[ATM] what causes coma?

[omegatroid at hotmail.com (Mutalib Abdallah)]

Where is the best focus when you have coma?  Are off-axis stars focused best 
on the same flat focal plane as on-axis stars, or is a curved focal plane 
required?   Perhaps some (but not all)of the coma could be conquered with a 
curved focal plane.

Also, I am still wondering what off axis coma looks like in a star test when 
you replace your eyepiece with a knife edge in a film can.


>From: "Good, Donald" <dgood@aha.org>
>To: 'Mark Holm' <mdholm@telerama.com>, ATM Mailing List <atm@atmlist.net>
>Subject: RE: [ATM] what causes coma?
>Date: Tue, 10 Feb 2004 11:30:34 -0600
>
>Eureka, I've got it.  After studying the article About Coma at:
>http://www.opticalmechanics.com/about_coma.htm
>I suddenly realize what coma is!!
>
>Mark, you are right, what I described previously was not coma, although I 
>am
>not sure that it is exactly  curvature of field.  Maybe it was a mix of
>curvature, coma, and caustic.  A definite error was the  implication that
>the "focus someplace else" was a focus to a point.  But lets let that go 
>and
>start over.
>
>In About Coma, James Mulherin describes several relationships of coma
>prominence to the angular distance from  the center of the field of view
>(FOV), to the F number of the mirror, and to other parameters.  And I
>believe  that, while he refers to parabolic and Newtonian and in one case,
>to "all telescopes of a given focal ratio",  he is actually referring to 
>the
>classical (parabolic) Newtonian in all cases.  As to Mark's question about
>coma in a spherical mirror, I will answer Yes, because I am going to relate
>coma directly to spherical  aberration.  I am also going to describe (I
>hope, in a simple, qualitative way - no math) the shape of coma  and the
>peculiar double ring in Figure 2.  In this explanation, the airy disk and
>diffraction effects will be  ignored.  Here goes.
>
>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.
>
>Now lets tilt the column of light (still parallel rays) a little over the
>spherical mirror, representing a  far point object near the edge of FOV.  
>We
>can easily make the tilt small enough that there is still a point  on the
>mirror away from the mirror center that is perpendicular to the axis of the
>light column although not  on that axis.  In other words, there is a
>parallel ray somewhere in the light column that strikes the mirror
>perpendicularly.  What is the effect of points E, B, and C along this new
>ray?  NO DIFFERENCE!!  Due to the  symmetry of a sphere, any ray
>perpendicular to the surface is equivalent.  The spherical aberration is
>exactly  the same.
>
>HERE IT IS!!
>Now lets change the mirror surface under the tilted light column very
>slightly, from a sphere to a parabola  along the original axis of the
>mirror.  What happens to these circles from the various cones centered on
>that  perpendicular (off-center) ray?  They are displaced perpendicular to
>that ray slightly, forming a series of  off-center circles (almost circles,
>there is a little flattening) that you see in the spot diagrams.  Oddly
>enough, both the inside focus and outside focus circles are displaced in 
>the
>same direction in proportion to their sizes, giving the teardrop shaped 
>spot
>diagram.  The small end of the teardrop represents the point focus of the
>"B" cone.  At best focus, the "E" cone and the "C" cone are represented by
>the large end of the teardrop, being nearly the same size and nearly
>concentric.  As the focus is change, one will get bigger and the other will
>get smaller.  So coma is the slight distortion of spherical aberration due
>to a parabaloid mirror instead of a spherical one.
>
>At least that is how I see it.  It seems so simple that I feel it must be
>the truth.
>Don Good
>
>
>
>
>-----Original Message-----
>From: Mark Holm [mailto:mdholm@telerama.com]
>Sent: Monday, February 09, 2004 8:56 PM
>To: ATM Mailing List
>Subject: RE: [ATM] what causes coma?
>
>
>I think Donald Good's explanation is really a description of field
>curvature, an abberation also present in many reflecting telescope
>designs.  With field curvature, if you could warp your detector to fit
>the curvature (possible with photographic film and plates if the
>curvature isn't too strong), the abberation would vanish.  With coma,
>the abberation would still be there, even with field curvature
>corrected, no?  Schmidt cameras have no coma, and, I think, no
>astigmatism, and most or all of the spherical abberation canceled by the
>corrector plate, but, at least in the "pure" design, there is major
>field curvature.
>
>The explanation at the OMI web site is probably technically correct, but
>I find it somewhat incomplete because, the way it describes coma makes
>it seem that coma could arise from a parabolic or spherical mirror.  I
>think spheres are coma free (if I am remembering what I have read
>correctly) but of course spheres have lots of spherical abberation.
>
>Maybe I am just not understanding what has been written.  Anybody else
>want to try an explanation that doesn't involve too much math?
>
>Mark Holm
>mdholm@telerama.com
>
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