Abstract

We performed a direct side-by-side comparison of a Shack–Hartmann wave-front sensor and a phase-shifting interferometer for the purpose of characterizing large optics. An expansion telescope of our own design allowed us to measure the surface figure of a 400-mm-square mirror with both instruments simultaneously. The Shack–Hartmann sensor produced data that closely matched the interferometer data over spatial scales appropriate for the lenslet spacing, and much of the <20-nm rms systematic difference between the two measurements was due to diffraction artifacts that were present in the interferometer data but not in the Shack–Hartmann sensor data. The results suggest that Shack–Hartmann sensors could replace phase-shifting interferometers for many applications, with particular advantages for large-optic metrology.

© 2000 Optical Society of America

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  1. B. M. Van Wonterghem, J. R. Murray, J. H. Campbell, D. R. Speck, C. E. Barker, I. C. Smith, D. F. Browning, W. C. Behrendt, “Performance of a prototype for a large-aperture multipass Nd:glass laser for inertial confinement fusion,” Appl. Opt. 36, 4932–4953 (1997).
    [CrossRef] [PubMed]
  2. See, for example, D. Malacara, Optical Shop Testing, 2nd. ed. (Wiley, New York, 1992) and numerous references therein.
  3. C. Koliopolis, “Simultaneous phase shift interferometer,” in Advanced Optical Manufacturing and Testing II, V. J. Doherty, ed., Proc. SPIE1531, 119–127 (1991).
    [CrossRef]
  4. R. Zacharias, E. Bliss, M. Feldman, A. Grey, M. Henesian, J. Koch, J. Lawson, R. Sacks, T. Salmon, J. Toeppen, L. Van Atta, S. Winters, B. Woods, C. LaFiandra, D. Bruns, “The National Ignition Facility (NIF) wavefront control system,” in Third International Conference on Solid State Lasers for Application to Inertial Confinement Fusion, W. H. Lowdermilk, ed., Proc. SPIE3492, 678–692 (1998).
    [CrossRef]
  5. B. M. Welsh, B. L. Ellerbroek, M. C. Roggemann, T. L. Pennington, “Fundamental performance comparison of a Hartmann and a shearing interferometer wave-front sensor,” Appl. Opt. 34, 4186–4195 (1995).
    [CrossRef] [PubMed]
  6. MiniFiz PMOD-100 HR, from Phase Shift Technology, 3480 E. Britannia Drive, Tucson, Ariz. 85706.
  7. Wavefront Sciences, 14810 Central Ave. SE, Albuquerque, N. Mex. 87123.
  8. See, for example, W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd. ed. (Cambridge University, Cambridge, England, 1994).
  9. D. R. Neal, W. J. Alford, J. K. Gruetzner, M. E. Warren, “Amplitude and phase beam characterization using a two-dimensional wavefront sensor,” in Third International Workshop on Laser Beam and Optics Characterization, A. Giesen, M. Morin, eds., Proc. SPIE2870, 72–82 (1996).
    [CrossRef]

1997

1995

Alford, W. J.

D. R. Neal, W. J. Alford, J. K. Gruetzner, M. E. Warren, “Amplitude and phase beam characterization using a two-dimensional wavefront sensor,” in Third International Workshop on Laser Beam and Optics Characterization, A. Giesen, M. Morin, eds., Proc. SPIE2870, 72–82 (1996).
[CrossRef]

Barker, C. E.

Behrendt, W. C.

Bliss, E.

R. Zacharias, E. Bliss, M. Feldman, A. Grey, M. Henesian, J. Koch, J. Lawson, R. Sacks, T. Salmon, J. Toeppen, L. Van Atta, S. Winters, B. Woods, C. LaFiandra, D. Bruns, “The National Ignition Facility (NIF) wavefront control system,” in Third International Conference on Solid State Lasers for Application to Inertial Confinement Fusion, W. H. Lowdermilk, ed., Proc. SPIE3492, 678–692 (1998).
[CrossRef]

Browning, D. F.

Bruns, D.

R. Zacharias, E. Bliss, M. Feldman, A. Grey, M. Henesian, J. Koch, J. Lawson, R. Sacks, T. Salmon, J. Toeppen, L. Van Atta, S. Winters, B. Woods, C. LaFiandra, D. Bruns, “The National Ignition Facility (NIF) wavefront control system,” in Third International Conference on Solid State Lasers for Application to Inertial Confinement Fusion, W. H. Lowdermilk, ed., Proc. SPIE3492, 678–692 (1998).
[CrossRef]

Campbell, J. H.

Ellerbroek, B. L.

Feldman, M.

R. Zacharias, E. Bliss, M. Feldman, A. Grey, M. Henesian, J. Koch, J. Lawson, R. Sacks, T. Salmon, J. Toeppen, L. Van Atta, S. Winters, B. Woods, C. LaFiandra, D. Bruns, “The National Ignition Facility (NIF) wavefront control system,” in Third International Conference on Solid State Lasers for Application to Inertial Confinement Fusion, W. H. Lowdermilk, ed., Proc. SPIE3492, 678–692 (1998).
[CrossRef]

Flannery, B. P.

See, for example, W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd. ed. (Cambridge University, Cambridge, England, 1994).

Grey, A.

R. Zacharias, E. Bliss, M. Feldman, A. Grey, M. Henesian, J. Koch, J. Lawson, R. Sacks, T. Salmon, J. Toeppen, L. Van Atta, S. Winters, B. Woods, C. LaFiandra, D. Bruns, “The National Ignition Facility (NIF) wavefront control system,” in Third International Conference on Solid State Lasers for Application to Inertial Confinement Fusion, W. H. Lowdermilk, ed., Proc. SPIE3492, 678–692 (1998).
[CrossRef]

Gruetzner, J. K.

D. R. Neal, W. J. Alford, J. K. Gruetzner, M. E. Warren, “Amplitude and phase beam characterization using a two-dimensional wavefront sensor,” in Third International Workshop on Laser Beam and Optics Characterization, A. Giesen, M. Morin, eds., Proc. SPIE2870, 72–82 (1996).
[CrossRef]

Henesian, M.

R. Zacharias, E. Bliss, M. Feldman, A. Grey, M. Henesian, J. Koch, J. Lawson, R. Sacks, T. Salmon, J. Toeppen, L. Van Atta, S. Winters, B. Woods, C. LaFiandra, D. Bruns, “The National Ignition Facility (NIF) wavefront control system,” in Third International Conference on Solid State Lasers for Application to Inertial Confinement Fusion, W. H. Lowdermilk, ed., Proc. SPIE3492, 678–692 (1998).
[CrossRef]

Koch, J.

R. Zacharias, E. Bliss, M. Feldman, A. Grey, M. Henesian, J. Koch, J. Lawson, R. Sacks, T. Salmon, J. Toeppen, L. Van Atta, S. Winters, B. Woods, C. LaFiandra, D. Bruns, “The National Ignition Facility (NIF) wavefront control system,” in Third International Conference on Solid State Lasers for Application to Inertial Confinement Fusion, W. H. Lowdermilk, ed., Proc. SPIE3492, 678–692 (1998).
[CrossRef]

Koliopolis, C.

C. Koliopolis, “Simultaneous phase shift interferometer,” in Advanced Optical Manufacturing and Testing II, V. J. Doherty, ed., Proc. SPIE1531, 119–127 (1991).
[CrossRef]

LaFiandra, C.

R. Zacharias, E. Bliss, M. Feldman, A. Grey, M. Henesian, J. Koch, J. Lawson, R. Sacks, T. Salmon, J. Toeppen, L. Van Atta, S. Winters, B. Woods, C. LaFiandra, D. Bruns, “The National Ignition Facility (NIF) wavefront control system,” in Third International Conference on Solid State Lasers for Application to Inertial Confinement Fusion, W. H. Lowdermilk, ed., Proc. SPIE3492, 678–692 (1998).
[CrossRef]

Lawson, J.

R. Zacharias, E. Bliss, M. Feldman, A. Grey, M. Henesian, J. Koch, J. Lawson, R. Sacks, T. Salmon, J. Toeppen, L. Van Atta, S. Winters, B. Woods, C. LaFiandra, D. Bruns, “The National Ignition Facility (NIF) wavefront control system,” in Third International Conference on Solid State Lasers for Application to Inertial Confinement Fusion, W. H. Lowdermilk, ed., Proc. SPIE3492, 678–692 (1998).
[CrossRef]

Malacara, D.

See, for example, D. Malacara, Optical Shop Testing, 2nd. ed. (Wiley, New York, 1992) and numerous references therein.

Murray, J. R.

Neal, D. R.

D. R. Neal, W. J. Alford, J. K. Gruetzner, M. E. Warren, “Amplitude and phase beam characterization using a two-dimensional wavefront sensor,” in Third International Workshop on Laser Beam and Optics Characterization, A. Giesen, M. Morin, eds., Proc. SPIE2870, 72–82 (1996).
[CrossRef]

Pennington, T. L.

Press, W. H.

See, for example, W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd. ed. (Cambridge University, Cambridge, England, 1994).

Roggemann, M. C.

Sacks, R.

R. Zacharias, E. Bliss, M. Feldman, A. Grey, M. Henesian, J. Koch, J. Lawson, R. Sacks, T. Salmon, J. Toeppen, L. Van Atta, S. Winters, B. Woods, C. LaFiandra, D. Bruns, “The National Ignition Facility (NIF) wavefront control system,” in Third International Conference on Solid State Lasers for Application to Inertial Confinement Fusion, W. H. Lowdermilk, ed., Proc. SPIE3492, 678–692 (1998).
[CrossRef]

Salmon, T.

R. Zacharias, E. Bliss, M. Feldman, A. Grey, M. Henesian, J. Koch, J. Lawson, R. Sacks, T. Salmon, J. Toeppen, L. Van Atta, S. Winters, B. Woods, C. LaFiandra, D. Bruns, “The National Ignition Facility (NIF) wavefront control system,” in Third International Conference on Solid State Lasers for Application to Inertial Confinement Fusion, W. H. Lowdermilk, ed., Proc. SPIE3492, 678–692 (1998).
[CrossRef]

Smith, I. C.

Speck, D. R.

Teukolsky, S. A.

See, for example, W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd. ed. (Cambridge University, Cambridge, England, 1994).

Toeppen, J.

R. Zacharias, E. Bliss, M. Feldman, A. Grey, M. Henesian, J. Koch, J. Lawson, R. Sacks, T. Salmon, J. Toeppen, L. Van Atta, S. Winters, B. Woods, C. LaFiandra, D. Bruns, “The National Ignition Facility (NIF) wavefront control system,” in Third International Conference on Solid State Lasers for Application to Inertial Confinement Fusion, W. H. Lowdermilk, ed., Proc. SPIE3492, 678–692 (1998).
[CrossRef]

Van Atta, L.

R. Zacharias, E. Bliss, M. Feldman, A. Grey, M. Henesian, J. Koch, J. Lawson, R. Sacks, T. Salmon, J. Toeppen, L. Van Atta, S. Winters, B. Woods, C. LaFiandra, D. Bruns, “The National Ignition Facility (NIF) wavefront control system,” in Third International Conference on Solid State Lasers for Application to Inertial Confinement Fusion, W. H. Lowdermilk, ed., Proc. SPIE3492, 678–692 (1998).
[CrossRef]

Van Wonterghem, B. M.

Vetterling, W. T.

See, for example, W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd. ed. (Cambridge University, Cambridge, England, 1994).

Warren, M. E.

D. R. Neal, W. J. Alford, J. K. Gruetzner, M. E. Warren, “Amplitude and phase beam characterization using a two-dimensional wavefront sensor,” in Third International Workshop on Laser Beam and Optics Characterization, A. Giesen, M. Morin, eds., Proc. SPIE2870, 72–82 (1996).
[CrossRef]

Welsh, B. M.

Winters, S.

R. Zacharias, E. Bliss, M. Feldman, A. Grey, M. Henesian, J. Koch, J. Lawson, R. Sacks, T. Salmon, J. Toeppen, L. Van Atta, S. Winters, B. Woods, C. LaFiandra, D. Bruns, “The National Ignition Facility (NIF) wavefront control system,” in Third International Conference on Solid State Lasers for Application to Inertial Confinement Fusion, W. H. Lowdermilk, ed., Proc. SPIE3492, 678–692 (1998).
[CrossRef]

Woods, B.

R. Zacharias, E. Bliss, M. Feldman, A. Grey, M. Henesian, J. Koch, J. Lawson, R. Sacks, T. Salmon, J. Toeppen, L. Van Atta, S. Winters, B. Woods, C. LaFiandra, D. Bruns, “The National Ignition Facility (NIF) wavefront control system,” in Third International Conference on Solid State Lasers for Application to Inertial Confinement Fusion, W. H. Lowdermilk, ed., Proc. SPIE3492, 678–692 (1998).
[CrossRef]

Zacharias, R.

R. Zacharias, E. Bliss, M. Feldman, A. Grey, M. Henesian, J. Koch, J. Lawson, R. Sacks, T. Salmon, J. Toeppen, L. Van Atta, S. Winters, B. Woods, C. LaFiandra, D. Bruns, “The National Ignition Facility (NIF) wavefront control system,” in Third International Conference on Solid State Lasers for Application to Inertial Confinement Fusion, W. H. Lowdermilk, ed., Proc. SPIE3492, 678–692 (1998).
[CrossRef]

Appl. Opt.

Other

MiniFiz PMOD-100 HR, from Phase Shift Technology, 3480 E. Britannia Drive, Tucson, Ariz. 85706.

Wavefront Sciences, 14810 Central Ave. SE, Albuquerque, N. Mex. 87123.

See, for example, W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd. ed. (Cambridge University, Cambridge, England, 1994).

D. R. Neal, W. J. Alford, J. K. Gruetzner, M. E. Warren, “Amplitude and phase beam characterization using a two-dimensional wavefront sensor,” in Third International Workshop on Laser Beam and Optics Characterization, A. Giesen, M. Morin, eds., Proc. SPIE2870, 72–82 (1996).
[CrossRef]

See, for example, D. Malacara, Optical Shop Testing, 2nd. ed. (Wiley, New York, 1992) and numerous references therein.

C. Koliopolis, “Simultaneous phase shift interferometer,” in Advanced Optical Manufacturing and Testing II, V. J. Doherty, ed., Proc. SPIE1531, 119–127 (1991).
[CrossRef]

R. Zacharias, E. Bliss, M. Feldman, A. Grey, M. Henesian, J. Koch, J. Lawson, R. Sacks, T. Salmon, J. Toeppen, L. Van Atta, S. Winters, B. Woods, C. LaFiandra, D. Bruns, “The National Ignition Facility (NIF) wavefront control system,” in Third International Conference on Solid State Lasers for Application to Inertial Confinement Fusion, W. H. Lowdermilk, ed., Proc. SPIE3492, 678–692 (1998).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Table layout of the test facility. The 100-mm (4-in.) beam enters a 6.8× Kepler telescope from the right, which has a folded optical path to reduce space requirements. A test surface is placed on the left side and is relay imaged by the telescope onto the transmission flat of the PSI and onto the lenslet plane of the SH sensor. The rectangular border represents the edges of the granite optical table: L1, L2, L3, L4, lenses; M1, M2, M3, mirrors; BS, beam splitter.

Fig. 2
Fig. 2

(a)–(c) Gray-scale surface difference maps (test surface minus reference-flat surface) and (d)–(f) double-difference maps of the SH sensor and PSI measurement data: (a) SH data (turbulent environment), average of 100 measurements, P–V = 628 nm, rms = 106 nm; (b) SH data (stable environment), average of 50 measurements, P–V = 644 nm, rms = 115 nm; (c) PSI data (stable environment), average of 24 measurements, P–V = 729 nm, rms = 116 nm; (d) SH (turbulent) PSI, P–V = 187 nm, rms = 26.5 nm; (e) SH (stable) PSI, P–V = 244 nm, rms = 29.6 nm; (f) SH (turbulent) SH (stable), P–V = 149 nm, rms = 28.7 nm. The double-difference maps in (d)–(f) were obtained after regridding the data to 512 × 512 arrays and subtracting residual tip/tilt aberrations, and each map covers a 366-mm subaperture of the 400-mm-square mirror surface.

Fig. 3
Fig. 3

Surface map of the residual difference between the SH data from Fig. 2(b) and the PSI data from Fig. 2(c), when the latter is averaged over groups of columns and rows to produce a 48 × 48 pixel map of the central 366-mm subaperture of the mirror surface and subtracted directly from the 48 × 48 pixel SH sensor map of the same region. The dominant systematic error is caused by the diffraction ring pattern that is present in the PSI data but not in the SH sensor data; the spatial rms is 24.9 nm, and the P–V is 150 nm.

Tables (2)

Tables Icon

Table 1 Design Specifications for the Interferometer System Componentsa

Tables Icon

Table 2 Parameter Definitions and Interferometer System Performance in Routine Operating Conditionsa

Equations (12)

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

Sx, y; t=Gx, y+Fx, y; t,
σSx,y;t2=σGx,y2+σFx,y;t2,
σSx,y;t2=1Nx,y Sx, y; t2-1Nx,y Sx, y; t2.
rms accuracy2=σGx,y2,
rms precision2=2σFx,y2¯,
rms repeatability2 14σGx,y2σG(x,y)4¯-σFx,y2¯for σGx,y  σFx,y;t,
σSH1-SH22=σSH12+σSH22,
σSH1-PS2=σSH12+σPS2+Δ2,
σSH2-PS2=σSH22+σPS2+Δ2,
Δ2=σSH1-PS2+σSH2-PS2-σSH1-SH222-σPS2=18 nm2,
σSH12=σSH1-PS2-σPS2-Δ2=18 nm2,
σSH22=σSH2-PS2-σPS2-Δ2=22 nm2.

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