Re: ATM Immersion Null Test for Aspheres

[Anthony Stillman <atmer@flash.net>]

>> delta s = R * k^6 * e^2 / 16  = (y^6 * e^2 / 16 * R^6 * lambda) wavelengths
>>
>> where y = k*R

>This looks like one of the residual terms in the power
>series for 1-sqrt(1 - y^2), which is the formula for
>sagitta.

Richard,

You are of course correct.  This first order null simply forces the k^2
term to zero.  This is explained in the derivation which I omitted so that
no one would  be "bored".

What I didn't understand, and still don't is the re-equation that includes
lambda.  First, the units don't work out.  Second, substitution doesn't
give this.  I've checked subsequent journals and looked in AO's index but
there appear to be no errata for this letter.  Curiously, today I noticed
under references for a seemingly unrelated paper that the technique was
presented in S&T April 1964 p242.  My collection of S&Ts is a little spotty
from before the 70's, perhaps someone else on the list can check this out
and report back.

While trying to fall asleep last night, it dawned on me that a layered null
might work as well or better.  Possibly allowing for the nulling of higher
order terms.  That is, two or more media layered above one another above
the test surface.  The different media having differing indices.  Obviously
for liquids, specific gravity and compatibility would be a concern.  I'm
still working through this, but I thought I'de mention it in case others
have already thought it out.

Anthony