Abstract

The star test is a useful tool for fast visual inspection of the aberrations of micro-objectives during final adjustment. One of its most valuable properties is that it permits instantaneous observation of the effect of adjustments of lens groups, for instance, the shifting element during on-axis coma adjustment. Sometimes, however, it is difficult to perform the star test, e.g., in the ultraviolet region, which represents a field of growing interest driven by applications in semiconductor inspection and metrology. In addition, it is difficult to display the point-spread functions with video cameras because of the high dynamic range needed. We present a simple work-around with which to overcome these problems. If an interferometer is available for quantitative wave-front analysis on the production line, the point-spread function may quite easily be computed from an interferogram of the wave front in the back focal plane of a micro-objective. We describe the achievement and application of such a simulated star test in various spectral regions, together with some of its useful applications, including real-time wave-front manipulation.

© 2003 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. W. T. Welford, “Star tests,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978), Chap. 11, pp. 251–379.
  2. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), Chap. IX, pp. 459–490.
  3. H. R. Suiter, Star Testing Astronomical Telescopes: A Manual for Optical Evaluation and Adjustment (Willman-Bell, Richmond, Va., 1994).
  4. J. J. Stamnes, Waves in Focal Regions, Propagation, Diffraction and Focusing of Light, Sound and Water Waves (Adam Hilger, Bristol, UK, 1986).
  5. J. Wesner, J. Heil, Th. Sure, “Reconstructing the pupil function of microscope objectives from the intensity PSF,” in Current Developments in Lens Design and Optical Engineering III, R. E. Fischer, W. J. Smith, R. B. Johnson, eds., Proc. SPIE4767, 32–43 (2002).
    [CrossRef]
  6. DUV camera: Proxicam HR 0, Proxitronic, Bensheim, Germany.
  7. Flow Cytometric Standards Corporation, San Juan, PR 00919-4344 (fcsc@caribe.net).
  8. Molecular Probes, Inc., Eugene, Ore. 97492-9165 (order@probes.com).
  9. Structure Probe, Inc., West Chester, Pa. 19381-0656 (spi3spi@2spi.com).
  10. Benchmark Technologies, Inc., Lynnfield, Mass. 01950 (info@benchmarktech.com).
  11. M. Françon, Optical Interferometry (Academic, New York, 1966), Chap. XI, pp. 201–210.
  12. P. Hariharan, “Multiple pass interferometry,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978), Chap. 7, pp. 218–230.
  13. Visible light lasers: He-Ne-laser Model 1653 (543 nm) and Ar-ion laser Model 210 (488 nm), JDS Uniphase Corporation, San Jose, Calif.
  14. Infrared laser: PPM10(1310-35)F2 diode laser (1310 nm), Power Technology, Inc., Little Rock, Ark. 72219.
  15. DUV laser: NU-00212-110 (266 nm), Nanolase, Meylan, France.
  16. Visible light camera: PCO-VC44/VC45-CCD-camera, PCO Computer Optics GmbH, Kelheim, Germany.
  17. Infrared camera: Micronviewer Model 7290, Electrophysics Corporation, Fairfield, N.J. 07004-2442.
  18. G. Schulz, J. Schwider, “Interferometric testing of smooth surfaces,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1976), Vol. XIII, pp. 93–167.
    [CrossRef]
  19. N. G. A. Taylor, “Spherical aberration in the Fizeau interferometer,” J. Sci. Instrum. 34, 399–402 (1957).
    [CrossRef]
  20. T. S. Kolomiitsova, N. V. Konstantinovskaya, N. A. Goiko, “Abnormal interference pattern in the testing of spherical surfaces,” Sov. J. Opt. Technol. 57, 727–729 (1990).
  21. Comité Consultatif International de la Radiodiffusion. CCIR video standard: 625 lines/frame, 25 frames/s, 1:2 interlace (for details see, for example, http://www.mtxindia.com/An1.htm) .
  22. Cortex CX-100 frame grabber: Stemmer PC-Systeme GmbH, Puchheim, Germany.
  23. ASUS TX97-E motherboard equipped with a 233-MHz Pentium MMX CPU: ASUS Computer International, Newark, Calif. 94560.
  24. Matrox Electronic Systems, Ltd., Dorval, Quebec H9P 2T4, Canada.
  25. E. O. Brigham, The Fast Fourier Transform (Prentice-Hall, Englewood Cliffs, N.J., 1974).
  26. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C (Cambridge U. Press, Cambridge, 1992).
  27. FFTW algorithm; see, for example, http://www.fftw.org/ . FFTW (acronym for fastest Fourier transform in the West) is a C subroutine library for computing the discrete Fourier transform in one or more dimensions.
  28. J. W. Goodman, Introduction to Fourier Optics McGraw-Hill, (New York, 1998), Chap. 2, pp. 4–29.
  29. C. J. R. Sheppard, P. Török, “Dependence of Fresnel number on aperture stop position,” J. Opt. Soc. Am. A 15, 3016–3019 (1989).
    [CrossRef]
  30. A. H. Nuttall, “On the quadrature approximation to the Hilbert-transform of modulated signals,” Proc. IEEE 54, 1458–1459 (1966).
    [CrossRef]
  31. A. W. Rihaczek, “Hilbert-transforms and the complex representation of real signals,” Proc. IEEE 54, 434–435 (1966).
    [CrossRef]
  32. R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965).
  33. M. Kujawinska, “Spatial phase measurement methods,” in Interferogram Analysis, Digital Fringe Pattern Measurement Techniques, D. W. Robinson, G. T. Reid, eds. (Institute of Physics, Bristol, UK, 1993), pp. 141–193, and references therein.
  34. T. Dresel, N. Lindlein, J. Schwider, “Empirical strategy for detection and removal of misalignment aberrations in interferometry,” Optik (Jena) 112, 304–308 (2001).
    [CrossRef]
  35. C. Roddier, “Interferogram analysis using Fourier transform techniques,” Appl. Opt. 25, 1668–1673 (1987).
    [CrossRef]
  36. M. Kujawinska, J. Wojciak, “High accuracy Fourier transform fringe pattern analysis,” Opt. Lasers Eng. 14, 325–339 (1991).
    [CrossRef]
  37. J. Koslowski, G. Serra, “Analysis of the complex phase error introduced by the application of the Fourier transform method,” J. Mod. Opt. 46, 957–971 (1999).
  38. J. Yanez-Mendiola, M. Servin, D. Malacara-Hernandez, “Reduction of the edge effects induced by the boundary of a linear-carrier interferogram,” J. Mod. Opt. 48, 685–693 (2001).
    [CrossRef]
  39. J. H. Massig, J. Heppner, “Fringe pattern analysis with high accuracy by use of the Fourier transform method,” Appl. Opt. 40, 2081–2088 (2001).
    [CrossRef]
  40. R. J. Hanisch, R. L. White, eds., The Restoration of HST Images and Spectra II, proceedings of a workshop held at the Space Telescope Science Institute, Baltimore, Md., 18–19November1993, and references therein.
  41. J. Krist, R. Hook, The Tiny Tim User’s Guide, October1997, http://scivax.stsci.edu/∼krist/tinytim.html .
  42. P. J. Shaw, D. J. Rawlins, “The point spread function of a confocal microscope: its measurement and use in deconvolution of 3D data,” J. Microsc. 163, 151–165 (1991).
    [CrossRef]
  43. J. A. Conchello, E. W. Hansen, “Enhanced 3D reconstruction from confocal scanning microscope images. 1. Deterministic and maximum likelihood reconstructions,” Appl. Opt. 29, 3795–3804 (1990).
    [CrossRef] [PubMed]
  44. J. A. Conchello, J. J. Kim, E. W. Hansen, “Enhanced three-dimensional reconstruction from confocal scanning microscope images. II. Depth discrimination versus signal-to-noise ratio in partially confocal images,” Appl. Opt. 33, 3740–3750 (1994).
    [CrossRef] [PubMed]
  45. J. A. Conchello, Computational Optical Sectioning Microscopy (Deconvolution), http://rayleigh.wustl.edu/∼josec/tutorials .
  46. T. J. Holmes, “Maximum-likelihood image reconstruction adapted for noncoherent optical imaging,” J. Opt. Soc. Am. A 5, 666–673 (1988).
    [CrossRef]

2001 (3)

T. Dresel, N. Lindlein, J. Schwider, “Empirical strategy for detection and removal of misalignment aberrations in interferometry,” Optik (Jena) 112, 304–308 (2001).
[CrossRef]

J. Yanez-Mendiola, M. Servin, D. Malacara-Hernandez, “Reduction of the edge effects induced by the boundary of a linear-carrier interferogram,” J. Mod. Opt. 48, 685–693 (2001).
[CrossRef]

J. H. Massig, J. Heppner, “Fringe pattern analysis with high accuracy by use of the Fourier transform method,” Appl. Opt. 40, 2081–2088 (2001).
[CrossRef]

1999 (1)

J. Koslowski, G. Serra, “Analysis of the complex phase error introduced by the application of the Fourier transform method,” J. Mod. Opt. 46, 957–971 (1999).

1994 (1)

1991 (2)

P. J. Shaw, D. J. Rawlins, “The point spread function of a confocal microscope: its measurement and use in deconvolution of 3D data,” J. Microsc. 163, 151–165 (1991).
[CrossRef]

M. Kujawinska, J. Wojciak, “High accuracy Fourier transform fringe pattern analysis,” Opt. Lasers Eng. 14, 325–339 (1991).
[CrossRef]

1990 (2)

T. S. Kolomiitsova, N. V. Konstantinovskaya, N. A. Goiko, “Abnormal interference pattern in the testing of spherical surfaces,” Sov. J. Opt. Technol. 57, 727–729 (1990).

J. A. Conchello, E. W. Hansen, “Enhanced 3D reconstruction from confocal scanning microscope images. 1. Deterministic and maximum likelihood reconstructions,” Appl. Opt. 29, 3795–3804 (1990).
[CrossRef] [PubMed]

1989 (1)

1988 (1)

1987 (1)

C. Roddier, “Interferogram analysis using Fourier transform techniques,” Appl. Opt. 25, 1668–1673 (1987).
[CrossRef]

1966 (2)

A. H. Nuttall, “On the quadrature approximation to the Hilbert-transform of modulated signals,” Proc. IEEE 54, 1458–1459 (1966).
[CrossRef]

A. W. Rihaczek, “Hilbert-transforms and the complex representation of real signals,” Proc. IEEE 54, 434–435 (1966).
[CrossRef]

1957 (1)

N. G. A. Taylor, “Spherical aberration in the Fizeau interferometer,” J. Sci. Instrum. 34, 399–402 (1957).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), Chap. IX, pp. 459–490.

Bracewell, R.

R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965).

Brigham, E. O.

E. O. Brigham, The Fast Fourier Transform (Prentice-Hall, Englewood Cliffs, N.J., 1974).

Conchello, J. A.

Dresel, T.

T. Dresel, N. Lindlein, J. Schwider, “Empirical strategy for detection and removal of misalignment aberrations in interferometry,” Optik (Jena) 112, 304–308 (2001).
[CrossRef]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C (Cambridge U. Press, Cambridge, 1992).

Françon, M.

M. Françon, Optical Interferometry (Academic, New York, 1966), Chap. XI, pp. 201–210.

Goiko, N. A.

T. S. Kolomiitsova, N. V. Konstantinovskaya, N. A. Goiko, “Abnormal interference pattern in the testing of spherical surfaces,” Sov. J. Opt. Technol. 57, 727–729 (1990).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics McGraw-Hill, (New York, 1998), Chap. 2, pp. 4–29.

Hansen, E. W.

Hariharan, P.

P. Hariharan, “Multiple pass interferometry,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978), Chap. 7, pp. 218–230.

Heil, J.

J. Wesner, J. Heil, Th. Sure, “Reconstructing the pupil function of microscope objectives from the intensity PSF,” in Current Developments in Lens Design and Optical Engineering III, R. E. Fischer, W. J. Smith, R. B. Johnson, eds., Proc. SPIE4767, 32–43 (2002).
[CrossRef]

Heppner, J.

Holmes, T. J.

Kim, J. J.

Kolomiitsova, T. S.

T. S. Kolomiitsova, N. V. Konstantinovskaya, N. A. Goiko, “Abnormal interference pattern in the testing of spherical surfaces,” Sov. J. Opt. Technol. 57, 727–729 (1990).

Konstantinovskaya, N. V.

T. S. Kolomiitsova, N. V. Konstantinovskaya, N. A. Goiko, “Abnormal interference pattern in the testing of spherical surfaces,” Sov. J. Opt. Technol. 57, 727–729 (1990).

Koslowski, J.

J. Koslowski, G. Serra, “Analysis of the complex phase error introduced by the application of the Fourier transform method,” J. Mod. Opt. 46, 957–971 (1999).

Kujawinska, M.

M. Kujawinska, J. Wojciak, “High accuracy Fourier transform fringe pattern analysis,” Opt. Lasers Eng. 14, 325–339 (1991).
[CrossRef]

M. Kujawinska, “Spatial phase measurement methods,” in Interferogram Analysis, Digital Fringe Pattern Measurement Techniques, D. W. Robinson, G. T. Reid, eds. (Institute of Physics, Bristol, UK, 1993), pp. 141–193, and references therein.

Lindlein, N.

T. Dresel, N. Lindlein, J. Schwider, “Empirical strategy for detection and removal of misalignment aberrations in interferometry,” Optik (Jena) 112, 304–308 (2001).
[CrossRef]

Malacara-Hernandez, D.

J. Yanez-Mendiola, M. Servin, D. Malacara-Hernandez, “Reduction of the edge effects induced by the boundary of a linear-carrier interferogram,” J. Mod. Opt. 48, 685–693 (2001).
[CrossRef]

Massig, J. H.

Nuttall, A. H.

A. H. Nuttall, “On the quadrature approximation to the Hilbert-transform of modulated signals,” Proc. IEEE 54, 1458–1459 (1966).
[CrossRef]

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C (Cambridge U. Press, Cambridge, 1992).

Rawlins, D. J.

P. J. Shaw, D. J. Rawlins, “The point spread function of a confocal microscope: its measurement and use in deconvolution of 3D data,” J. Microsc. 163, 151–165 (1991).
[CrossRef]

Rihaczek, A. W.

A. W. Rihaczek, “Hilbert-transforms and the complex representation of real signals,” Proc. IEEE 54, 434–435 (1966).
[CrossRef]

Roddier, C.

C. Roddier, “Interferogram analysis using Fourier transform techniques,” Appl. Opt. 25, 1668–1673 (1987).
[CrossRef]

Schulz, G.

G. Schulz, J. Schwider, “Interferometric testing of smooth surfaces,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1976), Vol. XIII, pp. 93–167.
[CrossRef]

Schwider, J.

T. Dresel, N. Lindlein, J. Schwider, “Empirical strategy for detection and removal of misalignment aberrations in interferometry,” Optik (Jena) 112, 304–308 (2001).
[CrossRef]

G. Schulz, J. Schwider, “Interferometric testing of smooth surfaces,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1976), Vol. XIII, pp. 93–167.
[CrossRef]

Serra, G.

J. Koslowski, G. Serra, “Analysis of the complex phase error introduced by the application of the Fourier transform method,” J. Mod. Opt. 46, 957–971 (1999).

Servin, M.

J. Yanez-Mendiola, M. Servin, D. Malacara-Hernandez, “Reduction of the edge effects induced by the boundary of a linear-carrier interferogram,” J. Mod. Opt. 48, 685–693 (2001).
[CrossRef]

Shaw, P. J.

P. J. Shaw, D. J. Rawlins, “The point spread function of a confocal microscope: its measurement and use in deconvolution of 3D data,” J. Microsc. 163, 151–165 (1991).
[CrossRef]

Sheppard, C. J. R.

Stamnes, J. J.

J. J. Stamnes, Waves in Focal Regions, Propagation, Diffraction and Focusing of Light, Sound and Water Waves (Adam Hilger, Bristol, UK, 1986).

Suiter, H. R.

H. R. Suiter, Star Testing Astronomical Telescopes: A Manual for Optical Evaluation and Adjustment (Willman-Bell, Richmond, Va., 1994).

Sure, Th.

J. Wesner, J. Heil, Th. Sure, “Reconstructing the pupil function of microscope objectives from the intensity PSF,” in Current Developments in Lens Design and Optical Engineering III, R. E. Fischer, W. J. Smith, R. B. Johnson, eds., Proc. SPIE4767, 32–43 (2002).
[CrossRef]

Taylor, N. G. A.

N. G. A. Taylor, “Spherical aberration in the Fizeau interferometer,” J. Sci. Instrum. 34, 399–402 (1957).
[CrossRef]

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C (Cambridge U. Press, Cambridge, 1992).

Török, P.

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C (Cambridge U. Press, Cambridge, 1992).

Welford, W. T.

W. T. Welford, “Star tests,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978), Chap. 11, pp. 251–379.

Wesner, J.

J. Wesner, J. Heil, Th. Sure, “Reconstructing the pupil function of microscope objectives from the intensity PSF,” in Current Developments in Lens Design and Optical Engineering III, R. E. Fischer, W. J. Smith, R. B. Johnson, eds., Proc. SPIE4767, 32–43 (2002).
[CrossRef]

Wojciak, J.

M. Kujawinska, J. Wojciak, “High accuracy Fourier transform fringe pattern analysis,” Opt. Lasers Eng. 14, 325–339 (1991).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), Chap. IX, pp. 459–490.

Yanez-Mendiola, J.

J. Yanez-Mendiola, M. Servin, D. Malacara-Hernandez, “Reduction of the edge effects induced by the boundary of a linear-carrier interferogram,” J. Mod. Opt. 48, 685–693 (2001).
[CrossRef]

Appl. Opt. (4)

J. Microsc. (1)

P. J. Shaw, D. J. Rawlins, “The point spread function of a confocal microscope: its measurement and use in deconvolution of 3D data,” J. Microsc. 163, 151–165 (1991).
[CrossRef]

J. Mod. Opt. (2)

J. Koslowski, G. Serra, “Analysis of the complex phase error introduced by the application of the Fourier transform method,” J. Mod. Opt. 46, 957–971 (1999).

J. Yanez-Mendiola, M. Servin, D. Malacara-Hernandez, “Reduction of the edge effects induced by the boundary of a linear-carrier interferogram,” J. Mod. Opt. 48, 685–693 (2001).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Sci. Instrum. (1)

N. G. A. Taylor, “Spherical aberration in the Fizeau interferometer,” J. Sci. Instrum. 34, 399–402 (1957).
[CrossRef]

Opt. Lasers Eng. (1)

M. Kujawinska, J. Wojciak, “High accuracy Fourier transform fringe pattern analysis,” Opt. Lasers Eng. 14, 325–339 (1991).
[CrossRef]

Optik (Jena) (1)

T. Dresel, N. Lindlein, J. Schwider, “Empirical strategy for detection and removal of misalignment aberrations in interferometry,” Optik (Jena) 112, 304–308 (2001).
[CrossRef]

Proc. IEEE (2)

A. H. Nuttall, “On the quadrature approximation to the Hilbert-transform of modulated signals,” Proc. IEEE 54, 1458–1459 (1966).
[CrossRef]

A. W. Rihaczek, “Hilbert-transforms and the complex representation of real signals,” Proc. IEEE 54, 434–435 (1966).
[CrossRef]

Sov. J. Opt. Technol. (1)

T. S. Kolomiitsova, N. V. Konstantinovskaya, N. A. Goiko, “Abnormal interference pattern in the testing of spherical surfaces,” Sov. J. Opt. Technol. 57, 727–729 (1990).

Other (31)

Comité Consultatif International de la Radiodiffusion. CCIR video standard: 625 lines/frame, 25 frames/s, 1:2 interlace (for details see, for example, http://www.mtxindia.com/An1.htm) .

Cortex CX-100 frame grabber: Stemmer PC-Systeme GmbH, Puchheim, Germany.

ASUS TX97-E motherboard equipped with a 233-MHz Pentium MMX CPU: ASUS Computer International, Newark, Calif. 94560.

Matrox Electronic Systems, Ltd., Dorval, Quebec H9P 2T4, Canada.

E. O. Brigham, The Fast Fourier Transform (Prentice-Hall, Englewood Cliffs, N.J., 1974).

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C (Cambridge U. Press, Cambridge, 1992).

FFTW algorithm; see, for example, http://www.fftw.org/ . FFTW (acronym for fastest Fourier transform in the West) is a C subroutine library for computing the discrete Fourier transform in one or more dimensions.

J. W. Goodman, Introduction to Fourier Optics McGraw-Hill, (New York, 1998), Chap. 2, pp. 4–29.

R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965).

M. Kujawinska, “Spatial phase measurement methods,” in Interferogram Analysis, Digital Fringe Pattern Measurement Techniques, D. W. Robinson, G. T. Reid, eds. (Institute of Physics, Bristol, UK, 1993), pp. 141–193, and references therein.

W. T. Welford, “Star tests,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978), Chap. 11, pp. 251–379.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), Chap. IX, pp. 459–490.

H. R. Suiter, Star Testing Astronomical Telescopes: A Manual for Optical Evaluation and Adjustment (Willman-Bell, Richmond, Va., 1994).

J. J. Stamnes, Waves in Focal Regions, Propagation, Diffraction and Focusing of Light, Sound and Water Waves (Adam Hilger, Bristol, UK, 1986).

J. Wesner, J. Heil, Th. Sure, “Reconstructing the pupil function of microscope objectives from the intensity PSF,” in Current Developments in Lens Design and Optical Engineering III, R. E. Fischer, W. J. Smith, R. B. Johnson, eds., Proc. SPIE4767, 32–43 (2002).
[CrossRef]

DUV camera: Proxicam HR 0, Proxitronic, Bensheim, Germany.

Flow Cytometric Standards Corporation, San Juan, PR 00919-4344 (fcsc@caribe.net).

Molecular Probes, Inc., Eugene, Ore. 97492-9165 (order@probes.com).

Structure Probe, Inc., West Chester, Pa. 19381-0656 (spi3spi@2spi.com).

Benchmark Technologies, Inc., Lynnfield, Mass. 01950 (info@benchmarktech.com).

M. Françon, Optical Interferometry (Academic, New York, 1966), Chap. XI, pp. 201–210.

P. Hariharan, “Multiple pass interferometry,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978), Chap. 7, pp. 218–230.

Visible light lasers: He-Ne-laser Model 1653 (543 nm) and Ar-ion laser Model 210 (488 nm), JDS Uniphase Corporation, San Jose, Calif.

Infrared laser: PPM10(1310-35)F2 diode laser (1310 nm), Power Technology, Inc., Little Rock, Ark. 72219.

DUV laser: NU-00212-110 (266 nm), Nanolase, Meylan, France.

Visible light camera: PCO-VC44/VC45-CCD-camera, PCO Computer Optics GmbH, Kelheim, Germany.

Infrared camera: Micronviewer Model 7290, Electrophysics Corporation, Fairfield, N.J. 07004-2442.

G. Schulz, J. Schwider, “Interferometric testing of smooth surfaces,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1976), Vol. XIII, pp. 93–167.
[CrossRef]

R. J. Hanisch, R. L. White, eds., The Restoration of HST Images and Spectra II, proceedings of a workshop held at the Space Telescope Science Institute, Baltimore, Md., 18–19November1993, and references therein.

J. Krist, R. Hook, The Tiny Tim User’s Guide, October1997, http://scivax.stsci.edu/∼krist/tinytim.html .

J. A. Conchello, Computational Optical Sectioning Microscopy (Deconvolution), http://rayleigh.wustl.edu/∼josec/tutorials .

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (12)

Fig. 1
Fig. 1

Schematic sketch of the Twyman-Green interferometer: 1, single-mode fiber; 2, point source; 3, achromatic collimating lens; 4, beam splitter; 5, reference mirror (one may tilt the reference wave by adjusting θ and adjust the optical path length of the reference arm by shifting the mirror along the z′ axis); 6, micro-objective with focal length f and pupil radius r p ; 7, spherical autocollimating mirror with radius R (field position y, and defocus z may be adjusted); 8, 9, system for imaging the pupil onto the CCD chip; 10, CCD camera; 11, thermal light source; 12, 14, collimating lenses; 13, interference filter; 15, pinhole; 16, glass flat for dispersion balancing of the two interferometer arms.

Fig. 2
Fig. 2

(a) Interferogram of the wave front in the pupil of an N-PLAN 40×/0.65 ∞/0.17/D objective at λ = 543 nm used with a cover slide of 170-μm thickness inserted between the front lens and the return sphere of the Twyman-Green interferometer. A substantial tilt of 10λ is introduced into the reference wave to get 20 fringes in the interferogram. (b) Fourier amplitude of (a). The amplitude is shown gray coded, and the zero-bias peak (labeled DC) is suppressed because it otherwise would dominate the image completely. The two PSFs (labeled ±1) are centered at ±carrier frequency. Pupil coordinates x, y and spectral coordinates k x , k y as well as carrier wave vector k r are indicated.

Fig. 3
Fig. 3

(a) Interferogram (intensity hologram) of the wave front in the pupil of a PL-Fluotar 50×/0.85 P/∞/0 objective at λ = 543 nm. The pronounced primary coma was introduced intentionally for this demonstration. (b) Reconstruction of the PSF obtained from the interferogram by imaging of the Fraunhofer diffraction pattern of (a) copied onto a transparency of 24 mm × 36 mm; see text for details. The zero-bias peak (labeled DC) and the diffraction maxima of different orders (labeled ±1, ±2) are clearly visible. The ±2 PSFs emerge as a result of the nonlinear graduation curve of the Xerox copy that we used to obtain the transparency.

Fig. 6
Fig. 6

Interferograms (a), (c), (e), (g), and (i) and the corresponding Fourier spectra (b), (d), (f), (h), and (j) of a PL-Fluotar 50×/0.85P/∞/0 objective with a peak-to-valley (PV) primary on-axis coma wave-front error of ≈1 fringe at λ = 543 nm for several orientations of the fringe pattern. The objective, into which coma was introduced intentionally to facilitate recording of this series, is the same as for Fig. 3. Note the similarity of (b) and Fig. 3(b). The PSFs move in frequency space according to the orientation of the tilt while they maintain their appearance.

Fig. 4
Fig. 4

(a), (c), (e) Interferograms and (b), (d), (f) the corresponding Fourier spectra of the wave front in the pupil of a PL-Fluotar 40×/0.70∞/0.17/D objective at λ = 543 nm used with a cover slide of thickness d = 170 μm. Note that fringe orientation and spacing are the same for each figure. Note also that the PSFs are similar in (b), (d), and (f) and differ only in size, while they occupy the same position in frequency space.

Fig. 5
Fig. 5

Interferograms (a), (c), (e), (g), and (i) and the corresponding Fourier spectra (b), (d), (f), (h), and (j) of a PL-APO 50×/0.90 U-V-I∞/0 objective at λ = 488 nm for different amounts of reference wave-front tilt. Note that the PSFs shift in frequency space while they maintain their appearance.

Fig. 7
Fig. 7

Interferograms (a), (c), (e), (g), and (i) and corresponding Fourier spectra (b), (d), (f), (h), and (j) of a PL-APO 50×/0.90 U-V-I ∞/0 objective at λ = 488 nm for a defocus ranging from ≈-1 fringe PV in (a) and (b) to ≈+1.3 fringes PV in (i) and (j). These values correspond to a defocus in the object space ranging from z ≈ -480 nm in (a) and (b) to z ≈ +530 nm in (i) and (j). The residual PV wave-front errors after the removal of defocus are ≈0.2 fringe of spherical wave-front error, ≈0.2 fringe of astigmatism, and ≈0.15 fringe of coma; the corresponding in-focus situation occurs approximately in the interferogram shown in (e). Only a magnified portion near +1 PSF is shown in the Fourier amplitude images.

Fig. 8
Fig. 8

Interferograms (a), (c), (e), (g), and (i) and the corresponding Fourier spectra (b), (d), (f), (h), and (j) of a PL-APO 50×/0.90 U-V-I ∞/0 objective at λ = 488 nm used with a cover slide of thickness d = 170 μm to introduce the pronounced spherical PV wave-front error of ≈1.3 fringes intentionally for this demonstration. The defocus ranges from ≈-1.7 fringes PV (corresponding to z ≈ -750 nm in the object space), where the PSF displays the circle of least confusion in (a) and (b), to ≈+2.6 fringes PV (corresponding to z ≈ +650 nm in object space), where the PSF displays the Gaussian focus in (i) and (j). The objective used here is the same as that used for the measurements shown in Fig. 7. In the Fourier amplitude images, only a magnified portion near +1 PSF is shown.

Fig. 9
Fig. 9

Interferograms (a), (c), (e), (g), and (i) and the corresponding Fourier spectra (b), (d), (f), (h), and (j) of a PL-Fluotar 50×/0.85P/∞/0 objective at λ = 543 nm. The defocus ranges from ≈-2.3 fringes in (a) and (b) (corresponding to z ≈ -1.3 μm in the object space) to ≈+1.7 fringes in (i) and (j) (corresponding to z ≈ +470 nm in the object space). The objective used here, into which we introduced the on-axis coma by intentionally driving the shifting element far off the axis, is the same as that used for the measurements shown in Figs. 3 and 6. In the Fourier amplitude images, only a magnified portion near the +1 PSF is shown.

Fig. 10
Fig. 10

Interferograms (a), (c), (e), (g), and (i) and the corresponding Fourier spectra (b), (d), (f), (h), and (j) of a 150×/0.90 DUV ∞/0 objective at λ = 266 nm. The images were recorded while the shifting element of the objective was moved along the direction indicated by the tail of the PSF until the initially present primary coma of ≈2 fringes PV was completely eliminated as shown in (j). Some remaining trefoil wave-front error is still present in (j). The granular background in the PSF images results from the speckles that are present in the interferograms.

Fig. 11
Fig. 11

Interferograms (a), (c), (e), (g), and (i) and the corresponding Fourier spectra (b), (d), (f), (h), and (j) of a 63×/0.70 1300 nm ∞/0 objective at λ = 1310 nm for a defocus ranging in equal steps from -4 μm in (a) and (b) to +4 μm in (i) and (j). The images show some residual astigmatic aberration as well as a small spherical wave-front error.

Fig. 12
Fig. 12

Real-time wave-front correction: (a) interferogram of a 40×/0.85 HCX PL APO CORR CS ∞/170 objective used with a 170-μm cover slide without immersion at λ = 543 nm, (b) the corresponding PSF. Some spherical wave-front error has been intentionally introduced for this demonstration. (c), (d) real and imaginary parts, respectively, of the reconstructed wave front with the original tilt, which has been removed in (e) and (f). In (g) and (h) the spherical aberration has been removed from the wave front. (i) Corrected interferogram and (j) the corresponding PSF, where the coma wave-front error, which is nearly completely hidden in (a) and (b) is now clearly exposed.

Equations (6)

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

Aobjx, y= Aobj,0x, yexpiϕobj,0x, y,
Arefx, y= Arx, yexpiϕrx, y,
Ix, y=| Aox, y|2+| Ar|2+2Aox, y Ar cosϕox, y-ϕrx, y,
Ix, y=Ir+ Iox, y+ Aox, yAr exp+iϕox, y+kr,xx+kr,yy+Aox, yAr exp-iϕox, y+kr,xx+kr,yy.
Aox, y= HAox, y= F-1-isignkxFAox, y,
Aox, y=Aox, y+iAox, y=F-12 stepkxFIhpx, y,

Metrics