Depth of Field Test - Method and Results (1 Viewer)

Ok, I've simmered down a bit now. I think it's best to take on only one Dunnism at a time, so I'll confine my comments to the claim that "stands to reason" from the quote below.


..."If you are a photographer, you know that when your aperture is wide open your photo has a shallow depth of field (so only the subject, or part of the subject, is in focus). When the aperture is narrow, you increase depth of field (so more of the world remains in focus).

It stands to reason that a binocular that is very bright will result in the user’s pupil constricting, thus increasing depth of field."...


Notice that this claim is for a real increase in optical DOF (not a subjective impression of DOF), caused by a change in the aperture and focal ratio of the eye from a rather small increase in light transmission.

Does this really make sense? If an increase in light transmission simply stimulates the eye's pupil to compensate by constricting then virtually all binoculars would appear equally bright. There wouldn't be any "very bright" ones. To use a Dunnish phrase, Pupil Constriction Peter would rob Higher Light Transmission Paul. Anyone who has compared an old single layer coated bin to a fully multi-coated one knows this doesn't happen, but never mind, let's assume it does. The supposed increase in optical DOF from a brighter image can be put to the test using the defocused star method I described earlier.

I picked two 7x50 binoculars with very different light transmission, a Nikon 7x50 Prostar with state of the art transmission in the 90-95% range and an old Leitz 7x50 with transmission around 75%. The difference in brightness between the two is quite obvious, but when I tested them for DOF using the defocused artificial star method I could see no difference at all. I should mention that I even increased the sensitivity of the test by using two closely spaced star points at a distance that caused the edges of the defocused discs to barely touch in both binoculars. Even a very slight difference in the size of the discs would have been visible.

Alas, this isn't the first time I've found myself dismayed by Pete Dunne breezily disseminating an optical myth of his own invention, without testing it or bothering to think it through.

These are some of my thoughts on Depth of Field calculations.

1. There are two lines to be considered. Optical DOF, calculations that are well defined and have a specific meaning and published algorithms from various sources, one set of which is attached as a jpg. For those who remember the pre-auto focus lenses that had the DOF scales printed on them.

2. The other is the mechanism of the human optical and perception system. These include such things as eye pupil diameter, depth perception and accommodation.

3. Since this is a binocular forum, and not a human interface-engineering forum, I have only concerned myself with the optical DOF of the instrument itself. Each individual will have to find out how they react to the instrument specifications as they apply to him or her.

For those of you who are familiar with photography, which appears to be many from comments on the forum, take your favorite DOF calculator for cameras and examine the outputs for the following conditions; 50 mm f:/4 (1x), 400 mm f:/4 (8x) and 500 mm f:/4 (10x). Notice the hyperfocal distances are 32.9m, 2105.7m ((400/50)^2 X 32.9) and 3290 m ((500/50)^2 X 32.9). Also check that the difference of the near and far focus distances when converted to diopters also matches the 64:1 and 100:1 ratios, allowing for round off errors in the calculator.

A binocular objective system is not much different than a camera except the focal plane replaces the film position and is a real image. The eyepiece functions to enlarge this real image by scaling the image (and DOF) to the desired magnification, maybe, adding aberrations. I have found the camera programs to be fair predictors of the optical DOF of binoculars when certain adjustments are made. The COC, or blur ratio, has to be modified because of magnification and the paper size has to be modified in the form of an aperture ratio. Once this is fit to observed data (i.e. scaling the camera data to fit field measurements) the resulting figures are approximately in the range of focus range uncertainty. I have checked this in the past by using a method similar to one posted in another thread and adjusting a camera program to match those measurements and then substituting binoculars of different powers.

This works well when the optical DOF is the limiting factor, like for young people who can dilate to 5 or 7 mm and have accommodations of > 2-3 diopters. For us older folks that can only dilate maybe 4 mm and have accommodations <2-3 diopters, then our own eyes are probably the limiting factor a lot of the time, probably limited to our accommodation. These considerations apply to other measured specifications of the optics also, for instance, someone measures the field curvature at 2 diopters then someone with an accommodation of greater than 2D will see the field a fairly flat and in focus but someone with 1 or 1.5D will see the edges with considerable defocus.

The optic system can be engineered/calculated to a desired status for the average observer, but can anyone predict how any given individual will perceive the image, no. If you are expecting any subjective or objective review to tell you what you will see, I think you will be unhappy with any result. At least with good objective measurements, if you know your limits and visual capabilities you will be able to make a better estimate of the expected performance. The same can apply to subjective reviews also, if the conditions the results were obtained under are included.

Just my thoughts and by no means definitive. Everyone have a very good rest of the year.

Ron

PS. Henry, I have occasionally used one other modification of your procedure to verify that the optical DOF is similar for a given power. I use one sphere with two light sources, one either side of the line of sight, so that I can adjust distance from, and the angle between, the defocus spots to bring them tangent. Great idea, your test

Henry, even with his faulty logic, dunne comes up with bright is good. And i have to say, even at mid price, brightness is good for all my viewing problems. It evens out some problems, such as my two eyes not being the same.

Ron,
Thanks for sharing your work in applying photographic DOF to binoculars. After my saying there's no way to do this, I see that you were already well along the path! I don't doubt the results that you give, so don't think that I'm arguing with you, but I was kind of surprised that the correlation between photography and binoculars is anything like good, because the systems seem very different to me. But I think I see how it can be. I'm just going to lay out how it seems to me, please correct me where I am wrong. I'm not pontificating, just testing my understanding, okay?

A camera forms a real image with a single, or "objective", lens. According to geometrical optics, there is but one focal distance for a given image distance. So, how does depth of field arise? In photography, it arises from the imperfect defining powers of the lens, and the medium. Photographic lenses are compromised to be sharp at the edges, and do not approach diffraction limitation even in the center. This is acceptable, because the grain/pixel structure of the medium could not resolve, at typical photographic focal lengths, diffraction limited sharpness. As long as the image of a point does not exceed that grain size, the image will appear as sharp as can be. The image can in fact be substantially defocused without the point spread function exceeding the spatial resolution of the medium. So, there's a range of object distances for a given image plane, called "depth of field", that will satisfy this criterion. To the extent that lenses and film/pixel resolution don't vary much, DOF is a useful and well-defined concept in photography, to the point where lenses are typically engraved showing depth of field about any setting.

Binoculars are different. If you consider the system independent of a "medium" (which would be the eye), the origin of depth of field is the inherent blurriness of the optic itself. This is limited by diffraction, but I am led to believe that in most binoculars, optical flaws dominate the diffraction blur. As long as enlargement of the image of a point due to misfocus does not exceed the optical blur, the image in the focal plane will be as sharp as it can be.

Folding in the eye may seem a can of worms, but is essential to complete a realistic picture of the situation. In the absence of visual astigmatism, an eye might resolve an angle of 1 arcmin through a well focused eyepiece. The more the eyepiece magnifies, the more visible the blur from the objective becomes, which qualitatively explains the perceived decrease in DOF with increased magnification. But, the fact that photographic and binocular DOF should agree (you say approximately, so I don't know how close you have found them to) is at first surprising. It suggests that binocular and camera lenses are of similar quality, which is not too surprising, but also that the angular resolution of the eye somehow is somehow comparable to the spatial resolution of film/CCD.

I should not be surprised. After all, photography gives results which look good to the eye at a casual glance, but on very close inspection often appear imperfect. Similarly, good binoculars give images which look very sharp in normal viewing, but flawed under boosted magnification. In other words, the quality of photography and binoculars both accurately match/barely exceed the eye's resolving power. Any better performance would be wasted, and poor engineering. So, photographic DOF might very well reasonably match binocular DOF.

Could you tell us what all the symbols in you equations represent? I'd like to work a couple of cases out and see what I get.
Ron

Hi RonH;

I am not going to try a full answer to this today, it would take too long and I would probably have to do some reading to get a coherent answer together. Today is going to be full.

I did take a simple test I did on a pair of compacts the other day and just threw the numbers into a DOF calculator this morning so you could see the correlation. A caution, do not expect the numbers to be exact. There is some focus error and I can not estimate a 100 micron blur diameter very well, it may be twice or half that.

http://www.birdforum.net/showpost.php?p=1355636&postcount=6 is were I made the field test. In the attached jpg, the first two columns are an approximation of those observations. Note, the calculator shows about a 1.7 diopter DOF and what I observed was about 1.9D.

PM me your email address an I will send you the full PDF that goes with the DOF calculator I use.

Hope this helps some.

Ron

For those interested in trying this you can download the free calculator at http://www.vanwalree.com/optics/vwdof.html also download the PDF manual, it is very useful and contains the formulas used.

Below is the way I modify the input to get around not knowing the focal length or f number. I do not use much anymore since I have found some quick estimates that suit my needs but would be interested in any feedback from real data as compared to the calculated values.
------------------------------------------------------------------------------------------------
Set focal length to aperature * power
Set f number to aperture

Set format to x,y size of aperture i.e. 14.142x14.142=20 mm (aperture * 0.707107).
Set COC to percentage of FOV in mm (.085% of 42 mm objective = .036 mm----- Note: change this COC value to match field data.
Note that the COC used so far is the default film values * 0.707107

Thanks Ron,
That is overwhelming and sufficient. The article linked at the bottom of the page is good reading. It is simple matter to transform spatial blur in the image plane to angular blur as viewed through an eyepiece. Then I guess one has to try on a few cases, experiment vs calculation, to discover his own personal tolerable blur criterion. I don't know if I'll ever get there, but this was a good learning experience already.
RonH

RonH and others;

During lunch I took the time to fit the field data a little better (first and last column) and included the input fields as an example.

Ron,
I think I'm on the right track. Computers give me the willies, so I used the equations for near and far points. I tried to reproduce your result with your 8x20 for an object distance of 30m. Not understanding your substitution, I simply guessed the focal ratio to be 4, and used your .019mm circle of confusion. I got:

near point: 22.1m, vs your 20.8m
far point: 46.5m, vs your 53.9m

I suppose the difference is due to my erroneous focal ratio. I am led to believe that roof binos are usually faster than f/4. I can get your results almost exactly with a focal ratio of 3.3. Then, 8x requires an eyepiece with a focal length of 8.3mm. Through such an eyepiece, the .019mm COC would appear to subtend 8 arcmin. A good eye can barely resolve 1 arcmin under the best conditions, 3 is usually more like it, and 8 is reasonable in this "stretch" situation. I presume you accepted a slight apparent blur.

So I think I get it, but please straighten me out if I don't.
Thank you,
RonH

Wow, this thread has a lot of great info. Kevin's "defocused sign" and Henry's "glitter points" sound great. I like the idea of an easy to use test and those are pretty simple. One thing about "larger disks" in that message, higher magnifications would show larger disks, correct? So it may be hard to compare say a 7x and 8x? I'll have to try.

To summarize the thread (let me know what I missed):
- Perceived DOF (the very generic and broad sense, not in a optical science sense) is dependent on a lot of variables, such as field curvature, eye dilation, light level, but is most dependent on magnification.
- DOF in an optical sense would be far more difficult to observe but can be calculated.
- Focus habits can also affect apparent depth of field (front/back focus)
- Tape measurement has calibrated numbers but the actual readings are too prone to error for even a subjective test.

BTW, could binoculars be designed at F4. That's a pretty fast focal ratio. I'd suspect F5.6 (like most scopes) or F8. An 8.3mm eyepiece in astronomy has to have a pretty advanced design to have any eye relief at all. I understand that eyepieces in bins are often the earlier, low eye relief design so wouldn't the actual eyepieces have to be in the 15-25mm range? I would be glad to see some published specs.

Thanks much.

Matt

Matt,

If you compare 7x and 8x bins using the a glitter point the defocused disc will be larger in the 8x because it's more out of focus, not because it's enlarged by higher magnification. If you see different sized discs in binoculars that are supposed to have the same magnification it's an indication that the magnifications are actually not the same.

Most binoculars have focal ratios around f/4 or lower. That's why the image usually looks pretty poor if the magnification is boosted very much. They're just not very good telescopes. However, in daylight the effective focal ratios are higher. For instance a 5mm exit pupil binocular with an f/4 objective will be stopped down to f/6.7 if the eye's pupil is closed to 3mm.

Specs for objective and eyepiece focal lengths are rare. I've measured a few directly and occasionally you can employ a trick or two to figure them out. If two binoculars in the same series use the same eyepiece and prism, but have different magnifications you can measure the difference in physical lengths to determine the focal lengths of the objectives. For example, the Nikon 8x30 and 10x35 EIIs use the same EP and prism. The difference in length measured from the objective glass is about 27mm, so you could say that each 1x of magnification in these binoculars equals about 13.5mm of objective focal length. The 10x35 has a 135mm f/3.86 objective and the 8x30 is 108mm f3.6 and, of course, the EP focal length is about 13.5mm.

Henry

As long as we are dragging this on, is it true that a porro in the same size as a roof, say 8x42, has more DOF? Yes or no, plus any math you want to add.

Tero,
I can't see why there would be difference for prism type. No math needed, prism type simply is not a parameter in the equations. There might be a DOF-like illusion from the Porro's increased stereo effect, like "the view has more depth", but not DOF in the strict sense of what distance range appears fairly sharp.
Ron

I have two 8x42 pairs, and I was not able to see one either, other than the porro was sharper, confusing me a bit.

Tero,
Well, an overall sharpness difference could sure throw you off. Some say the sharper bino will appear to have greater DOF, since, being sharper to begin with, it has more "headroom" for defocus tolerance. I'm not so sure. With a not-so-sharp binocular, a bit of additional blur might not stand out like it would when added to a very sharp image. Duh.
Ron

I just ran the numbers on some binoculars with the VWDOF Calculator that Surveyor posted.

But first a word of caution.

The DOF calculator was developed for cameras, not binoculars. So a bit of tweaking and guesswork is required for the calculator to output DOF estimates for binoculars.

As Surveyor suggests, here is the tweaking that is required to run your own numbers.


Second, as stated many times above, depth of field is used exclusively for terrestial use, particularly in close-up viewing. It has no place in astronomy viewing when all binoculars are focused upon infinity.

Next, binocular depth of field is influenced by prism design, eyepiece design, perceived sharpness, and eyeball dimensions of the observer, to mention a few of the variables that have been reported in the threads. Consequently, field tests have shown repeatedly that two different binoculars of the same dimensions may easily produce different DOF results for different situations and with different users.

Finally, DOF calculation should be done primarily to identify trends (or DOF gaps) in binocular collections.

. . .

Having said the above, here are a few estimates [er... tweakimates] on some common binocular sizes.


. . .

WOW, the lower power sizes are really DOF-friendly. If you do a lot of nature viewing during the day, I recommend you add one or two lower power models to your collection. My DOF gem is the Leupold Katmai 6x32 roof CF--where an extended DOF contributes greatly to obtaining quick, one-handed views. The Fujinon Polaris FMT-SX 7x50 porro IF is DOF friendly as well--although I must use both hands for this big guy.

Surveyor, thank you for posting the VWDOF Calculator. I may not have used it properly, but it did get me thinking about how important DOF can be in certain situations.

--Bob
Kentucky, USA

Even 7x is way more pronounced than 8x. A real advantage in my book. I may get a 6x eventually but I haven't found a problem yet that a 6x would solve. Though I am a hopeless gearhead so why need an excuse.

Matt_RTH said:

Even 7x is way more pronounced than 8x. A real advantage in my book. I may get a 6x eventually but I haven't found a problem yet that a 6x would solve. Though I am a hopeless gearhead so why need an excuse.

Click to expand...

Woodland birding.

Especially when they're in brush, they're singing or scolding, you are close but still can't see them so you have to scan depthwise in the brush.

I remember having problems like this using a Pentax WP 8x32 looking for a wren in a thicket. I wanted to ID it particularly because I'd seen lots of Bewick's Wrens in this location, a couple of Winter Wrens and I was curious if this was going to "complete the set" with a House Wren. I was perhaps 6 feet or a little more away from it.

I was sorry I hadn't brought the Yosemites.

I was birding at sun down with 10x42. Depth of field was poor. Is it because my eye is dilated?