Hi Mick,

I'm trying to follow along the numbers in these recent
posts. Couple random questions....

So you are doing interferometry at the radius of curvature,
which gives a large spherical error, and then manually
correcting or "nulling" out the spherical due to the
set up. OK, got it. What are the units on the
interferometry "Pri Spheric -0.625" in message #673?
Is it waves PTV, RMS, on the wavefront, on the surface, etc.?

I am always a little nervous when the corrections are
10 or 20 times bigger than the thing we are trying
to measure. But I guess there is no way around it.
Unless you can come up with a big flat mirror to test
against, or something like that.

If I just put a ruler on one of your sample igrams,
the error is about 2 fringes or 2 waves PTV on the
wavefront (at center of curvature). Does that sound
about right? Or is there a factor of two missing somewhere?

Back to Roddier. What camera / pixel scale / filter
did you use again? This is the 10 inch F/6 mirror?
What is the exact focal length?

- John B.


--- In roddier@yahoogroups.com, "m_hollimon" <mhholl@...> wrote:
>
> Dr. Biretta/Group -
>
> A careful further examination of the data in the comparison table of post #
673, plus some investigation into how the performance numbers are calculated by
the two applications, WinRoddier2.2 and OpenFringe, has produced some further
insights into the question of comparing results between the two.
>
> The reported Strehl ratios in the table are calculated from the value of the
normalized Zernike coefficient according to the algoritm:
>
> Strehl ratio = exp(-(2*pi*sigma)^2) Eq. 1
>
> where sigma is the rms value of the wavefront or surface error.
>
> If only the single value of primary spheric is considered, sigma, the rms
error, is numerically equal to the normalized coefficient value; for
WinRoddier2.2 this is:
>
> (Primary Spheric Zernike Coefficient)/(Reference Wavelength) Eq. 2
>
> this value is then used in Eq. 1 to obtain the reported Strehl ratio for
Primary Spheric alone.
>
> For WinRoddier2.2, the mathmatical methodology for obtaining the Primary
Spheric Zernike coefficient is not known.
>
> In the case of interferometry and OpenFringe, the rms value to be used to
calculate Strehl ratio must be obtained from the reported Zernike coefficient by
a consdierably more complex calculation.
>
> First a "software null correction" (necessary because a parabolic mirror is
being tested at its center of curvature, not is focal point) must be subtracted
from the listed Primary Spheric Zernike coefficient value:
>
> sc = Zernike value minus Null Correction Eq. 3
>
> Then this difference is squared and divided by a scaling factor used from
Zernike theory:
>
> S = sc^2/(Scale Factor) Eq. 4
>
> Next, the rms error sigma is calculated:
>
> Sigma = Sqrt(Sigma)* (wavelength of test laser)/(Reference wavelength) Eq.
5
>
> This final sigma value is then the one used in Eq. 1 to obtain the Strehl
ratio of Primary Spheric coefficient. In the case of the table in post # 673,
the rms value used to produce the Primary Spheric only Strehl ratio (0.983) is
0.021, not the 0.0396 value listed on the last line. Roddier and OpenFringe then
do in fact calculate quite different values of Strehl ratio, 0.934 versus 0.983
in this example.
>
> From the above it is readily apparent that the Strehl values from
interferometry are obtained using a number of factors from the interferometry
test (Null correction, laser wavelengths, etc.); further, the end results are
descriptors of a surface, not a wavefront. So direct and specific comparison of
Roddier and interferometric results may not be really meaningful, as the
underlying processing methods may be different. This then makes comparing the
two tests in a quantitative way rather difficult, particularly since
interferometry measures a mirror alone while Roddier measure a complete
telescope. As of now, it seems that comparisons need to be used mostly as sanity
checks, raising alerts if differences seem grossly out of proportion; comparing
numbers in the third decimal place may not mean much.
>
> There are probably many ways in which my interferometric measurement Strehl
ratios in the mid 0.90s (mirror) can evolve into Roddier measured results in the
low 0.80s (telescope).
>
> Mick Hollimon
> 11 June 09
> 8:53 PM PDT USA
>