Explaining Yaw free, distortionless & Yaw free/distortionless operation of a camera..

[Theodoros]

Most people think that yaw free operation of a camera is unimportant... They think that if you manage to work around things and have planes focused well enough it's the same...

Others think that if Scheimpflug's law is satisfied, (three planes crossing a line or near that) the operation is distortionless too...

The truth is different... Scheimpflug's law does state that three planes (the image area's plane, the subject's plane and the lens plane) should cross in a line... but it also assumes (which is never stated) that the projection radius of the cone projected in the image area should remain constant as it was if the subject was focused without any movements applied and thus, only a part of it in focus...

In other words it means that your camera is both yaw free and distortionless only if you can focus it without movements, then apply the movements you want (shifts & up downs included) and never have to refocus it... Otherwise (if you have to refocus it) there will be distortions (on all directions) involved in the image captured...

The more the focus will need corrections, the more the (distortion) error... The closer the subject's plane, the more evident the (distortion) error...

https://en.wikipedia.org/wiki/Scheimpflug_principle

[Nodda Duma]

Yes - I think - but there's a simpler way to think of it.

Distortion stems from the lens and is in part a function of field angle -- or at the image surface, the distance from the optical axis. Distortion can be thought of as a change in magnification vs. field angle -- because that's exactly what it is. The other aspect of a lens-based imaging system that affects magnification is lens-to-image plane distance and corresponding lens-to-object plane distance.

Introduce tilts in the lens or back and two things happen: 1) You've tilted the optical axis away from the mechanical center of the camera, shifting farther up the field-dependent distortion (field-dependent magnification) curve. 2) You've also introduced a linear magnification change due to the varying lens-to-image plane distances. Image plane, of course, is shorthand for plane of best focus, which is perpendicular to the optical axis.

The distortion/varying magnification has thus correspondingly increased and become asymmetrical.

[Doremus Scudder]

Yaw-free just keeps you from having to reposition the camera after making a swing when the camera has already had tilts applied. Sure, it takes an iteration or two, but it's pretty easy-peasy...

As for "distortion": We're dealing with a conical projection here. Any projection introduces some distortion; a lens introduces distortion at the edge compared to the center of the image. This is most evident with short focal-length lenses (oval rendering of round objects at the edges), but it's always there; it's a property of the conical projection. And, just like mapmakers, with their many projections (Mercator, cylindrical, Eckert, Mollweide, etc.), some distortion is always present in a projection.

The only important issue for us LF photographers is how we wish to render the subject on the film, which boils down to which conic section we choose for the film plane. The one and only thing that determines this is the position of the camera back in relation to lens plane. However, how planes are projected on the film is determined by the back position relative to the subject plane. This latter and choosing the plane of sharp focus are really the driving concerns that determine camera movements.

In other words, "distortionless" here is pretty meaningless, since there is always some. Which is the distorted image: one with converging verticals taken with no movements and the camera pointing upward at the top of a building or the one with parallel verticals taken after front rise has been applied? Most would say the former, but in reality, as long as the lens plane and the film plane are parallel, the projection is the same and there is no "distortion" in either by your definition. The image circle is still a circle and the radius is the same for both.

However, any time the lens plane and the film plane are not parallel, the projection at the film plane becomes a elliptical conic section, instead of a circle, with many different radii. Nevertheless, swings and tilts allows us to focus on other planes than the one parallel to the film plane. Any time you tilt to get the foreground sharp or swing to bring the plane of focus closer to one side or the other you are "distorting" the image by your radius-based definition. But, if we purposely alter the projection from circular to elliptical to get the image closer to our perception of reality, or to emphasize a particular plane of focus, or even to render objects larger at one place in the image than they would be with a "zero-position" shot, is that really "distortion," or are we simply choosing to use a different projection? I think its just the latter. The beauty of a view camera is that the photographer decides how the projection should be.

And, yaw-free really has nothing to do with which conic section the film plane ends up in. It's simply the relationship of the lens plane position to that of the film plane.

Doremus

[Nodda Duma]

Doremus - I think distortion in your example of non-parallel lens and film is really a magnification change across the image.

Distortion isn't a conical projection effect. It's a real aberration - a change in magnification vs field angle and is entirely a function of the lens design itself. Symmetrical lenses - amongst other designs - have zero distortion. Pinholes are free of distortion.

If distortion were a conical projection effect and couldn't be eliminated, then astrometry would not be possible.

We're all probably in agreement about the same effects, it's just a difference in semantics.

[Theodoros]

Hi Doremus... Nodda has it right I'm affraid... If you intercept a sphere at the same radius but with the center of it decentered to another point, the result plane (after intersecting the same sphere) will be an "egg" shape one instead of a circle, for a circle to exist (EDIT: ...in the projection cone...), there is no other way but to have an interception on the same axis being perpedicular to the base of the image cone (which then requires of the axis to pass through the center of the sphere)... Note that the center of the sphere projected towards the image area, is always the entrance pupil of the lens...

[Tin Can]

Too bad you guys don't use drawings.

Your words obfuscate.

I wonder about visualization on a photographic site.

Often.

[Theodoros]

The wikipedia link I used in the OP has all the drawings you need Randy... Only parameter that has to be considered is that they still ignore the change of the focusing plane's position (although they show it in blue) and thus the distortion that will be induced on the image area's plane (after a cone has been projected on it from a wrong position) - which is easy to visualize yourself (Imagine a sphere being sectioned from a center being a random point off center...) ...it is an "egg-shape" the "cut", ...isn't it?

[Pere Casals]

"Austrian army Captain Theodor Scheimpflug, who used it in devising a systematic method and apparatus for correcting perspective distortion in aerial photographs"

So... suprisingly Captain Theodor invented it to un-distort things.

As the LF learner that I am, I viewed a lot of times this image:

https://es.pinterest.com/pin/150448443772966725/

I was thinking that Tilt and Swing were ajusted to compensate vertical vs horizontal stretch, now I think that there is diagonal stretch, as image circle will be also an ellipse, but with a diagonal major axis...

Is it like this?


Anyway I guess that any distortion can be compensated with the enlarger by Tilt-Swing the projection lens, or the paper. Also it can be done with the scanned image, with PS. Does not?

[Theodoros]

"Austrian army Captain Theodor Scheimpflug, who used it in devising a systematic method and apparatus for correcting perspective distortion in aerial photographs"

So... suprisingly Captain Theodor invented it to un-distort things.

As the LF learner that I am, I viewed a lot of times this image:

https://es.pinterest.com/pin/150448443772966725/

I was thinking that Tilt and Swing were ajusted to compensate vertical vs horizontal stretch, now I think that there is diagonal stretch, as image circle will be also an ellipse, but with a diagonal major axis...

Is it like this?

Exactly... The theory only includes tilt and swing movements... it doesn't "compensate" for shifts or up-down movements or "parallel planes" as makers do... According to Scheimpflug's law, yaw free includes distortionless operation (other than using movement to have a third plane all in focus).... In other words the law doesn't allow for changing the focus point and thus induce distortions... It assumes that focusing stays constant (and thus operation is distortionless)!

Anyway I guess that any distortion can be compensated with the enlarger by Tilt-Swing the projection lens, or the paper. Also it can be done with the scanned image, with PS. Does not?

[/QUOTE]

No way! Distortions induced in an image captured as stereo (three axis perpendicular to each other), there is no way that can be corrected on a (two axis) plane...

[Nodda Duma]

Too bad you guys don't use drawings.

Your words obfuscate.

I wonder about visualization on a photographic site.

Often.

We're not crowded around a white board, and words have been used for centuries to relay technical information. The mind's eye is a wonderful illustrator in and of itself.