T3D Re: telescope eyepiece distortion

[john bercovitz <bercov@xxxxxxxxxxx>]

I got off-list mail suggesting that camera and telescope images 
are the same and I shouldn't make a distinction.  That's correct.  
I was being sloppy and not saying precisely what I meant because 
precisely what I meant takes more words.

I'm better at examples than at explanations so I will offer some 
examples and then try to tack on food for thought.  I will make 
the examples free of math.

1) If you take a picture of a wall that has dots equally spaced on 
it in a square array of rows and columns, then when you view that 
photo from any distance you choose which is not the ortho 
distance, it is as if you were getting closer to or farther from 
the wall than the camera was.  In this special case, a long lens 
really does "bring you closer".  If you view the photo through a 
lens, you want the lens to be free of distortion because that 
rectilinear array still has to be rectilinear no matter what 
distance you view the photo from or you're not really changing 
your distance from the wall, but instead you are messing up the 
picture.

2) A box kite is a solid made up of 12 lines.  An unrendered 
rectangular parallelpiped if you will.  It comprises two squares 
joined by four longer lines where all of the lines in the solid 
are parallel or perpendicular.  Now let's take a picture of a box 
kite end on.  According to where we set the camera relative to the 
kite, the two squares of the kite will subtend different angles at 
the camera relative to each other.  If we get one kite-length away 
from one end of the kite, then one square will be about twice the 
size of the other square on the photo.  Now if we view the photo 
from any distance but the ortho distance, the squares will be the 
wrong size relative to each other and we have perspective 
distortion.  If we try to correct the wrong-distance view by 
putting distortion into a viewing lens, we will bow the sides of 
the squares and that's no good so we quit trying that.

3) We arrange dots in a regular pattern on the inner surface of a 
sphere and we place a camera at the center of the sphere and we 
take a picture.  On the flat film plane, dots near the edge of the 
photo are much farther apart than dots near the center of the 
picture (assuming the lens is fairly wide angle) but this does not 
matter because when we view the picture from the ortho seat, the 
dot spacings will subtend the same angles at the eye as they did 
at the camera and so all of these subtended angles will still be 
equal.  If we view from too far back, we will see the dots at the 
edge of the photo grow farther apart.  If we view from too close 
in, we will see the dots at the edge of the photo grow closer 
together.  When I say grow farther apart or closer together, I 
mean relative to the spacing of the dots in the middle of the 
photo.  If we want to view from closer than the ortho distance, 
then we need to use a viewing lens which pumps up the distance 
between dots near the edge of the photo.  This sort of lens is 
said to have positive or pincushion distortion.

John B


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