted as argumentative (heaven forbid), and possibly a bit pompous (I’m trying to improve). Also, it occurred to me that it wouldn’t be too hard to try out Henry’s technique in the back yard. I managed to find a single red Xmas tree ornament, and the sun cooperated nicely. The trial was finished just a few minutes ago. I hope my eyesight wasn’t hurt permanently.
I decided to use all four of my Swarovski SLC’s to maintain as much similarity as possible; all roof, same manufacturer, same quality, equal owner affection, etc. They made for a nice 2x2 experiment design, — two 10x and two 8x, each pair having a large and small objective variant. Specifically, they were the 10x25, 10x42, 8x20, and 8x30.
There were two trial sets, each using a different sun angle. The second was better because the glitter point was at the top of the ball and made for an easier visualized disk. I should point out that when on-axis all binoculars produced a nice circular disk with a strong red fringe. Off-axis they rapidly changed to oblongs, whether vertically or horizontally. I should also add that when these disks were examined they were not stable; there was a 3-4 sec. waiting period to be perceived clearly as a disk. The impression is that my eye was accommodating, or more broadly speaking, “adapting”. Problem 1 — Whatever happens in the eye may influence the results. Solution — none that I can think of.
I did all subsequent comparisons with my left dominant eye.
Although Henry apparently uses two eyes to compare blur disks simultaneously, I would not recommend this because the eyes do not function independently. Binocular rivalry often cross-contaminates what each eye perceives, eliminating or averaging differences when they are small.
There were two primary questions: (1) were the 10x disks perceived to be larger than the 8x?, and (2) were the disks from larger objectives perceived to be a different size than those from smaller ones? After preliminary efforts to set up the binoculars at a uniform focusing distance, i.e., several leaves at the top of a tree two hundred feet away, it became evident that everything depended on how accurately that was done. A small change in infinity setting has a clear effect on disk size. Problem 2 — repeatability. Solution — do this several times to average out error. I did it three times, not enough.
The results were as follows:
1. 10x binoculars produced larger disks than 8x. Theory says they should be in the ratio of 100:64 (nonlinear), rather than 100:80 (linear). The difference looked more like theory would predict, but I wouldn’t stake my life on it.
2. For both 10x and 8x pairs the larger objective
consistently seemed to produce
slightly larger disks than the smaller ones.
3. Results 1 and 2 were replicated after resetting infinity focus thrice.
Discussion:
Result 1 is
possibly consistent with theory, result 2 is not. The larger objectives should produce greater DOF and, hence, smaller out-of-focus disk sizes. They appeared to be, however, slightly larger.
One explanation for result 2 might be that the two small objective (pocket) binoculars were slightly higher power than spec, or the large objective binoculars lower than spec, or some combination of the two. If disk size grows with the square of magnification, then any small difference would be exaggerated.
Another explanation is that this observer did not infinity focus the pocket binoculars in the same way as the larger ones. A procedure was used to approach infinity from a point beyond and work inwards, but there is no guarantee that this corresponded to an equivalent setting in each case. The focuser gains are different between the binoculars, with the pocket pairs involving more turns and possibly yielding more precision. High gain conversely, could produce more error.
Yet another explanation is that my perceptual estimates of size were contaminated by scene disparity, in particular, monocular field of view or distance cues. Pocket binoculars always have a smaller FOV than their full size mates. Size estimation has many pitfalls and this may simply have been one of them. Side by side comparison with both eyes, as mentioned above, has yet other complications, particularly a tendency to average out small differences — which would obviously bias the results to not seeing any.
Other comments:
1. There is no doubt that the visualized disk monotonically changes with defocus. Rack the focus wheel from one end to the other and observe it spread out or contract. I’m not sure if the growth is linear, but the disk will also grow larger beyond the observer’s infinity focus. (I have some residual concern about this, as relates to physical scaling.)
2. The procedure is, as Henry mentioned, easy to perform (although not so easy on the eyes.) I am concerned with the
visual adaptation process that obviously occurs when the out-of-focus glitter point is first addressed by the eye. This may involve several things including lens accommodation and pupil changes to minimize retinal blur. I certainly experience strain whatever it is. That being the case, it’s hard to know if the same physiological state obtains for each binocular. As I’ve mentioned on other threads, differences in pupil diameter affect both the effective aperture and f/# of the system. Hence, they constitute a problematic basis for a nasty observer effect.
3. In my opinion, although the present results do not support the theory that larger objectives, with longer focal lengths, have a greater DOF, they also don’t quite support the thesis that they are the same size either. Besides, the "null-hypothesis" can't be proven. All in all, I would say that the procedure, as ingenious as it is, is subject to sufficient vagary that it not likely to strongly verify nor refute theory. The weak point is that it's all based on size perception. Personally, I'm also not convinced that the adaptations required to perform the task don't mask the optical advantages that some believe a larger objective provides. But, that's just me. I need my theories disproven before I give up on them.
Thank you Henry for an interesting exercise, and I'm going to save my red ball for the future. It’s been fun, but now I need to take a nap.
Blue skies,
Ed