Abstract

The possibility to measure segmented wave-front thanks to lateral shearing interferometry using diffraction grating is presented and analyzed. Aside from the response of such technique, the dynamic range is evaluated and shown to be limited. To greatly extend this one, a new method based on the use of two colors, not necessarily monochromatic, combined with an innovative Fourier treatment, is proposed. The two-color proposed in this paper is a high dynamic and low sensitivity technique; it can be completed by a one-color analysis, with low dynamics and high sensitivity, to reach high precision measurements. The ability of this method to measure Keck-like wave-front is demonstrated thanks to a computational analysis. Finally, a first experimental measurement of an etched substrate by using a quadri-wave lateral shearing interferometer is detailed.

©2006 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Multiple-wave lateral shearing interferometry for wave-front sensing

J.-C. Chanteloup
Appl. Opt. 44(9) 1559-1571 (2005)

Two-dimensional wave-front reconstruction from lateral shearing interferograms

Peiying Liang, Jianping Ding, Zhou Jin, Cheng-Shan Guo, and Hui-tian Wang
Opt. Express 14(2) 625-634 (2006)

Phase measurement of a segmented wave front using PISton and TILt interferometry (PISTIL)

Maxime Deprez, Benoit Wattellier, Cindy Bellanger, Laurent Lombard, and Jérôme Primot
Opt. Express 26(5) 5212-5224 (2018)

References

  • View by:
  • |
  • |
  • |

  1. G. Chanan, M. Troy, F. Dekens, S. Michaels, J. Nelson, T. Mast, and D. Kirkman, “Phasing the Mirror Segments of the Keck Telescopes: The Broadband Phasing Algorithm,” Appl. Opt. 37, 140–155 (1998).
    [Crossref]
  2. G. Chanan, C. Ohara, and M. Troy, “Phasing the Mirror Segments of the Keck Telescopes II: The Narrow-band Phasing Algorithm,” Appl. Opt. 39, 4706–4714 (2000).
    [Crossref]
  3. G. Chanan, M. Troy, and E. Sirko, “Phase Discontinuity Sensing: A Method for Phasing Segmented Mirrors in the Infrared,” Appl. Opt. 38, 704–713 (1999).
    [Crossref]
  4. F. Shi, G. Chanan, C. Ohara, M. Troy, and D. C. Redding, “Experimental Verification of Dispersed Fringe Sensing as a Segment Phasing Technique using the Keck Telescope,” Appl. Opt. 43, 4474–4481 (2004).
    [Crossref] [PubMed]
  5. R. Diaz-Uribe and A. Jiménez-Hernández, “Phase measurement for segmented optics with 1D diffraction patterns,” Opt. Express 12, 1192–1204 (2004).
    [Crossref] [PubMed]
  6. V. V. Voitsekhovich, S. Bara, and V. G. Orlov “Co-phasing of segmented telescopes: A new approach to piston measurements,” A&A 382, 746–751 (2002).
  7. J. Primot, “Three-wave lateral shearing interfermometer,” Appl. Opt. 32, 6242–6249 (1993).
    [Crossref] [PubMed]
  8. J. Primot and L. Sogno, “Achromatic three-wave (or more) lateral shearing interferometer,” J. Opt. Soc. Am. A 12, 2679–6285 (1995).
    [Crossref]
  9. J.C. Chanteloup, “Multiple-wave lateral shearing interferometry for wave-front sensing,” Appl. Opt. 44, 1559–1571 (2005).
    [Crossref] [PubMed]
  10. J. Primot and N. Guérineau, “Extended Hartmann test based on the pseudoguiding property of a Hartmann mask completed by a phase chessboard,” Appl. Opt. 39, 5715–5720 (2000).
    [Crossref]
  11. S. Velghe, J. Primot, N. Gurineau, M. Cohen, and B. Wattellier, “Visible and Infrared Wave-Front Metrology by Quadri-Wave Lateral Shearing Interferometry,” in Optical Fabrication, Testing, and Metrology II, A. Duparré, R. Geyl, and L. Wang, eds. ,Proc. SPIE 5965, 596512-1–596512-8 (2005).
  12. B. Wattellier, M. Cohen, P. D’Oliveira, G. Doumy, P. Monot, and F. Reau, “New precompensation scheme for best focusing of a 30-fs femtosecond 10-TW laser beam using a four-wave lateral shearing interferometer,” Conference on Lasers and Electro-Optics Europe, p. 172 (2005).
    [Crossref]
  13. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982).
    [Crossref]
  14. D. Malacara, Optical Shop Testing (Wiley-Interscience, 1992), p. 126.
  15. K. Creath, “Step height measurement using two-wavelength phase-shifting interferometry,” Appl. Opt. 26, 2810–2816 (1987).
    [Crossref] [PubMed]
  16. C. Polhemus, “Two-wavelength interferometry,” Appl. Opt. 12, 2071–2074 (1973).
    [Crossref] [PubMed]
  17. A. J. den Boef, “Two-wavelength scanning spot interferometer using single-frequency diode lasers,” Appl. Opt. 27, 306–311 (1988).
    [Crossref]
  18. P. J. de Groot and S. Kishner, “Synthetic wavelength stabilization for two-color laser-diode interferometry,” Appl. Opt. 30, 4026–4033 (1991).
    [Crossref] [PubMed]
  19. M.P. Rimmer, “Method for evaluating lateral shearing interferograms,” Appl. Opt. 13, 623–629 (1974).
    [Crossref] [PubMed]
  20. K. R. Freischlad and C. L. Koliopoulos, “Modal estimation of a wave front from difference measurements using the discrete Fourier transform,” J. Opt. Soc. Am. A 3, 1852–1861 (1986).
    [Crossref]
  21. http://www.phasics.com.

2005 (2)

S. Velghe, J. Primot, N. Gurineau, M. Cohen, and B. Wattellier, “Visible and Infrared Wave-Front Metrology by Quadri-Wave Lateral Shearing Interferometry,” in Optical Fabrication, Testing, and Metrology II, A. Duparré, R. Geyl, and L. Wang, eds. ,Proc. SPIE 5965, 596512-1–596512-8 (2005).

J.C. Chanteloup, “Multiple-wave lateral shearing interferometry for wave-front sensing,” Appl. Opt. 44, 1559–1571 (2005).
[Crossref] [PubMed]

2004 (2)

2002 (1)

V. V. Voitsekhovich, S. Bara, and V. G. Orlov “Co-phasing of segmented telescopes: A new approach to piston measurements,” A&A 382, 746–751 (2002).

2000 (2)

1999 (1)

1998 (1)

1995 (1)

1993 (1)

1991 (1)

1988 (1)

1987 (1)

1986 (1)

1982 (1)

1974 (1)

1973 (1)

Bara, S.

V. V. Voitsekhovich, S. Bara, and V. G. Orlov “Co-phasing of segmented telescopes: A new approach to piston measurements,” A&A 382, 746–751 (2002).

Chanan, G.

Chanteloup, J.C.

Cohen, M.

S. Velghe, J. Primot, N. Gurineau, M. Cohen, and B. Wattellier, “Visible and Infrared Wave-Front Metrology by Quadri-Wave Lateral Shearing Interferometry,” in Optical Fabrication, Testing, and Metrology II, A. Duparré, R. Geyl, and L. Wang, eds. ,Proc. SPIE 5965, 596512-1–596512-8 (2005).

B. Wattellier, M. Cohen, P. D’Oliveira, G. Doumy, P. Monot, and F. Reau, “New precompensation scheme for best focusing of a 30-fs femtosecond 10-TW laser beam using a four-wave lateral shearing interferometer,” Conference on Lasers and Electro-Optics Europe, p. 172 (2005).
[Crossref]

Creath, K.

D’Oliveira, P.

B. Wattellier, M. Cohen, P. D’Oliveira, G. Doumy, P. Monot, and F. Reau, “New precompensation scheme for best focusing of a 30-fs femtosecond 10-TW laser beam using a four-wave lateral shearing interferometer,” Conference on Lasers and Electro-Optics Europe, p. 172 (2005).
[Crossref]

de Groot, P. J.

Dekens, F.

den Boef, A. J.

Diaz-Uribe, R.

Doumy, G.

B. Wattellier, M. Cohen, P. D’Oliveira, G. Doumy, P. Monot, and F. Reau, “New precompensation scheme for best focusing of a 30-fs femtosecond 10-TW laser beam using a four-wave lateral shearing interferometer,” Conference on Lasers and Electro-Optics Europe, p. 172 (2005).
[Crossref]

Freischlad, K. R.

Guérineau, N.

Gurineau, N.

S. Velghe, J. Primot, N. Gurineau, M. Cohen, and B. Wattellier, “Visible and Infrared Wave-Front Metrology by Quadri-Wave Lateral Shearing Interferometry,” in Optical Fabrication, Testing, and Metrology II, A. Duparré, R. Geyl, and L. Wang, eds. ,Proc. SPIE 5965, 596512-1–596512-8 (2005).

Ina, H.

Jiménez-Hernández, A.

Kirkman, D.

Kishner, S.

Kobayashi, S.

Koliopoulos, C. L.

Malacara, D.

D. Malacara, Optical Shop Testing (Wiley-Interscience, 1992), p. 126.

Mast, T.

Michaels, S.

Monot, P.

B. Wattellier, M. Cohen, P. D’Oliveira, G. Doumy, P. Monot, and F. Reau, “New precompensation scheme for best focusing of a 30-fs femtosecond 10-TW laser beam using a four-wave lateral shearing interferometer,” Conference on Lasers and Electro-Optics Europe, p. 172 (2005).
[Crossref]

Nelson, J.

Ohara, C.

Orlov, V. G.

V. V. Voitsekhovich, S. Bara, and V. G. Orlov “Co-phasing of segmented telescopes: A new approach to piston measurements,” A&A 382, 746–751 (2002).

Polhemus, C.

Primot, J.

Reau, F.

B. Wattellier, M. Cohen, P. D’Oliveira, G. Doumy, P. Monot, and F. Reau, “New precompensation scheme for best focusing of a 30-fs femtosecond 10-TW laser beam using a four-wave lateral shearing interferometer,” Conference on Lasers and Electro-Optics Europe, p. 172 (2005).
[Crossref]

Redding, D. C.

Rimmer, M.P.

Shi, F.

Sirko, E.

Sogno, L.

Takeda, M.

Troy, M.

Velghe, S.

S. Velghe, J. Primot, N. Gurineau, M. Cohen, and B. Wattellier, “Visible and Infrared Wave-Front Metrology by Quadri-Wave Lateral Shearing Interferometry,” in Optical Fabrication, Testing, and Metrology II, A. Duparré, R. Geyl, and L. Wang, eds. ,Proc. SPIE 5965, 596512-1–596512-8 (2005).

Voitsekhovich, V. V.

V. V. Voitsekhovich, S. Bara, and V. G. Orlov “Co-phasing of segmented telescopes: A new approach to piston measurements,” A&A 382, 746–751 (2002).

Wattellier, B.

S. Velghe, J. Primot, N. Gurineau, M. Cohen, and B. Wattellier, “Visible and Infrared Wave-Front Metrology by Quadri-Wave Lateral Shearing Interferometry,” in Optical Fabrication, Testing, and Metrology II, A. Duparré, R. Geyl, and L. Wang, eds. ,Proc. SPIE 5965, 596512-1–596512-8 (2005).

B. Wattellier, M. Cohen, P. D’Oliveira, G. Doumy, P. Monot, and F. Reau, “New precompensation scheme for best focusing of a 30-fs femtosecond 10-TW laser beam using a four-wave lateral shearing interferometer,” Conference on Lasers and Electro-Optics Europe, p. 172 (2005).
[Crossref]

A&A (1)

V. V. Voitsekhovich, S. Bara, and V. G. Orlov “Co-phasing of segmented telescopes: A new approach to piston measurements,” A&A 382, 746–751 (2002).

Appl. Opt. (12)

M.P. Rimmer, “Method for evaluating lateral shearing interferograms,” Appl. Opt. 13, 623–629 (1974).
[Crossref] [PubMed]

K. Creath, “Step height measurement using two-wavelength phase-shifting interferometry,” Appl. Opt. 26, 2810–2816 (1987).
[Crossref] [PubMed]

A. J. den Boef, “Two-wavelength scanning spot interferometer using single-frequency diode lasers,” Appl. Opt. 27, 306–311 (1988).
[Crossref]

P. J. de Groot and S. Kishner, “Synthetic wavelength stabilization for two-color laser-diode interferometry,” Appl. Opt. 30, 4026–4033 (1991).
[Crossref] [PubMed]

J. Primot, “Three-wave lateral shearing interfermometer,” Appl. Opt. 32, 6242–6249 (1993).
[Crossref] [PubMed]

G. Chanan, M. Troy, and E. Sirko, “Phase Discontinuity Sensing: A Method for Phasing Segmented Mirrors in the Infrared,” Appl. Opt. 38, 704–713 (1999).
[Crossref]

G. Chanan, C. Ohara, and M. Troy, “Phasing the Mirror Segments of the Keck Telescopes II: The Narrow-band Phasing Algorithm,” Appl. Opt. 39, 4706–4714 (2000).
[Crossref]

J. Primot and N. Guérineau, “Extended Hartmann test based on the pseudoguiding property of a Hartmann mask completed by a phase chessboard,” Appl. Opt. 39, 5715–5720 (2000).
[Crossref]

G. Chanan, M. Troy, F. Dekens, S. Michaels, J. Nelson, T. Mast, and D. Kirkman, “Phasing the Mirror Segments of the Keck Telescopes: The Broadband Phasing Algorithm,” Appl. Opt. 37, 140–155 (1998).
[Crossref]

C. Polhemus, “Two-wavelength interferometry,” Appl. Opt. 12, 2071–2074 (1973).
[Crossref] [PubMed]

F. Shi, G. Chanan, C. Ohara, M. Troy, and D. C. Redding, “Experimental Verification of Dispersed Fringe Sensing as a Segment Phasing Technique using the Keck Telescope,” Appl. Opt. 43, 4474–4481 (2004).
[Crossref] [PubMed]

J.C. Chanteloup, “Multiple-wave lateral shearing interferometry for wave-front sensing,” Appl. Opt. 44, 1559–1571 (2005).
[Crossref] [PubMed]

J. Opt. Soc. Am. (1)

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

Opt. Express (1)

Proc. SPIE (1)

S. Velghe, J. Primot, N. Gurineau, M. Cohen, and B. Wattellier, “Visible and Infrared Wave-Front Metrology by Quadri-Wave Lateral Shearing Interferometry,” in Optical Fabrication, Testing, and Metrology II, A. Duparré, R. Geyl, and L. Wang, eds. ,Proc. SPIE 5965, 596512-1–596512-8 (2005).

Other (3)

B. Wattellier, M. Cohen, P. D’Oliveira, G. Doumy, P. Monot, and F. Reau, “New precompensation scheme for best focusing of a 30-fs femtosecond 10-TW laser beam using a four-wave lateral shearing interferometer,” Conference on Lasers and Electro-Optics Europe, p. 172 (2005).
[Crossref]

D. Malacara, Optical Shop Testing (Wiley-Interscience, 1992), p. 126.

http://www.phasics.com.

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 (7)

Fig. 1.
Fig. 1. (a) A segmented wave-front W(x,y) constituted with two segments separated by a height h. (b) The corresponding optical path is a s-wide crenel of height h: Δ s,xW(x,y)=hCλ (x,y).
Fig. 2.
Fig. 2. Schematic profiles of two lateral shearing interferograms obtained with two different wavelengths λ1 and λ2 during the analysis of the segmented wave-front shown on fig. 1(a).
Fig. 3.
Fig. 3. Evolution of F λ 1 , σ , h versus σ when h=50µm and λ1=10µm.
Fig. 4.
Fig. 4. The two-color analysis has been applied to the wave-front presented on (a). The fig.(b) shows a simulated monochromatic interferogram generated by a QWLSI with an infinite SNR. The fig.(c) and (e) represent the reconstructed wave-fronts with respectively the noiseless interferogram and the noisy interferogram (SNR=8). The fig.(d) and (f) represent the average piston values of the 36 segments calculated on the original wave-front (dashed line) and on the reconstructed wave-front (solid line) shown on (c) and (e).
Fig. 5.
Fig. 5. Schematic test bench dedicated to the two-color analysis of etched substrates by quadri-wave lateral shearing interferometry.
Fig. 6.
Fig. 6. (a)The experimental interferogram at λ1. The axis x and y are given by the orientation of the bright spots. (b)The reconstructed wave-front thanks to a two-color analysis.
Fig. 7.
Fig. 7. A profile of the reconstructed wave-front along the line drawn on fig. 6(b).

Equations (12)

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

I ( x , y , z ) = 2 I 0 [ 1 + cos ( 2 π x p + k Δ s , x W ( x , y ) ) ] ,
H ( x , y ) = I 0 exp [ i θ ( x , y ) ] .
θ s = 2 π ( 1 λ 1 1 λ 2 ) h = 2 π λ s h ,
λ s = λ 1 λ 2 λ 2 λ 1 .
H λ s ( x , y ) = H λ 1 ( x , y ) H λ 2 * ( x , y ) = I 0 exp [ 2 i π λ s Δ s , x W ( x , y ) ] ,
B λ 1 , σ ( λ ) = B λ 1 exp [ 1 2 ( λ λ 1 σ ) 2 ]
I λ 1 , σ ( x , y ) = 2 I 0 0 + [ 1 + cos ( 2 π x p + 2 π λ h C λ ( x , y ) ) ] B λ 1 , σ ( λ ) d λ .
H λ 1 , σ ( x , y ) = I 0 A 0 + exp [ 2 i π λ h ] B λ 1 , σ ( λ ) d λ .
H λ 1 , σ ( x , y ) = I 0 B λ 1 exp [ 2 i π λ 1 h ] 0 + exp [ 2 i π h λ 1 2 λ λ 2 2 σ 2 ] d λ .
H λ 1 , σ ( x , y ) = H λ 1 ( x , y ) F λ 1 , σ , h
F λ 1 , σ , h = B λ 1 2 π exp [ 2 π 2 h 2 λ 1 4 σ 2 ] σ
σ opt = λ 1 2 2 π h

Metrics