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Re: [ATM] Is this Sphere good enough?

Don Ray wrote:

>I ran FIGURE using a 5 zone mask with a Sphere as the
reference with the following results:
P-V Error - 1/2.75
Strehl Ratio - 0.825
Surface RMS Error - 19.3
against a Parabola I get the following:
PV Error 1/1.25
Strehl Ratio 0.054
Surface RMS 63.5

I thought that concept of the Strehl (ratio) is clear to me.
Reading Don's post and some answers I realized That I am wrong.

While I thought that Strehl of the aberrated mirror is defined as
the ratio of the peak intensity in the image of the infinite far point source
of the aberrated mirror to the
MAXIMUM possible peak intensity in the image of the same source
as produced by the mirror of the same diameter and the same (?)  paraxial radius
of curvature
(which is -1 conic or ideal paraboloid).

>From Don's example and subsequent replies to his post I found that
aberrated mirror is not necessarily compared to ideal paraboloid  but
to any imaginable ideal conical (or even nonconical) surface mirror.

Consequence is that for each aberrated mirror there are as many Strehls
as there are reference surfaces chosen.

James Burrows in the "ATM Mathematics" cites: The Strehl ratio is
 "the ratio of the light intensity at the peak of the diffraction pattern of an
aberrated image
 to that at the peak of an aberration free image".

In this definition neither the reference surface diameter, ROC or conic constant
are mentioned.

I am puzzled how can sphere be reference surface because even if ideal
there is spherical aberration and image is therefore not aberration free
as requested in definition.

Further reading of the ATM Math  reveals that Strehl is defined ( at least
approximately)
in terms of the wavefront RMS deviation from the best fit PARABOLA.

Does that means that calculating wavefront RMS deviation from the best fit
sphere or
any other curve gives valid Strehl providing the nature of the referenced
surface is mentioned.

I thought that best fit paraboloid is implicitly understood when mentioning
Strehl.
But in that case even my assumption that reference paraboloid has equal diameter
and
paraxial  ROC as a aberrated mirror is also wrong because best fit paraboloid
has different ROC
from the aberrated mirror.

And finally what was meant by "aberration free" mirror in the Strehl definition.

I must be on terribly wrong tracks. Any help will be greatly appreciated.

Vladimir.





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