World's Best 8X42: The Zeiss 8X56FL (1 Viewer)

henry link said:

Ed,

Check out this DOF thread from Cloudy Nights. It has plenty of math to chew on. Note that I took a position on DOF and focal ratio similar to yours until I was set right by Jean-Charles Bouget and Holger Merlitz.

http://www.cloudynights.com/ubbthre...4,5,8,9,10&Number=268206&page=0&view=collapse

Today I cooked up another backyard technique for measuring depth of field. I think this one is less subjective.

I placed two identical small glass spheres at different distances, nearly in line with each other. One at about 8m and the other about 20m from my viewing position. The sun reflecting from the spheres produced glitter points. I focused one barrel of a binocular on the distant glitter point, then (without changing focus) moved the closer glitter point to the field center. The size of the out of focus glitter point indicates how far out of focus it is. A smaller circle indicates it's closer to being in focus. So the binoculars with the smallest out of focus circles have the widest DOF. The beauty part is that the size of the out of focus circle is visually quite stable. It's so far out of focus that my eye couldn't even attempt to accomodate to it. You don't have to try to judge whether one binocular is more or less out of focus than another at the closer distance, all that matters is the size of the circle. As for my results. I'll just say that so far they are consistent with magnification as the only important determinant, but I will keep playing with it. I hope others interested in the DOF question will try this and post results.

Henry

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Henry,

Thanks for finding the old CN thread. I read it through quickly, and have a general idea where Holger and Jean-Charles are coming from, but I'm not yet able to rationalize their approach with Warren Smith's definition. (Being one of the McGraw-Hill book series Editors I accept what he says as gospel.) Essentially, what it comes down to is this. If the DOF is constant for all binoculars having the same power, then the focal length of the objective should drop out of the defining equation for the DOF of the system. That would constitute a proof in my book. Naturally, empirical measurements should follow theory so long as they are valid, i.e., measure what they should measure.

Blue skies,
Ed
PS. I'm sure you saw EdZ's early posts on the thread.

henry link said:

One of Jean-Charles Bouget's posts in the link above contains some mathematically calculated figures for DOF at various magnifications.

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Thanks Henry.

I read the CN thread with great interest. Apparently, this matter is not well understood (or agreed upon) by many, particularly as it pertains to practical terrestrial binocular viewing. However, I'm inclined to believe there is an applicable formula, provided appropriate constraints are introduced. So, the simple one given by JCB was worth try. (Keep in mind, I am pure layman here.)

To see what the numbers looked like, I solved the formula for DOF (or as I understood the formula (d-d'). It seems that this would at least yield values that could show the degree of difference between magnifications. I then set up a spreadsheet to generate numbers for 6,7,8, and 10x, with the ability to vary the nominal viewing (perfect focus) distance. As well, I played around with the near focus distance (z) to see the effect. Incidentally, I did get the same results that JCB listed in the CN thread for distance in focus with infinity for given power (ie 8x was in focus from 64m to infinity while using 1m for "z" > note: the formula works for any unit of distance, so long as you're consistent throughout the calculation).

As expected, the lower powers yielded larger DOFs. For instance, at 75 feet, using near focus of 1.5 feet, the DOF of 6x came to 44', while 10x showed 25'. As a percent of the viewing distance, this would be 58% for 6x and 33% for 10x. Further, the difference in DOF between 6x and 10x, as a percent of viewing distance, came to 25% (for the above givens). Incidentally, the result when comparing 8x to 10x was 11%. I had expected more actually.

The interesting thing: There was a maximum percentage that I could generate for any magnification comparison. The 11% above was the highest percentage that I could generate for 8 vs 10x. In other words, by changing the viewing distance and/or near focus, there was a limit to the difference in DOF as a percent of viewing distance (for any two given mags). Also interesting was that the maximums occurred at typical birding distances, say 40'-120'.

I did struggle to get a firm near focus distance (represented by "z" in JCBs analysis) by personal measurement. I couldn't really convince myself of the concept. But, as I extensively varied the number around the figure given by JCB, I was able to still get the maximum percentages by varying the viewing distance, which never got extreme in terms of typical birding distances.

Another notion: I imagine that focus accomodation and acceptable blur issues are covered with the foregoing, because the subjectivity is built in with this (what I'm calling) near focus distance (z), which I expect varies from person to person. As well, although it certainly affected DOF at a given distance, changing "z" didn't really affect the ultimate comparison between different powers, only the distance at which they varied most.

Finally, I'm not totally convinced that the formula is perfect (or that is isn't). I'm also not completely confident that I executed it perfectly. However, the trends seemed quite logical, and fairly believable.

It would be interesting to compare such with the (non subjective) field tests being described here. I'm limited in my bino stable, but will be playing around to check feasibility.

Really, a more knowlegable person needs to do these calculations. I'm hopeful that a consensus can result from all the discussion.

Sorry for the ramble,

APS

APS

It has been some years since I generated this table and to be honest, I do not remember a whole lot of detail on the derivation of some of the variables. I was just looking to generate a baseline on a "standard set" to compare other optics against in a hope of being able to rate them and I am not wanting to repeat that process again. I still use this table for estimating and the only thing I can say about it is that it apears to support Henry contention that DOF is pretty much the same for instruments of the same power.

If you have the time or inclination, compare it to your spread sheet and let me know if it fits. Thanks

Ron

Surveyor said:

APS

It has been some years since I generated this table and to be honest, I do not remember a whole lot of detail on the derivation of some of the variables. I was just looking to generate a baseline on a "standard set" to compare other optics against in a hope of being able to rate them and I am not wanting to repeat that process again. I still use this table for estimating and the only thing I can say about it is that it apears to support Henry contention that DOF is pretty much the same for instruments of the same power.

If you have the time or inclination, compare it to your spread sheet and let me know if it fits. Thanks

Ron

Click to expand...

Ron,

I don't understand the table. Sorry The hyperfocal distance doesn't vary with effective aperture, altho it should diminish as f/# increases. Maybe I'm not readin it right.

Ed

elkcub said:

Ron,

I don't understand the table. Sorry The hyperfocal distance doesn't vary with effective aperture, altho it should diminish as f/# increases. Maybe I'm not readin it right.

Ed

Click to expand...

Ed;

It has been too many years since I delved into this and the table is left over. If memory serves (and I have reason to doubt that) as aperture increases, so does focal length (hence as aperture get larger, bins get longer), therefore f# stays approx. constant. I am not saying the table is accurate, may not even be of use, I just wondered if it would compare with APS's spreadsheet.

Ron

Surveyor said:

APS

... the only thing I can say about it is that it apears to support Henry contention that DOF is pretty much the same for instruments of the same power.

If you have the time or inclination, compare it to your spread sheet and let me know if it fits. Thanks

Ron

Click to expand...

Okay - When I initially compared the numbers, they did not match. Your DOF numbers were higher, and varied more with power. (Note: I am only looking at the target distance, magnification, and DOF.) However, I have been wondering all this time about a potential problem with the wording of the CN thread from which I got the formula. In one of his posts, "JCB" mentioned that he could focus his 10x40 at 15m and it would still be sharp down to 12m, for a "DOF" of 3m, which agreed with the formula. He never mentioned what the far (background) sharp distance that was. It seems like the total DOF would be the SUM of the distances BOTH in front of AND behind the target.

Considering this possibility, and the higher numbers, I just copied my work and solved for d (called it d") instead of d', with d' set to the target distance. Then, I added the two results together (presumably adding foreground and background sharp distances together). As you might expect, it had a very large effect. (Note that in my earlier post that I had expected higher nos.) I also tweaked "z" from 2' to 3' which brought my 10x number close to yours. What's interesting is how well the rest of the results also matched. Yours were still a little higher, but the trend was VERY similar. My calculated DOFs (at 50') were 20' for 10x, 32 for 8x, 43 for 7x, and 64 for 6x.

I then increased the object distance gradually. As expected, the DOF, especially at 6x, began to go very high. Just past 70', the formula blew up for 6x, giving negative numbers. I assume this was basically indicating infinity focus. When I got high enough for 7x to blow up, the foreground distance in focus was about 49'. In other words, at 7x, every thing from about 49' out to infinity will be in focus. That's in agreement with JCBs chart on the CN thread. I don't know if it's right or not, but I at least feel pretty good about the formula performing.

I'd like to see if other field measurements could confirm the accuracy (or failure) of this (or some other) math approach. I'd be glad to attach the Excel spreadsheet if someone will tell me how. This doesn't claim that power is the only significant factor, but might give a measure of HOW MUCH of a factor it is, with other things being equal.

APS

APSmith said:

Okay - When I initially compared the numbers, they did not match. Your DOF numbers were higher, and varied more with power. (Note: I am only looking at the target distance, magnification, and DOF.) However, I have been wondering all this time about a potential problem with the wording of the CN thread from which I got the formula. In one of his posts, "JCB" mentioned that he could focus his 10x40 at 15m and it would still be sharp down to 12m, for a "DOF" of 3m, which agreed with the formula. He never mentioned what the far (background) sharp distance that was. It seems like the total DOF would be the SUM of the distances BOTH in front of AND behind the target.

Considering this possibility, and the higher numbers, I just copied my work and solved for d (called it d") instead of d', with d' set to the target distance. Then, I added the two results together (presumably adding foreground and background sharp distances together). As you might expect, it had a very large effect. (Note that in my earlier post that I had expected higher nos.) I also tweaked "z" from 2' to 3' which brought my 10x number close to yours. What's interesting is how well the rest of the results also matched. Yours were still a little higher, but the trend was VERY similar. My calculated DOFs (at 50') were 20' for 10x, 32 for 8x, 43 for 7x, and 64 for 6x.

I then increased the object distance gradually. As expected, the DOF, especially at 6x, began to go very high. Just past 70', the formula blew up for 6x, giving negative numbers. I assume this was basically indicating infinity focus. When I got high enough for 7x to blow up, the foreground distance in focus was about 49'. In other words, at 7x, every thing from about 49' out to infinity will be in focus. That's in agreement with JCBs chart on the CN thread. I don't know if it's right or not, but I at least feel pretty good about the formula performing.

I'd like to see if other field measurements could confirm the accuracy (or failure) of this (or some other) math approach. I'd be glad to attach the Excel spreadsheet if someone will tell me how. This doesn't claim that power is the only significant factor, but might give a measure of HOW MUCH of a factor it is, with other things being equal.

APS

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APS;

Thanks for looking. As I have said it has been a long time since I looked at this stuff and a lot of it came from my brother who did some optics design at the cape just after college (long time ago). I was trying to remember some details when elkcub brought it up. The figures match a couple pair of bins I tried it with, but I used the bins to set the circle of confusion. Seems as if I remember using a blur ratio of aperture/300 or aperture/100 pi thinking that was about what I called acceptable blur. I have not read the article your are referring to and not really wanting to go through that process again unless it appears that it would be useful.

Thanks for checking and if I remember any more useful details about what I did I will PM to you so I do not start a contraversy over something I admittadly know very little about.

Ron

BTW just thought I would mention this. In the table, 1/2 the hyperfocal distance (+/-) would be the near blur limit and infinity the far blur limit. In the 7x case, about 65', so your 49' seems about right considering diff. in blur ratio.

Surveyor said:

Ed;

It has been too many years since I delved into this and the table is left over. If memory serves (and I have reason to doubt that) as aperture increases, so does focal length (hence as aperture get larger, bins get longer), therefore f# stays approx. constant. I am not saying the table is accurate, may not even be of use, I just wondered if it would compare with APS's spreadsheet.

Ron

Click to expand...

Ron,

Say again where this table came from. I thought you had 5 different binoculars/telescopes 6, 7, 8, 10, and 15x that were stopped down to five different apertures. Or did you have 25 instruments? :stuck:

In any case, it would be helpful if you could tell us the focal lengths involved.

I've attached a quick graph of your first column of hyperfocal distances in relation to my predictions using (M-1)^2. (M=magnification.) The scales don't correspond, but the important thing to note is the almost perfect growth prediction. So far, I'm happy.

I'll explain how this came about after checking my algebra.

Ed

Had a little time during lunch to think about this. This is just a speculative opinion. One of the reasons I believe that DOF may be mostly related to power without regard to f-number is that f-number is mostly a term borrowed from and directly related to photography. The f-number has a large effect on film but not much on vision. If we were working with film, a change from f5 to f4 would let us use ½ the shutter speed to expose the film and we know that film has no self-accommodation. If we are looking through a bin with a given exit pupil diameter, we see the image with the same brightness regardless of f-number (focal length’s and aperture set the value, unless we are stopping down the aperture) and our eyes can take whatever time they need to accommodate the image (or maybe our eyes adjust to the f-number needed) i.e. if looking at a image with a 4 mm exit pupil, the eyes will accommodate the DOF whether it is f4 or f6 or maybe even f10.

Of course this just an unsubstantiated opinion and opinions are just like……………….. and the theory may be just like Swiss cheese, full of holes

In daylight all mid-size and larger binoculars will have the same effective aperture due to the iris, and hence the only factor of significance will be the magnification and image distance, which together determination the image magnification i.e. the image size divided by the object size.

I would guess that as the light dims, so the iris will dilate, and the depth of field will increase. However, at a certain light level different receptors in the eye start to take over, and of course the optical properties of the eye change, due for example to the cornea. So it's far from clear (to me anyway) what will happen.

Surveyor said:

Had a little time during lunch to think about this. This is just a speculative opinion. One of the reasons I believe that DOF may be mostly related to power without regard to f-number is that f-number is mostly a term borrowed from and directly related to photography. The f-number has a large effect on film but not much on vision. If we were working with film, a change from f5 to f4 would let us use ½ the shutter speed to expose the film and we know that film has no self-accommodation. If we are looking through a bin with a given exit pupil diameter, we see the image with the same brightness regardless of f-number (focal length’s and aperture set the value, unless we are stopping down the aperture) and our eyes can take whatever time they need to accommodate the image (or maybe our eyes adjust to the f-number needed) i.e. if looking at a image with a 4 mm exit pupil, the eyes will accommodate the DOF whether it is f4 or f6 or maybe even f10.

Of course this just an unsubstantiated opinion and opinions are just like……………….. and the theory may be just like Swiss cheese, full of holes

Click to expand...

Well, surprisingly your thinking comes close to mine. Using a little algebra with the standard lens formula, it becomes evident that the DOF' (depth of focus) of a telescope reduces to:

Fo(fo/#)B/(1+m)^2

where Fo is the focal length of the objective, (fo/#) is its f-number, and B is the acceptable angular blur. This shows that the depth of focus of the binocular is directly proportional to the focal length and f-number of the objective, but inversely proportional to the square of the instrument’s magnification. In other words, the relationship with magnification is nonlinear as shown in the graph above. However, keep in mind that the observer can change pupil diameter dynamically, and when p < EP (= exit pupil) this modulates the objective’s f-number via the effective aperture.

Although this algebra affirms the great importance of magnification in determining depth of focus, it is not obvious, at first, why empirical measurements using distance tend not to show focal length as playing its rightful role in perceived depth of field. To explain this aspect of the problem, the most likely consideration is that although the instrument’s focal lengths and magnification are fixed, the observer controls the system aperture! Hence, within broad limits, the observer can, and probably does, adjust p to compensate for small percentage differences in focal length, thereby offsetting its apparent effect. To support this notion, it is well known that the pupil changes involuntarily in response to both emotional and cognitive events, a fact that has been exploited to study cognition experimentally and also to develop lie detection systems. Moreover, it is also understood that in normal vision the eye constantly seeks to minimize blur, which, with advancing age, cannot be accomplished very well through accommodation alone. Accordingly, in order to assess depth of field behaviorally, it is crucial to have experimental control over the observer’s momentary pupil diameter. Since this is not possible by direct intervention, pupil diameter would at least have to be monitored unobtrusively to establish the true state of the system.

In summary, then, perceived DOF falls off with the square of (m+1). Hence, magnification is indeed a dominant and perceptually measurable variable. DOF also increases proportionally to the F and (f/#) of the system (or F^2/A), but there is a serious perceptual measurement problem because the observer controls the effective aperture. Hence, what an observer perceives will depend upon his own involuntary and unconscious pupil responses, which are biologically designed to minimize blur, — the very thing he is trying to evaluate. This being the case, efforts to see (i.e., perceive) the effects of small changes in focal length on the object side of the optics will continue to be elusive.

However, the optical effects are still there, and on the image side there is every reason to believe that improved DOF' would enhance the quality of the view.

Blue skies,
Ed

"it is not obvious, at first, why empirical measurements using distance tend not to show focal length as playing its rightful role in perceived depth of field."

Focal length is already taken into account by the magnification. Consider a simple lens element. The longer the focal length, the greater the image magnification. Double the focal length, and you double the image magnification. all other things being equal.

Actually I am a little confused what you mean by the formula. What are you considering? A binocular or simple Newtonian reflecting telescope consists of a primary element focal length F1, and a magnifying element focal length F2. (Maybe I'm easily confused. And I don't even have the excuse of a nice bottle of cider to hand ...)

Leif,

Please read post #11. The focal length of the optical system involves both the objective and eyepiece focal lengths, the ratio of which determines the magnification of the system, m.

The standard lens formula is P = Po + Pe - d*Po*Pe, where P = 1/F. I set d=0 because the objective and eyepiece focal points correspond.

Substituting for F in the formula in post #11, the DOF' is seen to be inversely related to the square of (m+1).

If my reasoning is flawed I'd be grateful for having it corrected. That way I learn. Optics is not my first language. But, hopefully it won't be the death of me.

Scientifically, an observer (human or machine) can not be used to study a phenomenon that it influences by the act of observing it.

Blue skies,
Ed

I'm numb on the subject of DOF. I will, however, attest to the veracity of the "8x32SE look mushy and dull in sunlight" comment found in post #1. Truthfully, I would never have believed it had I not witnessed it with my own, aging eyes.

Earlier this evening, with SE in hand, I wandered afield in search of migrant waterfowl. Good fortune prevailed as I stumbled upon a lovely pair of Hooded Mergansers all gussied up in fresh, spring plumage. My first instinct was to go for the big, powerful Nikon scope, but precious daylight was slipping away and I had my trusty SE hanging lazily around my neck. Heck, I thought, the SE is just a miniature scope with an image about as good as it gets here on mother earth. As I raised my faithful companion, I just knew my baby blues were about to feast on the loveliest pair of courting divers I'd seen all day. It breaks my heart to admit the cold hard truth about the SE 8X32, Nikon model 7381, but the image I saw was exactly as Henry described. To identify what I saw as "mushy and dull" would be generous. Knowing Henry, he was overly kind in his analysis.

I suppose I should make amends for all my SE promotions but, truthfully, I never realized how mushy and dull it could be. I thought I field-tested it under rigorous conditions, but apparently I did not. Please allow me to set the record straight: The Nikon SE 8X32, model 7381 can be very mushy and quite dull EVEN in full daylight. It's even worse in low light. I sincerely regret any inconvenience I may have caused.

John

PS
Upon removing its objective caps, my SE 8X32 (Nikon model 7381) startled me with a supremely satisfying view of two lovebirds swimming and diving in the warm glow of an unseasonably warm, spring evening. Love may be mushy, but it sure isn't dull!

Leif said:

I suspect they made the right choice from a commercial viewpoint, as they want the 8x42 FL to sell in large quantities. Would most people see the difference?

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Leif,

I think with a side by side comparison they probably would. But even if not, their eyes could feel the difference. I made the experience that binoculars with a wide sweet spot and higher focal length are more comfortable for the eyes. The difference is more noticable after a long day of birding when the eyes got tired. I suppose because the eyes unconsciously try to work against the lost of sharpness across the field of view. Surely this depends on age as well as on fitness in general. Maybe this could be one of the secrets behind of what some people call 'ease of view' in binoculars.

Steve

elkcub said:

Scientifically, an observer (human or machine) can not be used to study a phenomenon that it influences by the act of observing it.

Blue skies,
Ed

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This is wrong.
If it were true, it would invalidate all of experimental science.

If the amount of influence is known, it will be taken into account. Meaningful conclusions from experiments can be drawn.

Thomas (scientist, professional)

elkcub said:

Leif,

Please read post #11. The focal length of the optical system involves both the objective and eyepiece focal lengths, the ratio of which determines the magnification of the system, m.

The standard lens formula is P = Po + Pe - d*Po*Pe, where P = 1/F. I set d=0 because the objective and eyepiece focal points correspond.

Substituting for F in the formula in post #11, the DOF' is seen to be inversely related to the square of (m+1).

If my reasoning is flawed I'd be grateful for having it corrected. That way I learn. Optics is not my first language. But, hopefully it won't be the death of me.

Scientifically, an observer (human or machine) can not be used to study a phenomenon that it influences by the act of observing it.

Blue skies,
Ed

Click to expand...

Hi Ed. Thanks for the reply. Optics is definitely not my first language either and thanks for reminding me of that formula.

One thing I will say though is not to confuse depth of focus and depth of field as they are not at all the same. Depth of focus is measured behind the binocular, and depth of field in front! I think it is depth of field we are interested in.

Leif

ThoLa said:

...
If the amount of influence is known, it will be taken into account. Meaningful conclusions from experiments can be drawn.

Thomas (scientist, professional)

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Thomas,

Perhaps I might have said "...influences to an unknown extent or in an uncontrollable way," which was really implicit in the statement. Otherwise, I'll stick with it since it's such a bedrock concept in behavioral science, and should be self-evident.

The observer's pupilary and accommodative responses (to an unknown extent or in an uncontrollable way) affect the outcome of a depth of field distance estimation task by modulating retinal blur. If you know how a lone observer might control or measure these physiological responses, I'm all ears. Those who have had lens replacement surgery can limit the problem to the pupilary mechanism, I guess, but that might be asking too much of the average person.

Ed (scientist, professional, ret.)

Leif said:

...
One thing I will say though is not to confuse depth of focus and depth of field as they are not at all the same. Depth of focus is measured behind the binocular, and depth of field in front! I think it is depth of field we are interested in.

Leif

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Hey Lief,

You've probably forgotten, but you pointed that out to me a few years ago, and it's kept me in focus ever since. :t:

Thanks,
Ed

elkcub said:

Hey Lief,

you pointed that out to me a few years ago

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Normally when someone says I am repeating myself, they mean from a few minutes back ...