Paper Resolution

[Patrick Troccolo]

I have been making many resolution tests on my camera lenses, with resolutions up to 80 lp/mm using the RIT test patterns. When I try to enlarge these patterns in my rigid Durst 138s at 2X, 3X, 4X & 6X with both a 100mm Schneider Componon or a 210mm Componon, all I have for resolution on my Ilford Multigrade V paper is a 10 to 12 lp/mm.
Has anyone measured paper resolution?

[Emmanuel BIGLER]

Patrick. You should give us some details on how you measure your final resolution on print. Finding only 10-12 lp/mm does not seem to match what I know from actual resolution of papers. The limiting resolution factor is probably elsewhere in your experiments.

20 years ago I tested traditional B&W paper by contact printing a USAF test target (fabricated on a chromium glass photomask) on a piece of photographic paper. I found a resolution above 50 lp/mm. This was traditional glossy baryt paper.

Ilfochrome paper is credited 63 lp/mm according to this official datasheet :
http://www.ilford.com/html/us_english/pdf/303e.pdf (http://www.ilford.com/html/us_english/pdf/303e.pdf)

Taking into account that the first light- sensitive layer in an Ilfochrome is certainley silver halide, I cannot imagine how the resolution of a glossy silver halide B&W paper could be only 10 lp/mm. Even a B&W Polaroïd print is credited something between 13 and 25 lp/mm.
http://www-unix.oit.umass.edu/~jpalma/scanning_bw.html (http://www-unix.oit.umass.edu/~jpalma/scanning_bw.html)

[Mark Sawyer]

Regarding lp/mm, the "l" is lines and the "mm" is millimeters, but don't both the "p" and the "/" mean "per"? (Hence, "lp/mm" reads "lines per per millimeters"?) Inconsequential, but little things sometimes bug me...

Anyways, I'd check the resolution coming through your enlarger lens with a good grain focuser just to see whether all those lines are reaching the paper. (And don't shake the enlarger.)

[Oren Grad]

Mark -

Actually, lp/mm stands for "line pairs per mm".

[Emmanuel BIGLER]

One line pair is one cycle, i.e. one bar plus one space to make one period of a grid.

In the above messages, please replace 'lp/mm' by : 'cycles per mm' and there will be no ambiguity.

In the photomask I used, when the bar is 5 microns wide and the space 5 microns wide, the period is 10 microns, the tested resolution is therefore 100 cycles per millimetres. I remember that I could read patterns with 10 microns bars plus 10 microns space, period 20 microns for a resolution of 50 cycles per millimetre or 50 lp/mm. This figure of 50 cycles/mm as well as the 63 cycles/mm for Ilfochrome exceeds by far the resolution of the human eye for a print examined at a 10" (250 mm) distance, where 7 cycles / mm is considered the resolution limit in visual observation.

[Neal Shields]

Back in 2002, I think feb. Ctein did an article in Photo Techniques Magazine titled: "Is your print paper sharp enough".

The short answer was: yes.

[Richard Littlewood]

could depend on the enlarger light. A condenser for example will give more in the way of sharpness than say the diffused cold cathode. A point source light is best if it's sharpness you want.

[paulr]

My experience suggests that with enlarging, fiber based paper does in fact limit resolution. This is based on the simple observation that the finest detail clearly defined through a focusing loupe (like a peak/micromega critical focuser) will not be visible at any magnification on the final print. Yes, the observations are made with the focuser sitting on a piece of the same paper stock, and no, that degree of change in focal plane would not be enough to make the difference I'm seeing.

I don't believe that tests made using a contact printed test target under pressure are applicable. A projection printed neg is going to have lower contrast (lower mtf) detail, and the surface of the paper will not be pressed flat. A test like this shows maximum resolveable detail under perfect (and therefore completely unrealistic) conditions.

That being said, I think the limits will only be aparent when looking at a print with a loupe. The paper doesn't seem to soften contrast at the moderately high resolutions (5lp/mm or so) that our eyes use most to determine sharpness. My own very informal tests have shown glossy paper to resolve at least 12lp/mm. This included wires on a window screen that were completely invisible to the naked eye at any distance but clearly defined when seen with a 4x loupe.

[Oren Grad]

Emanuel -

Thanks for sharing your results. Could you clarify on a few points?

> I tested traditional B&W paper by contact printing a USAF test target <

What was your contact printing setup? What size paper did you use? How did you hold the test target in contact with the paper?

> I found a resolution above 50 lp/mm. <

How did you examine the print to assess resolution?

> I remember that I could read patterns with 10 microns bars plus 10 microns space <

What standard did you use to judge that the test pattern at a given frequency had been unambiguously rendered in the print?

[Sal Santamaura]

Don't know why it didn't make the transition to lfphotography.info, but see what I said on the subject in this greenspun.com thread:


http://www.greenspun.com/bboard/q-and-a-fetch-msg.tcl?msg_id=004TDI (http://www.greenspun.com/bboard/q-and-a-fetch-msg.tcl?msg_id=004TDI)

[Mark Sawyer]

Oren-

Right you are on the "line pairs." Can't believe I never knew that...

[Oren Grad]

Mark -

No problem. We all know things that seem obvious in hindsight but that we didn't grasp until someone else helped show the way...

[Patrick Troccolo]

First, I want to thank you all for your comments.
I went to my enlarger today and using my grain magnifier found that the negative-enlarging lens combination was resolving 18 - 20 lp/mm at the paper plane for a negative (Tmax 100) made by my 150mm Schneider Super Symmar HM @ f16 that measured 75 lp/mm view by microscope of a RIT resolution target (high contrast).
The print, on Ilford multigrade V FB using grade 3 filtration, measured 12 lp/mm.
After viewing the Greenspun bboard, I'm going to buy a box of Bergger VC paper to see if I can have better resolution on my prints.
Granted, you can't see the difference with the eye, yet I want my prints to come closer to what my lenses and film can resolve than I'm getting now. Why waste all that effort and expense only to have it compromised by a paper.

[Sal Santamaura]

Patrick, I'm glad you're going to sample Bergger VC. Since that posting three years ago, I've switched to Bergger Graded NB. Sharpness wasn't the reason; tonal rendition of graded papers just seems more pleasing. Please give both papers a try!

[paulr]

"Why waste all that effort and expense only to have it compromised by a paper."

well, if you intend your prints to be viewed with a loupe, then more resolution makes sense. But if you intend them to be viewed normally, or even squinted at up close, then anything beyond 12lp/mm will be invisible. This has to do with the density of rods and cones on the human retina. It's based on current enough research that it's what Schneider engineers uses as a guideline when adjusting a lens's MTF response.

I would be more concerned with the VISIBLE factors that make a print appear sharp. More resolved detail beyond 11 lp/mm has no affect on this. But slight incrases in edge contrast in the neighborhood of 5lp/mm has a huge affect on it. There is zero corellation (in modern optical systems) between ability to resolve microscopic frequencies and ability to produce strong contrast at visible frequencies.

Beyond that, when you consider all the tonal qualities that actually make a print worth looking at, I wonder if microscopic resolution is really a worthwhile factor to consider when choosing a paper.

[Sal Santamaura]

"...then anything beyond 12lp/mm will be invisible."

Per Ctein, 30 lp/mm is required in a print for "perfect sharpness" as a result of our eyes' sensitivity to image acutance (edge sharpness).

[paulr]

I like a lot of Ctein's articles, but I have to say, he tends to conduct some pretty simple, homegrown experiments and then present his findings as fact. The kind of perceptual science involved in determining the limits of human resolution are very, very complex--way beyond anything Ctein has demonstrated in the articles I've seen, and certainly way beyond what anyone gets from a BS in physics in the 1970s. The perceptual science that Schneider uses is based on controlled experiments that take into account many more variables than anyone can in a darkroom.

The real issue is that microdetail has very little impact on our sense of sharpness. It's the relatively coarser detail at 4-7lp/mm that provides our brains with a sense of sharpness. What guys like Ctein frequently don't realize is that the things they're doing to increase resolution (maximum frequency rendered above a minimum modulation threshold) may well be increasing the modulation in the critical 4-7lp/mm range, and through that seperate process, increase your sense of sharpness.

This is important to lens designers, because they often need to compromise between resolving the finest detail and resolving less fine detail at higher contrasts. This is actually part of optimizing a lens for a particular magnification. An enlarger lens designed for lower magnifcations can relinquish some microdetail in order to provide higher contrast in the critical range, and therefore appear sharper.

I've seen a a print that resolves 20 lp/mm held side by side with a print of the same negative that resolves 5 lp/mm. The lower resolution print was tack sharp, and the higher resolution print was blurry! These were prints produced by Schneider to illustrate a point. They were both ugly. but it was interesting none the less.

[paulr]

I've just double checked some human optical research online.

Most subjective tests I've found (using printed samples illuminated with reflected light, using a viewing distance that corresponds to the average near-limit of human vision, 10 inches) find an actual maximum resolvable resolution of 6 to 7.5 line pairs per millimeter. At this point subjects were unable to distinguish between a bar pattern and a field of flat gray.

Actual retinal resolution limits are higher. The spacing of rods and cones on the human retina is about 2 microns, or 29 seconds of arc. This corresponds to an absolute maximum resolution of about 60 cycles (line pairs) per degree. If we accept that the near limit (closest focus distance) of the eye is 10 inches, that translates to 13.5 lp/mm maximum resolution. If you have unusually good eyes and can focus at 8 inches, you'd be able to resolve a maximum of 16.9 lp/mm.

These theoretical maximum values, while about half of what Ctein claims, are still much higher than what anyone can actually see on a print. They do not account for diffraction, optical aberations of the lens, and what is likely a reolution limiting function of our brain's optical processing, which exists to prevent aliasing and other interference patterns from becoming visible.

They also do not take into account the eye's extreme sensitivity to contrast. We can come closer to our retinal resolution limit when trying to resolve point sources of light. In these tests, the smallest separation at which we can define two point sources is used to calculate maximum resolveable frequency. The contrast of a bar chart or sinusoidal bar pattern is much lower, so our maximum resolveable frequency is much lower when looking at them. And the contrast of fine details in a photographic print is much lower still, no matter how much you paid for those lenses!

After looking at this research, it seems like Schneider's figure of 11-12 lp/mm is actually optimistic.

[Emmanuel BIGLER]

Details for Oren Grad
I used a glass/chromium photomask of size 3" as my test target. Not a film. The contrast of such an object is huge, the optical densiy of a chromium photomask is something like 3-4 depending on which wavelength is used ; I simply used an enlarger as my light source and projected an empty frame of the contact printing stuff. The photomask was simply pressed against the paper on another flat glass surface underneath to ensure a good overall flatness. Most probably I pressed by hand. When you simply contact print a microscope plate coated with photoresist even without pressing you easily get a resolution of 4-5 microns per cycle i.e. you easily get 100 cycles per mm. without a complex equipment.

For my silver halide contact prints, the results were examined with a metallographic microscope fitted with 10x and 20x lenses and 10x eyepieces. Resolving 50 lp/mm is an easy job for a 20x microscope lens. But on a few mm field. The criterion was rough and analogous to all sharpness criteria with a USAF test target, groups of 3 bars were clearly separated at a period of 20 microns. At the time I had access to an excellent micro-densitometer but my goal was not a very precise evaluation ; I was just curious to check what I could see and that was amazingy sharp.

Abous this experiment by contact printing being realistic or not, I simply want to comment quietly that the overall resolution of a print combines different factors. My point is that a traditional silver halide glossy paper itself is not the limiting factor, period. Now we can start discussing about other causes of lack of sharpness, but this is another story. If the projected image has already a low contrast, the optical transfer process plus de-focusing is to be blamed, not silver halide on paper. I'm not speaking of other papers with a well-marked texture, I'm just speaking about traditional glossy paper on a thin paper support.

If ILford can achieve more than 60 lp/mm with Ilfochrome (and Ilford know their product and would not state anything unrealistic), I cannot imagine that the resolution in the final colour print is better than the original resolution of the silver halide image which I asume present in the early stage of the Ilfochrome photochemical process (I assume that there is at least one layer of silver halides in Ilfochrome, I may be wrong).

[paulr]

My original observation about there being a practical resolution limit on an enlarged print actually had nothing to do with lack of sharpness. It was about a phenomenon that I noticed, and one that would only matter if you were in the habbit of looking at prints with a loupe, or if you were trying to scan a print in order to make a larger print from it.

Just a couple of general comments: when you're investigating sharpness, or lack of it, it's important to make a distinction between sharpness and resolution. sharpness is a subjective quality related to the edge contrast of details, and which corresponds pretty well with MTF at certain frequencies. Resolution is a pseudo-objective quality based on the highest frequency of detail visible, usually under some arbitrarily chosen set of conditions. It's possible to have very high resolution and very poor sharpness at the same time. And vice versa. So it's helpful not to confuse the issues.

It's also worthwhile to note that sharpness (and resolution) are not typically lost through bottlenecks or "limiting factors." They are lost progressively through every link of the image chain. Even the sharpest film degrades the image. A paper surface that can theoretically resolve a million line pairs per millimeter degrades the image. The air that the light passes through degrades the image. And the degradation is cumulative. If you take the MTF graphs of every link--the taking lens, the film/developer combination, the enlarging lens, the paper--and multiply them, you will get the MTF of the entire system. MTF values are less than 100%, with a handful of odd exceptions, so multiplying will always give you a smaller number. Unless there's a part of the signal chain that is hopelessly worse than the others (like, your enlarger is out of focus, or you're using a holga lens on your 8x10 camera, and wondering why things are a little fuzzy) you'll be able to get improved quality by making a significant improvement anywhere along the line.

[Patrick Troccolo]

Actually, it was Ctein's article in Phototechniques that started this chain of events for me. I realised that my prints were an order of magnitude away from the resolutions he stated and I began a study to understand final print resolution, using first principles and 1/Rt**2 = 1/R1**2 + 1/R2**2 etc., to see where the weak link in my chain of MTF degradation was. It wound up with the paper resolution. Funny how life is about these things.
If the limit to "sharpness" on the print is acutance, I'd like to be the one making the choice. I've made choices on the quality of lenses I've purchased, the film that was chosen to minimize grain and maximize resolution, the rigid enlarger (Durst 138s and not cheap) and large format view cameras (5X7), why not the paper.
I don't know what a high acutance paper would produce, wrt a high quality print, and maybe someone's already done that work and has handed us the result, I'd just like a choice, or at least to know why we're limited to 12 lp/mm.

[Oren Grad]

Emanuel -

Thanks very much for posting those details - exactly what I was looking for.

Paul -

Thanks for your further elaborations on this topic. I should say that my own "scientific" interest here is not primarily in what is the maximum spatial frequency that produces a visible effect. Rather, it's in accounting for why contact prints, at least in my experience, look different from even the most careful projection prints. I'm still inclined to believe that the phenomenon can be explained in terms of MTFs, but which spatial frequencies are the critical ones in accounting for this particular phenomenon remains an open question for me.

One familiar example of MTFs greater than 100% for at least one stage in the imaging chain: Kodak's current published MTFs for TMax films and Tri-X show modulation > 100% for "lower" frequencies (specific range varies by film, but it extends to relatively high frequencies with TMX). I think the usual explanation for this is edge and adjacency effects.

This reminds me of a question that may be related to the contact print issue: why does TMX tend to look soft, even when it is objectively rendering the subject with good contrast out to fairly high spatial frequencies?

[paulr]

Oren, I've been curious about the contact print phenomenon for a long time. You might be right that the difference has something to do with the shape of the MTF curve. I'm pretty sure it's about much more than just maximum sharpness ... I've seen some amazing contact prints that had "that look" but on close examination weren't really that sharp. I've also had a few strange experiences of being able to recognize something as an 8x10 contact print at a glance from across the room. One time I saw reproductions in a book over a friend's shoulder. They were candid looking, formally loose portraits. But something struck me and I asked my friend if those were 810 contacts. Turns out the book was by Nick Nixon ... handheld 8x10s of his family. I don't know what it is that jumped out at me, but something did.

The t-max question is an interesting one, too. I switched to tmx from agfapan 100 several years ago, and noticed a slight overall softer look ... in spite of the new film recording much, much more detail. Part of it might be the grain--the apx had a very crisp grain structure, which was lurking just beyond the range of visibility in my prints, but in tmx the grain is nowhere to be found. I doubt this is the whole story though. In the end, the slightly softer, smoother look grew on me, so i don't regret the move. I have to say the difference has been subtle. I get some very sharp prints from tmx ...they're just more likely to emphasize smoothness over edginess, which wasn't as much the case with the old film.

Incidentally, the reason film can be developed to 100%+ MTF is slightly artificial in most cases. It just means they're developing it to a higher contrast than whatever a neutral reference would be. Edge effects would be a more legitemate example of >100% MTF.

[Emmanuel BIGLER]

I totally agree with Paul R. that edge sharpness and MTF resolution for small modulations are different issues. The original message by Patrick Trocollo refers to a resolution limit in terms of estimated 10/12 lp/mm, i.e in terms of line pairs on a periodic test object. The original question refers to paper resolution. To both question an answer in terms of the USAF test target and separating groups of bars+spaces is IMHO, meaningful. We know that for extremly small modulations silver halide grains can be so small that 5000 lp/mm can be achieved on an holographic plate ; coating the same stuff on paper would certainly degrade actual resolution !!!! And we also know that holographic silver halide media are totally irrelevant to conventional photography, but it gives an idea of the potentiality of ultra-slow-sensitivity and ultra-fine grain silver halide processes.
I agree that 'contrast' and 'edge sharpess' are physiological notions to which we try to associate objective measurements, but this is difficult. Like in music, Fourier analysis of sound and images is not the ultimate key to solve all visual and physiological effects.
For example, some contact prints made from negatives developed in pyro exhibit a very special quality in terms of edge sharpness and "subtle feeling" which is amazing and for which I prefer not to elaborate any theory : some day I should try it myself by hands. This is also the joy of LF printing.
A musical similarity is : record a piano with a good microphone but cut by digital processing all the transients i.e. the very beginning of the sound. In terms of Fourier Analysis very few things are changed if you cut the starting transient signal and consider the quasi-steady state decay of sound, but the resulting sound without the transients is exactly like.... an accordion !!!! Hence, for the ear, edge sharpness ( a non linear effect) is probably more important that Fourier spectrum (in the model of small, linearized signals)!!! I'm quite sure that this also applies to the assesment of print sharpness.

[Oren Grad]

Paul -

> Part of it might be the grain--the apx had a very crisp grain structure, which was lurking just beyond the range of visibility in my prints <

Ah, but that's part of what's so tantalizing here - in your APX 100 example, we can't quite discern the grain as such, but there's some mechanism by which it's having a visible effect. In this respect I think TMX vs Delta 100 is a very interesting comparison - both look grainless in the small enlargements I make, but Delta 100 looks "edgier" to me and TMX looks softer, although both are superb in rendering fine detail.

> Incidentally, the reason film can be developed to 100%+ MTF is slightly artificial in most cases. It just means they're developing it to a higher contrast than whatever a neutral reference would be. <

Excellent point! I didn't think of that - it's like introducing an amplifier at one stage in the chain.

Emanuel -

> Like in music, Fourier analysis of sound and images is not the ultimate key to solve all visual and physiological effects... A musical similarity is : record a piano with a good microphone but cut by digital processing all the transients i.e. the very beginning of the sound. In terms of Fourier Analysis very few things are changed if you cut the starting transient signal and consider the quasi-steady state decay of sound, but the resulting sound without the transients is exactly like.... an accordion !!!! Hence, for the ear, edge sharpness ( a non linear effect) is probably more important that Fourier spectrum (in the model of small, linearized signals)!!! <

An alternative interpretation is that the Fourier spectrum really does capture the differences that matter; although they may be small when examined on a graph, if the difference occurs at frequencies to which the hearing system is disproportionately sensitive, the subjective effect can be substantial. Anyway, audio is more complicated in one respect - comparisons of live instruments versus recordings played through speakers are affected not only by effects of the recording/playback system on the frequency spectrum, but also by spatial effects associated with binaural hearing and the coupling of the sound transducer to the room - live instruments just behave differently from speakers in that respect. It would take a 3D Fourier spectrum - a record of how the Fourier spectrum varies through the listening space - to capture that, something that's theoretically straightforward but practically a real bear to implement and interpret.

I still want to think that the optical effects we're talking about, however subtle, have an explanation in terms of MTF - or, more properly, in terms of the coupling of MTF to the perceptual physiology of our visual system.

[paulr]

Emmanuel,
the sound analogy is a good one. But an even tougher one to comprehend. We should count ourselves lucky that we don't have to deal with human psychoacoustics when making pictures. As murky and complex as visual phenomena seem, the corresponding audio ones make them seem simple in comparison.
I'll bet that right now, in some dark parallel corner of the web, a bunch of recording and mastering engineers with nothing better to do are yelling their very similar, equally unproveable theories at each other!

[Oren Grad]

Forgot to add that sound is further complicated by being time-varying as well as space-varying. Paul's right - there's much more voodoo in audio...

[Patrick Troccolo]

I went back to the darkroom this morning and made contact prints of the 150mm Super Symmar HM lens resolution tests. Remember they had a resolution of 75 lp/mm and an enlarged print resolution of 12 lp/mm. I printed them with 3 different Ilford contrasts, 0, 2 & 4. The contact print resolutions were 28 lp/mm, 35lp/mm & 40 lp/mm.
Add that to your contact print vs. enlarged print comments.
BTW, I've never been able to make a print from an enlarger that matched a contact print.

[Patrick Troccolo]

Do you guys ever do any experiments, or is it all about a social medium?

[Sal Santamaura]

Contact print numerical paper resolution were you use the identical negative on Bergger VC and/or graded paper would be most interesting. Please post your results if you do run either of those tests.

[paulr]

has anyone ever made a 1:1 projection print (basically, contact print size but with an enlarger)?
I've always had it in the back of my mind to do this. to try to make 2 identical prints, one by contact and one by projection, to see what the subjective differences are.

[Mark Sampson]

The contact print would be (slightly) sharper and contrastier, because the image will not have passed through a lens. Can't argue with the laws of physics.

[Oren Grad]

Paul -

Yes, several years ago I tried comparing a 4x5 contact print with a 4x5 projection print of the same negative. The projection print was pretty good, but it was easy to tell them apart. However, the projection print had to be suboptimal for at least two reasons - first, I didn't have on hand an enlarging lens optimized for 1:1 - I was just using a garden-variety EL-Nikkor computed for the usual range of 2x enlargement and beyond. Second, the grain focusers I have on hand don't do well near life-size, and I'm not sure focus was optimal, though it had to have been pretty close. In this experiment as in so many others, it's not easy to hone one's technique to the point where one can be confident that the results are limited by the tools and materials rather than slop on the part of the user.

[paulr]

"The contact print would be (slightly) sharper and contrastier, because the image will not have passed through a lens. Can't argue with the laws of physics"

I'd bet the contact print would be sharper too. but i'm also interested other qualities, like rendering of tones.

And I wouldn't assume that the laws of physics as we understand them would predict anything with certainty in cases like this. Observed reality is often more complicated and interesting than predictions based on simple laws.

For example, in the contact print case, there's the issue of a difused light source, and light scattering in different ways than it does with the projection print, which is capable of focusing on the actual emulsion layer. I doubt this (or similar effects) would actually make the projection print sharper, but they're examples of the kinds of complications that can make results interesting.

And yeah, I think you'd want to use a 1:1 process lens like a g-claron (which I don't have) to get the best results.

[Patrick Troccolo]

Paul, thanks for the suggestion on 1:1 printing, I went back into the darkroom this morning to try your idea. By the way, it's easier to adjust a bellows extension for 1:1 and then adjust focus by moving the head. I focused on paper and could easily view 40 lp/mm in the grain magnifier. The print was made on contrast 4 and was carefully printed for equal line/space pairs. The print has a resolution of 12-14 lp/mm.
With the same focus setting, I printed a negative that I had a very good contact print of, wrt contrast, tones. The subject was El Capitan in Yosemite, basically a rock wall. What was striking was, at a reading distance of 10"-12", the noticeably sharper contact print. The contact print was more pleasing, jumped out at you. The "enlarged" print was lacking life when compared side-to-side with the contact.
On studing the contact print, it was the local "contrast" that made me feel it was sharper. High acutance made the details just "pop".

[Patrick Troccolo]

Has anyone ever used an unsharp mask for printing? I understand it helps for edge sharpness.

[Emmanuel BIGLER]

Many thanks indeed to Patrick T. to share his experiments with us. I like very much the idea of a fair competition between a contact print from a 4"x5" neg and a 1:1 "enlarged" print from the same neg.

And let's try to argue "with" or "against" the laws of physics (I hope that Mark S. will
allow me to argue ;-);-)

First, I agree with Paul R. that even a good 6-element enlarging lens is usually designed for a magnification ratio between 2x and 10X, sometimes up to 20X for the APO series, but definitely not for 1:1. Special 1:1 enlarging lenses exist as well as the good ol' process lenses (apo-ronar, etc..) but I'm not sure that the issue is actually here. Anyway, let us stop down the enlarging lens to an "engraved" f/16 which is actually an effective f/32 at 1:1 ratio as far as diffraction (and photometric) effects are concerned.

Assume that stopped down this way the lens is pretty close to being diffraction-limited ; a conservative evaluation of the cut-off period @ zero contrast is 32 microns ; actually a really diffraction-limited lens @ f/32 can provide some contrast up to about 22 cycles per mm if we consider 0.7 micron as a reference wavelength (again, this is conservative since B&W paper is sensitive to 0.4 / 0.5 micron wavelengths). So let's assume, based on the laws of physics, that we resolve up to 30 microns for a visible period, this is about 30 cycles per mm, again a factor about 4 above the reasonable visual limit of 7 cycles per mm for a print seen from 10" (250mm).

So there is something that does not work
- either the lens is actually 2x to 4x worse than the theoretical diffraction limit, which I do not believe at all @f/16 (N_eff : effective f/32 @1:1 ratio),
- or the sharpness criterion based on the ultimate visible cycle @ zero contrast due to diffraction equal to (N_eff x lambda) is irrelevant to the evaluation of the visual quality in a good paper print.

My feeling is that the 2nd idea is closer to reality than the 1st, i.e., for sure, it is good to check what is the actual resolution limit for the image of small periodic objects like the USAF test chart, but this is not a sufficient criterion for a reasonable assessment of a good print.

Since we like to refer to the laws of physics, it is interesting to mention here what the laws of physics say as far as the resolution limit of a contact print are. Basically there are two limiting factors :
- a geometrical blurring effect (the simple geometrical shadow-cast effect)
- a Fresnel diffraction effect.

The geometrical effect is simply the fact that if the light source is seen under an angle "theta" from the contact printer and if there is a small gap "g" between the paper and the negative you should expect a resolution limit due to a simple shadow-cast effect
r_geom ~= (theta x g).

So a diffuse light source (theta = big) for contact printing yields a certain lack of sharpness w/respect to a point source (theta = small), for the same value of the air gap "g".

The Fresnel diffraction effect, in the unrealistic limit of a perfectly collimated beam (theta = 0) yields another blurring effect r_diff which is about the square root of lambda x g i.e.

r_diff ~= (lambda x g )^(1/2)

where lambda is the wavelength of light.

Assume that we need a resolution criterion of 30 microns, consider a light source of about 1 radian wide (~60 degrees) we are allowed an air-gap of 30 microns. In a traditional contact printing frame we are probably better than that, I have no idea. As far as the Fresnel diffraction effect is concerned, take a very pessimistic value of 1 micron for the wavalength lambda, we are allowed an air-gap of 900 microns ((900)^(1/2) = 30) i.e. about 1 millimetre in order to reach a 30 microns resolution limit ! so it is clear that in a contact print, diffraction is absolutely negligible whereas in an enlarging lens used to its optimum f-stop, diffraction is definitely non-negligible since at the best f-stop aberrations and diffraction contribute half and half.

At the first glance, the conclusion could be simple : want nice sharp prints ? no problem, use a large format camera an contact-print !! Achieving 40 cycles per mm, i.e. a limit cycle of 25 microns sounds reasonable with a modern lens covering 8"x10" and modern film. Achieving the same with an enlarging lens is certainly more difficult.

There is another very difficult issue which is the comparison of noise between and enlarged negative and a contact print. The noise you see on an enlarged print with a focusing loupe device is not simply the geometrically enlarged pattern of film grains, the statistics of density fluctuations is heaviliy modified when passing throught a lens. And this "noise transfer effect" is certainly different in a contact print.

[Emmanuel BIGLER]

a small corection to the above figures : the theoretical limit period @zero contrast for an effective F/32, diffraction-limited lens @ 0.7 microns wavelength is : 32 x 0.7 = 22 microns, i.e. about 45 cycles per mm (1000/22). This does not change the conclusions i.e. that it is extremely dificult to achieve this resolution in an enlarged print.