Abstract

Continuing to develop the sine condition test (SCTest), we show how violations of the generalized sine condition can be used to align a three-mirror anastigmat (TMA). This paper shows how the linear aberrations measured using the sine condition, along with aberrations that have constant field dependence, can be used to align a system. We discuss the design of the test hardware needed to align a TMA and the procedure for alignment. Using simulation, we then investigate the behavior of the alignment SCTest for various levels of mirror misalignment, mirror fabrication errors, and misalignment of the test equipment. All of these tests show that the alignment SCTest can successfully align an optical system.

© 2014 Optical Society of America

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2013 (2)

2012 (2)

D. R. Blanco, “Near-perfect Collimation of Wide-Field Cassegrain Telescopes,” Publ. Astron. Soc. Pac. 124, 36–41 (2012).
[CrossRef]

T. Agócs, L. Venema, V. Korkiakoski, and G. Kroes, “Optimizing optical systems with active components,” Proc. SPIE 8450, 84505F (2012).
[CrossRef]

2011 (2)

2010 (1)

J. H. Burge, C. Zhao, and S. H. Lu, “Use of the Abbe sine condition to quantify alignment aberrations in optical imaging systems,” Proc. SPIE 7652, p. 765219 (2010).
[CrossRef]

2008 (2)

A. M. Hvisc and J. H. Burge, “Alignment analysis of four-mirror spherical aberration correctors,” Proc. SPIE 7018, 701819 (2008).
[CrossRef]

K. P. Thompson, T. Schmid, and J. P. Rolland, “The misalignment induced aberrations of TMA telescopes,” Opt. Express 16, 20345–20353 (2008).
[CrossRef]

2003 (1)

J. H. Burge and R. P. Angel, “Wide-field telescope using spherical mirrors,” Proc. SPIE 5174, 83 (2003).
[CrossRef]

2000 (1)

L. Noethe, “Final alignment of the VLT,” Proc. SPIE 4003, 382–390 (2000).
[CrossRef]

1998 (1)

H. N. Chapman and D. W. Sweeney, “Rigorous method for compensation selection and alignment of microlithographic optical systems,” Proc. SPIE 3331, 102–113 (1998).
[CrossRef]

1996 (1)

B. McLeod, “Collimation of fast wide-field telescopes,” Publ. Astron. Soc. Pac. 108, 217–219 (1996).
[CrossRef]

1995 (1)

R. K. Bhatia, “Telescope alignment: is the zero-coma condition sufficient?” Proc. SPIE 2479, 354–363 (1995).
[CrossRef]

1979 (1)

Agócs, T.

T. Agócs, L. Venema, V. Korkiakoski, and G. Kroes, “Optimizing optical systems with active components,” Proc. SPIE 8450, 84505F (2012).
[CrossRef]

Angel, R. P.

J. H. Burge and R. P. Angel, “Wide-field telescope using spherical mirrors,” Proc. SPIE 5174, 83 (2003).
[CrossRef]

Backes, M.

A. Hoecker, P. Speckmayer, J. Stelzer, J. Therhaag, E. von Toerne, H. Voss, M. Backes, T. Carli, O. Cohen, A. Christov, D. Dannheim, K. Danielowski, S. Henrot-Versille, M. Jachowski, K. Kraszewski, A. Krasznahorkay, M. Kruk, Y. Mahalalel, R. Ospanov, X. Prudent, A. Robert, D. Schouten, F. Tegenfeldt, A. Voigt, K. Voss, M. Wolter, and A. Zemla, “TMVA—toolkit for multivariate data analysis,” PoS ACAT:040, p. 62, arXiv:physics/0703039 (2007).

Bhatia, R. K.

R. K. Bhatia, “Telescope alignment: is the zero-coma condition sufficient?” Proc. SPIE 2479, 354–363 (1995).
[CrossRef]

Blanco, D. R.

D. R. Blanco, “Near-perfect Collimation of Wide-Field Cassegrain Telescopes,” Publ. Astron. Soc. Pac. 124, 36–41 (2012).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University, 1999).

Burge, J. H.

S. Lampen, M. Dubin, and J. H. Burge, “Design and optimization of the sine condition test for measuring misaligned optical systems,” Appl. Opt. 52, 7099–7108 (2013).
[CrossRef]

S. Lampen, M. Dubin, and J. H. Burge, “Design and optimization of the sine condition test for measuring misaligned optical systems,” Appl. Opt. 52, 7099–7108 (2013).

S. Lampen, M. Dubin, and J. H. Burge, “Implementation of sine condition test to measure optical system misalignments,” Appl. Opt. 50, 6391–6398 (2011).
[CrossRef]

J. H. Burge, C. Zhao, and S. H. Lu, “Use of the Abbe sine condition to quantify alignment aberrations in optical imaging systems,” Proc. SPIE 7652, p. 765219 (2010).
[CrossRef]

A. M. Hvisc and J. H. Burge, “Alignment analysis of four-mirror spherical aberration correctors,” Proc. SPIE 7018, 701819 (2008).
[CrossRef]

J. H. Burge and R. P. Angel, “Wide-field telescope using spherical mirrors,” Proc. SPIE 5174, 83 (2003).
[CrossRef]

T. T. Elazhary, C. Zhao, P. Zhou, and J. H. Burge, “The generalized sine condition,” submitted to J. Opt. Soc. Am. A.

Carli, T.

A. Hoecker, P. Speckmayer, J. Stelzer, J. Therhaag, E. von Toerne, H. Voss, M. Backes, T. Carli, O. Cohen, A. Christov, D. Dannheim, K. Danielowski, S. Henrot-Versille, M. Jachowski, K. Kraszewski, A. Krasznahorkay, M. Kruk, Y. Mahalalel, R. Ospanov, X. Prudent, A. Robert, D. Schouten, F. Tegenfeldt, A. Voigt, K. Voss, M. Wolter, and A. Zemla, “TMVA—toolkit for multivariate data analysis,” PoS ACAT:040, p. 62, arXiv:physics/0703039 (2007).

Chapman, H. N.

H. N. Chapman and D. W. Sweeney, “Rigorous method for compensation selection and alignment of microlithographic optical systems,” Proc. SPIE 3331, 102–113 (1998).
[CrossRef]

Christov, A.

A. Hoecker, P. Speckmayer, J. Stelzer, J. Therhaag, E. von Toerne, H. Voss, M. Backes, T. Carli, O. Cohen, A. Christov, D. Dannheim, K. Danielowski, S. Henrot-Versille, M. Jachowski, K. Kraszewski, A. Krasznahorkay, M. Kruk, Y. Mahalalel, R. Ospanov, X. Prudent, A. Robert, D. Schouten, F. Tegenfeldt, A. Voigt, K. Voss, M. Wolter, and A. Zemla, “TMVA—toolkit for multivariate data analysis,” PoS ACAT:040, p. 62, arXiv:physics/0703039 (2007).

Cohen, O.

A. Hoecker, P. Speckmayer, J. Stelzer, J. Therhaag, E. von Toerne, H. Voss, M. Backes, T. Carli, O. Cohen, A. Christov, D. Dannheim, K. Danielowski, S. Henrot-Versille, M. Jachowski, K. Kraszewski, A. Krasznahorkay, M. Kruk, Y. Mahalalel, R. Ospanov, X. Prudent, A. Robert, D. Schouten, F. Tegenfeldt, A. Voigt, K. Voss, M. Wolter, and A. Zemla, “TMVA—toolkit for multivariate data analysis,” PoS ACAT:040, p. 62, arXiv:physics/0703039 (2007).

Cook, L. G.

L. G. Cook, “Three-mirror anastigmatic optical system,” U.S. patentUS4265510 A (May5, 1981).

Danielowski, K.

A. Hoecker, P. Speckmayer, J. Stelzer, J. Therhaag, E. von Toerne, H. Voss, M. Backes, T. Carli, O. Cohen, A. Christov, D. Dannheim, K. Danielowski, S. Henrot-Versille, M. Jachowski, K. Kraszewski, A. Krasznahorkay, M. Kruk, Y. Mahalalel, R. Ospanov, X. Prudent, A. Robert, D. Schouten, F. Tegenfeldt, A. Voigt, K. Voss, M. Wolter, and A. Zemla, “TMVA—toolkit for multivariate data analysis,” PoS ACAT:040, p. 62, arXiv:physics/0703039 (2007).

Dannheim, D.

A. Hoecker, P. Speckmayer, J. Stelzer, J. Therhaag, E. von Toerne, H. Voss, M. Backes, T. Carli, O. Cohen, A. Christov, D. Dannheim, K. Danielowski, S. Henrot-Versille, M. Jachowski, K. Kraszewski, A. Krasznahorkay, M. Kruk, Y. Mahalalel, R. Ospanov, X. Prudent, A. Robert, D. Schouten, F. Tegenfeldt, A. Voigt, K. Voss, M. Wolter, and A. Zemla, “TMVA—toolkit for multivariate data analysis,” PoS ACAT:040, p. 62, arXiv:physics/0703039 (2007).

Dubin, M.

Elazhary, T. T.

T. T. Elazhary, C. Zhao, P. Zhou, and J. H. Burge, “The generalized sine condition,” submitted to J. Opt. Soc. Am. A.

Henrot-Versille, S.

A. Hoecker, P. Speckmayer, J. Stelzer, J. Therhaag, E. von Toerne, H. Voss, M. Backes, T. Carli, O. Cohen, A. Christov, D. Dannheim, K. Danielowski, S. Henrot-Versille, M. Jachowski, K. Kraszewski, A. Krasznahorkay, M. Kruk, Y. Mahalalel, R. Ospanov, X. Prudent, A. Robert, D. Schouten, F. Tegenfeldt, A. Voigt, K. Voss, M. Wolter, and A. Zemla, “TMVA—toolkit for multivariate data analysis,” PoS ACAT:040, p. 62, arXiv:physics/0703039 (2007).

Hoecker, A.

A. Hoecker, P. Speckmayer, J. Stelzer, J. Therhaag, E. von Toerne, H. Voss, M. Backes, T. Carli, O. Cohen, A. Christov, D. Dannheim, K. Danielowski, S. Henrot-Versille, M. Jachowski, K. Kraszewski, A. Krasznahorkay, M. Kruk, Y. Mahalalel, R. Ospanov, X. Prudent, A. Robert, D. Schouten, F. Tegenfeldt, A. Voigt, K. Voss, M. Wolter, and A. Zemla, “TMVA—toolkit for multivariate data analysis,” PoS ACAT:040, p. 62, arXiv:physics/0703039 (2007).

Hvisc, A. M.

A. M. Hvisc and J. H. Burge, “Alignment analysis of four-mirror spherical aberration correctors,” Proc. SPIE 7018, 701819 (2008).
[CrossRef]

Jachowski, M.

A. Hoecker, P. Speckmayer, J. Stelzer, J. Therhaag, E. von Toerne, H. Voss, M. Backes, T. Carli, O. Cohen, A. Christov, D. Dannheim, K. Danielowski, S. Henrot-Versille, M. Jachowski, K. Kraszewski, A. Krasznahorkay, M. Kruk, Y. Mahalalel, R. Ospanov, X. Prudent, A. Robert, D. Schouten, F. Tegenfeldt, A. Voigt, K. Voss, M. Wolter, and A. Zemla, “TMVA—toolkit for multivariate data analysis,” PoS ACAT:040, p. 62, arXiv:physics/0703039 (2007).

Kingslake, R.

R. Kingslake, Lens Design Fundamentals, 2nd ed. (Academic, 2010).

Korkiakoski, V.

T. Agócs, L. Venema, V. Korkiakoski, and G. Kroes, “Optimizing optical systems with active components,” Proc. SPIE 8450, 84505F (2012).
[CrossRef]

Kraszewski, K.

A. Hoecker, P. Speckmayer, J. Stelzer, J. Therhaag, E. von Toerne, H. Voss, M. Backes, T. Carli, O. Cohen, A. Christov, D. Dannheim, K. Danielowski, S. Henrot-Versille, M. Jachowski, K. Kraszewski, A. Krasznahorkay, M. Kruk, Y. Mahalalel, R. Ospanov, X. Prudent, A. Robert, D. Schouten, F. Tegenfeldt, A. Voigt, K. Voss, M. Wolter, and A. Zemla, “TMVA—toolkit for multivariate data analysis,” PoS ACAT:040, p. 62, arXiv:physics/0703039 (2007).

Krasznahorkay, A.

A. Hoecker, P. Speckmayer, J. Stelzer, J. Therhaag, E. von Toerne, H. Voss, M. Backes, T. Carli, O. Cohen, A. Christov, D. Dannheim, K. Danielowski, S. Henrot-Versille, M. Jachowski, K. Kraszewski, A. Krasznahorkay, M. Kruk, Y. Mahalalel, R. Ospanov, X. Prudent, A. Robert, D. Schouten, F. Tegenfeldt, A. Voigt, K. Voss, M. Wolter, and A. Zemla, “TMVA—toolkit for multivariate data analysis,” PoS ACAT:040, p. 62, arXiv:physics/0703039 (2007).

Kroes, G.

T. Agócs, L. Venema, V. Korkiakoski, and G. Kroes, “Optimizing optical systems with active components,” Proc. SPIE 8450, 84505F (2012).
[CrossRef]

Kruk, M.

A. Hoecker, P. Speckmayer, J. Stelzer, J. Therhaag, E. von Toerne, H. Voss, M. Backes, T. Carli, O. Cohen, A. Christov, D. Dannheim, K. Danielowski, S. Henrot-Versille, M. Jachowski, K. Kraszewski, A. Krasznahorkay, M. Kruk, Y. Mahalalel, R. Ospanov, X. Prudent, A. Robert, D. Schouten, F. Tegenfeldt, A. Voigt, K. Voss, M. Wolter, and A. Zemla, “TMVA—toolkit for multivariate data analysis,” PoS ACAT:040, p. 62, arXiv:physics/0703039 (2007).

Lampen, S.

Lu, S. H.

J. H. Burge, C. Zhao, and S. H. Lu, “Use of the Abbe sine condition to quantify alignment aberrations in optical imaging systems,” Proc. SPIE 7652, p. 765219 (2010).
[CrossRef]

Mahalalel, Y.

A. Hoecker, P. Speckmayer, J. Stelzer, J. Therhaag, E. von Toerne, H. Voss, M. Backes, T. Carli, O. Cohen, A. Christov, D. Dannheim, K. Danielowski, S. Henrot-Versille, M. Jachowski, K. Kraszewski, A. Krasznahorkay, M. Kruk, Y. Mahalalel, R. Ospanov, X. Prudent, A. Robert, D. Schouten, F. Tegenfeldt, A. Voigt, K. Voss, M. Wolter, and A. Zemla, “TMVA—toolkit for multivariate data analysis,” PoS ACAT:040, p. 62, arXiv:physics/0703039 (2007).

McLeod, B.

B. McLeod, “Collimation of fast wide-field telescopes,” Publ. Astron. Soc. Pac. 108, 217–219 (1996).
[CrossRef]

Mertz, L.

Noethe, L.

L. Noethe, “Final alignment of the VLT,” Proc. SPIE 4003, 382–390 (2000).
[CrossRef]

Ospanov, R.

A. Hoecker, P. Speckmayer, J. Stelzer, J. Therhaag, E. von Toerne, H. Voss, M. Backes, T. Carli, O. Cohen, A. Christov, D. Dannheim, K. Danielowski, S. Henrot-Versille, M. Jachowski, K. Kraszewski, A. Krasznahorkay, M. Kruk, Y. Mahalalel, R. Ospanov, X. Prudent, A. Robert, D. Schouten, F. Tegenfeldt, A. Voigt, K. Voss, M. Wolter, and A. Zemla, “TMVA—toolkit for multivariate data analysis,” PoS ACAT:040, p. 62, arXiv:physics/0703039 (2007).

Prudent, X.

A. Hoecker, P. Speckmayer, J. Stelzer, J. Therhaag, E. von Toerne, H. Voss, M. Backes, T. Carli, O. Cohen, A. Christov, D. Dannheim, K. Danielowski, S. Henrot-Versille, M. Jachowski, K. Kraszewski, A. Krasznahorkay, M. Kruk, Y. Mahalalel, R. Ospanov, X. Prudent, A. Robert, D. Schouten, F. Tegenfeldt, A. Voigt, K. Voss, M. Wolter, and A. Zemla, “TMVA—toolkit for multivariate data analysis,” PoS ACAT:040, p. 62, arXiv:physics/0703039 (2007).

Robert, A.

A. Hoecker, P. Speckmayer, J. Stelzer, J. Therhaag, E. von Toerne, H. Voss, M. Backes, T. Carli, O. Cohen, A. Christov, D. Dannheim, K. Danielowski, S. Henrot-Versille, M. Jachowski, K. Kraszewski, A. Krasznahorkay, M. Kruk, Y. Mahalalel, R. Ospanov, X. Prudent, A. Robert, D. Schouten, F. Tegenfeldt, A. Voigt, K. Voss, M. Wolter, and A. Zemla, “TMVA—toolkit for multivariate data analysis,” PoS ACAT:040, p. 62, arXiv:physics/0703039 (2007).

Rolland, J. P.

Schmid, T.

Schouten, D.

A. Hoecker, P. Speckmayer, J. Stelzer, J. Therhaag, E. von Toerne, H. Voss, M. Backes, T. Carli, O. Cohen, A. Christov, D. Dannheim, K. Danielowski, S. Henrot-Versille, M. Jachowski, K. Kraszewski, A. Krasznahorkay, M. Kruk, Y. Mahalalel, R. Ospanov, X. Prudent, A. Robert, D. Schouten, F. Tegenfeldt, A. Voigt, K. Voss, M. Wolter, and A. Zemla, “TMVA—toolkit for multivariate data analysis,” PoS ACAT:040, p. 62, arXiv:physics/0703039 (2007).

Speckmayer, P.

A. Hoecker, P. Speckmayer, J. Stelzer, J. Therhaag, E. von Toerne, H. Voss, M. Backes, T. Carli, O. Cohen, A. Christov, D. Dannheim, K. Danielowski, S. Henrot-Versille, M. Jachowski, K. Kraszewski, A. Krasznahorkay, M. Kruk, Y. Mahalalel, R. Ospanov, X. Prudent, A. Robert, D. Schouten, F. Tegenfeldt, A. Voigt, K. Voss, M. Wolter, and A. Zemla, “TMVA—toolkit for multivariate data analysis,” PoS ACAT:040, p. 62, arXiv:physics/0703039 (2007).

Stelzer, J.

A. Hoecker, P. Speckmayer, J. Stelzer, J. Therhaag, E. von Toerne, H. Voss, M. Backes, T. Carli, O. Cohen, A. Christov, D. Dannheim, K. Danielowski, S. Henrot-Versille, M. Jachowski, K. Kraszewski, A. Krasznahorkay, M. Kruk, Y. Mahalalel, R. Ospanov, X. Prudent, A. Robert, D. Schouten, F. Tegenfeldt, A. Voigt, K. Voss, M. Wolter, and A. Zemla, “TMVA—toolkit for multivariate data analysis,” PoS ACAT:040, p. 62, arXiv:physics/0703039 (2007).

Sweeney, D. W.

H. N. Chapman and D. W. Sweeney, “Rigorous method for compensation selection and alignment of microlithographic optical systems,” Proc. SPIE 3331, 102–113 (1998).
[CrossRef]

Tegenfeldt, F.

A. Hoecker, P. Speckmayer, J. Stelzer, J. Therhaag, E. von Toerne, H. Voss, M. Backes, T. Carli, O. Cohen, A. Christov, D. Dannheim, K. Danielowski, S. Henrot-Versille, M. Jachowski, K. Kraszewski, A. Krasznahorkay, M. Kruk, Y. Mahalalel, R. Ospanov, X. Prudent, A. Robert, D. Schouten, F. Tegenfeldt, A. Voigt, K. Voss, M. Wolter, and A. Zemla, “TMVA—toolkit for multivariate data analysis,” PoS ACAT:040, p. 62, arXiv:physics/0703039 (2007).

Therhaag, J.

A. Hoecker, P. Speckmayer, J. Stelzer, J. Therhaag, E. von Toerne, H. Voss, M. Backes, T. Carli, O. Cohen, A. Christov, D. Dannheim, K. Danielowski, S. Henrot-Versille, M. Jachowski, K. Kraszewski, A. Krasznahorkay, M. Kruk, Y. Mahalalel, R. Ospanov, X. Prudent, A. Robert, D. Schouten, F. Tegenfeldt, A. Voigt, K. Voss, M. Wolter, and A. Zemla, “TMVA—toolkit for multivariate data analysis,” PoS ACAT:040, p. 62, arXiv:physics/0703039 (2007).

Thompson, K. P.

Venema, L.

T. Agócs, L. Venema, V. Korkiakoski, and G. Kroes, “Optimizing optical systems with active components,” Proc. SPIE 8450, 84505F (2012).
[CrossRef]

Voigt, A.

A. Hoecker, P. Speckmayer, J. Stelzer, J. Therhaag, E. von Toerne, H. Voss, M. Backes, T. Carli, O. Cohen, A. Christov, D. Dannheim, K. Danielowski, S. Henrot-Versille, M. Jachowski, K. Kraszewski, A. Krasznahorkay, M. Kruk, Y. Mahalalel, R. Ospanov, X. Prudent, A. Robert, D. Schouten, F. Tegenfeldt, A. Voigt, K. Voss, M. Wolter, and A. Zemla, “TMVA—toolkit for multivariate data analysis,” PoS ACAT:040, p. 62, arXiv:physics/0703039 (2007).

von Toerne, E.

A. Hoecker, P. Speckmayer, J. Stelzer, J. Therhaag, E. von Toerne, H. Voss, M. Backes, T. Carli, O. Cohen, A. Christov, D. Dannheim, K. Danielowski, S. Henrot-Versille, M. Jachowski, K. Kraszewski, A. Krasznahorkay, M. Kruk, Y. Mahalalel, R. Ospanov, X. Prudent, A. Robert, D. Schouten, F. Tegenfeldt, A. Voigt, K. Voss, M. Wolter, and A. Zemla, “TMVA—toolkit for multivariate data analysis,” PoS ACAT:040, p. 62, arXiv:physics/0703039 (2007).

Voss, H.

A. Hoecker, P. Speckmayer, J. Stelzer, J. Therhaag, E. von Toerne, H. Voss, M. Backes, T. Carli, O. Cohen, A. Christov, D. Dannheim, K. Danielowski, S. Henrot-Versille, M. Jachowski, K. Kraszewski, A. Krasznahorkay, M. Kruk, Y. Mahalalel, R. Ospanov, X. Prudent, A. Robert, D. Schouten, F. Tegenfeldt, A. Voigt, K. Voss, M. Wolter, and A. Zemla, “TMVA—toolkit for multivariate data analysis,” PoS ACAT:040, p. 62, arXiv:physics/0703039 (2007).

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A. Hoecker, P. Speckmayer, J. Stelzer, J. Therhaag, E. von Toerne, H. Voss, M. Backes, T. Carli, O. Cohen, A. Christov, D. Dannheim, K. Danielowski, S. Henrot-Versille, M. Jachowski, K. Kraszewski, A. Krasznahorkay, M. Kruk, Y. Mahalalel, R. Ospanov, X. Prudent, A. Robert, D. Schouten, F. Tegenfeldt, A. Voigt, K. Voss, M. Wolter, and A. Zemla, “TMVA—toolkit for multivariate data analysis,” PoS ACAT:040, p. 62, arXiv:physics/0703039 (2007).

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Figures (16)

Fig. 1.
Fig. 1.

General illustration of an optical system with finite conjugates. Annotations are—O, object point; I, conjugate image point; B, point on EP; C, point on XP conjugate to B; εo,off-axis object point; εi, conjugate off-axis image point; S^o, unit vector pointing from O to B; θo, angle of S^o with respect to the axis; S^i, unit vector from I to C; θi, angle of S^i with respect to the axis. Text and image similar to [3].

Fig. 2.
Fig. 2.

Block diagram of the alignment SCTest applied to a generic UUT.

Fig. 3.
Fig. 3.

(a) Small sample of projection grating pattern and (b) locations of orders at intermediate image plane.

Fig. 4.
Fig. 4.

Nominal design of TMA. (a) Side view of layout; (b),(c) rotated views of layout; and (d) close-up of intermediate image and image plane.

Fig. 5.
Fig. 5.

Spot diagrams of TMA system at its operational wavelength of 4 μm. Sections have different scales. (a) Nominal design performance—scale 100 μm, (b) performance of misaligned TMA—scale 400 μm, and (c) performance of misaligned TMA after M3 position was adjusted to correct center of the field performance—scale 400 μm.

Fig. 6.
Fig. 6.

(a) Side view of alignment SCTest with 0 and ±1 orders in y direction and (b) rotated view of (a) and close-up of the intermediate image and aperture plane.

Fig. 7.
Fig. 7.

(a) Side view of alignment SCTest with 0 and ±1 orders in x direction and (b) rotated view of (a) and close-up of the intermediate image and aperture plane.

Fig. 8.
Fig. 8.

Flow diagram of the alignment simulation process.

Fig. 9.
Fig. 9.

Distribution of the mean rms spot size across field for the starting mirror configuration and the aligned system. Area under curve is normalized to one.

Fig. 10.
Fig. 10.

(a) Cumulative distribution function of the aligned rms spot size, showing the percent of data equal to or less than a given rms spot size. (b) Distribution of the mean rms spot size across field for the aligned system, as well as the gamma fit to estimate the peak rms spot size, as well as the thresholds shown in (a). Area under curve normalized to one.

Fig. 11.
Fig. 11.

Improvement of rms spot size through alignment with respect to the starting rms spot size.

Fig. 12.
Fig. 12.

Change in rms spot size during alignment for six sample trials.

Fig. 13.
Fig. 13.

Improvement of TMA performance after perturbation of TMA mirrors for the tolerances in Table 3. (a) Starting rms spot size shown in blue with square data points and aligned rms spot size shown in red with circular data points and (b) Aligned rms spot size.

Fig. 14.
Fig. 14.

Performance of alignment in the presence of the test equipment perturbations for the three examples given in Table 5.

Fig. 15.
Fig. 15.

Improvement of TMA performance after perturbation of mirror fabrication parameters for the tolerances in Table 7. (a) Starting rms spot size shown in blue with square data points and aligned rms spot size shown in red with circular data points and (b) Aligned rms spot size.

Fig. 16.
Fig. 16.

Improvement of TMA performance after perturbation of all DOFs of the mirror position, all DOFs of the test equipment, and the radius and conic constant of the TMA mirrors for the tolerances in Table 9. (a) Starting rms spot size shown in blue with square data points and aligned rms spot size shown in red with circular data points and (b) aligned rms spot size.

Tables (11)

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Table 1. Summary of Case Study Conclusions

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Table 2. TMA Design Specifications

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Table 3. Tolerances of TMA Mirror Sets

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Table 4. Results of TMA Mirror Simulation

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Table 5. Starting and Aligned rms Spot Size for Test Equipment Misalignment Example

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Table 6. Test Equipment Set

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Table 7. Tolerances of TMA Fabrication Mirror Sets

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Table 8. Results of TMA Fabrication Mirror Simulation

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Table 9. Combined Simulation Tolerances and Results

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Table 10. TMA Prescription

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Table 11. Corners of FOV

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

Wo=S^o·εo
WI=S^i·εi.
WPME=WoWI,
WPME=S^o·εoS^i·εi.
Jo,ij=δziδxj,
Jo=UWVT.
JoVi=SiUi
δx=Vcomp1WcompUcompTz(x),

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