New AOS Zernike references¶
The AOS operates using the following steps:
- Find donuts
- Fit donuts to a Zernike pupil decomposition
- Compare the measured Astigmatism and Coma Zernike coefficients against reference values, according to the following expression:
a_i(Measured)[x,y] = a_i(Reference)[x,y] + Delta_i + ThetaX_i * y + ThetaY_i * x
where i is the Zernike index (5,6 Astigmatism and 7,8 Coma) and x,y are Focal Plane coordinates
- Transform from the Delta_i and ThetaX,Y_i to Hexapod decenter & tip/tilt
Thus, you can see that the reference serves as the AOS set-point, ie. the hexapod is adjust until the Zernike terms of
the wavefront match the reference.
Current AOS Zernike reference meshes¶
The current AOS reference meshes were built from a single image, exposure number 159627, taken on Dec 8, 2012 which had reasonably good IQ, and had rather high donut density. At the time I checked that the Zernike values in the Focus&Alignment CCDs from this image were close to the Zernike values found in the Science CCDs (and those were from exposure number 134239, out of focus by +1500microns, taken September 15th, close to Zenith and with the hexapod alignment settings Steve Kent found at first light)
What I discovered some time later is that the Zernike set-points are not quite set optimally given this procedure. However, the distance from what I think is optimal is not all that large in wavefront terms - only about 0.2-0.3 waves. But I do think that this is large enough that it is worth improving.
New AOS Zernike reference meshes¶
To better optimize the wavefront I have adopted the following procedure:
- Build a high statistics Zernike reference for the Science CCDs from around 50 images taken at 1.5mm out-of-focus on November 20, 2012
- Adjust the Zernike values for Astigmatism and Coma so that the average across the focal plane is zero and for Astigmatism also adjust the Zernike values so that the slope across the focal plane is zero. This adjustment corresponds to dialing in the ideal hexapod alignment (as well as the ideal primary mirror Astigmatism)
- Next, build a high statistics Zernike reference for the Focus&Alignment CCDs from 8 science images taken on September 5, 2013. I chose this date because these had very good donut statistics, taken when the AOS was running smoothly.
- Finally, I adjusted the Zernike values for the Focus&Alignment references such that there was good continuity from the edge of the Science CCDs across to the neighboring Focus&Alignment CCDs.
So, there are two important differences here. First, I adjusted the Zernike values in the Science CCDs to ideal values, and second, I adjusted the Zernike values in the FandA CCDs to match the Science CCD values.
The plots below show the Astigmatism (Z5,Z6) and Coma (Z7,Z8) for both Science and FandA chips after this procedure.
Effect of these new AOS Zernike reference meshes¶
Using these new references will produce an offset in the hexapod setting compared to the previous references of (Diff = Old-New, as corrections)
dx: 838 microns
dy: -1269 microns
these correspond to changes in the Coma of 0.22 for Z7 and 0.28 for Z8.
Improvement in IQ¶
I think there should be a modest but noticeable improvement in IQ with these new meshes. Using a result from Chris Davis we expect that the quadrature change in FWHM as a function of decenter can be expressed as:
Delta FWHM^2 = 0.035 * (dx/1000)^2
with FWHM in arcsec and dx in microns.
So if we are 800 and 1200 microns from optimal, we expect a change in FWHM^2 of 0.07. At the median IQ of 0.9" that
corresponds to an improvement to 0.86, and if we are at the very best IQ of 0.7" that implies an improvement to 0.65".