Abstract

An interferometric fringe scanner was used for the Technology Mirror Assembly (TMA) x-ray telescope, built by Perkin-Elmer as a technology demonstration for the Advanced X-Ray Astrophysics Facility (AXAF). We discuss advanced data processing features, implemented during a follow-on project to improve the mirror’s midfrequency errors still further. Data processing techniques include interleaving of multiple scans, and optimal smoothing and interpolation of the interleaved data onto a uniform grid. We discuss the underlying mathematics behind the processes, the motivation in terms of recovering the highest possible spatial frequencies from the data, and some sample results.

© 1988 Optical Society of America

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References

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  1. A. Slomba, L. Montagnino, “Subaperture Testing for Mid-Frequency Figure Control on Large Aspheric Mirrors,” Proc. Soc. Photo-Opt. Instrum. Eng. 429, 114 (1983).
  2. A. Slomba, R. Babish, P. Glenn, “Mirror Surface Metrology and Polishing for AXAF TMA,” Proc. Soc. Photo-Opt. Instrum. Eng. 597, 40 (1985).
  3. P. Glenn, A. Slomba, “Derivation of Requirements for Surface Quality and Metrology Instrumentation for AXAF TMA,” Proc. Soc. Photo-Opt. Instrum. Eng. 597, 55 (1985).
  4. A. Gelb, Ed., Applied Optimal Estimation (MIT Press, Cambridge, MA, 1974).

1985 (2)

A. Slomba, R. Babish, P. Glenn, “Mirror Surface Metrology and Polishing for AXAF TMA,” Proc. Soc. Photo-Opt. Instrum. Eng. 597, 40 (1985).

P. Glenn, A. Slomba, “Derivation of Requirements for Surface Quality and Metrology Instrumentation for AXAF TMA,” Proc. Soc. Photo-Opt. Instrum. Eng. 597, 55 (1985).

1983 (1)

A. Slomba, L. Montagnino, “Subaperture Testing for Mid-Frequency Figure Control on Large Aspheric Mirrors,” Proc. Soc. Photo-Opt. Instrum. Eng. 429, 114 (1983).

Babish, R.

A. Slomba, R. Babish, P. Glenn, “Mirror Surface Metrology and Polishing for AXAF TMA,” Proc. Soc. Photo-Opt. Instrum. Eng. 597, 40 (1985).

Glenn, P.

A. Slomba, R. Babish, P. Glenn, “Mirror Surface Metrology and Polishing for AXAF TMA,” Proc. Soc. Photo-Opt. Instrum. Eng. 597, 40 (1985).

P. Glenn, A. Slomba, “Derivation of Requirements for Surface Quality and Metrology Instrumentation for AXAF TMA,” Proc. Soc. Photo-Opt. Instrum. Eng. 597, 55 (1985).

Montagnino, L.

A. Slomba, L. Montagnino, “Subaperture Testing for Mid-Frequency Figure Control on Large Aspheric Mirrors,” Proc. Soc. Photo-Opt. Instrum. Eng. 429, 114 (1983).

Slomba, A.

A. Slomba, R. Babish, P. Glenn, “Mirror Surface Metrology and Polishing for AXAF TMA,” Proc. Soc. Photo-Opt. Instrum. Eng. 597, 40 (1985).

P. Glenn, A. Slomba, “Derivation of Requirements for Surface Quality and Metrology Instrumentation for AXAF TMA,” Proc. Soc. Photo-Opt. Instrum. Eng. 597, 55 (1985).

A. Slomba, L. Montagnino, “Subaperture Testing for Mid-Frequency Figure Control on Large Aspheric Mirrors,” Proc. Soc. Photo-Opt. Instrum. Eng. 429, 114 (1983).

Proc. Soc. Photo-Opt. Instrum. Eng. (3)

A. Slomba, L. Montagnino, “Subaperture Testing for Mid-Frequency Figure Control on Large Aspheric Mirrors,” Proc. Soc. Photo-Opt. Instrum. Eng. 429, 114 (1983).

A. Slomba, R. Babish, P. Glenn, “Mirror Surface Metrology and Polishing for AXAF TMA,” Proc. Soc. Photo-Opt. Instrum. Eng. 597, 40 (1985).

P. Glenn, A. Slomba, “Derivation of Requirements for Surface Quality and Metrology Instrumentation for AXAF TMA,” Proc. Soc. Photo-Opt. Instrum. Eng. 597, 55 (1985).

Other (1)

A. Gelb, Ed., Applied Optimal Estimation (MIT Press, Cambridge, MA, 1974).

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Figures (8)

Fig. 1
Fig. 1

Conceptual view of the TMA fringe scanner that measures axial mirror profiles.

Fig. 2
Fig. 2

Basic interpretation of fringe scanner data. Data points are equally spaced in the optical path difference (ODP) but are unequally spaced along the scan.

Fig. 3
Fig. 3

Intuitive approach to interleaving. Two hypothetical scans are shown, where the sampled points of one scan lie midway between the sampled points of the other. First the scans are shown interleaved using obviously incorrect relative piston and tilt. Then, the intuitively correct interleaving is shown.

Fig. 4
Fig. 4

Average surface profile using the previous linear interpolation method.

Fig. 5
Fig. 5

Average surface profile using the new Kalman filtering method.

Fig. 6
Fig. 6

Root mean square (rms) scan-to-scan variation using the previous linear interpolation method (average variation = 0.0034 μm).

Fig. 7
Fig. 7

Root mean square (rms) scan-to-scan variation using the new Kalman filtering method (average variation = 0.0011 μm).

Fig. 8
Fig. 8

Integrated power spectral density (PSD) function using first the previous linear interpolation method and then the new Kalman filtering method.

Equations (8)

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S = ( 1 2 ) n = 1 NSCN 1 m = ( n + 1 ) NSCN i , j = 1 NFRN × ( y n , i y m , j ) 2 W n , i ; m , j ,
W n , i ; m , j = corr ( x n , i x m , j ) ,
y n , i = y 0 n , i + A n + B n x n , i ,
S = ( 1 2 ) n , m , i , j [ ( y 0 n , i + A n + B n x n , i ) ( y 0 m , j + A m + B m x m , j ) ] 2 × corr ( x n , i x m , j ) .
d S / d A n = d S / d B n = 0 for all n > 1 .
y optimal = ( y 1 V 2 + y 2 V 1 ) / ( V 1 + V 2 ) ,
V optimal = 1 / ( 1 / V 1 + 1 / V 2 ) .
F ( f ) = f f max PSD ( f ) d f ,

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