Archived posting to the Leica Users Group, 1998/02/05

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Subject: Re: [Leica] Re: Distortion
From: "Henning J. Wulff" <>
Date: Thu, 5 Feb 1998 20:22:45 -0800

Danny (and anyone else who might still be listening),

>In the interest of gaining a better understanding of the complex issues we're
>discussing, I wish you wouldn't be brief. I have tried to explain my
>points in detail
>in the interest of both, teaching something and offering to learn.
>1) In an ideal (fully corrected) lens, used on flat film, perspective
>rendition is the same for all lenses, no matter the construction type and
>focal length. As the field of view increases, the corners of the image
>relate less and less to our usual visual interpretation, and we call that
>perspective distortion.
>I've been looking for a written proof of this for a very long time, but
>when Sidney
>Ray or Stroebel/Zakia write about perspective distortions, their examples
>are always
>entirely based on true wide angle and long focus designs; never retrofocus or
>telephoto versions.
>Information about the telephoto effect is very scarce and what is
>available is vague
>enough to teach little of its severity (or lack of severity). This
>retrofocus effect I'm
>arguing is something that I (and many others) have noticed in practice.
>I've tried to
>explain many reasons that it can (and to my mind, does) exist.
>I realise (now at least) that you strongly disagree, but isn't your
>assertion (of
>perspective rendition being equal per focal length, whether emulated or
>not) more a
>question of interpretation of the texts than it is of a steadfast optical

So, assiduously avoiding being brief, herewith the longer version:

Please believe me Danny when I say that this is not a matter of
interpretation of the texts. A lot has been written about this that is
vague, misleading and even downright untrue, by people who should know

Lenses redirect light, but they follow all the laws of geometry which are
most easily comprehensible when studying the imaging of a pinhole camera.
This, I'm sure you know, is the perfect imaging system if interference is
not allowed for, ie, the ray properties of light would dictate that it is a
perfect imaging system. The focal length is the distance the pinhole is
from the film plane (note that the term 'plane' is important), there is no
distortion, and, as can be readily seen, a 180 degree wide scene needs an
infinite film plane to record it. An infinitesimally small pinhole in an
infinitely thin membrane will provide a perfectly sharp, completely
aberration free image, with only light falloff to contend with (again,
discounting wave/particle theory).

Now introduce a lens. Let us say that this lens (which is necessary to get
us away from the wave/particle theory induced diffraction, and to also
incidentally allow us to shoot with film of less than infinite speed) has
some problems - a not unrealistic assumption :-). It has variable
magnification, ie, if shooting a line of buildings of the same height from
across the street, the buildings directly across are imaged at 10mm height,
and the ones further down either side, 45 degrees from the one directly
across, are imaged at 8mm, even though in real life they are the same
height (and would be rendered the same by a pinhole camera). This lens has
'barrel distortion', ie, if the base of the buildings goes through the
center of the image, the top of the buildings would be bowed so that the
straight line formed by the top of the buildings in real life would be
closer to the base line at the edges of the image than at the center.

People can only see a very narrow angle sharply at any one time, in
practice only a few degrees. 3 degrees to each side, everything is all
fuzzy already, but our 'peripheral vision', which accepts basic shapes,
colors, and especially movement, encompasses at times more than 180
degrees. Sharpness (or rather, acuity) falls off fairly gradually, so that
for areas equivalent to a 21mm lens on 35mm film, we perceive the geometry
well enough so that our brain can process the imperfect image from our eyes
and tell us what the geometry really is. (This is as far as I'm going with
the 'reality' of objects around us :-)). Extrapolation will tell you that
our processing of the 180 degree extent of our peripheral vision is
imperfect, as we do not see objects at infinity to the right and left of us
the same size as those across the street from us. To make up for our very
narrow cone of true visual acuity, we scan continually, looking directly at
a number of points; our brain then puts all the image inputs together to
form a sharp, geometrically correct perception of the world.

The Leica does not scan (we'll leave the Leicinas out of it).

Here you can start to see the problem humans have with perspective
distortion. The buildings mentioned that are 45 degrees off-axis are
substantially further away from us (and appear smaller when we, scanning,
look at them), yet we require in a 'distortion free' lens that they be
rendered the same height. You can realize that a lens which has barrel
distortion (a lessening of magnification the further items are off-axis)
will render objects smaller in the corners than a lens with no reduction in
magnification. We therefore perceive such a lens as having less
'perspective distortion' than a lens with no linear distortion.

A 'usual' lens for photographic work, at its best, images flat plane to
flat plane with no linear distortion. Fisheyes, for this purpose, are not
'usual', nor is any lens that introduces lots of distortion, or images from
or onto curved surfaces.

A retrofocus lens tries to do the same, while clearing the mirror in an
SLR, or imaging the scene onto a Polaroid back which is further back yet. A
telephoto lens also tries to do the same, while reducing the total length
of the assembly from that required by a standard long focus lens. The
geometric imperatives remain the same, and if linear distortion (change in
magnification) is kept to zero, the rendering of the image will be the same.

A retrofocus lens consists basically of two parts; a light collecting cell
or set of cells, and a relay lens that bundles the collected light so that
the angle of light from the rear of the lens is smaller than the angle of
the same ray incident on the lens, while keeping the geometry 'correct',
ie, no change in magnification. A telephoto lens does the opposite; it
spreads the light so that the exit angle from the lens is grater than the
incident angle. It has 'collector' cells and relay cells that spread the
light. A teleconverter is a relay lens that spread the light further. A 2x
converter approximately doubles the exit angle for the same incident ray as
the prime lens would by itself. A teleconverter will make any non-telephoto
long focus (or other 'standard') lens into a telephoto.

Retrofocus lenses produce design problems which lead to them having complex
distortion curves, ie, a whole lot of complex magnification changes across
the angle of view. These are best explored with poorly corrected (for
distortion) lenses from the sixties and seventies. A good example is the
18mm/4 Nikkor. When viewing through a low distortion viewfinder (there
aren't a lot around!) buildings can look strange. Over most of the field
there is strong barrel distortion (reduction in magnification), up to about
10mm from the center; then this reverses so that there is no distortion at
around 12 to 14mm from the center (magnification the same as at the
center), then beyond that 'pincushion' distortion (magnification greater
than at the center, parallel lines diverge) grows rapidly to the corners.
This lead to the appearance at the edges of 'moustache' shaped lines that
were straight in nature. The overall effect of this is that due to the
barrel distortion over most of the field (reduction in magnification),
retrofocus lenses do not tend to image off-axis objects as large as a
zero-distortion lens would, and this agrees better with our 'scanning'
method of seeing, so it appears that this lens has less perspective
distortion. In the furthest reaches of the corners, the perspective
distortion would, of course, be worse, but they make up only a small
fraction of the whole image area, and often do not contain full images of
objects. Partial objects, which in these corners would be imaged quite
large, are not as readily seen as distorted.

So that is why retrofocus lenses often appear to produce less perspective
distortion. If they had the same degree of (very low) linear distortion as
non-retrofocus lenses, their rendering would be the same.

BTW; telephotos basically have pincushion distortion (straight lines
diverge when off axis), and designers have to work their butts off to try
to correct for that, and the cos 4th law effects of telephoto lenses are
worse than regular long focus lenses, but because the angle of view and the
exit angle of the lens are both very small, this usually matters little.

I spent many years in physics at University, and finally I get to use some
of it! :-).

   *            Henning J. Wulff
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