Re: [Leica] Re: Distortion

[dannyg1 <dannyg1@IDT.NET>]

Henning ,

As you know, the principal difference between a retrofocus and a symmet, is that the
symmet images at (or close to) its focal length and the retrofocus provides some room 
at the rear by placing a divergent group in front of a convergent one, effectively
shifting nodal planes back, behind the lens.

Considering that the angle of oblique projection controls the amount of wide angle
effect stretching and that the severity of this stretching is the principal image
'quality' that the viewer discerns/uses to separate a wide angle from longer focal
lengths; it follows that our perception of 'strong' perspective is heavily influenced by
any exaggeration of it.

It's also true that, when the focal plane plane is brought closer to the lens rear, the 
Angle of view/field angle or covering power (all the same guys) must be increased in 
order for the image to fully cover that plane. The image cone, projected by the
symmetrical lens will also become more angularly extreme.

It follows then, that the wide angle effect, dependant on the increased oblique
projection is also exaggerated. It follows again, that the human perception of the 
wide angle effect, whether physical or phsychological, is influenced by this 
exaggeration and this results in a heightened depth perception within that 
rendering (the best example being the identical stretching
effect in the marginal image of a wide field view lens, of otherwise normal focal
length).

Here's the description of "Marginal distortion" from a 1960 edition of the Focal
encyclopedia (under heading Perspective, pg. 821):

"A further cause of apparantly incorrect distortion in photographs arises because the
photographic recording surface is flat, whereas the retina of the eye is curved.
The perspective images of at the edge of a picture, particularly of a wide angle
photograph, are drawn out because the picture plane is flat and so becomes
increasingly oblique away from the center of the field. But the image projected on
the retina of the eye by objects in the field of vision falls on a spherical surface, with
all points the same distance from the eye, so that the perspective is no different at the
edges from what it is at the centre.
To a man standing in front of a row of identical posts stretching away to either side,
the apparant diameter of the posts gets gradually smaller as they get farther away.
But to a camera from the same position, the posts actually get wider and wider away
from the centre because each successive post records its image at a point further
from the lens and on an increasingly oblique surface. The result of this disparity
between the visual and the photographic perspective is that the eye rejects as false the
drawn out perspective of objects towards the edges of wide angle photographs. "

You've answered :

> With regard to perspective rendering, what matters is the angle of
> incidence on the lens, not the angle of the rays between the film and the
> lens. You can have whatever type of relay lenses you want behind the
> collector lenses, and as long as you wind up with no linear distortion, you
> won't change the perspective rendering. The lens - to - film angle does, as
> you mentioned, affect the eveness of illumination, with the result that
> retrofocus lenses don't suffer the full effect of the cos-fourth law. And,
> as you quite rightly pointed out, the viewing distance/image size
> relationship is critical if one wants to overcome perspective distortion
> effects.

Isn't the angle of incidence the trace of a ray from the surface of an object and, 
wouldn't it be imaged by the lens as a point to focused point, earth to film?

I'm particularly interested in this physical truth:

"The lens - to - film angle does, as you mentioned, affect the eveness of illumination,
with the result that retrofocus lenses don't suffer the full effect of the cos-fourth
law."

My understanding is that this lessened (retrofocus) falloff provides optical proof that 
the image is projected more directly and so, suffers less oblique projection distortion
effect.

(in regards to the Nikon OP fisheye)
> which produces images with _no_ falloff
> to the edges due to its orthographic projection formula. (Some of this
> stuff is on my web site).

A circular fisheye lacks light fall off by projecting light, subject to film, in an 
equidistant fashion, center and edge (I'll look at your site soon). It is my 
understanding that it does this by projecting to film with equivalent magnification. 
I could be wrong (and may well be considering that lensless/pinhole images aren't 
rendered like a fisheye) but do remember from my younger days, the problems 
cartographers have with translating a circular world (in perspective terms) to a flat 
surface.
I remember from those lectures that the translations were best done by gradually
varying the magnification of the continents, as the perspective receded away from 
the central viewpoint. 

In effect, the trick was to undo perspective to the same degree that it
occurred. I have always thought that this was how lenses worked, having higher
refractive power at the element periphery than the center and they look to me as
though they do work like this, even on paper/raytracings.

Regards,
Danny Gonzalez