Round Robin Mirror Test Interferometery, High Resolution Robo, and Manual Foucault Comparison


  1. Introduction

The purpose of this report is to investigate:


To first question is the easiest to answer. I have the mirror surface profiles from both of my test system. If these two independent systems produce similar surface profiles I can assume they are accurate. It is even better if they also match a published profile for these mirrors. For mirror b all of that is true.


The second question is harder. The surface profiles can be computed from the published data. But we don’t have a known good profile. The plots of the data very more than I would like to see. I would like several independent measures of the profiles to agree within a tolerance. I could not find that kind of profile data except on mirror B. So my approach is to validate my test systems against mirror B. Once my systems is validated against B then maybe I can use it to generate the surface for mirror C.


It will compare analysis of Round Robin Mirrors done with high resolution Robotic Foucault, Interferometry, and Manual Foucault. The high resolution robotic Foucault was developed by me. The hardware was inspired by James Lerch’s robotic tester. The testing algorithm I derived from work done by Mike Peck at http://pw1.netcom.com/~mpeck1/astro/autof/autof.htm. I will not discuss the details of the algorithm here except to say that it uses as many zones as there are pixels across the mirror under test to get a large number of samples. I believe this generates an accurate surface profile better than the normal Foucault procedure because of the higher sample density. The interferometry uses a Bath style interferometer with analysis software that I derived and upgraded from FringeXP written by Dave Rowe.


My intent is to show that I have captured a true representation of the surface with my interferometer and high resolution robo so that my data can be used as a reference for the analysis of the Manual Foucault data


Those not interested in my validation can skip directly to the Foucault surface analysis graph at the end. To see how well the testers matched the surface.


  1. Robo to Interferometry Validation

Validation of high resolution robo Foucault was done by measuring 3 different mirrors and comparing the results with analysis done by 3 independent test systems and 2 testers. The resulting surface error profiles of each mirror were compared to the profile from High Res Robo data using Sixtests software by Jim Burrows. The analysis for mirror one was done by Steve Koehler comparing High Res Robo data to the symmetrical terms extracted from the test data taken by James Mulherin. See http://www.visi.com/~mkoehler/18-64/analysis.pdf for details. Figure 5. summarizes the results. The second comparison was done by me comparing high res robo data and the interferometery profile of mirror B taken by Roger Ceragioli at the University of Arizona http://alice.as.arizona.edu/~rogerc/Round%20Robin%20Interferometry.html. Figures 2, 3, and 4 below show the comparison.


A third comparison was done between my interferometer data and High Res Robo and will be shown in Figures 2 and 3 below.


  1. Interferometry

I will start by showing the surface as computed by my Bath interferometer. Figure 1. is the 2D contour plot from my interferometer of mirror B. It is the computed average from 29 interferograms. Three groups of about ten each taken with different tilts to help average sampling errors due to fringe orientation. Diameter 2 was horizontal for the measurments. As other testers found, I too found this mirror had very little astigmatism that rotated with the mirror. Most of it comes from test stand and my interferometer setup so the astigmatism terms are disabled in the analysis. Coma did rotate with the mirror but because that can be adjusted out with collimation those terms are also disabled.



Table 1. shows the statistics for the computed Zernike terms from the 29 interferograms. The Zernike terms are ordered according to Wyant at http://www.optics.arizona.edu/jcwyant/Zernikes/ZernikePolynomials.htm. Notice that the standard deviations for the terms is very small. I think that shows that I have taken enough data to be accurate.


Diameter 1 is rotated version of the above so I’m not going to present that data. The major features of this mirror are a high annular ring at about 75% radius and a small hill close into the center on the right side. We can see these features in the 3D plot and profiles shown next.




Figure 1. 2D contour map and zernike data for Mirror B with Diameter 2 horizontal computed by OG (FringeXP enhanced).

Figure 1a. 3D surface plot of mirror in Figure 1.

For the statisticians Table 1 lists the stats gathered for the Zernike terms.


Table 1. Complete list of Zernike values computed and their variation for 29 images.

Mean STD MIN MAX MODE

Piston -6.038 0.305 -7.400 1.380 -5.937

X Tilt -4.292 0.752 -8.768 0.903 -5.007

Y Tilt 4.039 0.543 0.158 7.366 0.559

Defocus -0.265 0.013 -0.412 -0.139 -0.215

X Astig 0.003 0.023 -0.276 0.275 -0.000

Y Astig 0.038 0.003 0.000 0.076 0.029

X Coma -0.097 0.006 -0.143 -0.010 -0.091

Y Coma 0.094 0.008 -0.025 0.173 0.052

Spherical -0.843 0.003 -0.883 -0.813 -0.833

X Trefoil 0.010 0.002 -0.028 0.032 0.002

Y Trefoil 0.023 0.006 -0.040 0.103 0.016

X 2nd Astig -0.029 0.003 -0.068 0.004 -0.032

Y 2nd Astig 0.001 0.002 -0.030 0.019 0.000

X 2nd Coma 0.029 0.002 0.011 0.052 0.023

Y 2nd Coma -0.026 0.003 -0.053 -0.002 -0.017

2nd Spherical -0.019 0.002 -0.038 0.013 -0.024

X Tetrafoil -0.010 0.003 -0.042 0.035 -0.012

Y Tetrafoil 0.005 0.002 -0.015 0.019 0.006

2nd X Trefoil -0.011 0.002 -0.030 0.006 -0.008

2nd Y Trefoil -0.008 0.002 -0.036 0.010 -0.013

3rd X Astig -0.002 0.002 -0.020 0.024 -0.008

3rd Y Astig 0.011 0.003 -0.019 0.039 0.029

3rd X Coma -0.001 0.002 -0.025 0.017 -0.004

3rd Y Coma -0.008 0.002 -0.025 0.016 -0.004

3rd Spherical 0.025 0.002 0.005 0.058 0.019

26 -0.003 0.002 -0.020 0.014 -0.011

27 0.004 0.002 -0.018 0.022 0.002

28 -0.006 0.002 -0.021 0.024 -0.009

29 0.009 0.002 -0.016 0.025 0.014

30 -0.008 0.002 -0.027 0.009 -0.005

31 0.000 0.002 -0.018 0.016 0.006

32 0.001 0.002 -0.025 0.033 -0.009

33 -0.002 0.002 -0.021 0.017 -0.002

34 0.028 0.002 0.005 0.054 0.018

35 -0.030 0.003 -0.064 -0.012 -0.032

36 0.072 0.002 0.049 0.101 0.075

37 -0.004 0.002 -0.023 0.024 -0.005

38 -0.004 0.003 -0.033 0.026 -0.010

5th Spherical -0.002 0.002 -0.018 0.020 0.001

6th Spherical 0.002 0.002 -0.024 0.019 0.002

7th Spherical -0.006 0.001 -0.020 0.013 -0.004

8th Spherical -0.010 0.001 -0.030 0.004 -0.013


  1. Interferometery and Robo profile comparison


Figure 2. below is a surface error plot for diameter 2 computed by my analysis software (OG). It shows both the interferometer profile (blue) and high resolution robotic Foucault in Black. Only the spherical terms are used from the interferometry data because that is about all the Foucault test sees.

Figure 2 Diameter 2 robo and interferometer wavefront error in waves



Figure 3 Averager profile by Roger Ceragioli

The profile that Roger Ceragioli computed is displayed in Figure 3. As you can see there is a close resemblance.

Figure 4 Diameter 1 interferogram and robo wavefront error in waves



Figure 4. is a comparison of Robo measured diameter 1 with the profile computed using the interferometery spherical Zernike terms.


Figure 5 Torus Mirror 18-64 interferometer and Robo profiles


Figure 5. Shows and excerpt from Steve Koehlers paper comparing my high res robo measurement of his mirror with interferometry done by James Mulherin.


I use Figures 2. through 5. as verification that the high resolution Foucault technique is measuring accurately as best as can be expected within Foucault limitations. Last I show the full mirror diameter 2 interferometery profile using all the Zernike Terms but Astig and Coma. You can see from this that the Black Foucault data is some sort of blend of the left and right profiles. It is not a straight average of the left and right halves. I have computed such and they do not fit exactly.

Figure 6 Diameter 2 Interferometer with all terms on and robo profile surface error in nanometers.


  1. Manual Foucault profile Comparison

The following data was derived from the Round Robin report published by Scott Rychnovsky. I used Frontsix to prepare the data for input into FigureXP. FigureXP was used because James Lerch modified it so that I could export the profiles into a spreadsheet to compare them. Figure 5. is the comparison for Mirror B diameter 1. The reference surface from high res robo is the thick blue line. The manual testers used a six zone mask that has a much lower resolution than robo so we would expect some divergence especially in the center and at the edge where they have no data. The best matches were by Michael Mills, Jim Haven, and Scott Rychnovsky. These people were also the best matches on Mirror C.


Figure 7 Round Robin Surface profiles compared to High Res Robo. Surface error in nanometers




Next Figure 8. is the comparison of Round Robin Mirror C Surface Profile. This mirror has about ¼ astigmatism that will not show up in the analysis. That has been demonstrated clearly in the round robin roport. The purpose here is compare the robo and the manual testers to one another.

Figure 8 Round Robin Mirror C Diameter 1Surface profiles. Error in nanometers