47 replies to this topic

[Henry Link]

Jean-Charles,

I think that in your example of the two 7X50's the light cones would not be identical. Imagine that one pair has an objective with a 147mm focal length and the other 210mm. The first will have a focal ratio of f/7 and the second a focal ratio of f/10 when both are stopped down to 21mm. Of course an actual 7X21 mini binocular would have a much lower focal ratio under these conditions since it's entire objective would be utilized, giving it a focal ratio of perhaps f/4.

I believe there is a little difference in the focal lengths of those two Zeiss binoculars. The FL's appear to me to have a lower than average focal ratio of about f/3.5-3.6 (to compensate for the extra physical length that results from using AK prisms), while the Classics that use Schmidt-Pechan prisms (8X30, 10X40) appear to be around f/4. If the optical systems were identical a careful look might show a little more DOF in the Classic, but the FL's use a focusing element instead of a moving objective and a very different eyepiece design which may have some effect on DOF.

Henry

[JCB]

Henry,

In my example of the two 7x50's, the light cones are different after the objective lenses, but identical inside the eye. To understand DOF, you have to imagine that the eye is a lens which focalise the light on the retina, as drawn in my figure. DOF is controlled by the incoming light cone on the retina, not the incoming light cone on the focal plane of the objective lens.

Binoculars work in a much more complex way than a single camera lens.

Jean-Charles

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[KennyJ]

Jean Charles,

Thank you for your very clear diagrams.

I appreciate your simplification.

Not that I'm any wiser about what DOES create "depth of field" as a result , mind you :-)

Kind regards to one of our two great diagram specialists !

Kenny

[Henry Link]

Jean-Charles,

It appears that we agree on one point. Two binoculars with the same magnification and the same focal length objectives can have different depth of fields provided one has a smaller aperture than the other, as in the example I gave of the stopped down 7X50. Where we continue to see things differently, however, concerns the influence of the objective's focal ratio on DOF when aperture remains constant. Your diagrams didn't quite convince me and I will try to explain why.

The longer focal length objective in my example not only reduces the steepness of the objective light cone compared to the short one but also demands a change in the optical system beyond the objective's focal plane, in that the focal length of the eyepiece has to be increased to maintain the same magnification. Since the longer focal length eyepiece has a lower magnification factor it also has a less steep light cone and wider DOF in focusing on the aerial image from the objective.

I tend to use a hands (eyes) on approach rather than a mathematical one so I confess that I didn't pick my 7X50 examples completely out of thin air. I actually have a very short focal length 7X50, a US Military M19 which has a focal length of 150mm. While I 'm uncertain about the exact focal length of the Nikon Prostar it appears to be the more normal 190-200mm. I didn't use these as a specific example because the optics are different in more ways than just objective focal length, but I did compare them in regard to depth of field. The Nikon has noticeably more which does convince my eyes that two binoculars with the same magnification and the same aperture can have different DOF's, whatever the reasons may be.

Henry

[btschumy]

Yuri, the owner of TEC (Telescope Engineering Corporation) recently responded to a question about depth of field on the TEC Yahoo group. Here is what he says:

Permited defocusing in microns could be calculated by formula:
Def. (mk) = 2 L F/DxF/D , where L - wave length, F/D - focal ratio.
fro F/7 it would be : 2 x 0.555 x 7 x 7 = 54mk
For simplicity you can remember appr. formula:
permited defocusing in microns is equal square of f-ratio of your scope.
For F/15 MAC it would be 225mk, for f/7 APO it would be appr. 50mk
and for the last one you should take in acount the field curvature of high power
eyepice, like Supermono 6, since it has defocusing ~110mk.
Someone may say how about an eye accomodation - it could hel but in
general everyone prefer observe in relax condition, secondly our best
accomodation was at the age, when we didnot have scopes!
BTW, our ability to accomodation may be easy checked - defocus slightly the
star image and check if you can return sharp image back by straining your
eye! I bet it is not easy!
Best regards,
Yuri

If I understand his reply correctly, this seems to imply that DOF is simply a function of focal ratio.

[holger_merlitz]

Hello Jean-Charles,

Your results on DOF for a binocular is in agreement with whatever I was able to figure out so far. In fact, magnification and (effective) exit pupil appear to be the dominating parameters. Here, 'effective' means the smaller of both, the observer's eye-pupils and the exit pupil. I must admit that not all aspects are clear to me. The following approach to analyse this problem was suggested by Walter E. Schoen on a German discussion board:

The thin-lens equation

1/F = 1/G + 1/B

relates the distance of the object to be observed (G) with the focal length (F) and the distance of its image (B). A telescope is essentially made of two lenses, and the above relation is valid for both of them, the objective, and the ocular, for which we shall write

1/f = 1/b + 1/g

Now we assume that the binocular is focused to infinity. This means that the ocular is positioned in a way that the focal plane of the objective is on top of the focal plane of the ocular. Each object with large distance produces a sharp image in this particular plane, and the image 'B' of the objective coincides with the object 'g' of the ocular. Now we assume the object is coming closer. Its image 'B' is therefore shifting away from this plane, and since we keep the telescope focused on infinity, the ocular's image 'b' of the 'object 'B' becomes unsharp. One approach is to calculate the distance, to which the eye has to focus in order to get this image 'b' back into focus. The reciprocal value of this distance is the diopter-value the eye has to accommodate. With some arithmetic, and using V = F/f (magnification) and f+F = g+B = distance between objective and ocular one can obtain

b = G/Vˆ2 - f - f/V

(actually, when I tried to verify this relation, I got the opposite sign, but, being no professional, I may have messed up some conventions used for optical computations).

As an example, Walter E. Schoen computes the numbers for a compact 10x50 binocular with F=100mm, f=10mm. The distance of the object is G = 100m = 100000mm:

b = 100000/10ˆ2 - 10 - 10/10 [mm] = 1000 - 10 - 1 [mm] = 989 [mm]

Use the reciprocal to obtain the diopter (1 dbt = 1/1000mm):

1000/989 dpt = 1,0111 dpt

Now the same calculation with another 10x50, this time less compact with F=200mm and f=20mm:

b = 100000/10ˆ2 - 20 - 20/10 [mm] = 1000 - 20 - 2 [mm] = 978 [mm]


1000/978 dpt = 1,0225

which is essentially the same. This means that the focal length has almost none impact on the DOF. It is the magnification which dominates.

Actually, we do not want to care about accommodation when discussing DOF, because this is a parameter which strongly depends on the observer. An alternative approach does start in the same way as described above, but allows a certain amount of unsharpness of the final image, for example 3.4 angular minutes. Here it can be shown that the effective exit pupil size becomes the second parameter (but I have not yet understood how exactly this is calculated). A smaller effective exit pupil increases DOF.

In summary it seems to be that only magnification and effective exit pupil are dominating factors for DOF. Focal length has some influence but not much. However, I am not sure how well the assumptions made for these calculations are satisfied. For example, a binocular is not made of thin lenses. Only professionals may be able to figure out the validity of these assumptions, maybe with the help of ray-tracing software.

With regards,
Holger

[JCB]

Holger,

Thank you so much for your posting ! I was secretly hoping that an highly learned person in binoculars would come with accurate calculations. I think it has happened.
I'll examine your answer carefully as soon as I'll have enough time, but I'm happy to notice that the calculations you have outlined are far simpler than mine, and yet lead to the same conclusion, despite the fact that they are quite different. Thank you again.


Kenny, Henry, and others,

I'm fully aware that my diagram proves nothing. It was only the starting point for my rather complicated calculations, and I don't want bother everyone with them in this discussion. I ought to make a little web page to detail them, but the reality is that I haven't the energy to do it correctly with mathematical formulae. The fact remains that only a mathematical approach (or a precise ray-tracing, as suggested by Holger Merlitz) can give an accurate answer to this very interesting question.
Remember however that, in my opinion, even if we come to an agreement on the tiny influence of the focal length, there are still unknown reasons which must explain why binoculars with equal magnification have different depth of field.

Jean-Charles

[Henry Link]

Jean-Charles,

I did some careful visual experiments today (I'm no mathematician) which have brought me around to your view. I compared the DOF in a number of 8X30's (with focal lengths from about 108 to 132mm) to one that I made by stopping down a CZJ 8X50 Octarem ( focal length about 190-200mm) and an 8X30 telescope I made by stopping down a Takahashi FC-50 ( focal length 400mm) combined with a 48mm eyepiece. I could observe small differences in DOF, but none were clearly related to objective focal length. The scope, which I expected to have huge DOF actually had a little less than several of the 8X30 binoculars. The stopped down Octarem was about equal to the widest of the 8X30's, but not better. None of the 8X optics had as much DOF as a 6X24 Kern I tried under the same conditions.

The small differences I saw among the 8X30's (Nikon E, Zeiss (west) B porro, Swarovski Habicht porro, Kern, Fujinon FMTR-SX) must be related to eyepiece design since they are all quite similar otherwise (except for the air spaced objective in the Zeiss). This must also be the explanation for the greater DOF I see in the 7X50 Prostar compared to the M19.

Henry

[JCB]

Henry,

Very interesting ! Your experiments are as good as tons of mathematics.


Holger,

Here are a few comments :
- your calculations are right, b is negative. If the image formed by the objective is located between the focal plane of the eyepiece and the eyepiece lens, the conjugate of this image is a virtual image on the same side than the original image.

- The focal length of the objective has almost no importance, but if we examine carefully the results, the DOF decreases slightly when the focal length increases, which is the opposite of what we could imagine without calculations.

- The results can be found with the formula I wrote in a previous post :

1/z = M².(1/d'-1/d)

Here d is infinity, z=b , M=V and d'=G.
We have therefore : b=G/V² which is nearly the same as the formula on your post, in which the negligible terms have been omitted.
(For V=10 and G=100000 mm, we find b=1000 mm)
My formula is not rigorously exact, but is more general because it is also valid when the binoculars are not focused to infinity, but to the distance d.

I think it's worth doing some applications of this formula :
We suppose that the binoculars are focused to infinity, and that with naked eye we can see sharply objects without accommodation if they are 1 m away. Then DOF are :
For a 7x binocular : 49 m to infinity
For a 8x binocular : 64 m to infinity
For a 10x binocular : 100 m to infinity
For a 12x binocular : 144 m to infinity
People more than 60 years old, lacking in eye accommodation, and who have to rapidly focus between two distances (like birders), have to very carefully examine the drawbacks of high power binoculars, considering their poor depth of field.

- I made a figure in order to show the influence of the effective eye pupil.

Jean-Charles

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[holger_merlitz]

Hi Jean-Charles,

thanks for the additional explanations! From the figure it is quite clear why the object, when out of focus, looks 'sharper' once the exit pupil size is reduced. This obviously leads to a deeper DOF (quite the same as in photography).

Putting the numbers together we know why the Fujinon 7x50 seems to have an excellent DOF: First of all, its magnification is low, and your table demonstrates how the DOF increases when magnification is reduced. Then, during day time, the eye-pupils are narrow, decreasing the effective exit pupil and thereby further increasing DOF. Also, it is well known that the image of the Fujinon is, due to its excellent coating, brighter than comparable binoculars. This may, at least to a little extent, further reduce the eye-pupil size to further increase DOF.

I think we are on the way to understand these things.

Thanks a lot,

Holger

[BobinKy]

I was reading through some of the older threads and thought this thread on Depth of Field includes several good comments worthy of re-reading.

[BobinKy]

Here is a link to an intriguing discussion on binocular depth of field that took place last month on Bird Forum.

[EdZ]

As mentioned both in that thread and here in previous discussions, it is important to differentiate whether or not the discussion of depth of field refers strictly to on-axis view or the view across the entire filed of view. Different aspects affect each perception.
Curvature and Depth of Field

edz

[Rich N]

After comparing my Zeiss 7x42FL and 10x42FL, in the daytime, I think the reason my 7x seems to have greater depth of field is because of the smaller image scale. The greater depth of field between the two is just an illusion. At 10x it is much easier to see if something is a bit out of focus. The smaller image scale of the 7x just gives the impression greater depth of field but objects a few yards in front and behind the point of focus are still out of focus.

Rich

[BobinKy]

I just ran the numbers on some binoculars with the VWDOF Calculator that Surveyor posted in the Bird Forum link.

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. Set format to x,y size of aperture, such as 22.6 x 22.6 = 32mm (objective size x 0.707107)

Set COC to percentage, such as .085% x 32 = COC (.085% x objective size = COC). [I know this is a bit of a tweak!]

Set focal length, such as 6 x 32 = 192mm (power x objective size = focal length). [Another tweak!]

Set F number to objective size. 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. 6x32 . . . size
20 meters . . . object distance
14 meters . . . near point of focus
38 meters . . . far point of focus
24 meters . . . depth of focus

7x50 . . . size
20 meters . . . object distance
15 meters . . . near point of focus
30 meters . . . far point of focus
15 meters . . . depth of focus

8x32 . . . size
20 meters . . . object distance
16 meters . . . near point of focus
27 meters . . . far point of focus
11 meters . . . depth of focus

8.5x44 . . . size
20 meters . . . object distance
16 meters . . . near point of focus
26 meters . . . far point of focus
10 meters . . . depth of focus

10x50 . . . size
20 meters . . . object distance
17 meters . . . near point of focus
24 meters . . . far point of focus
7 meters . . . depth of focus

. . .

6x32 . . . size
50 meters . . . object distance
23 meters . . . near point of focus
Infinity . . . far point of focus
Infinity . . . depth of focus

7x50 . . . size
50 meters . . . object distance
27 meters . . . near point of focus
360 meters . . . far point of focus
333 meters . . . depth of focus

8x32 . . . size
50 meters . . . object distance
30 meters . . . near point of focus
147 meters . . . far point of focus
117 meters . . . depth of focus

8.5x44 . . . size
50 meters . . . object distance
32 meters . . . near point of focus
120 meters . . . far point of focus
88 meters . . . depth of focus

10x50 . . . size
50 meters . . . object distance
35 meters . . . near point of focus
86 meters . . . far point of focus
51 meters . . . depth of focus

16x70 . . . size
50 meters . . . object distance
43 meters . . . near point of focus
60 meters . . . far point of focus
17 meters . . . depth of focus . . .

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.

I hope you find the above useful.

[James S]

Here is a link to an intriguing discussion on binocular depth of field that took place last month on Bird Forum.

Is birdforum down or out of business? I cannot click through this link.

[Mark9473]

Couldn't reach Birdforum either, just now.

[Bob K]

I haven't been able to get on Bird Forum for the last day and 1/2.

[EdZ]

Hmm, works for me, but maybe past problems have been fixed.

The Birdforum discussion confirms the long-ago discussion that took place here regarding low power being the greatest influence. Keep in mind that discussion relates ONLY to the on-axis image. The reference link I gave above deals with an entirely different topic, Curvature and Depth of Field, which I'm sure is often a "mistaken identity" issue that many people may be seeing and not realize.

edz

[MacGee]

They're moving to new servers. I don't really understand the bit about your ISP not being able to find the address.

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[MacGee]

Latest.

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