P3D Re: formats & focal lengths

["Dr. George A. Themelis" <DrT-3d@xxxxxxxxxxxxxxxxxxxxxxxxxxx>]

>Perspective is the relationship (location and size) of different
>subjects within a scene.  Perspective is only effected by the
>positioning of the taking lens with respect to the subjects in the
>scene.  The focal length of the taking lens does not effect
>perspective.

Thanks Brian Reynolds <reynolds@xxxxxxxxx> for a well written piece.
If this is the official definition of perspective then there is no
question that the focal length of the taking lens has nothing to do
with it.

There are still a few questions in my mind:  What does "wide angle 
perspective" mean?  Why are lenses separated in "wide angle" and 
"long" lenses if the focal length has nothing to do with perspective?
Why is a "normal" lens in a given format conventionally defined as 
having a focal length equal to the diagonal of the image?

That's where viewing conditions enter into the picture.

There is something called "correct viewing perspective".  This occurs 
when an image is viewed from a distance equal to the FL of the taking 
lens (time the magnification if the image is magnified in printing or 
projection).  If the image is viewed from distances significantly 
longer or shorter then this "correct" distance then a distortion 
occurs.  

Empirical observations confirm that an image of a certain size is 
viewed comfortably for a distance equal to the diagonal of that image.
If a picture is taken with a "normal" lens then chances are that it
will be viewed with the correct perspective.  If a picture is taken
with a "wide angle" lens then most probably it will be viewed from
much longer than the correct perspective, resulting in a "wide
angle" distortion where the space appears to be stretched in the z
direction.  The opposite happens if the picture is recorded with a
longer lens where space appears to be compressed when the picture is
viewed from a distance much shorter than the correct perspective.

Our main interest, stereo photography, offers a good tool to visualize
these deformations more intensely that 2D photography.  Hence the terms
"stretch" (for wide angle perspective) and "squash" (for long lens
perspective).  As we know, it is not the taking lens that creates 
these deformations but the mismatch of taking/viewing angles of view.
But because our viewers have fixed lenses and our stereo projections
a certain given setup, chances are that short or long lenses in our
cameras will create the corresponding perspective deformations.

I consulted Rudolf Kingslake's "Optics in Photography".  The first
chapter of the book is titled "Perspective".  Kingslake makes a
distinction between what he calls "True" and "Apparent" perspective.
"True" perspective is determined by the distance of the camera from
the scene and has nothing to do with the FL of the taking lens, just
as Brian defined it.  "Apparent" perspective has to do with the
viewing conditions.  Kingslake writes:

"There are two independent ways of varying the perspective in a
photograph: 1) By moving the camera lens relative to the object, 
2) by moving the eye relative to the finished print.  The first
movement controls the true perspective in the photograph, which is
fixed once the photograph is taken.  The second movement changes the
apparent perspective of the photograph and thus indirectly affects the
ultimate appearance of the scene.  For the perspective to be correct,
the photographic print must appear to the observer just as the 
original scene appeared to the photographer.  This will occur only if
the print is viewed from its correct center of perspective."

Finally, an off the record comment.  I think as a society we are
obsessed with wide angle images.  We have made the 35mm the standard
lens for 35mm film photography and we are screaming for more (field
of view).  We routinely view images from much further away than the
correct center of perspective (no one is sitting one diagonal away 
from the TV screen!)  We are so used to wide angle perspective that
we don't find gross perceptive deformations objectionable.  The worse
offenders are newspaper reporters.  I remember when my wife was in a
newspaper story about daycare centers.  The photographer used the
widest possible lens and came so close to the near object that the
lady and child in front were occupying half the picture with their
heads while my wife and daughter's heads were tiny-tiny in the back.
If you stick this picture in front of your nose, it might make sense
but at an arm's length distance, it is terrible!  Yet I am sure most
people find it cute.  But what gets me is this real deformation found
in some super wide angle lenses where people's heads close to the 
corners look eggshaped (with main axis towards the center) instead of 
round!  This looks really ugly and I feel sorry for the victims of
ultra wide photography!

George Themelis