Bob Atkins - Really wrong Optics!

Comments on the Really Right Stuff "white paper" on photographic resolution

By Dr. Bob Atkins

In a recent (12/96) "White Paper" from Really Right Stuff (RRS), they discuss what's needed for sharp images. In the end, they conclude what you'd (correctly) expect. Use a sturdy tripod and head, stop the lens down a couple of stops, don't use a multiplier unless you have to, and so on. Unfortunately, their attempts to explain the underlying optical principles fall far short of the mark. In fact the "facts" given are misleading, incorrect and/or incomplete. I don't want to reproduce the whole thing here (nor, given the copyright laws, am I allowed to), but I will give examples of some of the errors in the document and some of the logical problems with their arguments. Bad science is bad science and shouldn't go unchallenged.

Part I

"How good are current 35mm lenses" is their opening. Here they discuss the resolution of lenses, measured by the microscopic examination of the aerial image of a resolution test chart imaged by the lens and compare it to the theoretical diffraction limit. This should raise an immediate red flag for anyone who has a sound background in optics. You know what's coming. They are about to conclude that if a lens shows resolution to the theoretical limit, then the lens must be close to a perfect (diffraction limited) lens. Sorry, but this is just not the case. Why it isn't the case is explained in detail in an article on my web page concerning the measurement of aerial image resolution . You need to understand this, so visit the link now!

When they say that the "resolution" of the lens is better wide open, what exactly does "resolution" in this context mean? If it means the ultimate resolution in the aerial image, that's OK. If it means anything other than that, then it isn't OK.

The fact that they observe aerial image resolution decreasing as a lens is stopped down should not, repeat not, be taken as any indication of the performance of the lens at any spatial frequency (lp/mm) other than the one being directly measured.

Part II

"But what's the best resolution on film" is their second page. Here it gets bad again. For example they make the statement (and in their own bold type!) "Best lens resolution is achieved when shooting wide open, but best film resolution is at ~f22 (or smaller)". Now it isn't easy to dig out what they are trying to say here. What does "best lens resolution" mean? Best resolution at the resolution limit in the aerial image - maybe. But that bears no relation at all to the best resolution on film or the best resolution in the range that can be recorded on film (between 0 and about 150 lp/mm). It's a number unrelated to any lens property other than ultimate resolution in the aerial image and that's not something of any practical value or interest to photographer! "Film resolution" isn't related to the lens at all. It's the resolving power of the film and that's a number which stands on its own. If they mean "best resolution on film", they're still wrong - and clearly they don't mean that since they later conclude that best resolution on film comes at about f8! They do say the following:

"film resolution has been shown to vary appreciably with aperture, and resolving power is always highest when the light source area is minimized, to retard dispersion".

Err, I just don't understand that. It sounds like Star Trek speak (... one must adjust the phase initiator coils in order to align the tachyon field generators ...). They might be trying to say that dispersion (by which they may mean the scattering of light in the emulsion?) is minimized when the image point spread function (smallest possible spot) is minimized - but that happens at wide apertures (f5.6-f8), not at small apertures (f22) where diffraction makes the point spread function larger! They might be saying that dimmer images (at f22?) cause less dispersion, which is true but has no bearing on resolution in the real world (or underexposed images would be sharper!!). Despite trying my best to understand what they are saying, I can't. It makes no sense at all.

They then go on to list a table showing resolution on film as a function of aperture which peaks at f8 (no big surprise, "f8 and be there" has always been the photographer's motto!). They don't say how they got the table [actually this isn't true, RRS say they got the table from data supplied by Charles Sleicher with his lens testing chart. What I should have said is that there is no explanation of how the numbers in the table were derived] and, in fact, they can't logically get the table based on the "facts" presented earlier! They've left something out completely. I know what it is (and I believe it's wrong anyway!) but you are never going to guess from the text! It involves (what I think are incorrect) assumptions about the depth of focus in relation to the thickness of film. Anyway, here's the table

f2.8	80 lp/mm
f4.0	90 lp/mm
f5.6	95 lp/mm
f8.0	100 lp/mm
f11	95 lp/mm
f16	80 lp/mm

Also, much is made of the empirical relationship (empirical - relying on experience or observation alone, often without due regard for system and theory - Websters!) between film, lens and system resolution. This relationship is often given as:

1/R_s² = 1/R_f² + 1/R_l²

where R_s is the final system resolution, R_f is the film resolution and R_l is the lens resolution. This relationship is quoted in many texts, including publications by Kodak (P315 - Scientific Imaging) and in "Image Clarity" by John Williams. It is certainly a relationship which can give a decent approximation of system resolution under some conditions. However it is not based on any sound theory and can, in fact, be shown to give erroneous results when used improperly. There is no reason why the exponent should be 2. Some studies have shown a better fit with smaller exponents in the region of about 1.5, but even then, it's still empirical - it applies only under the conditions used for the experiment in which it was determined. Here's why it can fail (and fail badly) at times.

The only way to truly calculate system resolution is via multiplication of the MTF of the film by the MTF of the lens [Actually you should use the OTF, optical transfer function, the MTF being the absolute value of the OTF. However MTF is more commonly obtained and in most practical cases works just fine]. This is soundly based in optical theory and gives an exact solution. For this you need to know the MTF of the lens and the MTF of the film over the spatial frequency range you are interested in (typically between 1 and around 200 lp/mm). If you know those functions you can calculate system resolution. Now the empirical formula above uses just two numbers, film and lens resolution limits (i.e. the point at which the film and lens MTF values drop below some fixed value, say 0.01). To predict the system resolution, those two numbers would have to predict the MTF of the lens and film at all other (lower) spatial frequencies. They don't!. As I showed above, lens resolution has zero value in predicting the shape of the MTF curve. Now if you take a set of lenses which have low aberration values (say less then 0.25 wavelengths of wavefront error), then you can make an approximate predication of the shape of the MTF curve from the limit of lens resolution. Under those circumstances you can use the empirical relationship to approximate system resolution. However, if you take a lens with significantly higher aberrations and use the empirical relationship, you get an invalid predication of system resolution. You could be way off (indeed you probably would be!). In practice, this means that while system resolution calculations via the empirical relationship may be ballpark accurate with the lens stopped down (say f5.6 and smaller), they may be way off for large apertures (say f1.0 to f4, depending on the lens). This can get you into all sorts of problems trying to explain why you don't see optimum performance wide open, when your measured "lens resolution" is highest wide open!

Part III

"Doublers" - They say that doublers always reduce resolution - and this is true. They give an example of a doubler used on a lens at f8, yielding an effective f16 lens. They then point to their table which shows maximum resolution at f8 as 100 lp/mm and maximum resolution at f16 as 80 lp/mm and say "look - resolution drops even for a perfect lens and doubler!". My comment is yes, but ... you typically don't use a doubler on a lens at f8. You are much more likely to use it on an f2.8 or f4 lens (300/2.8, 400/2.8, 500/4 or 600/4). In that case you go from f2.8 to f5.6, or from f4 to f8. Now, take their "resolution on film vs. aperture" table (shown above). At f2.8 they show maximum resolution of 80 lp/mm, at f4 90 lp/mm at f5.6 95 lp/mm and at f8 100 lp/mm. By their logic, this shows that you get an improvement of resolution when you add a doubler to a fast lens!! You can't have it both ways. They have already shown (in part 1) that lenses have higher resolving power when used at full aperture, via the aerial image testing, so you can't argue (using their logic) that lenses get better in performance when they are stopped down.Clearly we have a problem here, related to both the misinterpretation of experimental data and the application of faulty logic.

Bryan Geyser of RRS has pointed out to me that he was thinking of the practice of adding doublers to macro lenses to improve working distance, and in that case small apertures are often used. In this case the loss of the two stops results in lowered resolution because diffraction is the dominant aberration. It's not really the doubler which is causing the drop in resolution, it's the effective aperture being so small. You would drop the resolution by just about the same amount if you simply stopped down two stops rather than adding a doubler. The danger with a doubler is that some people might not appreciate that the two stop loss in aperture directly translates into decreased resolution due to diffraction when working at small apertures. This topic is touched on in the article on sharpness at the DOF limits elsewhere on these pages (see the table and the drop in resolution of the in focus image at smaller apertures).

The diffraction issue isn't so important at larger apertures because diffraction (for almost all lenses) isn't the dominant aberration at large apertures (it's usually spherical aberration in the center of the field, with coma and astigmatism added as you move out to the edges of the field).

Conclusion

All in all, the attempts at explaining the role of optics in determining the resolution on film aren't impressive. They make no mention of the true causes of changes in resolution with aperture, which is the reduction of the wavefront error via reduction in lens aberrations (principally spherical aberration for the center of the image field in lenses used at wide apertures). They don't seem to realize that lenses can have significant amounts of spherical aberration and still appear to resolve out to the theoretical resolution limit when the aerial image is examined.

It's a pity this paper contains so much which is in error because it makes RRS look like they don't know what they are talking about, whereas in fact, RRS make some of the very best equipment you can buy. They make superbly well engineered quick release plates for arca-swiss type QR systems, and excellent brackets and other mechanical parts to assist photographers. The quality of their products is unquestionable. I wouldn't hesitate for one second to buy anything they manufacture. I certainly wouldn't go to them for technical advice on optics though!

RRS can be contacted at (805) 528 6321 or via FAX at (805) 528 7964. They do not have a web page or public email address.

My recommendations for the best sharpness conditions based only on optical considerations are as follows:

Shoot high quality, fast prime lenses at f5.6.
Shoot consumer type lenses and zooms at f8.
Don't use multipliers unless you have to.

These apertures represent the point at which aberrations are minimized. Open up more and spherical aberration will degrade the image, close down more and diffraction will degrade the image. In 99% of cases this will give you maximum sharpness of the in-focus image in the center of the frame. Of course you may have to open up more if you want a faster shutter speed, or stop down more if you want greater depth of field or add a multiplier if you need a longer focal length. While these actions may reduce the maximum theoretical image shapness slightly, they may result in a much improved overall result, so of course we all do them!