From: "Richard F.L.R. Snashall" 
To: ATM List 
Reply-To: "Richard F.L.R. Snashall" 




Jim Burrows wrote:
>
> At 09:42 2003-06-02 +0100, Richard F.L.R. Snashall wrote:
>
>> Has anyone here considered the possibility of using something a stronger
>> than Strehl ratio?  I'm thinking about something like the expected
>> value of the error from the centroid, given intensity squared as the
>> weighting function; or something like that.
>
>
> The Strehl ratio is awfully hard to beat - it's got physics (wave
> optics), history (Lord Rayleigh on), and the academic optics community
> consensus behind it.  In fact, your "something" sounds like
an intuitive
> definition of the Strehl ratio .  I don't want to discourage the
> search, however - maybe an ATM can come up with something better.
> Single-number mirror evaluations are nice and crisp, but one might start
> with Suiter's preference, the EER, p. 197 (he decides to go
> single-number, too, EER(1)).
>

If EER stands for something like Encircled Energy Ratio, it sounds just
like what I was describing.  The definition that I was ruminating would be
the typical:

     Integ( i^2 * ( Y - Ybar ) . ( Y - Ybar ) ) / Integ( i^2 )

where Ybar (both Y and Ybar being vectors) is the vector centroid in the
focal plane/surface:

     Integ( i^2 * Y ) / Integ( i^2 )

and i^2 is the squared intensity, which would include diffractive effects. 
The i^2 stuff should act like weighting, and, I think, pretty much wash,
but may make a difference when you have to consider such things as
vignetting.

The ratio part would come from normalizing this to some standard, say:

        1.22 * D / lambda

or maybe the equivalent value computed for a "standard" aperture
and wavelength.

        Rick S.

>         -- Jim Burrows
>         -- mailto://burrjaw{at}earthlink.net
>         -- http://home.earthlink.net/~burrjaw
>         -- Seattle N47.4723 W122.3662 (WGS84)
>
>

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