Trying to understand the optics of stacked lenses

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mgoodm3
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Trying to understand the optics of stacked lenses

Post by mgoodm3 »

My first post here and it is a technical one. :D I mainly image coins and do a lot of close-up in the 1:1 to 10:1 range for fine details.

The optics of stacked lenses is a bit of a mystery to me and I have been trying to wrap my head around the concepts involved.

My best interpretation of the basic optics is that the normally mounted lens is imaging the exit pupil of the reverse mounted lens (which is really its entrance pupil since it is reversed). The sucess of this by the normally monted lens seems to based on the sizes of the pupils in the normally mounted lens and the reversed lens - where it is better to have a larger one on the reversed lens (helped by a large aperture) and a smaller one on the normally mounted lens (helped by a smaller max aperture).

The position of the pupils seems to be the reason that there is variablility in which lenses work well together. In an ideal world the two pupils will be superimposed on each other. This seems to be best illustrated by a microscope where the eye relief (ie. exit pupil) should be superimposed on the entrance pupil of your eye.

Seems like cameras don't have that luxury of superimpostition unless you get lucky. With a distance between the two pupils, the field of view of the normally mounted lens seems to come into play - so a long focal length helps on the normally mounted lens and again a large exit pupil on the reversed lens is good.

Not sure if the exit pupil of the reversed lens has a field of view since the image is not projected on the normally mounted lens.

The aperture of the two lenses are another point entirely, but they are workable by just avoiding vignetting whenever possible.

Am I way off base or am I on the right track? I have had to piece these tidbits together from various optics sources.

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Post by rjlittlefield »

mgoodm3, welcome aboard! :D

You're basically on the right track, but I can't tell about a couple of the finer points.

What I'd like to do is go clear down to basic optics. If we try staying up at the level of terms like "exit pupil", it's very likely that what you get from my words will be different from what I tried to put there.

So...

First, remember that what any lens does is to collect a bundle of diverging light rays from each point on the subject, and bend those rays so they come back together again at a point on the sensor.

In between those two points, the bundle of light rays assumes some complicated shape that is basically a sequence of truncated cones. Each lens element changes the angle of the cone. In addition, the sides of the cone can be cut off, or clipped, when the bundle passes through any aperture, such as the lens diaphragm or too near the edge of a lens element.

In the simplest case, all bundles are clipped by the same aperture. The apparent position & size of that aperture for light entering the lens is called the "entrance pupil". Similarly the apparent position & size of that aperture for light leaving the lens is called the "exit pupil".

Most single lenses are designed so that they fit this simplest case -- all bundles are clipped by the same aperture, and it is straightforward to talk about the entrance and exit pupils as being the apparent position of that aperture.

When you stack lenses, life gets more complicated.

Ideally, the exit pupil of the front lens lies at the same place as the entrance pupil of the rear lens. In that case, it is still true that all bundles will be clipped by the same physical aperture. That aperture might be the one in the front or the one in the rear, and it doesn't matter which because exactly the same rays make it through the lens in either case.

However, this situation is very uncommon.

More commonly, the exit pupil of the front lens lies somewhat in front of the entrance pupil of the rear lens. In that case, bundles of light can be clipped by the front aperture, or the rear aperture, or both, depending on where they happen to originate in the subject field. Vignetting occurs when some or all of the light rays from the edge of the subject field cannot pass through both the front and the rear apertures.

It is probably easy to see that this problem gets worse as the two pupils move apart. Some lenses, particularly telephoto designs, have their pupils buried deep inside the lens. You can immediately see this by just stopping down the lens, looking into its front end, and seeing where the aperture appears to be. If the aperture appears to be far back from the front surface of the lens, then you can anticipate more problems trying to use that lens as part of a stack.

I think this description agrees with almost everything you wrote.

The bit I'm puzzling over is where you write that "the normally mounted lens is imaging the exit pupil of the reverse mounted lens". Normally I read that phrase "is imaging" to mean "is focusing on", and that is emphatically not the case with stacked lenses. (Contrast this with the situation where you use a magnifying glass to focus on the exit pupil of a microscope eyepiece, in order to see whether the objective lens is being filled properly by the condenser.)

I spent quite some time a couple of years ago, puzzling out how apertures work and what some of their stranger effects can be. You might find the writeup helpful as background reading: http://www.janrik.net/PanoPostings/NoPa ... xPoint.pdf .

Hope this helps, and again, welcome aboard! :D

--Rik

mgoodm3
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Post by mgoodm3 »

Thanks for the reply. I am glad that I have the right basic idea. I have gleaned quite a bit of useful practical optics from this forum. I recently pulished a book on coin photography and decided to work on a second project - photomacrography for coins. I have found it to be a much more technical subject and I would like to at least have a basic understanding of the processes involved. I have read multiple books on optics (very painful) and have tried to avoid the ugly math and stick to the concepts. Stacked lenses were the one thing that is not covered well anywhere that I can tell.

When I was "imaging the exit pupil" I was mainly referring to the fact that I would only like to accept light into the front lens that has passed through the aperture of the reversed lens - anything else means vignetting.

I want to provide some set of basic rules to help people pick lenses for stacking.

1) reversed lens: short focal length so you actually get some mag.
2) reversed lens fast: maximizes the size of the exit pupil.
3) front lens: long for narrow field of view and also getting decent mag.
4) front: slower to minimize the size of the entrance pupil. Ithink that this is independent of the aperture setting??
5) add extension help decrease vignetting although inc. magnif.
6) prayer

I will have to post some photos sometime. I have done just about every macro technique that I can find out there. I would also like to explore telecentric lenses a little and see if there is any application to the world of coins ( I can imagine some applications but don't know if practical).

Mark.

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Post by rjlittlefield »

mgoodm3 wrote:have tried to avoid the ugly math and stick to the concepts
Me too. When I teach math, I tell my students that having a concept solid beats memorizing a formula any day.
4) front: slower to minimize the size of the entrance pupil. I think that this is independent of the aperture setting??
No, to the question. The entrance pupil is exactly the aperture, as seen through the refracting elements in front of it. Stopping down the aperture also shrinks the entrance pupil. BTW, your use of "front" seems confusing to me. I use "front" to mean the lens that is nearer the subject, the one that is reversed. The other one I call "rear". I don't know if there is a standardized terminology for these things.
6) prayer
Absolutely. In my experience, asking for patience and acceptance is particularly useful. Insight is also worth a shot, but that's less often granted.
I would also like to explore telecentric lenses a little and see if there is any application to the world of coins.
There is quite a bit in the forum archives about these. They are a pet topic of mine. I will provide whatever assistance I can.

--Rik

mgoodm3
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Post by mgoodm3 »

I'll just have to stick to referring to the lenses as "normally mounted" and "reverse mounted" and try to avoid the confusion.

Actually having the pupils based upon the active aperture makes me happy. A lot of the references I have seen almost imply that the pupils are a fixed quantity and I was having trouble dealing with that.

It would seem that having a slow normally mounted lens wouldn't make a lot of difference. My own gut feeling is that the field of view is more important (narrow for a long lens ) makes more difference in how two lenses may interact. Although if the position of the pupils are very close to each other, the field of view is less important and the size becomes more important.

My own experience with setting up stacked combinations is that I will open both lens wide open and stop down the normally mounted lens one stop short of where vignetting sets in. I will then be able to stop down the reversed lens to a sharper aperture (such as f8 ) and things work pretty well ( at least for the combos that I have tried).

I have seen various places where they say to leave one or the other lenses wide open and I just don't see that in real life. I get sharper images by getting both lenses as close to their sharpest aperture as I can.

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Post by rjlittlefield »

mgoodm3 wrote:I have seen various places where they say to leave one or the other lenses wide open and I just don't see that in real life. I get sharper images by getting both lenses as close to their sharpest aperture as I can.
I have seen those same recommendations. Often the authors seem very emphatic that their way is the right way. Presumably each author has some reason for believing so strongly in the correctness of their own position. I suspect it's because they all have experiences, and those experiences have differed. (The alternative is to suspect that some of these people hold strong opinions without evidence, and surely no one would be guilty of that. :roll: )

Personally, I've never played much with stacked lenses, I've never seen careful experiments, and I've never read a very convincing or detailed analysis of how two non-superimposed apertures play together across a finite field.

For the single point that's on-axis, traditional analysis says that only one of the apertures will clip the ray bundle and it doesn't matter which one because the same peripheral rays will be clipped in either case. The second aperture might act as a baffle for stray light, and thus increase the contrast, but it should not otherwise affect the image. Note however that increasing the contrast does increase the apparent sharpness as well. It's hard to tease these things apart.

For points that are off-axis, the situation is not so clear to me. In that case, the bundle can be clipped in part by one aperture and in part by the other. I think I can imagine cases where stopping down each aperture eliminates rays that are particularly bad for that piece of the lens combination, while still letting enough light pass through to form an acceptably uniform (non-vignetted) image. But I haven't thought that through carefully, and I have no idea whether it occurs in practice.

I would be very interested to see a carefully done experiment that demonstrates improved image quality from stopping down both lenses.

Are you in a position to do that?

--Rik

mgoodm3
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Post by mgoodm3 »

What's funny with a few of the combinations I have tried is that once I get rid of the vignetting with the aperture on the normally mounted lens by opening it up, the aperture on the reversed lens can be adjusted without significant effect on the vignetting up to a certain point (ie. it acts like a normal aperture).

I notice two forms of vignetting with stacked lenses.

1) Total black where you can see the outline of the aperture
2) More subtle with just the center being slightly brighter than the periphery. (some of the rays being picked off by an aperture??)

I am doing MTF testing (Imatest software) on all of the lens combinations/techniques that I can scrape up and I plan to start playing with the stacked varieties soon. I have found that stacked lens tend to produce very high quality images even at higher magnifications, although I haven't put a number to that quality as of yet.

MTF testing has been very instructive for me.

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Post by rjlittlefield »

Here is a model that may help us to think about this.

Imagine a subject field that is entirely black except for a single bright spot.

That bright spot emits light rays, some of which pass through the first aperture and continue on toward the second aperture.

At the plane of the second aperture, the bundle of rays forms a patch of light that has the shape of the first aperture. The size of this patch tracks the size of the first aperture.

For simplicity, assume that both apertures are circular.

Depending on the diameters of the apertures and where the bright spot is located in the subject field, the patch of light in the plane of the second aperture may (1) lie completely inside the second aperture, or (2) completely surround the second aperture, or (3) overlap the edge of the second aperture, or (4) be completely outside the second aperture.

Case 1: If the patch lies completely inside the second aperture, then the second aperture has no effect at that point in the subject field. If this occurs for all points in the field, then you will see no vignetting, and the first aperture will entirely control exposure and depth-of-field. This situation is most likely if the rear lens is wide open and the front (reversed) lens is stopped down.

Case 2: If the patch completely surrounds the second aperture, then the first aperture has no effect at that point. If this occurs for all points in the field, then again you will see no vignetting, but now the second aperture will entirely control exposure and depth-of-field. This situation is most likely if the front (reversed) lens is wide open and the rear lens is stopped down.

Case 4: If the patch lies completely outside the second aperture, then no light will get through the lens combination for that point in the subject field. This is your first type of vignetting, with a black border. This situation is most likely if both lenses are stopped down a long ways.

Case 3: The most interesting situation is when the edge of the patch overlaps the edge of the second aperture. In this case, some but not all of the light rays get through the second aperture, so the resulting image is dimmed for that point in the field. In addition, because both apertures clip the ray bundle, its shape is liable to be very far from circular. This can have interesting effects on both DOF and bokeh. This situation is most likely if both lenses are stopped part way down, so that both the second aperture and the patch of light cast by the first aperture are fairly large.

Notice that case 3 can never occur in the center of the subject field, because then the patch is centered on the second aperture and we have either case 1 or case 2.

Notice also that we can never have a sharp transition from cases 1&2 to case 4. As the bright point moves out from the center of the field, the patch of light gradually slides off center with respect to the second aperture. For a while they are likely to completely overlap (case 1 or 2 -- no dimming at all), then they will gradually overlap less and less (case 3 -- progressively darker away from center), and finally they may not overlap at all (case 4 -- black border).

I am sorry this is such a long-winded explanation for what's really a simple phenomenon. No doubt a well-drawn diagram or two would get the idea across in much less space, but diagrams take a long time to draw, and then they always need at least some explanation too. :(

Anyway, the short summary is to think in terms of a hole (the second aperture) and a patch of light (rays that get through the first aperture). The type and extent of vignetting you get depends on the size of the hole, the size of the patch, and the distance the patch moves off-center as you shift attention from center to edge of the subject field. That last part, in turn, depends on the separation between the pupils (more separation, more movement), which is why it doesn't work well when the pupils are far apart.

Switching subjects, I am interested to hear more about your MTF testing. I have the impression that traditionally this is done with a crisp black-and-white test target. What do you use as a target at high magnifications?

--Rik

Joseph S. Wisniewski
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A quick note on terminology...

Post by Joseph S. Wisniewski »

rjlittlefield wrote:BTW, your use of "front" seems confusing to me. I use "front" to mean the lens that is nearer the subject, the one that is reversed. The other one I call "rear". I don't know if there is a standardized terminology for these things.
Yes, there is, but I dislike it. Lefkowitz used "prime" for the lens closes to the camera and "supplemental" lens for the lens closest to the subject. Shaw continued this use. If Lefkowitz and Shaw agree on terminology, we're pretty well stuck with it, unless heroic effort is made to change it. I think it's worth the effort in this case.

This "prime" and "supplement" usage is terribly confusing, for two different reasons.

First, the lens closest to the subject isn't a "supplement", it's the one doing most of the work. If any lens is the "primary", it is the front lens. The lens closest to the camera is performing a job more like an extension tube or bellows, it's just getting the other lens "away" from the camera a bit. (If you read up on "infinity optics" in microscopes, the lens closest to the subject performs the function of the microscope "objective", the one closest to the camera performs the function of the "tube lens").

Second, the lens closest to the camera could be a "zoom" lens. In Lefkowitz's day, this was rare. In 2008, it's very common. And in 2008, "prime" is also used to mean "not a zoom".
mgoodm3 wrote:I'll just have to stick to referring to the lenses as "normally mounted" and "reverse mounted" and try to avoid the confusion.
I believe that will actually cause more confusion. Bjorn Rorslett (is he active in these forums?) shows one example on his site: the 105mm "Bellows Nikkor" performs much better when mounted in the forward orientation in front of a telephoto lens. (Shaw specifically shows the Nikon short mount 105mm reversed in front of a telephoto, and that is one lens that definitely performs better forward mounted. Forward mounting is a little more complicated, though).

I extend this in the Macronomicon, with examples of enlarger lenses mounted "unreversed" in front of telephotos.

Current literature (the stacking article on Nikonians", Bjorn's articles, my own articles, the macro classes I teach at MPW, and my upcoming book "The Macronomicon" all use "front" and "rear". I think that those terms will make this discussion flow smoother.

Joseph S. Wisniewski
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Musing on coupling and aperture...

Post by Joseph S. Wisniewski »

I'm just going to ramble a bit, because I have a lot of thoughts on this subject in my head already, so I won't be "quoting" and "answering" as much as I normally do.

I always hated the term "stacking" lenses. I much prefer "coupling", because it captures the concept of a "partnership" between the lenses...

How familiar are you with the concepts of "diffraction" and "effective aperture"?

There are a number of ways to view the relationships of magnification, aperture, and focal length. Entrance and exit pupil will, obviously, drive you crazy, because they're not going to be coincident, they're going to reside well within their respective lenses. Neither lens will image the pupil of the other, both lenses are imaging infinity when seen from their respective focal planes.

Nevertheless, the pupil locations relative to the front and rear nodes is useful for calculating the pupillary magnification factor. The math for that is described in Lefkowitz, and I'll leave you to dig it up. If both lenses are focused to infinity, pupillary magnification can be ignored...

We'll stick with the terms "front lens" as the lens closest to the subject, and "rear lens" as the one mounted to the camera, as this agrees with the majority of existing literature.

In general, you want a fast lens for the front lens and for the rear lens. The rear, for the reasons you cited earlier, reduction of vignetting. The front, because we need it for resolution.

You talked of magnifications up to 10x. For coupled lenses focused to infinity, the magnification is the ratio of the focal length of the rear lens to the front lens. Picture the 10x combination of a 20mm in front of a 200mm.

If the rear lens is fast enough to prevent vignetting, the effective aperture is the aperture of the front lens multiplied by the magnification, in this case, f2.8*10x = f28.

Now, lets visit our old friend, the Cambridge In Color Diffraction Calculator

http://www.cambridgeincolour.com/tutori ... graphy.htm

We see that for a common 12mp 1.6x crop DSLR, the diffraction limit is around f8. f28 is 3-1/2 stops past that, so we're definitely looking at serious image softening. It's probably not important where we control the aperture, because we'd want that front lens wide open all the time.

But for lower magnifications, controlling the aperture properly becomes more critical. Whenever you couple two lenses, the "best" place to control the aperture isn't at the iris of either lens, it's someplace in between. If the ratio is 1:1 (identical lenses) the place to control the aperture is right in the space between the lenses. As the ratio gets larger, the best place to control aperture moves towards the iris of the front lens, but it never actually reaches the iris of the front lens (that would require that the ratio of rear lens to front lens approach infinity). At small ratios (say from 1:1 to 4:1) the "best" place is still between the lenses, and this can be done by rigging "Waterhouse stops" between the lenses. A "Waterhouse stop" is just a black disc with a hole in the center. I make them from thin plastic sheet, spray painted flat black. This will provide much better contrast and control of aberrations than controlling aperture with the front lens or the rear lens.

My "interlens" aperture holder is part of my lens "coupler". For many years, I have made my couplers from pairs of Cokin P-rings. These offer greater mechanical strength and better quality threads than any "off-the-shelf" coupler. They also make it easy to add a "stop holder", just make a thin spacer between the P-rings that you bolt together, and slide the stop into that space.

It is also possible to mount an actual iris diaphragm (I got mine from Edmund optical) in a P-ring lens coupler. Here's a bit more on how I did it...

http://photo.net/nikon-camera-forum/00OtlZ

http://photo.net/nikon-camera-forum/00PKz5

You may find, once you've gotten exposure correct with the interlens stop, you then want to adjust the apertures on both the front and the rear lens to reduce the stray light, as Rik so wisely pointed out.

As the ratio passes 3:1 or so, the "best" control is usually closer to the iris of the front lens than to the space between the lenses, so you can forget the Waterhouse stop or iris, and control aperture from the front lens. You still need to control flare by adjusting the aperture of the rear lens. But remember to calculate that effective aperture, you may find 4:1 or 5:1 is where you want to leave the front lens wide open. That same 20mm in front of a 105mm gives just over 5x, and takes us down to f14. Too much for a 1.6x crop digital, so on one of those, we'd probably never stop down. For 35mm film or a "full frame" DSLR, we might stop down one stop, but no more than that.

If you have the interlens aperture coupler, you can also adjust that for optimal contrast control.

rjlittlefield
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Post by rjlittlefield »

Joseph, thanks for chiming in here.

First off, let me offer the opinion that "rambling" is great. The risk with "quoting and answering" is that it lets the other person set the path of the discussion. Sometimes there are better paths, particularly when the initial poster is uncertain even how to think about the problem. Waterhouse stops may be out of scope for many of mgoodm3's intended audience, but discussing their advantages certainly helps to clarify the issues.

Second, I'd like to thank you specifically for those links to other discussions on photo.net. Very interesting reading indeed.

A point of clarification, just to be sure that we're all on the same page. Does "Lefkowitz" refer to his "Manual of Close-Up Photography" that is conveniently available through Amazon et.al., or are you referring to another publication?

--Rik

mgoodm3
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Post by mgoodm3 »

There's a lot of info here that I will try to digest.

I will refer to the lenses as front and rear in the future since that seems to be the industry standard.

The waterhouse stop is interesting and I may play with the idea a little for myself - as mentioned, my audience is barely comfortable with the concept of stacked (coupled) lenses.

Regarding MTF testing:

The imatest software uses slant line black/white interfaces. The target that I use is from Applied Image Inc (they have a ton of different targets). It's a standard digicam test pattern (ISO 12233) and has multiple slant lines on it. they also make a pattern with just a slant line on it. The whole test pattern is 20 x 26 mm so it roughly fills and SLR screen at 1:1.

The chrome on glass pattern I have seems too work well for all of the magnifications that I have played with so far and seems to be made with more than enough resolution capability for most purposes.

I have learned a lot of MTF testing. It gives a good indication of what works best at what magnification. I use it to test which aperture is the sharpest for various lenses. For now, all I have tested is sharpness in the center of the field. I plan on doing testing on the edge of the field also.

Takes a lot of time to do it because you can't really judge by eye which image is sharpest. You just have to take multiple pics at various focus levels to find the best. I am buying a verticle micrometer stage to make adjusting the height a little easier. Coins work best with a vertical camera and adjusting the height of the camera is difficult (also applies to stacking images).

mgoodm3
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Post by mgoodm3 »

Oh, I use MTF50 and MTF10. MTF50 seems to be roughtly the sharp/unsharp dividing line. MTF10 is roughly the max resolution.

The software works with RAW images and I do all of the testing without sharpening to helps standardize the numbers a little.

Joseph S. Wisniewski
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Post by Joseph S. Wisniewski »

rjlittlefield wrote:Joseph, thanks for chiming in here.
Rik, you are quite welcome.
rjlittlefield wrote: First off, let me offer the opinion that "rambling" is great. The risk with "quoting and answering" is that it lets the other person set the path of the discussion. Sometimes there are better paths, particularly when the initial poster is uncertain even how to think about the problem. Waterhouse stops may be out of scope for many of mgoodm3's intended audience, but discussing their advantages certainly helps to clarify the issues.
Glad you liked the rambling. Sometimes, that's just how my thought processes (or what's left of them) work.
rjlittlefield wrote: Second, I'd like to thank you specifically for those links to other discussions on photo.net. Very interesting reading indeed.
Glad you enjoyed. Coupling has always been a popular technique for field work, and there's a lot of that at photo.net.
rjlittlefield wrote: A point of clarification, just to be sure that we're all on the same page. Does "Lefkowitz" refer to his "Manual of Close-Up Photography" that is conveniently available through Amazon et.al., or are you referring to another publication?
Yes, that is indeed the one. My favorite macro book.

Chock full of good advice and fun "tinkering" stuff like how to build your own Aristophot style macro stand using black pipe and flanges...

Now, what I need is a good "micro" book. Something for scope use.

And I've got to get off my rear and finish the Macronomicon.

g4lab
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Post by g4lab »

If I may chime in too. Lefkowitz is a book that most members of this forum ought to have on their shelves. I certainly saved me a lot of time and film and made me much more comfortable shooting macro and to a lesser extent micro. Somewhat prior to the widespread advent of the internet I hooked up with a photo bookseller and paid an outrageous price for the book because he happened to have a hard bound copy. Even though the price was high I was very happy to have it and still am even though it is totally pre digital.

As the chips get bigger it won't matter as much.

There was a great book on microscopy by George Herbert Needham called Practical Use of the Microscope Published in the sixties by Charles Thomas of Springfield IL it is seriously showing its age but after trying to find a copy since about 1977 I got one from England (English printing too) on ebay. It predates things like infinity correction, fiber optics, let alone CF and ED objectives. But I still love it because when I first read it in the late seventies it was not quite as out of date and I learned a great deal from it. There is an earlier edition by the same author with the same title that is not the one you want. Needham was a biological microscopist at the U of Cal San Francisco if I remember correctly.

A bit more recent is Roger P. Loveland's Photomicrography A Comprehensive Treatise in two volumes from the Wiley Optics monograph series. Written about 1973 it is newer than the above and a great all time classic. Loveland was the head microscopist at the Eastman Kodak company in Rochester and took a lot of pictures of photo emulsion grain. Unfortunately I don't own these volumes, I have only had them out of university libraries for extended periods of time until the librarians asked me to return them. They do appear on the internet but I have not gotten around to buying copies myself yet. The McCrone Research Institute in Chicago had BOTH the above titles available as reprint on demand books until a few years ago. I think you could still get reprints if you tried but they are a little pricey. ($150) And the McCrone store also has lots of other titles.

Finally two books I have been happy to have by Alfred A. Blaker are Field Photography Beginning and Advanced Techniques and Handbook for Scientific Photography.

I have tried to continue to look at similar books that are newer when I find myself in university libraries. But I have not found anything yet that seems as good as the above authors. Certainly nothing that ever appears at regular bookstores.

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