To: atm{at}shore.net
From: MLThiebaux 
Reply-To: MLThiebaux 


Jeff, I appreciate your confirmation of the error analysis.  And it is
important to emphasize, as you did, that the first two effects depend on
the assumption of a spherical departure from flatness (i.e. a nonrandom,
smoothly convex or concave figure of revolution).

Martial Thiebaux
Rawdon hills, Nova Scotia


"Jeff Anderson-Lee"  wrote

>Of the three factors below, (1) and (2) assume that the P-V error is
>spherical as opposed to random.  If that is the case, then the analysis
>holds true.  If not, the only factor remaining is (3), and assuming
>rpv=random peak-valley error:
>
>    wave-front-error = 1.414*rpv
>
>So for the equation below to be the dominating factor, we must have:
>
>    rvp < .2025 * 1/2 * E,
>
>or approximately
>
>    rpv < E/10
>
>Jeff Anderson-Lee
>Sacramento, CA
>>
...
>>
>> There are 3 effects that reduce the error:
>>
>> 1. Only part of the diagonal is used in forming an on-axis star image.
>Let's call this area the "small" ellipse. ...
>> ...
>> 2. The slightly spherical diagonal should be compared to the nearest
>HYPERBOLOID, not to the perfect plane....
>> ...
>> 3. The optical path difference at 45 degrees incidence is sqrt(2) times
>the normal separation (not a factor of 2 as in normal incidence).
>>...
>> Combining the 3 effects, we find the wavefront error is
>>
>>        .2025 * 1/2 * 1.414 * E = .286 lambda,
>>
>> not great but it's just an example and the point should be clear.

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