[ScoutMan]

Have there been any comparisons made say between the Leupold Cascade (8x42) Porro and the other 6X+ bins like the Yosemite, Raven, and Raptor?

[FrankD]

Depth of Field or Depth of Focus?

The depth of field difference between the 8x42 Cascade porro and the 6x bins like the Yosemite, Raven, etc... is fairly noticeable and should be substantially different (favoring the 6x) simply because of the difference in magnification.

The term depth of focus is something I have not really seen used except here on Birdforum (I am giving Steve C. credit as I believe he was the first to coin the term). The depth of focus on the Cascades is very good simply because of the moderate-slow focusing speed, the porro design and the excellent apparent depth of field for an 8x binocular. The depth of focus on the 8x Cascade is very good in my opinion and entirely similar with the 6.5x Raven I just compared it to.

[elkcub]

Originally Posted by FrankD

Depth of Field or Depth of Focus?
...
The term depth of focus is something I have not really seen used except here on Birdforum (I am giving Steve C. credit as I believe he was the first to coin the term). The depth of focus on the Cascades is very good simply because of the moderate-slow focusing speed, the porro design and the excellent apparent depth of field for an 8x binocular. The depth of focus on the 8x Cascade is very good in my opinion and entirely similar with the 6.5x Raven I just compared it to.

"Depth of field" and "depth of focus" are conjugate concepts in optics. One applies to the object side, and the other to the image side. In general, any relationship proved in one domain can be transformed into an equivalent relationship in the other, but the transformation isn't always intuitive. For one thing, longitudinal vs lateral magnification needs to be considered. So, smart as he is, Steve C. didn't coin the term.

This is one of those cases, I'm afraid, where the strict optical meaning and everyday usage of "depth of field" are not mutually supportive. First, the optical concept is monocular in nature, not binocular. Still, most folks report what they see binocularly, and think of their perceptions as resulting from an inherent property of the binoculars. In fact, because binoculars (and telescopes, in general) are afocal devices, they simply can not possess a finite depth of field. Optically, they alter the depth characteristics of the observer's eyes inversely with magnification (M), or M-squared, depending on whether we are talking in the image or object domains.

Leaving that aside, I am convinced that there are observable differences between binoculars of the same power in terms of their apparent field depth. I would even go so far as to say these impressions have been supported by legitimate evidence of focusing differences between objects near and far, — binocularly and monocularly. We might, then, call this the Depth of Field Paradox.

I'm hoping to cobble together a plausible explanation for the paradox, but I don't think it will turn out to be entirely within the framework of the instrument's optics. Rather, I believe the nature of the visual process itself must be included. But, I'm getting ahead of myself... nap time.

Ed

[FrankD]

Very educational Ed and thank you for the correction on the origins of the term depth of focus. Do you have similar info to share on depth of focus as you did with depth of field?

FWIW I agree with your distinction between actual, measurable depth of field from a scientific perspective (monoculars in particular) and the apparent depth of field that most individuals experience based on the particular binocular and personal sensory abilities.

[Howard220]

Frank, for all the years I've been a photographer the term "depth of field" was meant to mean how much near through far in a photograph is rendered acceptably sharp. As you probably know, all things being equal when setting up a shot, the smaller the aperture of the lens' diaphragm, the more near-to-far is in acceptable focus. (Note there is but ONE plane of focus. The emphasis here is on the term "acceptable.") So by varying the aperture, you can vary the.. depth of... focus....

Some years ago someone came along in a posting somewhere that corrected the term "depth of field," saying that what we really mean is "depth of focus." Considering the above, it makes perfect sense to me.

[FrankD]

Some years ago someone came along in a posting somewhere that corrected the term "depth of field," saying that what we really mean is "depth of focus." Considering the above, it makes perfect sense to me.

Hmm, interesting Howard. I was thinking of the terms as mutually exclusive and not entirely inter-related. Maybe Steve can come on and repost the description of depth of focus that he had been using. My interpretation of Steve's description was how far you could rotate the focus wheel back and forth from "perfect focus" for your eyes and still receive close to perfect focus with the image. That may or may not be what the actual technical description of "depth of focus" really is but it was the term I had been using to describe this particular optical characteristic. If there is another more appropriate term for what I am describing then I will be happy to start using it.

[Howard220]

Yeah, I really don't know. In reference to binoculars, you may be right about that particular term. HOWEVER... ;-) Thinking about your description, I believe a *good* binocular snaps into focus on the viewed object. You are always certain you've got it. My Swift Audubon 804R's are like that. One of lesser optical quality allows you to focus back and forth, never easily finding the perfect focus. My Nikon Sportstar 8x25's are like that.

[FrankD]

That is true about the "snapping into focus" however there are bins that do have that snap and yet allow you to retain that snap over a limited, and yet useful, distance of the focus range.

[elkcub]

Originally Posted by FrankD

Very educational Ed and thank you for the correction on the origins of the term depth of focus. Do you have similar info to share on depth of focus as you did with depth of field?

FWIW I agree with your distinction between actual, measurable depth of field from a scientific perspective (monoculars in particular) and the apparent depth of field that most individuals experience based on the particular binocular and personal sensory abilities.

Rather than oversimplifying, the following 3 pages from Warren J. Smith's Modern Optical Engineering (1990) pretty much says it all in a most elegant and concise way. Be brave. Start at the bottom of pg. 145. Keep in mind that the "system," in our discussion, is a telescope being used for viewing. Namely, we are putting together an afocal instrument with a focal eye. The total system is focal.

Equation 6.10 is particularly important, and easy to miss. "...The depth of field and the depth of focus are related by the longitudinal magnification of the system." Most people don't understand longitudinal magnification, and that little factoid eluded me for some time. It accounts for differences between various analysts' results, some finding DOF to be inversely related to m and some m'-squared.

Unfortunately for those who would like to marvel at the DOF of their own hybrid bio-optical systems (binoculars), it depends upon the instantaneous focal length and aperture of the eye, scaled by the effective magnification of the binocular-telescope. These parameters are constantly changing due to accommodation (i.e., eye focus changes), pupil dilation (i.e., brightness modulation), and manual focusing (i.e., voluntary working distance changes). Assessing it by observation is similar to eating Jello with chopsticks. For the most part, however, except for some overlapping ranges of working magnification at near distances (i.e., pathological cases), binoculars with higher magnification will produce smaller system DOF, or DOF'

Again, it's all based on definitions, and folks are free to define things as they wish. However, using the technical development above, is there anything stated as to the width of the field that is in or out of focus? Or, is the development based on axial targets, — which I think is the case. Global assessments of the whole field in terms of focus-distance relationships are quite a different kettle of fish, and that's where I believe the visual process enters back stage. The visual process is busy putting together a 3-dimensional representation from two partially overlapping 2-dimensional images, and visual perceptions we report result from the interaction of the retinal stimulation and these processes.

Sorry to be long in the tooth, and getting preachy besides. Comments/corrections are welcome. Discussion even more.

Ed

[dustyview]

Good post, Ed. Thanks for the information. The only thing that I can add that may be of interest is that "acceptable" in photographic lens terms, while it may have originally been based on resolution (film grain), in fact varies by manufacturer. About 12 yrs. ago I bought my first new Hasselblad system, and was a little disappointed to see that Zeiss' estimation of acceptable hyperfocal blur in the 80mm T* Planar was too much for my eyes. Finally, after a few letters back and forth, Hasselblad admitted that I needed to scale the DOF estimates down at least a full stop to get the results (acceptable DOF/sharpness) I required. I've experienced this with other makers, but not to the same degree.

[elkcub]

Originally Posted by dustyview

Good post, Ed. Thanks for the information. The only thing that I can add that may be of interest is that "acceptable" in photographic lens terms, while it may have originally been based on resolution (film grain), in fact varies by manufacturer. About 12 yrs. ago I bought my first new Hasselblad system, and was a little disappointed to see that Zeiss' estimation of acceptable hyperfocal blur in the 80mm T* Planar was too much for my eyes. Finally, after a few letters back and forth, Hasselblad admitted that I needed to scale the DOF estimates down at least a full stop to get the results (acceptable DOF/sharpness) I required. I've experienced this with other makers, but not to the same degree.

Hi Dustyview,

Interesting. Since film grain size is physically measurable (and assuming some common reference film) one would think the camera manufacturers would not play around with the blur criterion for marketing purposes. What is this world coming to? :)

Ed

[FrankD]

Very nice Ed. Thank you. I am going to read it over a second time to make sure I understand it correctly. However, it seems that his comments specifically about binoculars ring true to what we had both been saying earlier.

[henry link]

Ed,

I'm looking forward to your work on this subject. Something new will be welcome. We've both been around the block a few times with the DOF subject.

Frank,

There is a good enough definition of Depth of Focus in lenses and the distinction between it and Depth of Field at Wikipedia here:

http://en.wikipedia.org/wiki/Depth_of_focus

Under this definition Depth of Focus in binoculars would be measured internally at the objective focal plane (analogous to the film or sensor plane in a camera lens) and plays no role in determining Depth of Field at the eye.

I think its not a good idea to throw a number of unrelated optical and mechanical characteristics into a undifferentiated subjective Depth of Field bin. We know impressions of DOF are affected by such unrelated things as focus speed, field curvature, and severity of axial aberrations and defects. But, we'll have a very poor understanding of what's happening optically if we assume that a binocular with high field curvature has excellent DOF or that one with a fast focus gearing has low DOF. For instance, very high field curvature could create the impression that a 10x binocular has wider DOF than an 8x binocular with a flat field, when, in fact, the very opposite is true. In this example try thinking of the planes of sharp focus in the binocular fields as bowls. In the 8x flat field binocular the bowl is shallow, but thick walled. In the 10x binocular with high field curvature the bowl is deep but thin walled. DOF is the thickness of the bowl wall, not the depth of the bowl.

Henry

[elkcub]

(Henry Link)...I think its not a good idea to throw a number of unrelated optical and mechanical characteristics into a undifferentiated subjective Depth of Field bin. We know impressions of DOF are affected by such unrelated things as focus speed, field curvature, and severity of axial aberrations and defects. But, we'll have a very poor understanding of what's happening optically if we assume that a binocular with high field curvature has excellent DOF or that one with a fast focus gearing has low DOF.

Coming around the block for the nth time, I've arrived at the conclusion that saying the same thing for the (n+1)th time will probably not produce a different result. Good idea or not, it's safe to say that people will continue to "...throw a number of unrelated optical and mechanical characteristics into an undifferentiated subjective Depth of Field bin."

There are two aspects to this. First, there seems to be a belief that theoretical optics terms always have a real counterpart that can be observed directly. This is not the case. Second, in this instance there is obviously a compelling if not universal perception, which people find very difficult calling anything but "depth of field." This is probably because the phrase is the most accurate description of the common perception.

So what's more important, that everyone be disciplined to use the optical terms correctly, or that we begin to examine and understand the underlying reason why people have this perception?

As users of binoculars, we should, in my view, be more interested in recognizing and explaining common observer responses, than in retaining the purity of discourse about abstract optical concepts. For example, "...such unrelated things as focus speed, field curvature, and severity of axial aberrations and defects..." really are related. They are related by the common perception of apparent DOF. The questions are how and why?

I'm glad the example of field curvature correction came up, since I have a growing belief that it has particularly strong interactions with a visual process known as the horopter, which is intimately related to the perception of spatial depth. (Even BF's spelling checker doesn't recognize that word, but Google hits are abundant.) In effect, the brain is accustomed to certain image relationships on the two retinas that are most likely compromised, to one degree or another, by focus changes and other optical effects over the projection field. The commonly used phrase "natural view," I believe, is probably related to these relationships with the horopter. But, unfortunately, I'm not aware of any applicable visual science in this area. Most studies seem to be related to abnormal vision, such as muscular imbalance or abnormal differences in magnification between the eyes.

Ok, you made me say it, Henry. Hopefully, I have not offended you or anyone else.

Ed

[henry link]

Ed,

Purist I may be, but the problem I see with lumping many causes together into a subjective impression of DOF is that each cause has a very different implication for the quality of the optics (as usual I'm talking about properties the optical instrument). If an impression of "shallow" DOF comes from an absence of field curvature I would consider that to be a good thing, but if the same impression comes from excessive aberrations that would be a bad thing. Focuser speed would be an optically neutral cause and a sample specific defect like astigmatism would be a red herring since it could occur in any binocular. Perhaps it's naive, but I'm inclined to attribute most reports of differences in DOF to simple mistakes, observations that are made too casually. Even if the raw observations are correct, I think they're still not very useful for evaluating optics without establishing the specific cause.

"Horopter", something totally new to me, if it turns out to be another cause related to the eye brain system should be an interesting addition to the list, once you've explained it.

Henry

[jcbouget]

I have already made some comments in the past about this subject. In the beginning there is nothing new, I am just trying to describe things with my own words.

Binoculars by themselves don’t have DOF characteristics. Right. The optical system that is interesting for us is the combination (binocular + eye), in which the eye itself is considered as an optical system, with an aperture stop, a focal length, a focal plane, etc. In this compounded optical system, the depth of focus is what happens on the retina, and has no practical interest.
We are interested only in what happens in the object space, so we must talk about the depth of field.

If the eye pupil is supposed to be constant, for example 2 mm, calculations prove that the depth of field of the system (binocular + eye), for very distant objects, is inversely proportional to M-squared. This fact is not questionable. My binoculars have magnifications going from 7x to 22x, and I have never noticed that the DOF performances were not closely related to magnifications.

In real life, the eye pupil is not constant, and theoretically this has an effect on the depth of field. In practice, I wonder if the wideness of the apparent field of view can modify the eye pupil. Imagine two 10x50 binoculars, one with a 50° AFOV, and the other with 65° wide angle eyepieces. In the latter there is more light that enters the eye, and perhaps in this case the eye pupil contracts more than in the 50° binocular, giving in consequence a better DOF. It’s just an hypothesis.

But the main issue about DOF is the fact that the eye itself has a built-in focus mechanism, that is continuously operating, regardless of our will. With the naked eye, who worry about depth of field ? This seems to be a problem only with binoculars. If we accepted to focus continuously our eyes behind binoculars as we do in ordinary life, most binoculars would have impressive depth of field.
So if people report different DOF with binoculars having identical magnification, it is probably because one binocular allows more easily the eye to focus by itself.
I strongly believe that optical aberrations of the binoculars play an important role, even if the image looks sharp. By modifying the optical image projected onto the retina, the aberrations introduced by the binocular change the habits of the brain, and the automatic focus ability can be flawed by this change.
I have noticed that if binoculars have very low level of optical aberrations (this is visible only with the booster method), it is often more easy to allow the eye to focus on nearby objects than to touch the focus wheel. On the contrary, I’ve found this is almost impossible with imperfect binoculars, which require to tune continuously the focus wheel.

Another related factor is the fact that there are two images, and the aberrations are almost always different between the two barrels. If one barrel is extremely good, the focused image still appears very sharp, but the aberrations in the worst barrel can contribute to the lack of the percieved DOF. Again, it’s just an hypothesis.

I have thought about another factor : the alignment of the two images. Even if the alignment (collimation) is correct, producing no strain or headache, a small residual misalignment changes the habits of our brain. I would not be surprised if a small vertical divergence for example resulted in a lack of DOF for some people, just because the eyes are in a uncommon situation and don’t react as usual.

Food for thought…

Jean-Charles

[Kevin Purcell]

Imagine two 10x50 binoculars, one with a 50° AFOV, and the other with 65° wide angle eyepieces. In the latter there is more light that enters the eye, and perhaps in this case the eye pupil contracts more than in the 50° binocular

See

http://www3.interscience.wiley.com/j...62279/abstract

The effect of field of view size on steady-state pupil diameter
Philip A. Stanley and A. Kelvin Davies
Sowerby Research Centre, British Aerospace (Operations) Ltd, FPC 267, PO Box 5, Filton, Bristol BS12 7QW, UK

ABSTRACT
Studies of the relationship between luminance and pupil diameter have produced widely differing results. This research note explores the possibility that this is due, in part, to differences in the size of the adapting fields used by various workers. We present measurements of pupil diameter as a function of luminance for a variety of field subtenses. The results indicate a consistent trend for smaller subtenses to produce less pupil constriction. For field diameters of up to 25°, replotting the data in terms of corneal flux density (i.e. the product of luminance and subtended area) causes an approximate convergence onto a single function described by

D = 7.75 − 5.75 [(F/846)^0.41/((F/846^0.41 + 2)]

where D is the pupil diameter (mm) and F is the corneal flux density (cd m−2 deg2). This equation should be of some practical use in estimation of natural pupil diameter.

Received: 9 June 1994 Revised form: 13 November 1994

DIGITAL OBJECT IDENTIFIER (DOI)
10.1046/j.1475-1313.1995.9400019v.x About DOI

You should be able to calculate pupil diameter from this if you know the transmission of the bin and the illuminance of the scene.

In real life I doubt it makes much difference. Just my guess.

[jcbouget]

I have corrected some strange mistakes in English in my previous text. I am sorry if there are other mistakes.

Originally Posted by Kevin Purcell

See

http://www3.interscience.wiley.com/j...62279/abstract

Thank you for this article !

In real life I doubt it makes much difference. Just my guess.

It’s my opinion too. But light of the environment can also enter the eye if the eyecups are not efficient enough. I will examine this formula.

Jean-Charles

[Surveyor]

Originally Posted by jcbouget

I will examine this formula.

Jean-Charles

Jean-Charles;
Interesting timing. Last weekend I had to make some rough estimates of my pupil diameter/iris diameter for a related experiment. The data may be of some use to you and I would like to know what you determine. Attached is the raw data for my imperfect eyes.

These are probably very limited data points. My 60+ year old eyes just do not have the range they used to.

Best
Ron

[FrankD]

So if people report different DOF with binoculars having identical magnification, it is probably because one binocular allows more easily the eye to focus by itself.

I find this an interesting hypothesis. I know you mentioned it to some degree earlier but what specific optical/design characteristics in a binocular do you think would contribute to this flexibility?

Thank all of you for the discussion. For whatever reason I seem to be following it much more readily this time.

[ronh]

Thanks to all for this interesting discussion. Might as well chip in my little bit of confusion. Although I am certainly one of their unwitting victims, I don't know what to say, do, or think about the things that masquerade as DOF, so I will confine my statements to the bona fide variety.

Formulae for DOF from photography can be simply modified from film grain to eyepiece and visual acuity. I have done this, and the results are generally consistent with most people's experience that big, low powered binoculars have the greatest DOF. But, I have not made any measurements.

I agree with Jean-Charles that the individual's focus accomodation is not accounted for in the mechanical relationships from photography. (Gee, I wish I had focus accomodation. My eyes are so stiff, I am practically a camera.)

For me, the eye pupil opening is a major effect. In bright daylight, my 7x50 seems to have a very nice DOF and focus is forgiving. But at night, striving to separate the closest double stars, I find that I must focus within a relatively narrow 0.2 diopter range for the best results.

Finally, I have a nutty idea that might help understand the m-squared formula intuitively. Higher magnifications show a more detailed picture of the scene, so it is easier to see a small focusing error. This contributes to the perception that higher magnifications have a shallower view, but only gives a factor of m. The size of the defocus blur, for a given linear defocus (ie, for a given mm of motion of the focusing element), scales with magnification, giving another factor of m. Thus, m-squared.
Ron

[ThoLa]

[quote=FrankD;1529973]I find this an interesting hypothesis. ...

no, it isn't. it is nonsense.
the eye#s ability to focus is an intrinsic ability and is in no way influenced by a binocular or any other instrument you put in front of it.
it is governed by biological factors alone: by the flexibility of the eye lens and the action of the tiny muscles that work on the lens.
The single most important factor that determines the performance of this system is AGE. With advancing age it inevitably gets more difficult; the lens of the eye loses flexibility, the muscles grow weaker.
No external tool "allows" to overcome bitter biological reality.

T

[henry link]

On the question of measuring pupil dilation with binoculars in front of the eye I've had good results using an out of focus artificial star. For sunlight measurements I set the binocular for infinity focus and examine a glitter point of the sun reflected in a Christmas tree ornament placed about 10' away. The out of focus disc is a pretty well focused image of the eye's pupil or the binocular exit pupil depending on which is smaller. For lower light situations I use a pinhole over a flashlight beam. Of course, at night actual stars can be used.

Just now I made a crude measuring caliper from a piece of stiff wire and measured my pupils with two 8x30 binoculars in front of my eyes. I picked an old Zeiss 8x30B Porro with a 50 degree field and a Nikon 8x30 E II with a 70 degree field to test Jean-Charles very reasonable idea that a smaller apparent field might cause the pupil to open larger. Measurements were made by placing the wire just in front of the objectives and bending it into a "U" shape until the tips of the wire barely show at opposite edges of the image of the pupil. In sunlight I measured an effective aperture of about 18mm for both binoculars (18mm aperture= 2.25mm eye pupil). I could detect no significant difference. I used a flashlight with a pinhole placed in a deeply shaded area under some shrubs for a lower light measurement. The result was about 28mm for each binocular (3.5mm eye pupil). Once again the difference between the two binoculars was too close too call, but I had a slight impression that my pupil was a tiny bit larger looking through the Nikon, the opposite of what I would expect.

BTW, this test is also useful for revealing how much off-axis vignetting is present at different light levels. Just move the disc toward the edge of the field to see the vignette.

Henry

[elkcub]

I've looked into the literature several times with less than perfect satisfaction. For practical purposes, however, the answer seems to be that the pupil responds primarily to light delivered to the foveal area of the retina, and less to the periphery. Most of the data relating pupil diameter to ambient illumination show considerable inter-personal variation, altho there is a good average approximation formula available...somewhere.

It doesn't provide the formula I was looking for, but this article has much value. As usual, the data come from opthalmology, just to give credit. You might say it also gives new meaning to the phrase "nit picking".

Note: Just realized that the article links to http://www.pc.ibm.com/ww/healthycomp...vdt13eyec.html, which presents the famous Reeves (1920) data. Still, no formula. :(

Ed

BTW, Henry, that seems to be a great method for measuring PD.

[elkcub]

Originally Posted by henry link

Ed,

Purist I may be, but the problem I see with lumping many causes together into a subjective impression of DOF is that each cause has a very different implication for the quality of the optics (as usual I'm talking about properties the optical instrument). If an impression of "shallow" DOF comes from an absence of field curvature I would consider that to be a good thing, but if the same impression comes from excessive aberrations that would be a bad thing. Focuser speed would be an optically neutral cause and a sample specific defect like astigmatism would be a red herring since it could occur in any binocular. Perhaps it's naive, but I'm inclined to attribute most reports of differences in DOF to simple mistakes, observations that are made too casually. Even if the raw observations are correct, I think they're still not very useful for evaluating optics without establishing the specific cause.

"Horopter", something totally new to me, if it turns out to be another cause related to the eye brain system should be an interesting addition to the list, once you've explained it.

Henry

Actually, I really don't disagree with anything you've said by way of instrument evaluation on an optical basis, except that in a few instances the presence of an aberration may be arguably beneficial for the user. One example is distortion, for reasons that Holger Merlitz (and Jean-Charles) has articulated. The value of moderate field curvature has been debated, and I tend to side with the moderates on that one. Although not an aberration, the optimum intensity/frequency distribution at the retina would argue for some kind of filtering, and not simply a total brightness criterion to identify what's "good" vs "bad." The article in my previous post should expose that elephant in the examining room.

...If an impression of "shallow" DOF comes from an absence of field curvature I would consider that to be a good thing, but if the same impression comes from excessive aberrations that would be a bad thing.

Henry, even you must have realized the complete ambiguity of that precious statement. Go to the head of the class!

The human visual process is concerned with creating a valid internal (mental, if you will) representation of the physical, 3-D world around us. That is so obvious we are functionally blind to it, unless something goes wrong with our eyes. At that point, the criterion for goodness quickly becomes the quality of that "internal representation." So, perhaps we differ in that I orient to the manner in which the instrument manages to retain important qualities of the normal internal mapping. Relative distance perception is high on the list.

The horopter is a theory of how the brain utilizes information on the two retinas, and concerns the mathematically complex determination of retinal correspondence. Most modern work goes back to the German genius H. von Hemholtz (1867). That it is a theory makes it no less valid (factual) than concepts of mass, gravity, or evolution, and like them it is under constant scientific debate. The recent theory has been expanded to what is called the "extended horopter" and is very complicated. Apparently, after 150 yrs., they have finally proved a conclusion by Hemholtz, whose analysis was too "dense" to comprehend.

Although I could make an effort to come up with a simple definition, the Internet is full of them (not always in agreement). But, in my view it would be like jumping into the middle of optics with a definition of wave front aberrations. For starters, a full-text .pdf file of Kenneth Ogel's 1962 lecture can be downloaded here: http://www.iovs.org/cgi/content/abstract/1/4/446. It summarizes the field up to that point. His last sentence is "...Mathematics has been avoided!"

Ed