Perspective Myth and Maths

[Jack]

Sorry Tim,

What Sashin said -- it IS just like I wrote it. If you are seeing distortions with a front lens tilt, your tilt is NOT axial around the lens center, period. Don't fret though, not all lens flanges are perfectly centered and some camera designs don't center their tilt and swing axes very well, so some combinations simply don't work the way they should.

 

[dick]

Yes but you will also 'distort' even if they *are* axial with the lens center. Adding {rear} tilt means that one end of the sensor is further away from the lens..... than the other end of the sensor...

Hence if one side of the image is magnified more than the other, you have a distortion...

Tim

Tim: I would not describe it as distortion.

I think that, theoretically the orientation of the lens should only change the position of the plane of sharpest focus, and magnification depends on the ratios between distances from the (nodal point of the) lens to the subject image and the subject.

...so it is the distance from the lens that counts, not the distance to the lens plane.

If you have a row of identical poles at an angle to the sensor plane, the image of the far pole would be smaller (perspective). You can correct (eliminate) the perspective by using rear swing, or making the back parallel to the line of poles. This is "correction" or "projection" rather than "distortion".

The lens is "just" a device to allow us to use wider apertures, so, until you come to worry about DOF and POSF, you can think of the lens as a pin hole... but the position of the theoretical pin hole is determined by focus.

If you have a mathematical bent, you can spend a week reading Merklinger's "Focusing the View Camera" and using the formulae to calculate anything you want to. I think all the formulae are also in Wikipedia.