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Thread: Diffraction Limit on Macro Lenses

  1. #1

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    Diffraction Limit on Macro Lenses

    Hi, I searched for an answer to this question on the forum but did not find it. So here is my question: what is the diffraction limit on modern macro lenses, for example the Rodenstock 180mm f5.6 APO-Macro-Sironar lens?

    I have been shooting flowers at 1:1 on 4x5 and 5x7 with this lens set to f64 to maximize DOF, and the results seem OK on my computer. However, I have not printed any of my photos at 16"x20" or larger yet (I like printing my images in the 16"x20" to 32"x40" size range). I know regular lenses are diffraction limited at about f22, but I was wondering if macro lenses were designed differently such that the diffraction limit kicks in at f32 or f45.

    I would like to maximize DOF without getting into visible diffraction (I usually photograph landscapes at f32 without noticing any diffraction; at f45 I start to see some diffraction). I usually print my scanned photos at 300DPI or 360DPI (EPSONs). Can anyone suggest usable apertures for modern macro lenses, formulas for figuring it out, and/or online information on the subject?

    Daniel

  2. #2

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    Re: Diffraction Limit on Macro Lenses

    f22, but if you are happy at f32 then use it.

  3. #3

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    Re: Diffraction Limit on Macro Lenses

    Dan, the standard rule of thumb is that diffraction limited resolution is 1500/(effective aperture). For lenses with pupillary magnification = 1 (that's most of the lenses we use), effective aperture is aperture set * (1 + magnification).

    So, at 1:1 with f/64 set effective aperture is f/128 and the highest resolution possible is 1500/128, i.e., about 12 lp/mm at very low contrast. Shooting at f/64 limits you to contact printing; enlargements will look fuzzy.

    One of the paradoxes of macro work is that stopping down can reduce depth of field. To learn more about this, read:

    Gibson, H. Lou. Close-Up Photography and Photomacrography. 1970. Publication N-16. Eastman Kodak Co. Rochester, NY. 98+95+6 pp. The two sections were published separately as Kodak Publications N-12A and N-12B respectively. Republished in 1977 with changes and without the 6 page analytic supplement, which was published separately as Kodak Publication N-15. 1977 edition is ISBN 0-87985-206-2.

    This is the most terrifying book on photographic technique I've ever read.

    Incidentally and all kidding aside, unless you like uniformly fuzzy prints there no DoF to speak of at 1:1, regardless of the aperture used. If you like uniformly fuzzy prints, don't use a lens, use a pinhole.

    Cheers,

    Dan

  4. #4

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    Re: Diffraction Limit on Macro Lenses

    The diffraction limit has nothing to do with the lens but only depends on the relative f/no. or more precisely the physical size of the aperture opening. A convenient metric for determining the size of an Airy disc diameter (the size of a resolvable spot on the film) is obtained by considering light at 400 nm wavelength. Then the diameter of the minimum resolvable spot is equal to the f/no in microns. Thus the Airy disc diameter at f/22 is 22 um. The diameter at f/64 is 64 um. The diameter at f/1.2 is 1.2 um!

    One can convert a 22um spot to lines per mm (l/mm.) by dividing 1000 (1000 um per mm.)by the Airy disc diameter. Then get line pairs per mm. (lp/mm.) by dividing again by 2. So your f/22 represents about 22.5 lp/mm. and your f/64 equals about 8 lp/mm. f/5.6 the common maximum diameter of large format lenses is equivalent to about 90 lp/mm. as a diffraction limit.

    Of course above says nothing about the optics in the lens which can degrade the image further although in some cases can offer some suttle but minor optical improvements. And we can all quibble about using the diameter of an Airy disc (the first dark fringe in the diffraction pattern) as a standard but it is a readily observable and measurable phenomena.

    Nate Potter, Austin TX.

  5. #5

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    Re: Diffraction Limit on Macro Lenses

    The diffraction limit for the plane of focus may be different from that for the DoF limits. Once the lens is essentially diffraction limited, further stopping down decreases sharpness in PoF. At the DoF limits, there is the additional tradeoff between defocus blur and diffraction; stopping down decreases the former but increases the latter. Eventually, diffraction predominates, and stopping down further gives less overall sharpness.

    As long as the combined blurring from defocus and diffraction is imperceptible, the tradeoff of sharpness at the DoF limits vs. that in the PoF isn't relevant. Sharpness in the PoF is always greater than that at the DoF limits, and if the sharpness at the DoF limits is acceptable, the sharpness in the PoF will be acceptable as well. The tradeoff may become an issue when great DoF is needed, especially in close-up work.

    In his article in the March/April issue of Photo Techniquesi (available on this web site as GIF images), Paul Hansma discusses the combined effects of defocus and diffraction. I also discuss it in my paper Depth of Field in Depth (on this web site, in PDF) under Combined Defocus and Diffraction. Although Hansma and I take quite different approaches, we come up with very similar rules for optimal f-number. Hansma gives

    N = sqrt(375 Δv),

    where N is the f-number and Δv is the focus spread. I give

    N = 20 sqrt(Δv)

    for 12 lp/mm in the negative.

    It should be noted that we both give the case of infinity focus (i.e., zero magnification). For close-up work, the effective f-number must be used, i.e., N (1 + m), where N is the marked f-number and m is the magnification. At 1:1, this cuts the optimal f-number in half.

  6. #6
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    Re: Diffraction Limit on Macro Lenses

    One comment: "Diffraction-limited" is high praise for a telescope objective. It means that the lens faults are so minor that diffraction controls the image quality.

    Thus, I think it's more useful to ask at what point diffraction causes more problem than stopping down solves. As Nathan has described, diffraction increases as the aperture decreases. So, a smaller aperture will always show more diffraction than a larger aperture.

    But lens faults and depth of field are the competing influences. Most people want to know the sweet spot of a given lens, where further stopping down shows net degradation--diffraction gets worse faster than improvements from correcting lens faults and increasing depth of field.

    In the macro range, depth of field is always a gigantic issue, and the larger the format, the easier it is to get into the macro range just taking pictures of normal subjects. My suspicion is that for most images, it would be rather hard for an image to be ruined by diffraction (limited in enlargeability, perhaps, but not ruined), while not having sufficient depth of field or correcting for aberrations (such as field curvature, etc.) can ruin the result at any print size. The challenge is finding the aperture that balances those competing influences, and that point is different for every lens and subject, it seems to me.

    For copy work or other technical application, one might have a specific performance standard, such as a print of X size that requires a resolution of Y line pairs/mm, which can then be backed into a calculation. For three-dimensional subjects, however, I suspect this has little to do with the results.

    A 16x20 is a 4x enlargement. If the visual standard is 5 line pairs/mm, then you need at least 20 line pairs/mm in the original image. Based on Nathan's numbers, f/22 is indeed your limit. But you'll have to ensure that the other influences on the image don't do worse things than the minor problem you might see at, say, f/32.

    Rick "perfection is unattainable" Denney

  7. #7

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    Re: Diffraction Limit on Macro Lenses

    Rick, I agree that in most cases, diffraction isn't what ruins an image. But this changes in close-up work, so that there really can be a visible tradeoff between DoF and overall sharpness. There's a good example on p. 84 of Lester Lefkowitz's The Manual of Close-Up Photography.

  8. #8

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    Re: Diffraction Limit on Macro Lenses

    Dan, I was writing my reply when you posted yours. It should be noted that the approach Hasma takes (i.e., root-square combination of defocus and diffraction blur spots) is essentially the same as Gibson took in 1960, when his analytic section was first published. So the idea is hardly new--it just hasn't received a lot of attention.

    It should be noted that Gibson apparently made an error in his basic formula for DoF (2nd ed., Vol. II, p. 95), using overall magnification (subject to final image) rather than magnification in the negative. When the error is corrected, it is seen that nearly all the difference between getting all the magnification in the negative (e.g., large format, contact print) and from enlarging the negative is due to loss of sharpness in the negative emulsion.

    In 1955, H.H. Hopkins developed a more theoretically solid approach calculating the MTF for combined defocus and diffraction. I used Hopkins's approach, and that my results were very similar to Hansma's suggests that the root-square combination of defocus and diffraction at least captures a fair amount of what's happening.

    But it doesn't always seem to work. In the same issue of Photo Techniques that I mentioned, Stephen Peterson attempts to find the minumum f-number that would give acceptable sharpness (his article is also available on this web site). In effect, his technique subtracts diffraction blur from total blur, and he eventually arrives at an f-number beyond which the desired sharpness cannot be achieved. I got far less correlation between his maximum f-number and that predicted by calculating MTFs with Hopkins's method than I did with Hansma's optimal f-number; in fact, I got much better correlation with the method many people on this forum have long used, i.e.,

    N = Δv / 2c,

    where c is the circle of confusion. It's possible to regard this value as a minimum f-number and Hansma's as a maximum. Unfortunately, in close-up work, the minimum can sometimes be greater than the maximum, suggesting that you can't get there from here. The value from this formula is greater than Peterson's; the actual value is probably somewhere in between.

  9. #9

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    Re: Diffraction Limit on Macro Lenses

    Jeffs' additional comments on the added effects of defocus has reminded me of the OPs' original desire to maximize the DoF for macro work. I think it has been mentioned here, maybe even by me, that there is a technique to obtain infinite depth of focus with a macro setup by using a scanning technique. This is variously called Scanning Light Photography as well as other terminology. It's been around for a long time.

    The idea is to illuminate the plane of focus, which would include the defocus regions to an acceptable circle of confusion, using two or three slits of light that are of a thickness approximating the thickness of the plane of acceptable focus and intercept that plane exactly and be coplanar with that plane throughout the field of view. Then the subject is translated through the slit illumination at a uniform rate and a velocity
    that is consistent with a proper exposure dose. (Not so easy to explain briefly).

    If interested Google C. J. Kazilek, "Scanning Light Photography" for a description with images and references.

    It needs to be a pretty sophisticated setup but I used it some years ago for documenting some MMIC modules with considerable success. If the OP is really serious about great depth of field this cannot be beat.

    A unique feature is that the image obtained has no perspective distortion since every part of the subject is always the same distance from the camera.

    Nate Potter, Austin TX.

  10. #10

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    Re: Diffraction Limit on Macro Lenses

    The technique Nate describes is also known as multi-plane scanning. Sidney Ray's Applied Photographic Optics gives a brief description, as well as several other references.

    Another alternative is software combination of images at various focus distances. It doesn't need a sophisticated setup, but it's obviously more of a chore with LF than with small- or medium-format digital. And it benefits from a stationary subject, which can be tough with flowers.

    I've not personally used either technique, so I can't offer much additional comment.

    Perhaps after providing a lot more information than the OP may have wanted, an attempt at practical answer to his question might be appropriate. Let's assume that DoF as well as sharpness in the plane of focus is important, and consider an example at 1.0 magnification, and for which the focus spread is 10 mm. Using my formula for optimal f-number at the DoF limits,

    N = 20 sqrt(10) / (1 + 1) = 32 .

    There's no point in using a smaller aperture because the image will get less sharp, even at the DoF limits. Assuming the standard 4x5 CoC of 0.1 mm, the conventional geometrical formula gives

    N = 10 / [2 x 0.1 x (1 + 1)] = 25 ,

    so it should be possible to get the desired DoF. The geometrical formula ignores diffraction, and probably underestimates the minimum f-number, so a better value might be 32, the same as given for the optimal f-number.

    What happens if the minimum f-number is greater than the optimal? Use the optimal, because using a greater f-number will make the image less sharp. When this happens, you can't get the desired DoF, and you also may be getting sharpness at the DoF limits at the expense of that in the plane of focus, and may need to decide which is more important.

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