Leonard Evens

8-Jun-2006, 09:09

Warning. This is highly technical, and it won't be of any practical interest, except possibly for people doing tilts with lenses of highly asymetric design, such as telephoto lenses.

If you fix the tilt angle, then it is known that, as you focus, the plane of exact focus rotates about a line, called the hinge line. The hinge line is also where the planes bounding the DOF region meet. If the back is vertical, the hinge line is located a certain distance, determined by the focal length and tilt angle, below the lens. Every analysis of this that I've seen, including my own, treats the lens as a point. The one exception is a diagram in Scheimpflug's original patent, as shown by Merklinger, which seems to suggest that the hinge line is in a plane through the tilt axis---see below---and parallel to the film plane. My intuition suggests that this should be right, at least if the pupil magnification is close to 1. (Otherwise, for DOF calculation, one would presumbly have to tilt about a line through the entrance pupil and use the plane, parallel to the film plane, containing the entrance pupil, but that is just a guess.)

A related question is where the tilt axis should be. Merklinger's discussion seems to suggest it should be the front nodal point, and my guess is that is right. But Merklinger's further comments suggest that one might use some other axis, even one in the film plane, and that would change the location of the hinge line.

My problem is that I've just read what Sidney F. Ray has to say about the matter briefly in Applied Photographic Optics, 3rd ed. In the text, he suggests that one use the rear nodal point to tilt about, and in a diagram, he shows the wedge shaped DOF region as being centered on a line in the film plane. I am pretty sure his diagram is wrong, unless one tilts about an axis in the film plane, since it conflicts with what Wheeler, Merklinger, and everyone else I know has looked at it, including myself, thinks. But I've been wrong before.

Any ideas? If someone has already done the analysis, I would like to know before I try to plunge in.

P.S. Just reading through various section of Ray, I've already found two other errors in formulas, which look almost like typos. This would not be unusual in a book of such scope, and I suspect there are a lot more. (The copy editor who did my mathematics book told me people still find errors in recent editions of Dickens novels.) I've written to the publisher to see if there is a list of errata, but if anyone already has one, please let me know.

If you fix the tilt angle, then it is known that, as you focus, the plane of exact focus rotates about a line, called the hinge line. The hinge line is also where the planes bounding the DOF region meet. If the back is vertical, the hinge line is located a certain distance, determined by the focal length and tilt angle, below the lens. Every analysis of this that I've seen, including my own, treats the lens as a point. The one exception is a diagram in Scheimpflug's original patent, as shown by Merklinger, which seems to suggest that the hinge line is in a plane through the tilt axis---see below---and parallel to the film plane. My intuition suggests that this should be right, at least if the pupil magnification is close to 1. (Otherwise, for DOF calculation, one would presumbly have to tilt about a line through the entrance pupil and use the plane, parallel to the film plane, containing the entrance pupil, but that is just a guess.)

A related question is where the tilt axis should be. Merklinger's discussion seems to suggest it should be the front nodal point, and my guess is that is right. But Merklinger's further comments suggest that one might use some other axis, even one in the film plane, and that would change the location of the hinge line.

My problem is that I've just read what Sidney F. Ray has to say about the matter briefly in Applied Photographic Optics, 3rd ed. In the text, he suggests that one use the rear nodal point to tilt about, and in a diagram, he shows the wedge shaped DOF region as being centered on a line in the film plane. I am pretty sure his diagram is wrong, unless one tilts about an axis in the film plane, since it conflicts with what Wheeler, Merklinger, and everyone else I know has looked at it, including myself, thinks. But I've been wrong before.

Any ideas? If someone has already done the analysis, I would like to know before I try to plunge in.

P.S. Just reading through various section of Ray, I've already found two other errors in formulas, which look almost like typos. This would not be unusual in a book of such scope, and I suspect there are a lot more. (The copy editor who did my mathematics book told me people still find errors in recent editions of Dickens novels.) I've written to the publisher to see if there is a list of errata, but if anyone already has one, please let me know.