Articles on DOF when tilting

[Leonard Evens]

I have put two articles on aspects of depth of field for tilted standards on my web page at

www.math.northwestern.edu/~len/photos/

The first article, entitled` View Camera Geometry,' is a highly technical article on the geometry of the subject. It uses concepts from projective geometry, some calculus, and lots of trigonometry. It requires a fairly good background in the relevant mathematics, so I don't recommend it for general readers, even for those with a strong background in technical areas. I wanted to get it all straight in my mind, whatever it took to do so, and I think I've accomplished that. In the process I was able to solve some of the problems arising when one tries to analyze these matters.. The article is complete, except for correcting typos and minor revision of language which will continue..

The second article, entitled `Depth of Field for the Tilted Lens', is still a work in progress. It is an attempt to describe some of the results of the first article without a lot of equations. (There may be a few, but they won't be essential to understanding the discussion.) It should be understandable to a much larger audience. Bu t it does assume some familiarity with technical concepts in view camera photography, such as the Scheimpflug and Hinge Rules, circles of confusion, the wedge shape of the DOF region for tilted lens plane, and similar concepts. I made some effort to explain all that, but it would be a lot to absorb for someone not already familiar with the ideas. The major aim of the article is to show why in most circumstances, you can ignore the effect of tilting on the shape of the circle of confusion, and to indicate under what circumstances the effect might be large enough to matter. In the process, other interesting issues come up.

I welcome comments about either article, but I would be very surprised if I got many about the first article. The second article is another matter, and I hope to get many useful suggestions about how I should proceed.

[Joanna Carter]

Hi Leonard

Well, as to the first article, personally, it went straight over my head I have found Merklinger's articles to be of much more use as they not only cover the maths, which is if only vague interest, they also provide some very practical examples of what happens to the image when I do this or that. Theory is all well and good for those who make their own lenses but, for most photographers, real world demonstrations are worth a thousand formulae.

Nonetheless, the articles look impressive, it's just that I, as a photographer, just wouldn't bother reading them

[kev curry]

I don't have the specialist knowledge to understand the articles either but on
the above discourtesy shown to another mans commendable efforts............
A classic response of ignorance to that which it cant understand.

[Joanna Carter]

On the above discourtesy shown to another mans commendable efforts............
A classic response of ignorance to that which it cant understand.

Kev, Leonard asked for comments, I simply replied from my POV. that is not intended as discourtesy, simply to express that such effort may be commendable but not necessary to take a great picture.

Heck, I don't have a problem with admitting ignorance of things I not only don't understand, it was hard enough picking the bones out of Merklinger's excellent articles.

Leonard, I hope you didn't take my comments as being derogatory, if anything, it is I that am simple enough to make pictures without knowing the science

[Paul O]

Kev, having known Joanna for a few years now I can assure you that she is the last person to be discourteous. She is, however, one of the few people I know who will give you an honest opinion - if you ask for one that is! I am sure that Leonard is prepared for al sorts of comments/criticism after all he did ask for responses.

A classic problem with the internet is that the typed word cannot often convey emotion and expression so there are times when comments are misunderstood or taken out of context. The sooner people realise and accept this the less backbiting or kneejerk response will unecessarily disrupt forum threads/posts. The comments made by Joanna were simply her opinion - having been asked by the author for comments. By you adopting the role of "defending" the author you have simply opened this thread to be a mudslinging contest.

I have no background/interest in maths or the science of scheimpflug/tilt - as long as it works in my photos I am happy! If, however, you are interested in the science/maths behind these principles then I'm sure that Leonard's articles will give you hours of enjoyable reading.

My own opinion on the articles is that they have NO relevance to me as a photographer - I have a similar opinion of Merklinger's work - but if some benefit from these then great!

I would not consider my comments to be discourteous?

Paul

[steve simmons]

There is an article in the Free Section of the View Camera web site complete with diagrams called Field Camera Movements that might be helpful

www.viewcamera.com


steve simmons

[chris_4622]

There is an article in the Free Section of the View Camera web site complete with diagrams called Field Camera Movements that might be helpful

www.viewcamera.com


steve simmons

Might be helpful to whom? Leonard?
This is totally inappropriate. He is announcing a couple of articles he wrote and asked for comments on the articles.

[Leonard Evens]

With respect to Joanna, I wasn't surprised at what she said, and I took no offense. I had already made the point that even the second article would be tough going for most people. It is still possible that someone like Joanna, if she has the time and inclination, might be able to make some useful suggestions on the basis of things she already knows. I did put in some remarks about points that Merklinger left out. I suggest she take a second look, but I certainly don't think she has any obligation to do so. It may be clearer as the diagrams are added. and the explanations are refined. She shouldn't even have looked at the first article.

With respect to Doremus Scudder's beautifully illustrated article in View Camera Magazine, referred to by Steve Simmons, as far as I am concerned, the more the merrier. I plan at a later date also to write such a practical guide, which may be of greater interest to someone like Joanna, but it certainly won't be the last word on the subject. Different people approach the use of movements in different ways, and no one approach works for everyone.

One problem with such treatments, though, is that almost everyone has one or more misconceptions about movements and their effects, and I don't exclude myself from that characterization. I've had serious misunderstandings, which, in some cases, took me years to resolve. Doremus's error, which he has readily admitted, is his description of the the depth of field region on page 28. This differs from that given by Merklinger and summarized in my second article. One of the advantages of a rigorous analysis is that the mathematics usually---unfortunately not always---leads you to the truth, whatever your preconceptions. So having done the analysis, I am in a much better position to distinguish fact from misconception.

Such analysis may also lead you to insights, which might otherwise have escaped your notice. For example, It may be well know to others, but I've never seen an exposition of exactly how the depth of field wedge, in the tilted case, unfolds itself on the ground glass, and I didn't think of looking at it until recently. It turns out that for each distance from the lens, there is a `window' on the ground glass of what it in focus at that distance, and its height stays more or less constant as the window moves across the frame from background to foreground. The height of the window is proportional to the f-number. It turned out that knowing this gave me an insight about how to extend what I can see on the ground glass as I stop down to what I can't see, because the image is too dim, as I stop down further. That can be valuable as a check on the method I use to pick the proper aperture to get the necessary DOF. It might also be helpful to people who prefer to do as much visually as possible, using calculations or tables only when necessary.

Finally, let me emphasize a couple of points which perhaps I didn't stress strongly enough about the two articles.

The first article would only be fully understandable by a trained mathematician or someone with equivalent background. Other people shouldn't even look at it.

The second article is primarily concerned with a technical point that most people aren't even aware of, but which has been a point of confusion since Wheeler first raised it. I wanted to explain, without a lot of equations, just what the situation was. I've been thinking about this for years, but only recently did I realize it could be attacked successfully using techniques from projective geometry. I believe I now have completely solved the technical problem. To understand what is involved there, equations entirely aside, you should have a firm PICTURE in your mind about how the the circle of confusion is formed and why it affects calculations of depth of field. Without that, it would be hopeless even to see why there is a problem to be concerned about. There are some people out there who do understand circles of confusion very well, understand the point raised by Wheeler, who would be able to follow the second article. Those people are the intended audience for the second article, but anyone who is willing to put in the work and who is interested enough may gain some enlightenment from it. Also, important to me, such people may be able to help me improve the exposition, if they are so inclined. But, of course, advice such as, "this is a worthless piece of junk" is not very helpful.

Let me make one other plea. Often these forums go off on some interesting tangent, and that becomes the main focus of the thread. This happens to me quite often, so I find it hard to get any useful feedback about something I say or ask about. I hope that won't happen in this thread.

[BrianShaw]

Thanks, Leonard. Complex math (complex in my mind, not yours) tends to make me hyperventilate. I'm hyperventilating right now. I've skimmed the articles and will read when I have more time. But a question about "hinge line". Is that line a theoretical, or does it have anything to do with the len/film board hinges physically being on the rail, rather than on the middle of the standard as on my Cambo.

[Leonard Evens]

Thanks, Leonard. Complex math (complex in my mind, not yours) tends to make me hyperventilate. I'm hyperventilating right now. I've skimmed the articles and will read when I have more time. But a question about "hinge line". Is that line a theoretical, or does it have anything to do with the len/film board hinges physically being on the rail, rather than on the middle of the standard as on my Cambo.

Let me say that even for a mathematician like myself, with years of experience teaching multidimensional calculus, the visualization required to understand view camera geometry is mind stretching. At times I've made physical aids, but they are difficult to make and hard to interpret. I've also benefited by using the program Maple, which draws three D diagrams and allows you to rotate them to view from different points of view. But even with all that, it is not easy.

The hinge line is not a part of your camera. It has nothing to do with the mechanical attachments of the standards to the rail. I don't think of it as being `theoretical' because I feel I can see where it is. Visualize where you expect the exact subject plane to pass near your camera. For example, often that plane might be the ground in front of you. Next, visualize the front standard, in its original untilted vertical position extended outward, mainly downward. That is what I call the reference plane. Those two planes intersect in the hinge line. It doesn't have an actual material existence, in the sense you could hang something on it, but most physicists would consider it as having a `physical' existence. I think most people who have throughly absorbed Merklinger's tutorials can sort of `see' it sitting there below the lens. I know I can, but not from any special ability I have.

The hinge line has the same kind of physical existence as the Scheimpflug line, which is where the lens plane and the image plane intersect. The difference is that if you focus by moving the rear standard, the hinge line stays fixed, but the Scheimplfug line moves with the standard. The basic problem about thinking about movements is that as one thing changes, everything else ha a tendency also to change, so keeping track of just what is where, and what the optical effects of it all might be, is very difficult. So anything that stays fixed is a great help. As you focus by moving the rear standard, the exact subject plane rotates about the hinge line. As you move the standard closer to the lens, it rotates downward, and as you move the standard away from the lens, it moves upward. Also, the DOF wedge is constrained between upper and lower plane which meet at the hinge line, and define, roughly speaking, the limits of what is in focus on either side of the exact subject plane. And, as you focus by moving the rear standard, that whole wedge rotates about the hinge line.

Although no higher mathematics is involved in what I described above, there is no getting around the fact that it is involved. In fact, I have to do pretty much what anyone else would do in trying to visualize it; my advanced mathematical knowledge doesn't help much. The only edge I might have over you is that I've spent years thinking about three dimensional geometry. If you want to understand what is going on, you do have to work at it. Eventually it should become clear, and when you do understand the geometry, it will help you understand how to use movements.

I think the single most important thing that many people don't know is that the tilt angle is determined just by the focal length and the distance to the hinge line. The subject plane is more or less fixed by the nature of the scene, and that determines the position of the hinge line, so, for fixed focal length determines the tilt angle. That means you should first fix the tilt angle on the baiss of where you think the subject plane goes and not fiddle with it much afterwards. Sometimes, you may want to make small adjustments, but not major changes.

People often tell you to ignore all that and just pay attention to what is on the ground glass. To me, that is like telling someone to fly an airplane entirely by what is on a view screen without having any understanding of the three dimensioal space occupied by the airplane. It can be done, but it is not the easy and most intuitive way to proceed. Every one of us is capable of some amount of three D visualization. Our ancestors couldn't have survived without it. Unfortunately, conditions of modern life don't help one refine that understanding. But I firmly believe view camera photographers should work at mastering the 3 dimensional aspects of the subject if they want to be able to understand what they are doing. Otherside, you end up just repeating what seemed to work before.

By the way, the main purpose of the second article is to elaborate on the 'roughly speaking' statement above.