[ATM] what causes coma?

[stuart452 at earthlink.net (Stuart Hutchins)]

Donald's explanation of spherical aberration is one of the best word
descriptions I've seen. But a spherical mirror where the aperture is at the
mirror shows coma as well as spherical aberration.

In the Schmidt camera, the aperture is located at the center of curvature of
the mirror, and it is smaller than the mirror.  So an off axis bundle of
rays is still centered on the center of curvature.  That is what defeats the
coma.  The corrector plate then corrects spherical aberration.

We really need to use diagrams to explain these things, because word
pictures are interpreted differently by different people, causing confusion.

Stuart


----- Original Message -----
From: "Good, Donald" <dgood@aha.org>
To: "'Mark Holm'" <mdholm@telerama.com>; "ATM Mailing List"
<atm@atmlist.net>
Sent: Tuesday, February 10, 2004 10:30 AM
Subject: RE: [ATM] what causes coma?


> Point 1 - A column of parallel incoming light, the diameter D of the
mirror
> and on axis with the mirror  (light from an infinitely far point source on
> axis) will focus to a point on the axis in a parabolic mirror.   This
> represents the object at the center of FOV.
>
> Point 2 - That same column of light in a spherical mirror will not focus
to
> a point, but to a range of points  along the axis at approximately one
half
> of the radius of curvature of the sphere.  This range of points is  the
> cause of spherical aberration.  Light reflected from the edge of the
mirror
> will focus closer to the  mirror than light reflected from the central
> region of the mirror.
>
> Lets look more closely at spherical aberration.  Light reflected from the
> edge zone forms a cone (shell, not  solid) of light that focuses at a
> distance E from the mirror on the axis.  Light reflected from the central
> zone forms another cone of light that focuses at a distance C from the
> mirror on the axis.  C is a little  greater than E.  The "best" focus is
> some point B on the axis between E and C which represents the focus of a
> cone from some intermediate radius of the mirror.  Lets put a small
circular
> piece of paper between E and C  perpendicular to the axis and on center,
> representing the focal plane.  Close to E, the "E" cone focuses to a
point,
> but the "C" cone has not reached focus and is cut off, forming a circle.
> The "B" cone also forms a  smaller concentric circle.  As the paper is
moved
> toward C, the "B" and "C" circles get smaller until at B,  the "B" cone
> reaches a point and then at C, the "C" cone reaches a point.  At the same
> time, the "E" cone starts to expand past its focus forming a circle of
> increasing diameter.  Between B and C, the "B" circle also starts to
expand,
> and beyond C all circles are expanding.  At B, we have a point focus of
the
> "B" cone, an expanding circle of the "E" cone and a shrinking circle of
the
> "C" cone.  Of course, all the other  intermediate cones are either
expanding
> in proportion between the edge zone and the "B" zone and shrinking in
> proportion between the "B" zone and the central zone.  This lack of common
> focus IS spherical aberration.