Abstract

We report the application of interferometry to the form measurement of a family of highly astigmatic optical surfaces. These measurements are based on a null test that employs a double-pass off-axis test arrangement with a tilted test surface and a reference sphere. This arrangement provides a perfect null test for an ellipsoid of revolution, or prolate spheroid. Its application is illustrated in detail in the presentation of results for the measurement of a specific family of eight differing surfaces that are incorporated into the K-Band Multi-Object Spectrometer Integral Field Unit. All surfaces measured here are sufficiently close to a prolate spheroid to justify its practical application. We discuss the application of the technique as a flexible low-cost approach for the generation of null interferograms in the measurement of a variety of complex surfaces.

© 2011 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
  3. C. M. Dubbeldam and D. J. Robertson, “Freeform diamond machining of complex monolithic metal optics for innovative astronomical applications,” Proc. SPIE 6149, 61490R(2006).
    [CrossRef]
  4. J. Schmoll, D. J. Robertson, C. M. Dubbeldam, F. Bortoletto, L. Pina, R. Hudec, E. Prieto, C. Norrie, and S. Ramsey-Howat, “Optical replication techniques for image slicers,” New Astron. Rev. 50, 263–266 (2006).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2010 (3)

S. Rolt, A. K. Kirby, and D. J. Robertson, “Metrology of complex astigmatic surfaces for astronomical optics,” Proc. SPIE 7739, 77390R (2010).
[CrossRef]

J. Burke and D. S. Wu, “Calibration of spherical reference surfaces for Fizeau interferometry a comparative study of methods,” Appl. Opt. 49, 6014–6023 (2010).
[CrossRef]

J. Nijenhuis, R. Hamelinck, and B. Braam, “Meeting highest performance requirements for lowest price and mass for the M1 segment support unit for E-ELT,” Proc. SPIE 7733, 77332H (2010).
[CrossRef]

2009 (1)

2008 (5)

P. Rees, R. Content, C. M. Dubbeldam, I. Lewis, S. Rolt, S. Todd, and I. Tosh, “Management of optical interfaces in the VLT KMOS instrument,” Proc. SPIE 7017, 701707(2008).
[CrossRef]

S. Rolt, C. M. Dubbeldam, D. J. Robertson, and D. A. Ryder, “Design for test and manufacture of complex multi-component optical instruments,” Proc. SPIE 7102, 71020A (2008).
[CrossRef]

F. Z. Fang, X. D. Zhang, and H. T. Hu, “Cylindrical coordinate machining of optical freeform surfaces,” Opt. Express 16, 7323–7329 (2008).
[CrossRef] [PubMed]

R. Gilmozzi and J. Spyromilio, “The 42 m European ELT: status” Proc. SPIE 7012, 701219 (2008).
[CrossRef]

S. Rolt and D. J. Robertson, “Diamond machining of aspherical mirrors and mirror arrays for integral field units: part II (metrology),” Proc. SPIE 7018, 70183S (2008).
[CrossRef]

2006 (4)

C. M. Dubbeldam and D. J. Robertson, “Freeform diamond machining of complex monolithic metal optics for innovative astronomical applications,” Proc. SPIE 6149, 61490R(2006).
[CrossRef]

J. Schmoll, D. J. Robertson, C. M. Dubbeldam, F. Bortoletto, L. Pina, R. Hudec, E. Prieto, C. Norrie, and S. Ramsey-Howat, “Optical replication techniques for image slicers,” New Astron. Rev. 50, 263–266 (2006).
[CrossRef]

W. Preuss and K. Rickens, “Precision machining of integral field units,” New Astron. Rev. 50, 332–336 (2006).
[CrossRef]

R. Content, “Slicer system of KMOS,” New Astron. Rev. 50, 374–377 (2006).
[CrossRef]

2005 (1)

K. Garrard, T. Bruegge, J. Hoffman, T. Dow, and A. Sohn, “Design tools for freeform optics,” Proc. SPIE 5874, 58740A(2005).
[CrossRef]

1992 (1)

1988 (1)

J. M. Sasian, “Design of null correctors for testing of astronomical optics,” Opt. Eng. 27, 1051–1056 (1988).

1985 (1)

1984 (1)

1976 (1)

1971 (1)

1969 (1)

R. Crane, “Interference phase measurement,” Appl. Opt. 8, 538–542 (1969).

1966 (2)

1934 (1)

F. Zernike, “Beugungstheorie des Schneidenverfahrens und seiner verbesserten Form, der Phasenkontrastmethode,” Physica 1, 689–704 (1934).
[CrossRef]

1918 (1)

F. Twyman, “Interferometers for the experimental study of optical systems from the point of view of the wave theory,” Philos. Mag. 35(205), 49–58 (1918).

Bortoletto, F.

J. Schmoll, D. J. Robertson, C. M. Dubbeldam, F. Bortoletto, L. Pina, R. Hudec, E. Prieto, C. Norrie, and S. Ramsey-Howat, “Optical replication techniques for image slicers,” New Astron. Rev. 50, 263–266 (2006).
[CrossRef]

Braam, B.

J. Nijenhuis, R. Hamelinck, and B. Braam, “Meeting highest performance requirements for lowest price and mass for the M1 segment support unit for E-ELT,” Proc. SPIE 7733, 77332H (2010).
[CrossRef]

Bruegge, T.

K. Garrard, T. Bruegge, J. Hoffman, T. Dow, and A. Sohn, “Design tools for freeform optics,” Proc. SPIE 5874, 58740A(2005).
[CrossRef]

Burke, J.

Content, R.

P. Rees, R. Content, C. M. Dubbeldam, I. Lewis, S. Rolt, S. Todd, and I. Tosh, “Management of optical interfaces in the VLT KMOS instrument,” Proc. SPIE 7017, 701707(2008).
[CrossRef]

R. Content, “Slicer system of KMOS,” New Astron. Rev. 50, 374–377 (2006).
[CrossRef]

Crane, R.

R. Crane, “Interference phase measurement,” Appl. Opt. 8, 538–542 (1969).

Dörband, B.

Dow, T.

K. Garrard, T. Bruegge, J. Hoffman, T. Dow, and A. Sohn, “Design tools for freeform optics,” Proc. SPIE 5874, 58740A(2005).
[CrossRef]

Dubbeldam, C. M.

P. Rees, R. Content, C. M. Dubbeldam, I. Lewis, S. Rolt, S. Todd, and I. Tosh, “Management of optical interfaces in the VLT KMOS instrument,” Proc. SPIE 7017, 701707(2008).
[CrossRef]

S. Rolt, C. M. Dubbeldam, D. J. Robertson, and D. A. Ryder, “Design for test and manufacture of complex multi-component optical instruments,” Proc. SPIE 7102, 71020A (2008).
[CrossRef]

C. M. Dubbeldam and D. J. Robertson, “Freeform diamond machining of complex monolithic metal optics for innovative astronomical applications,” Proc. SPIE 6149, 61490R(2006).
[CrossRef]

J. Schmoll, D. J. Robertson, C. M. Dubbeldam, F. Bortoletto, L. Pina, R. Hudec, E. Prieto, C. Norrie, and S. Ramsey-Howat, “Optical replication techniques for image slicers,” New Astron. Rev. 50, 263–266 (2006).
[CrossRef]

Everhart, E.

Fang, F. Z.

Garrard, K.

K. Garrard, T. Bruegge, J. Hoffman, T. Dow, and A. Sohn, “Design tools for freeform optics,” Proc. SPIE 5874, 58740A(2005).
[CrossRef]

Gilmozzi, R.

R. Gilmozzi and J. Spyromilio, “The 42 m European ELT: status” Proc. SPIE 7012, 701219 (2008).
[CrossRef]

Hamelinck, R.

J. Nijenhuis, R. Hamelinck, and B. Braam, “Meeting highest performance requirements for lowest price and mass for the M1 segment support unit for E-ELT,” Proc. SPIE 7733, 77332H (2010).
[CrossRef]

Hoffman, J.

K. Garrard, T. Bruegge, J. Hoffman, T. Dow, and A. Sohn, “Design tools for freeform optics,” Proc. SPIE 5874, 58740A(2005).
[CrossRef]

Holleran, R. T.

Hu, H. T.

Hudec, R.

J. Schmoll, D. J. Robertson, C. M. Dubbeldam, F. Bortoletto, L. Pina, R. Hudec, E. Prieto, C. Norrie, and S. Ramsey-Howat, “Optical replication techniques for image slicers,” New Astron. Rev. 50, 263–266 (2006).
[CrossRef]

Kirby, A. K.

S. Rolt, A. K. Kirby, and D. J. Robertson, “Metrology of complex astigmatic surfaces for astronomical optics,” Proc. SPIE 7739, 77390R (2010).
[CrossRef]

Lewis, I.

P. Rees, R. Content, C. M. Dubbeldam, I. Lewis, S. Rolt, S. Todd, and I. Tosh, “Management of optical interfaces in the VLT KMOS instrument,” Proc. SPIE 7017, 701707(2008).
[CrossRef]

Liu, D.

Luo, Y.

MacGovern, A. J.

Nijenhuis, J.

J. Nijenhuis, R. Hamelinck, and B. Braam, “Meeting highest performance requirements for lowest price and mass for the M1 segment support unit for E-ELT,” Proc. SPIE 7733, 77332H (2010).
[CrossRef]

Noll, R. J.

Norrie, C.

J. Schmoll, D. J. Robertson, C. M. Dubbeldam, F. Bortoletto, L. Pina, R. Hudec, E. Prieto, C. Norrie, and S. Ramsey-Howat, “Optical replication techniques for image slicers,” New Astron. Rev. 50, 263–266 (2006).
[CrossRef]

Parks, R. E.

Pina, L.

J. Schmoll, D. J. Robertson, C. M. Dubbeldam, F. Bortoletto, L. Pina, R. Hudec, E. Prieto, C. Norrie, and S. Ramsey-Howat, “Optical replication techniques for image slicers,” New Astron. Rev. 50, 263–266 (2006).
[CrossRef]

Preuss, W.

W. Preuss and K. Rickens, “Precision machining of integral field units,” New Astron. Rev. 50, 332–336 (2006).
[CrossRef]

Prieto, E.

J. Schmoll, D. J. Robertson, C. M. Dubbeldam, F. Bortoletto, L. Pina, R. Hudec, E. Prieto, C. Norrie, and S. Ramsey-Howat, “Optical replication techniques for image slicers,” New Astron. Rev. 50, 263–266 (2006).
[CrossRef]

Purcell, D.

D. Purcell, “Interferometric technique for microstructure metrology, using an index matching liquid,” D. Phil. thesis, University of North Carolina at Charlotte (2010).

Ramsey-Howat, S.

J. Schmoll, D. J. Robertson, C. M. Dubbeldam, F. Bortoletto, L. Pina, R. Hudec, E. Prieto, C. Norrie, and S. Ramsey-Howat, “Optical replication techniques for image slicers,” New Astron. Rev. 50, 263–266 (2006).
[CrossRef]

Rees, P.

P. Rees, R. Content, C. M. Dubbeldam, I. Lewis, S. Rolt, S. Todd, and I. Tosh, “Management of optical interfaces in the VLT KMOS instrument,” Proc. SPIE 7017, 701707(2008).
[CrossRef]

Rickens, K.

W. Preuss and K. Rickens, “Precision machining of integral field units,” New Astron. Rev. 50, 332–336 (2006).
[CrossRef]

Robertson, D. J.

S. Rolt, A. K. Kirby, and D. J. Robertson, “Metrology of complex astigmatic surfaces for astronomical optics,” Proc. SPIE 7739, 77390R (2010).
[CrossRef]

S. Rolt, C. M. Dubbeldam, D. J. Robertson, and D. A. Ryder, “Design for test and manufacture of complex multi-component optical instruments,” Proc. SPIE 7102, 71020A (2008).
[CrossRef]

S. Rolt and D. J. Robertson, “Diamond machining of aspherical mirrors and mirror arrays for integral field units: part II (metrology),” Proc. SPIE 7018, 70183S (2008).
[CrossRef]

J. Schmoll, D. J. Robertson, C. M. Dubbeldam, F. Bortoletto, L. Pina, R. Hudec, E. Prieto, C. Norrie, and S. Ramsey-Howat, “Optical replication techniques for image slicers,” New Astron. Rev. 50, 263–266 (2006).
[CrossRef]

C. M. Dubbeldam and D. J. Robertson, “Freeform diamond machining of complex monolithic metal optics for innovative astronomical applications,” Proc. SPIE 6149, 61490R(2006).
[CrossRef]

Rodgers, J. M.

Rolt, S.

S. Rolt, A. K. Kirby, and D. J. Robertson, “Metrology of complex astigmatic surfaces for astronomical optics,” Proc. SPIE 7739, 77390R (2010).
[CrossRef]

P. Rees, R. Content, C. M. Dubbeldam, I. Lewis, S. Rolt, S. Todd, and I. Tosh, “Management of optical interfaces in the VLT KMOS instrument,” Proc. SPIE 7017, 701707(2008).
[CrossRef]

S. Rolt and D. J. Robertson, “Diamond machining of aspherical mirrors and mirror arrays for integral field units: part II (metrology),” Proc. SPIE 7018, 70183S (2008).
[CrossRef]

S. Rolt, C. M. Dubbeldam, D. J. Robertson, and D. A. Ryder, “Design for test and manufacture of complex multi-component optical instruments,” Proc. SPIE 7102, 71020A (2008).
[CrossRef]

S. Rolt, “Form measurement of complex freeform surfaces by tilted interferometry,” in Proceedings of the ASPE Summer Topical Meeting Precision Interferometric Metrology (American Society for Precision Engineering, 2010), pp. 40–45.

Ryder, D. A.

S. Rolt, C. M. Dubbeldam, D. J. Robertson, and D. A. Ryder, “Design for test and manufacture of complex multi-component optical instruments,” Proc. SPIE 7102, 71020A (2008).
[CrossRef]

Sasian, J. M.

J. M. Sasian, “Design of null correctors for testing of astronomical optics,” Opt. Eng. 27, 1051–1056 (1988).

Schmoll, J.

J. Schmoll, D. J. Robertson, C. M. Dubbeldam, F. Bortoletto, L. Pina, R. Hudec, E. Prieto, C. Norrie, and S. Ramsey-Howat, “Optical replication techniques for image slicers,” New Astron. Rev. 50, 263–266 (2006).
[CrossRef]

Shafer, D.

Sohn, A.

K. Garrard, T. Bruegge, J. Hoffman, T. Dow, and A. Sohn, “Design tools for freeform optics,” Proc. SPIE 5874, 58740A(2005).
[CrossRef]

Spyromilio, J.

R. Gilmozzi and J. Spyromilio, “The 42 m European ELT: status” Proc. SPIE 7012, 701219 (2008).
[CrossRef]

Tian, C.

Tiziani, H. J.

Todd, S.

P. Rees, R. Content, C. M. Dubbeldam, I. Lewis, S. Rolt, S. Todd, and I. Tosh, “Management of optical interfaces in the VLT KMOS instrument,” Proc. SPIE 7017, 701707(2008).
[CrossRef]

Tosh, I.

P. Rees, R. Content, C. M. Dubbeldam, I. Lewis, S. Rolt, S. Todd, and I. Tosh, “Management of optical interfaces in the VLT KMOS instrument,” Proc. SPIE 7017, 701707(2008).
[CrossRef]

Twyman, F.

F. Twyman, “Interferometers for the experimental study of optical systems from the point of view of the wave theory,” Philos. Mag. 35(205), 49–58 (1918).

Wang, L.

Wu, D. S.

Wyant, J. C.

Yang, Y.

Zernike, F.

F. Zernike, “Beugungstheorie des Schneidenverfahrens und seiner verbesserten Form, der Phasenkontrastmethode,” Physica 1, 689–704 (1934).
[CrossRef]

Zhang, X. D.

Appl. Opt. (8)

J. Opt. Soc. Am. (1)

New Astron. Rev. (3)

R. Content, “Slicer system of KMOS,” New Astron. Rev. 50, 374–377 (2006).
[CrossRef]

J. Schmoll, D. J. Robertson, C. M. Dubbeldam, F. Bortoletto, L. Pina, R. Hudec, E. Prieto, C. Norrie, and S. Ramsey-Howat, “Optical replication techniques for image slicers,” New Astron. Rev. 50, 263–266 (2006).
[CrossRef]

W. Preuss and K. Rickens, “Precision machining of integral field units,” New Astron. Rev. 50, 332–336 (2006).
[CrossRef]

Opt. Eng. (1)

J. M. Sasian, “Design of null correctors for testing of astronomical optics,” Opt. Eng. 27, 1051–1056 (1988).

Opt. Express (2)

Philos. Mag. (1)

F. Twyman, “Interferometers for the experimental study of optical systems from the point of view of the wave theory,” Philos. Mag. 35(205), 49–58 (1918).

Physica (1)

F. Zernike, “Beugungstheorie des Schneidenverfahrens und seiner verbesserten Form, der Phasenkontrastmethode,” Physica 1, 689–704 (1934).
[CrossRef]

Proc. SPIE (8)

S. Rolt and D. J. Robertson, “Diamond machining of aspherical mirrors and mirror arrays for integral field units: part II (metrology),” Proc. SPIE 7018, 70183S (2008).
[CrossRef]

R. Gilmozzi and J. Spyromilio, “The 42 m European ELT: status” Proc. SPIE 7012, 701219 (2008).
[CrossRef]

J. Nijenhuis, R. Hamelinck, and B. Braam, “Meeting highest performance requirements for lowest price and mass for the M1 segment support unit for E-ELT,” Proc. SPIE 7733, 77332H (2010).
[CrossRef]

K. Garrard, T. Bruegge, J. Hoffman, T. Dow, and A. Sohn, “Design tools for freeform optics,” Proc. SPIE 5874, 58740A(2005).
[CrossRef]

C. M. Dubbeldam and D. J. Robertson, “Freeform diamond machining of complex monolithic metal optics for innovative astronomical applications,” Proc. SPIE 6149, 61490R(2006).
[CrossRef]

S. Rolt, A. K. Kirby, and D. J. Robertson, “Metrology of complex astigmatic surfaces for astronomical optics,” Proc. SPIE 7739, 77390R (2010).
[CrossRef]

P. Rees, R. Content, C. M. Dubbeldam, I. Lewis, S. Rolt, S. Todd, and I. Tosh, “Management of optical interfaces in the VLT KMOS instrument,” Proc. SPIE 7017, 701707(2008).
[CrossRef]

S. Rolt, C. M. Dubbeldam, D. J. Robertson, and D. A. Ryder, “Design for test and manufacture of complex multi-component optical instruments,” Proc. SPIE 7102, 71020A (2008).
[CrossRef]

Other (2)

S. Rolt, “Form measurement of complex freeform surfaces by tilted interferometry,” in Proceedings of the ASPE Summer Topical Meeting Precision Interferometric Metrology (American Society for Precision Engineering, 2010), pp. 40–45.

D. Purcell, “Interferometric technique for microstructure metrology, using an index matching liquid,” D. Phil. thesis, University of North Carolina at Charlotte (2010).

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Figures (9)

Fig. 1
Fig. 1

Component integrated into mounting block.

Fig. 2
Fig. 2

Basic Twyman–Green interferometer arrangement.

Fig. 3
Fig. 3

Schematic of null-test arrangement.

Fig. 4
Fig. 4

Generalized sketch of spheroid surface showing two foci.

Fig. 5
Fig. 5

Basic experimental setup. The tilt angle of the component is 72 ° . Note the large included angle between the interferometer and reference sphere arms, amounting to about 144 ° .

Fig. 6
Fig. 6

Interferogram without null-test procedure.

Fig. 7
Fig. 7

Interferogram with null-test procedure.

Fig. 8
Fig. 8

Typical form error (in nanometers).

Fig. 9
Fig. 9

Higher-order form error (in nanometers).

Tables (6)

Tables Icon

Table 1 Form Definitions for the Eight Component Configurations, Expressed in Terms of Zernike Polynomials a

Tables Icon

Table 2 Slow and Fast Axis Radii, Nominal Radii, and Tilt Angles for All Eight Component Types

Tables Icon

Table 3 Major Sources of Measurement Uncertainty by Origin and Broken Down into Zernike Polynomials a

Tables Icon

Table 4 Form Errors in Nanometers RMS for All Eight Components into the Nominal 5.2 mm Diameter Pupil a

Tables Icon

Table 5 Form Errors in Nanometers RMS for All Eight Components into Restricted Optical Footprint a

Tables Icon

Table 6 Zernike Form Contributions for Outer Segment of the Proposed E-ELT Primary Telescope Mirror a

Equations (6)

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

r = r 0 1 ε cos θ ,
z = x 2 / r 0 1 + 1 ( 1 + k ) x 2 / r 0 2 ,
R = r 0 1 ε 2 = R 1 R 2 ,
cos θ = 1 ε 2 = 1 + k = R 1 R 2 .
Δ θ = sin θ Δ z R ,
Δ R = ( cos 2 θ cos θ ) Δ z .

Metrics