Telescope Reviews: Curvature and Depth of Field

Small Binoculars
Curvature and Depth of Field

We often see remarks by users, this or that binocular has greater depth of field. This is far more often something we would hear from a terrestrial viewer rather than an astronomy viewer. In astronomy, all objects appear in a flat plane at infinity, but terra views are much different. It is very easy to understand how a terra viewer can be focused on a target 50M away and either sees the foreground scenery in focus or out of focus. There is a complex formula (it has been presented by others in this forum, HM, JCB, HL, etc.) that shows magnification holds a strong correlation to depth of field. That aside, a binocular that shows more of the scene in focus appears to have a greater depth of field.

True depth of field is actually a measure of the range of clear sharp image seen for the precise focus of the central area of the lens. Generally, that range may be realatively short, is strongly influenced by magnification and is probably restricted to the central aberration free area of the fov, perhaps the central 40-50% of fov. However, perception of depth of field is actually viewed over a fairly wide portion of the entire field of view (fov). Obviously, more images across the fov, some nearer and some further that appear in focus, leads to the perception of greater depth of field. As JCB so astutely noted, "Now, why people find that binoculars with equal magnification have quite different depth of field? I think that the perceived depth of field in binoculars is determined by other parameters..." This little study may show a possiblity why all may not be due to the direct correlation of magnification<>dof and how curvature may contibute to perceived dof.

Of course, many binoculars, even some of the best, when looking at stars at infinity, appear out of focus as you look at the images further out in the fov. Not uncommon at all, this is due to a variety of aberrations. Most often there is some loss of pinpoint focus or image quality across the fov due to one or a mix of the following; field curvature; spherical aberration; astigmatism; coma and chromatic aberration. (Pin cushion and barrel distortion move the image but do not change the appearance of the image, so would have little to no visual affect on sharpness of image).

[Recognizing that distortion actually refers to image movement and not appearance, from here on out, I will use the term “distortion” to refer to the collective loss of image quality due to all the above aberrations, and hopefully you will excuse the misuse of the term.]

Of the aberrations mentioned above only one can be changed by refocusing, field curvature. Field curvature appears because the outer portion of the field of view may have a different focal point than the center. The focal length increases as you move further out in the fov. You can't get both the center and the edge of the fov in focus at the same time but you can get one or the other in focus.

Curvature of field (change in focal length off-axis) can be reduced by using a field flattener. Without the flattener, the outer portions of the field will be slightly out of focus when the center is in focus. Instead of focused pinpoints in the outer field, in the presence of curvature, the star points would be slightly out of focus. Curvature has the tendency to enlarge and blur the circles of light that form the stars in the outer field. Points further out in the fov would be more out of focus and therefore more blurred. (Curvature would cause slightly enlarged circles, assuming no other aberrations are present. However there are almost always other aberrations present, so the distorted image is never that clean).

A field flattener is used to help insure much of the entire field is in focus at the same time. With the use of a field flattener, stars in the outer field will be focused and appear just as stars in the center (again, assuming no other aberrations are present). The field flattener does not eliminate spherical aberration, astigmatism, coma or chromatic aberration.

You can easily test for the amount of curvature contributing to the off-axis image distortion. My method is this. Focus the center precisely on a double star (nu Draco, or some other easy known double), in this case a nice even double star of approx. 1 arcmin separation. Move the star to various points in the fov; I chose to test at 50% out, 70% and 90%. The image will distort to some extent, take note of how much. If the image distorts to the point where the pair of stars begin to merge, then you are seeing 1 arcmin of total distortion at that point in the view. For small binoculars, this is a fairly common amount of total distortion in images between 50 to 80% out from center. Having noted the total distortion, refocus with the image at each point. If you can refocus ALL of the distortion OUT and make the images fine pinpoints at that point in the fov, then ALL of the distortion was contributed by field curvature. By watching to see how much of the distortion can be removed with refocusing, you can estimate how much field curvature contributes to total image distortion at these points in the fov. The portion that cannot be improved by refocusing is due to other aberrations, not part of this topic.

An astronomer would prefer all binoculars to have as little field curvature as possible so the entire plane of the fov has as little distortion as possible. It is not unusual to find that a binocular with much less sharpness out at 60 or 70% in the fov has a much greater amount of field curvature than a binocular which appears sharp out to 80-90% of the fov. A terrestrial viewer might want to consider how field curvature affects the view, and may in fact find field curvature to be a useful aberration. While it does nothing to add to depth of field further distant than the plane of focus, field curvature provides for closer objects to appear in focus as they range out across the fov.

Here’s a sampling of field curvature measured for a few binoculars.
Curvature arcsec/ total distortion arcsec at 50-70 and 90% out in fov
50%---70%---90%
15/20 15/25 30/40 Nikon SE 12x50
15/15 40/45 60/75 Nikon Act Extreme 12x50
10/10 30/30 45/45 Fujinon FMT-SX 10x50
15/30 30/60 90/160 Nikon Act Extreme 10x50
15/20 25/50 60/120 Fujinon BFL 8x42
50/60 120/170 150/300 Nikon Action Extreme 8x40
50/60 100/120 200/300 Nikon Act Extreme 8x40

What these numbers mean:
15/20 30/45 60/75 Nikon SE 10x42
The Nikon SE 10x42 was measured to have total distortion of point image at 50-70 and 90% out in the fov. At 50% out total distortion was 20 arcsec. At 70% out it was 45 arcsec and at 90% out the total image distortion due to all aberrations was 75 arcsec. Refocusing at 50% out I was able to remove nearly all of the 20 arcsec distortion leaving an estimated 5 arcsec of image distortion. Therefore, at 50% out, the amount due to curvature is 15 arcsec. At 70% out I could refocus out all but 15 arcsec, therefore 30 arcsec is due to curvature. At 90% out I could refocus to a limit of about 15 arcsec remaining, therefore 60 arcsec is due to curvature.

Examples of depth of field compared with curvature:
The Nikon AE 8x40 which has a great deal of curvature (approx 50-60 arcsec curvature at 50-60% out, about 120 arcsec at 70% out), when focused at 50m, 40m appears sharpest at 30% out 30m appears shapest at 50% out, 25m is clear at about 60% out and 15m is clearly sharp at 70% out.
The Fujinon BFL 8x42 has less field curvature (approx 15-20 arcsec curvature at 50-60% out, about 25 arcsec at 70% out). When focused at 50m, 40m appears sharper at 30% out, 30m appears shaper at 50% out, but 25m cannot be seen at all.
The Nikon AE 8x40 has greater curvature and more near targets in focus across the fov. It appears to have a greater depth of field, and this may be because it's greater curvature allows more close objects to come into focus as you use more of the off-axis fov.

The Nikon AE 12x50 which has more curvature (about 40 arcsec at 70% out, approx 60 arcsec curvature at 90% out), when focused at 50m, 40m appears sharpest at 40% out 30m appears shapest at 60% out, 25m is clear at about 80% out.
The Nikon SE 12x50 has less field curvature (15 arcsec at 70% out and approx 30 arcsec curvature at 90% out). When focused at 50m, 40m appears sharper at 70% out and the 30m target is barely focused at 90% out. The 25m target cannot be focused at all.
The Nikon AE 12x50 has greater curvature and greater near depth of field.

It seems clear from this correlation that the binoculars with greater field curvature have the perception of greater depth of field in front of the focus point. Therefore, it may stand to reason, a binocular with more field curvature may provide a greater “near” depth of field for the terra user. (of course that won't do you any good if all the birds you want to see are in the same tree sitting on branches between 45m-55m away). Also, it may be that a field flattener lens, which would be desirable for an astro viewer to get as flat a field as possible, might work against a terrestrial viewer looking for the greatest depth of field.

Just a thought in depth.

edz

Edited by EdZ (01/31/08 01:58 PM)

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