Abstract

We have developed a math model relating the measured parameters of the Technology Mirror Assembly (TMA) to its final performance. This scalar scattering model is valid for large and small amplitude features. It allows the user to specify power spectral densities and/or autocovariance functions within any spatial bandwidth, including microroughness. We present new TMA data in the bandwidth of ~0.1–1000 mm−1, predicting performance and comparing them with x-ray test data. We also account for assembly, alignment, and particulate contamination. Finally, we comment on improved performance expected after repolishing.

© 1988 Optical Society of America

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References

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  1. P. Glenn, A. Slomba, R. Babish, “TMA Mirror Quality Requirements and Achievements,” Proc. Soc. Photo-Opt. Instrum. Eng. 640, 45 (1986).
  2. L. Van Speybroeck et al., “Correspondence Between AXAF TMA X-Ray Performance and Models Based Upon Mechanical and Visible Light Measurements,” Proc. Soc. Photo-Opt. Instrum. Eng. 597, 20 (1985).
  3. D. A. Schwartz et al., “X-Ray Testing of the AXAF Technology Mirror Assembly (TMA) Mirror,” Proc. Soc. Photo-Opt. Instrum. Eng. 597, 10 (1985).
  4. P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963).
  5. R. Noll, P. Glenn, J. Osantowski, “An Optical Surface Analysis Code (osac),” Proc. Soc. Photo-Opt. Instrum. Eng. 362, 78 (1982).
  6. P. Glenn, “Space Telescope Performance Prediction Using the osac Code,” Opt. Eng. 25, 10261986); Proc. Soc. Photo-Opt. Instrum. Eng. 571, 164 (1985).
    [CrossRef]
  7. R. Noll, P. Glenn, “Mirror Surface Autocovariance Functions and Their Associated Visible Scattering,” Appl. Opt. 21, 1824 (1982).
    [CrossRef] [PubMed]
  8. P. Reid, P. Glenn, “Measurement of Micro Roughness and Effects of Detector Bandwidth and Finite Width,” Proc. Soc. Photo-Opt. Instrum. Eng.830, (1987), in press.
  9. L. Van Speybroeck, “Dust,” Smithsonian Astrophysical Observatory Internal Memorandum (27Mar.1987).

1986 (2)

P. Glenn, A. Slomba, R. Babish, “TMA Mirror Quality Requirements and Achievements,” Proc. Soc. Photo-Opt. Instrum. Eng. 640, 45 (1986).

P. Glenn, “Space Telescope Performance Prediction Using the osac Code,” Opt. Eng. 25, 10261986); Proc. Soc. Photo-Opt. Instrum. Eng. 571, 164 (1985).
[CrossRef]

1985 (2)

L. Van Speybroeck et al., “Correspondence Between AXAF TMA X-Ray Performance and Models Based Upon Mechanical and Visible Light Measurements,” Proc. Soc. Photo-Opt. Instrum. Eng. 597, 20 (1985).

D. A. Schwartz et al., “X-Ray Testing of the AXAF Technology Mirror Assembly (TMA) Mirror,” Proc. Soc. Photo-Opt. Instrum. Eng. 597, 10 (1985).

1982 (2)

R. Noll, P. Glenn, J. Osantowski, “An Optical Surface Analysis Code (osac),” Proc. Soc. Photo-Opt. Instrum. Eng. 362, 78 (1982).

R. Noll, P. Glenn, “Mirror Surface Autocovariance Functions and Their Associated Visible Scattering,” Appl. Opt. 21, 1824 (1982).
[CrossRef] [PubMed]

Babish, R.

P. Glenn, A. Slomba, R. Babish, “TMA Mirror Quality Requirements and Achievements,” Proc. Soc. Photo-Opt. Instrum. Eng. 640, 45 (1986).

Beckmann, P.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963).

Glenn, P.

P. Glenn, A. Slomba, R. Babish, “TMA Mirror Quality Requirements and Achievements,” Proc. Soc. Photo-Opt. Instrum. Eng. 640, 45 (1986).

P. Glenn, “Space Telescope Performance Prediction Using the osac Code,” Opt. Eng. 25, 10261986); Proc. Soc. Photo-Opt. Instrum. Eng. 571, 164 (1985).
[CrossRef]

R. Noll, P. Glenn, J. Osantowski, “An Optical Surface Analysis Code (osac),” Proc. Soc. Photo-Opt. Instrum. Eng. 362, 78 (1982).

R. Noll, P. Glenn, “Mirror Surface Autocovariance Functions and Their Associated Visible Scattering,” Appl. Opt. 21, 1824 (1982).
[CrossRef] [PubMed]

P. Reid, P. Glenn, “Measurement of Micro Roughness and Effects of Detector Bandwidth and Finite Width,” Proc. Soc. Photo-Opt. Instrum. Eng.830, (1987), in press.

Noll, R.

R. Noll, P. Glenn, “Mirror Surface Autocovariance Functions and Their Associated Visible Scattering,” Appl. Opt. 21, 1824 (1982).
[CrossRef] [PubMed]

R. Noll, P. Glenn, J. Osantowski, “An Optical Surface Analysis Code (osac),” Proc. Soc. Photo-Opt. Instrum. Eng. 362, 78 (1982).

Osantowski, J.

R. Noll, P. Glenn, J. Osantowski, “An Optical Surface Analysis Code (osac),” Proc. Soc. Photo-Opt. Instrum. Eng. 362, 78 (1982).

Reid, P.

P. Reid, P. Glenn, “Measurement of Micro Roughness and Effects of Detector Bandwidth and Finite Width,” Proc. Soc. Photo-Opt. Instrum. Eng.830, (1987), in press.

Schwartz, D. A.

D. A. Schwartz et al., “X-Ray Testing of the AXAF Technology Mirror Assembly (TMA) Mirror,” Proc. Soc. Photo-Opt. Instrum. Eng. 597, 10 (1985).

Slomba, A.

P. Glenn, A. Slomba, R. Babish, “TMA Mirror Quality Requirements and Achievements,” Proc. Soc. Photo-Opt. Instrum. Eng. 640, 45 (1986).

Spizzichino, A.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963).

Van Speybroeck, L.

L. Van Speybroeck et al., “Correspondence Between AXAF TMA X-Ray Performance and Models Based Upon Mechanical and Visible Light Measurements,” Proc. Soc. Photo-Opt. Instrum. Eng. 597, 20 (1985).

L. Van Speybroeck, “Dust,” Smithsonian Astrophysical Observatory Internal Memorandum (27Mar.1987).

Appl. Opt. (1)

Opt. Eng. (1)

P. Glenn, “Space Telescope Performance Prediction Using the osac Code,” Opt. Eng. 25, 10261986); Proc. Soc. Photo-Opt. Instrum. Eng. 571, 164 (1985).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (4)

R. Noll, P. Glenn, J. Osantowski, “An Optical Surface Analysis Code (osac),” Proc. Soc. Photo-Opt. Instrum. Eng. 362, 78 (1982).

P. Glenn, A. Slomba, R. Babish, “TMA Mirror Quality Requirements and Achievements,” Proc. Soc. Photo-Opt. Instrum. Eng. 640, 45 (1986).

L. Van Speybroeck et al., “Correspondence Between AXAF TMA X-Ray Performance and Models Based Upon Mechanical and Visible Light Measurements,” Proc. Soc. Photo-Opt. Instrum. Eng. 597, 20 (1985).

D. A. Schwartz et al., “X-Ray Testing of the AXAF Technology Mirror Assembly (TMA) Mirror,” Proc. Soc. Photo-Opt. Instrum. Eng. 597, 10 (1985).

Other (3)

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963).

P. Reid, P. Glenn, “Measurement of Micro Roughness and Effects of Detector Bandwidth and Finite Width,” Proc. Soc. Photo-Opt. Instrum. Eng.830, (1987), in press.

L. Van Speybroeck, “Dust,” Smithsonian Astrophysical Observatory Internal Memorandum (27Mar.1987).

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Figures (6)

Fig. 1
Fig. 1

Typical grazing incidence scatter profile from a single longitudinal mirror strip, showing the severe elongation in the tangential direction. Because of the elongation, the integral over a circular region can be approximated by an integral over an infinite strip which is inscribed by the circle. (This approximation holds as long as the circle in question is large enough that, if its size were multiplied by the reciprocal of the grazing angle, it would encircle a large portion of the energy. The excellent accuracy of this approximation for TMA is discussed in the text.)

Fig. 2
Fig. 2

Sample dust scatter result (x-ray energy = 1.49 keV, total scatter fraction = 0.289).

Fig. 3
Fig. 3

Sample dust scatter result (x-ray energy = 6.40 keV, total scatter fraction = 0.338).

Fig. 4
Fig. 4

Comparison of predicted encircled energies in a 1-sec of arc diam image circle. Order of hatched bars: (1) x-ray data; (2) 0.6-sec of arc core, 13.5-Å roughness; (3) 3.0-sec of arc core, 13.5-Å roughness; (4) 3.0-sec of arc core, 16.1-Å roughness; (5) 3.0-sec of arc core, 16.1-Å roughness, plus dust.

Fig. 5
Fig. 5

Comparison of predicted encircled energies in a 8-sec of arc diam image circle. Order of hatched bars: (1) x-ray data; (2) 0.6-sec of arc core, 13.5-Å roughness; (3) 3.0-sec of arc core, 13.5-Å roughness; (4) 3.0-sec of arc core, 16.1-Å roughness; (5) 3.0-sec of arc core, 16.1-Å roughness, plus dust.

Fig. 6
Fig. 6

Comparison of predicted encircled energies in a 20-sec of arc diam image circle. Order of hatched bars: (1) x-ray data; (2) 0.6-sec of arc core, 13.5-Å roughness; (3) 3.0-sec of arc core, 13.5-Å roughness; (4) 3.0-sec of arc core, 16.1-Å roughness; (5) 3.0-sec of arc core, 16.1-Å roughness, plus dust.

Tables (1)

Tables Icon

Table I Tabulation of Old and New TMA Surface Measurementsa

Equations (6)

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d P / d Ω total = ( Strehl d P / d Ω spec ) + d P / d Ω spec d P / d Ω scat ;
Strehl = exp [ 2 ( k σ sin α ) ] 2 ;
EE ( r ) = ( s 2 + t 2 ) 1 / 2 r d s d t d P / d Ω total ( s , t ) .
EE ( r ) = r + r d t + d s d P / d Ω total ( s , t ) .
EE ( r ) = Strehl r + r d t [ d P / d t spec + FT ( FT ( d P / d t spec ) { exp [ 4 π k g ( λ X / α ) ] 1 } ) ] ,
EE conv = 1 exp { ln ( 1 EE 1 ) * ln ( 1 EE 2 ) / ln [ ( 1 EE 1 ) ( 1 EE 2 ) ] } ,

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