Abstract

An improved multi-shear algorithm is proposed to reconstruct a two-dimensional wavefront from multiple phase differences measured by lateral shearing interferograms with different tilts. The effects of the tilt errors in the wavefront are analyzed and a compensation method is developed. Unbiased estimators are added to Fourier coefficients of the phase differences to eliminate the tilt errors adaptively. The algorithm is immune to the tilt errors and the wavefront under test can be recovered exactly. Computer simulation and optical test demonstrated that the proposed algorithm has higher recovery accuracy than the existing multi-shear algorithms.

© 2014 Optical Society of America

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References

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  1. D. Francis, R. P. Tatam, and R. M. Groves, “Shearography technology and applications: a review,” Meas. Sci. Technol. 21(10), 102001 (2010).
    [Crossref]
  2. M. P. Rimmer and J. C. Wyant, “Evaluation of large aberrations using a lateral-shear interferometer having variable shear,” Appl. Opt. 14(1), 142–150 (1975).
    [Crossref] [PubMed]
  3. P. Bon, G. Maucort, B. Wattellier, and S. Monneret, “Quadriwave lateral shearing interferometry for quantitative phase microscopy of living cells,” Opt. Express 17(15), 13080–13094 (2009).
    [Crossref] [PubMed]
  4. C. Falldorf, C. von Kopylow, and R. B. Bergmann, “Wave field sensing by means of computational shear interferometry,” J. Opt. Soc. Am. A 30(10), 1905–1912 (2013).
    [Crossref] [PubMed]
  5. P. Bon, G. Maucort, B. Wattellier, and S. Monneret, “Quadriwave lateral shearing interferometry for quantitative phase microscopy of living cells,” Opt. Express 17(15), 13080–13094 (2009).
    [Crossref] [PubMed]
  6. X. Liu, Y. Gao, and M. Chang, “A new lateral shearing interferometer for precision surface measurement,” Opt. Lasers Eng. 47(9), 926–934 (2009).
    [Crossref]
  7. P. Liang, J. Ding, Z. Jin, C. S. Guo, and H. T. Wang, “Two-dimensional wave-front reconstruction from lateral shearing interferograms,” Opt. Express 14(2), 625–634 (2006).
    [Crossref] [PubMed]
  8. C. Elster and I. Weingärtner, “Exact wave-front reconstruction from two lateral shearing interferograms,” J. Opt. Soc. Am. A 16(9), 2281–2285 (1999).
    [Crossref]
  9. C. Elster, “Exact two-dimensional wave-front reconstruction from lateral shearing interferograms with large shears,” Appl. Opt. 39(29), 5353–5359 (2000).
    [Crossref] [PubMed]
  10. A. Dubra, C. Paterson, and C. Dainty, “Wave-front reconstruction from shear phase maps by use of the discrete Fourier transform,” Appl. Opt. 43(5), 1108–1113 (2004).
    [Crossref] [PubMed]
  11. J. Villa, G. García, and G. Gómez, “Wavefront recovery in shearing interferometry with variable magnitude and direction shear,” Opt. Commun. 195(1-4), 85–91 (2001).
    [Crossref]
  12. G. García-Torales, G. Paez, M. Strojnik, J. Villa, J. L. Flores, and A. González Alvarez, “Experimental intensity patterns obtained from a 2D shearing interferometer with adaptable sensitivity,” Opt. Commun. 257(1), 16–26 (2006).
    [Crossref]
  13. B. Bravo-Medina, G. Garcia-Torales, R. Legarda-Sáenz, and J. L. Flores, “Wavefront recovery Fourier-based algorithm used in a vectorial shearing interferometer,” Proc. SPIE 8867, 88670Z (2013).
    [Crossref]
  14. Y. F. Guo, H. Chen, J. Xu, and J. Ding, “Two-dimensional wavefront reconstruction from lateral multi-shear interferograms,” Opt. Express 20(14), 15723–15733 (2012).
    [Crossref] [PubMed]
  15. H. Schreiber, “Measuring wavefront tilt using shearing interferometry,” Proc. SPIE 5965, 59659Y (2005).
    [Crossref]
  16. Z. Q. Yin, “Exact wavefront recovery with tilt from lateral shear interferograms,” Appl. Opt. 48(14), 2760–2766 (2009).
    [Crossref] [PubMed]
  17. X. Chen, Y. Li, G. Ding, and L. Lei, “Wavefront reconstruction with tilt from two shearing interferograms,” in Proceedings of IEEE Conference on Cross Strait Quad-Regional Radio Science and Wireless Technology (Harbin, 2011), pp. 202–205.
    [Crossref]
  18. C. Elster and I. Weingärtner, “Solution to the shearing problem,” Appl. Opt. 38(23), 5024–5031 (1999).
    [Crossref] [PubMed]
  19. S. H. Zhai, J. Ding, J. Chen, Y. X. Fan, and H. T. Wang, “Three-wave shearing interferometer based on spatial light modulator,” Opt. Express 17(2), 970–977 (2009).
    [Crossref] [PubMed]

2013 (2)

C. Falldorf, C. von Kopylow, and R. B. Bergmann, “Wave field sensing by means of computational shear interferometry,” J. Opt. Soc. Am. A 30(10), 1905–1912 (2013).
[Crossref] [PubMed]

B. Bravo-Medina, G. Garcia-Torales, R. Legarda-Sáenz, and J. L. Flores, “Wavefront recovery Fourier-based algorithm used in a vectorial shearing interferometer,” Proc. SPIE 8867, 88670Z (2013).
[Crossref]

2012 (1)

Y. F. Guo, H. Chen, J. Xu, and J. Ding, “Two-dimensional wavefront reconstruction from lateral multi-shear interferograms,” Opt. Express 20(14), 15723–15733 (2012).
[Crossref] [PubMed]

2010 (1)

D. Francis, R. P. Tatam, and R. M. Groves, “Shearography technology and applications: a review,” Meas. Sci. Technol. 21(10), 102001 (2010).
[Crossref]

2009 (5)

P. Bon, G. Maucort, B. Wattellier, and S. Monneret, “Quadriwave lateral shearing interferometry for quantitative phase microscopy of living cells,” Opt. Express 17(15), 13080–13094 (2009).
[Crossref] [PubMed]

P. Bon, G. Maucort, B. Wattellier, and S. Monneret, “Quadriwave lateral shearing interferometry for quantitative phase microscopy of living cells,” Opt. Express 17(15), 13080–13094 (2009).
[Crossref] [PubMed]

X. Liu, Y. Gao, and M. Chang, “A new lateral shearing interferometer for precision surface measurement,” Opt. Lasers Eng. 47(9), 926–934 (2009).
[Crossref]

Z. Q. Yin, “Exact wavefront recovery with tilt from lateral shear interferograms,” Appl. Opt. 48(14), 2760–2766 (2009).
[Crossref] [PubMed]

S. H. Zhai, J. Ding, J. Chen, Y. X. Fan, and H. T. Wang, “Three-wave shearing interferometer based on spatial light modulator,” Opt. Express 17(2), 970–977 (2009).
[Crossref] [PubMed]

2006 (2)

G. García-Torales, G. Paez, M. Strojnik, J. Villa, J. L. Flores, and A. González Alvarez, “Experimental intensity patterns obtained from a 2D shearing interferometer with adaptable sensitivity,” Opt. Commun. 257(1), 16–26 (2006).
[Crossref]

P. Liang, J. Ding, Z. Jin, C. S. Guo, and H. T. Wang, “Two-dimensional wave-front reconstruction from lateral shearing interferograms,” Opt. Express 14(2), 625–634 (2006).
[Crossref] [PubMed]

2005 (1)

H. Schreiber, “Measuring wavefront tilt using shearing interferometry,” Proc. SPIE 5965, 59659Y (2005).
[Crossref]

2004 (1)

A. Dubra, C. Paterson, and C. Dainty, “Wave-front reconstruction from shear phase maps by use of the discrete Fourier transform,” Appl. Opt. 43(5), 1108–1113 (2004).
[Crossref] [PubMed]

2001 (1)

J. Villa, G. García, and G. Gómez, “Wavefront recovery in shearing interferometry with variable magnitude and direction shear,” Opt. Commun. 195(1-4), 85–91 (2001).
[Crossref]

2000 (1)

C. Elster, “Exact two-dimensional wave-front reconstruction from lateral shearing interferograms with large shears,” Appl. Opt. 39(29), 5353–5359 (2000).
[Crossref] [PubMed]

1999 (2)

C. Elster and I. Weingärtner, “Exact wave-front reconstruction from two lateral shearing interferograms,” J. Opt. Soc. Am. A 16(9), 2281–2285 (1999).
[Crossref]

C. Elster and I. Weingärtner, “Solution to the shearing problem,” Appl. Opt. 38(23), 5024–5031 (1999).
[Crossref] [PubMed]

1975 (1)

M. P. Rimmer and J. C. Wyant, “Evaluation of large aberrations using a lateral-shear interferometer having variable shear,” Appl. Opt. 14(1), 142–150 (1975).
[Crossref] [PubMed]

Bergmann, R. B.

C. Falldorf, C. von Kopylow, and R. B. Bergmann, “Wave field sensing by means of computational shear interferometry,” J. Opt. Soc. Am. A 30(10), 1905–1912 (2013).
[Crossref] [PubMed]

Bon, P.

P. Bon, G. Maucort, B. Wattellier, and S. Monneret, “Quadriwave lateral shearing interferometry for quantitative phase microscopy of living cells,” Opt. Express 17(15), 13080–13094 (2009).
[Crossref] [PubMed]

P. Bon, G. Maucort, B. Wattellier, and S. Monneret, “Quadriwave lateral shearing interferometry for quantitative phase microscopy of living cells,” Opt. Express 17(15), 13080–13094 (2009).
[Crossref] [PubMed]

Bravo-Medina, B.

B. Bravo-Medina, G. Garcia-Torales, R. Legarda-Sáenz, and J. L. Flores, “Wavefront recovery Fourier-based algorithm used in a vectorial shearing interferometer,” Proc. SPIE 8867, 88670Z (2013).
[Crossref]

Chang, M.

X. Liu, Y. Gao, and M. Chang, “A new lateral shearing interferometer for precision surface measurement,” Opt. Lasers Eng. 47(9), 926–934 (2009).
[Crossref]

Chen, H.

Y. F. Guo, H. Chen, J. Xu, and J. Ding, “Two-dimensional wavefront reconstruction from lateral multi-shear interferograms,” Opt. Express 20(14), 15723–15733 (2012).
[Crossref] [PubMed]

Chen, J.

S. H. Zhai, J. Ding, J. Chen, Y. X. Fan, and H. T. Wang, “Three-wave shearing interferometer based on spatial light modulator,” Opt. Express 17(2), 970–977 (2009).
[Crossref] [PubMed]

Chen, X.

X. Chen, Y. Li, G. Ding, and L. Lei, “Wavefront reconstruction with tilt from two shearing interferograms,” in Proceedings of IEEE Conference on Cross Strait Quad-Regional Radio Science and Wireless Technology (Harbin, 2011), pp. 202–205.
[Crossref]

Dainty, C.

A. Dubra, C. Paterson, and C. Dainty, “Wave-front reconstruction from shear phase maps by use of the discrete Fourier transform,” Appl. Opt. 43(5), 1108–1113 (2004).
[Crossref] [PubMed]

Ding, G.

X. Chen, Y. Li, G. Ding, and L. Lei, “Wavefront reconstruction with tilt from two shearing interferograms,” in Proceedings of IEEE Conference on Cross Strait Quad-Regional Radio Science and Wireless Technology (Harbin, 2011), pp. 202–205.
[Crossref]

Ding, J.

Y. F. Guo, H. Chen, J. Xu, and J. Ding, “Two-dimensional wavefront reconstruction from lateral multi-shear interferograms,” Opt. Express 20(14), 15723–15733 (2012).
[Crossref] [PubMed]

S. H. Zhai, J. Ding, J. Chen, Y. X. Fan, and H. T. Wang, “Three-wave shearing interferometer based on spatial light modulator,” Opt. Express 17(2), 970–977 (2009).
[Crossref] [PubMed]

P. Liang, J. Ding, Z. Jin, C. S. Guo, and H. T. Wang, “Two-dimensional wave-front reconstruction from lateral shearing interferograms,” Opt. Express 14(2), 625–634 (2006).
[Crossref] [PubMed]

Dubra, A.

A. Dubra, C. Paterson, and C. Dainty, “Wave-front reconstruction from shear phase maps by use of the discrete Fourier transform,” Appl. Opt. 43(5), 1108–1113 (2004).
[Crossref] [PubMed]

Elster, C.

C. Elster, “Exact two-dimensional wave-front reconstruction from lateral shearing interferograms with large shears,” Appl. Opt. 39(29), 5353–5359 (2000).
[Crossref] [PubMed]

C. Elster and I. Weingärtner, “Solution to the shearing problem,” Appl. Opt. 38(23), 5024–5031 (1999).
[Crossref] [PubMed]

C. Elster and I. Weingärtner, “Exact wave-front reconstruction from two lateral shearing interferograms,” J. Opt. Soc. Am. A 16(9), 2281–2285 (1999).
[Crossref]

Falldorf, C.

C. Falldorf, C. von Kopylow, and R. B. Bergmann, “Wave field sensing by means of computational shear interferometry,” J. Opt. Soc. Am. A 30(10), 1905–1912 (2013).
[Crossref] [PubMed]

Fan, Y. X.

S. H. Zhai, J. Ding, J. Chen, Y. X. Fan, and H. T. Wang, “Three-wave shearing interferometer based on spatial light modulator,” Opt. Express 17(2), 970–977 (2009).
[Crossref] [PubMed]

Flores, J. L.

B. Bravo-Medina, G. Garcia-Torales, R. Legarda-Sáenz, and J. L. Flores, “Wavefront recovery Fourier-based algorithm used in a vectorial shearing interferometer,” Proc. SPIE 8867, 88670Z (2013).
[Crossref]

G. García-Torales, G. Paez, M. Strojnik, J. Villa, J. L. Flores, and A. González Alvarez, “Experimental intensity patterns obtained from a 2D shearing interferometer with adaptable sensitivity,” Opt. Commun. 257(1), 16–26 (2006).
[Crossref]

Francis, D.

D. Francis, R. P. Tatam, and R. M. Groves, “Shearography technology and applications: a review,” Meas. Sci. Technol. 21(10), 102001 (2010).
[Crossref]

Gao, Y.

X. Liu, Y. Gao, and M. Chang, “A new lateral shearing interferometer for precision surface measurement,” Opt. Lasers Eng. 47(9), 926–934 (2009).
[Crossref]

García, G.

J. Villa, G. García, and G. Gómez, “Wavefront recovery in shearing interferometry with variable magnitude and direction shear,” Opt. Commun. 195(1-4), 85–91 (2001).
[Crossref]

Garcia-Torales, G.

B. Bravo-Medina, G. Garcia-Torales, R. Legarda-Sáenz, and J. L. Flores, “Wavefront recovery Fourier-based algorithm used in a vectorial shearing interferometer,” Proc. SPIE 8867, 88670Z (2013).
[Crossref]

García-Torales, G.

G. García-Torales, G. Paez, M. Strojnik, J. Villa, J. L. Flores, and A. González Alvarez, “Experimental intensity patterns obtained from a 2D shearing interferometer with adaptable sensitivity,” Opt. Commun. 257(1), 16–26 (2006).
[Crossref]

Gómez, G.

J. Villa, G. García, and G. Gómez, “Wavefront recovery in shearing interferometry with variable magnitude and direction shear,” Opt. Commun. 195(1-4), 85–91 (2001).
[Crossref]

González Alvarez, A.

G. García-Torales, G. Paez, M. Strojnik, J. Villa, J. L. Flores, and A. González Alvarez, “Experimental intensity patterns obtained from a 2D shearing interferometer with adaptable sensitivity,” Opt. Commun. 257(1), 16–26 (2006).
[Crossref]

Groves, R. M.

D. Francis, R. P. Tatam, and R. M. Groves, “Shearography technology and applications: a review,” Meas. Sci. Technol. 21(10), 102001 (2010).
[Crossref]

Guo, C. S.

P. Liang, J. Ding, Z. Jin, C. S. Guo, and H. T. Wang, “Two-dimensional wave-front reconstruction from lateral shearing interferograms,” Opt. Express 14(2), 625–634 (2006).
[Crossref] [PubMed]

Guo, Y. F.

Y. F. Guo, H. Chen, J. Xu, and J. Ding, “Two-dimensional wavefront reconstruction from lateral multi-shear interferograms,” Opt. Express 20(14), 15723–15733 (2012).
[Crossref] [PubMed]

Jin, Z.

P. Liang, J. Ding, Z. Jin, C. S. Guo, and H. T. Wang, “Two-dimensional wave-front reconstruction from lateral shearing interferograms,” Opt. Express 14(2), 625–634 (2006).
[Crossref] [PubMed]

Legarda-Sáenz, R.

B. Bravo-Medina, G. Garcia-Torales, R. Legarda-Sáenz, and J. L. Flores, “Wavefront recovery Fourier-based algorithm used in a vectorial shearing interferometer,” Proc. SPIE 8867, 88670Z (2013).
[Crossref]

Lei, L.

X. Chen, Y. Li, G. Ding, and L. Lei, “Wavefront reconstruction with tilt from two shearing interferograms,” in Proceedings of IEEE Conference on Cross Strait Quad-Regional Radio Science and Wireless Technology (Harbin, 2011), pp. 202–205.
[Crossref]

Li, Y.

X. Chen, Y. Li, G. Ding, and L. Lei, “Wavefront reconstruction with tilt from two shearing interferograms,” in Proceedings of IEEE Conference on Cross Strait Quad-Regional Radio Science and Wireless Technology (Harbin, 2011), pp. 202–205.
[Crossref]

Liang, P.

P. Liang, J. Ding, Z. Jin, C. S. Guo, and H. T. Wang, “Two-dimensional wave-front reconstruction from lateral shearing interferograms,” Opt. Express 14(2), 625–634 (2006).
[Crossref] [PubMed]

Liu, X.

X. Liu, Y. Gao, and M. Chang, “A new lateral shearing interferometer for precision surface measurement,” Opt. Lasers Eng. 47(9), 926–934 (2009).
[Crossref]

Maucort, G.

P. Bon, G. Maucort, B. Wattellier, and S. Monneret, “Quadriwave lateral shearing interferometry for quantitative phase microscopy of living cells,” Opt. Express 17(15), 13080–13094 (2009).
[Crossref] [PubMed]

P. Bon, G. Maucort, B. Wattellier, and S. Monneret, “Quadriwave lateral shearing interferometry for quantitative phase microscopy of living cells,” Opt. Express 17(15), 13080–13094 (2009).
[Crossref] [PubMed]

Monneret, S.

P. Bon, G. Maucort, B. Wattellier, and S. Monneret, “Quadriwave lateral shearing interferometry for quantitative phase microscopy of living cells,” Opt. Express 17(15), 13080–13094 (2009).
[Crossref] [PubMed]

P. Bon, G. Maucort, B. Wattellier, and S. Monneret, “Quadriwave lateral shearing interferometry for quantitative phase microscopy of living cells,” Opt. Express 17(15), 13080–13094 (2009).
[Crossref] [PubMed]

Paez, G.

G. García-Torales, G. Paez, M. Strojnik, J. Villa, J. L. Flores, and A. González Alvarez, “Experimental intensity patterns obtained from a 2D shearing interferometer with adaptable sensitivity,” Opt. Commun. 257(1), 16–26 (2006).
[Crossref]

Paterson, C.

A. Dubra, C. Paterson, and C. Dainty, “Wave-front reconstruction from shear phase maps by use of the discrete Fourier transform,” Appl. Opt. 43(5), 1108–1113 (2004).
[Crossref] [PubMed]

Rimmer, M. P.

M. P. Rimmer and J. C. Wyant, “Evaluation of large aberrations using a lateral-shear interferometer having variable shear,” Appl. Opt. 14(1), 142–150 (1975).
[Crossref] [PubMed]

Schreiber, H.

H. Schreiber, “Measuring wavefront tilt using shearing interferometry,” Proc. SPIE 5965, 59659Y (2005).
[Crossref]

Strojnik, M.

G. García-Torales, G. Paez, M. Strojnik, J. Villa, J. L. Flores, and A. González Alvarez, “Experimental intensity patterns obtained from a 2D shearing interferometer with adaptable sensitivity,” Opt. Commun. 257(1), 16–26 (2006).
[Crossref]

Tatam, R. P.

D. Francis, R. P. Tatam, and R. M. Groves, “Shearography technology and applications: a review,” Meas. Sci. Technol. 21(10), 102001 (2010).
[Crossref]

Villa, J.

G. García-Torales, G. Paez, M. Strojnik, J. Villa, J. L. Flores, and A. González Alvarez, “Experimental intensity patterns obtained from a 2D shearing interferometer with adaptable sensitivity,” Opt. Commun. 257(1), 16–26 (2006).
[Crossref]

J. Villa, G. García, and G. Gómez, “Wavefront recovery in shearing interferometry with variable magnitude and direction shear,” Opt. Commun. 195(1-4), 85–91 (2001).
[Crossref]

von Kopylow, C.

C. Falldorf, C. von Kopylow, and R. B. Bergmann, “Wave field sensing by means of computational shear interferometry,” J. Opt. Soc. Am. A 30(10), 1905–1912 (2013).
[Crossref] [PubMed]

Wang, H. T.

S. H. Zhai, J. Ding, J. Chen, Y. X. Fan, and H. T. Wang, “Three-wave shearing interferometer based on spatial light modulator,” Opt. Express 17(2), 970–977 (2009).
[Crossref] [PubMed]

P. Liang, J. Ding, Z. Jin, C. S. Guo, and H. T. Wang, “Two-dimensional wave-front reconstruction from lateral shearing interferograms,” Opt. Express 14(2), 625–634 (2006).
[Crossref] [PubMed]

Wattellier, B.

P. Bon, G. Maucort, B. Wattellier, and S. Monneret, “Quadriwave lateral shearing interferometry for quantitative phase microscopy of living cells,” Opt. Express 17(15), 13080–13094 (2009).
[Crossref] [PubMed]

P. Bon, G. Maucort, B. Wattellier, and S. Monneret, “Quadriwave lateral shearing interferometry for quantitative phase microscopy of living cells,” Opt. Express 17(15), 13080–13094 (2009).
[Crossref] [PubMed]

Weingärtner, I.

C. Elster and I. Weingärtner, “Exact wave-front reconstruction from two lateral shearing interferograms,” J. Opt. Soc. Am. A 16(9), 2281–2285 (1999).
[Crossref]

C. Elster and I. Weingärtner, “Solution to the shearing problem,” Appl. Opt. 38(23), 5024–5031 (1999).
[Crossref] [PubMed]

Wyant, J. C.

M. P. Rimmer and J. C. Wyant, “Evaluation of large aberrations using a lateral-shear interferometer having variable shear,” Appl. Opt. 14(1), 142–150 (1975).
[Crossref] [PubMed]

Xu, J.

Y. F. Guo, H. Chen, J. Xu, and J. Ding, “Two-dimensional wavefront reconstruction from lateral multi-shear interferograms,” Opt. Express 20(14), 15723–15733 (2012).
[Crossref] [PubMed]

Yin, Z. Q.

Z. Q. Yin, “Exact wavefront recovery with tilt from lateral shear interferograms,” Appl. Opt. 48(14), 2760–2766 (2009).
[Crossref] [PubMed]

Zhai, S. H.

S. H. Zhai, J. Ding, J. Chen, Y. X. Fan, and H. T. Wang, “Three-wave shearing interferometer based on spatial light modulator,” Opt. Express 17(2), 970–977 (2009).
[Crossref] [PubMed]

Appl. Opt. (5)

M. P. Rimmer and J. C. Wyant, “Evaluation of large aberrations using a lateral-shear interferometer having variable shear,” Appl. Opt. 14(1), 142–150 (1975).
[Crossref] [PubMed]

C. Elster, “Exact two-dimensional wave-front reconstruction from lateral shearing interferograms with large shears,” Appl. Opt. 39(29), 5353–5359 (2000).
[Crossref] [PubMed]

A. Dubra, C. Paterson, and C. Dainty, “Wave-front reconstruction from shear phase maps by use of the discrete Fourier transform,” Appl. Opt. 43(5), 1108–1113 (2004).
[Crossref] [PubMed]

Z. Q. Yin, “Exact wavefront recovery with tilt from lateral shear interferograms,” Appl. Opt. 48(14), 2760–2766 (2009).
[Crossref] [PubMed]

C. Elster and I. Weingärtner, “Solution to the shearing problem,” Appl. Opt. 38(23), 5024–5031 (1999).
[Crossref] [PubMed]

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

C. Falldorf, C. von Kopylow, and R. B. Bergmann, “Wave field sensing by means of computational shear interferometry,” J. Opt. Soc. Am. A 30(10), 1905–1912 (2013).
[Crossref] [PubMed]

C. Elster and I. Weingärtner, “Exact wave-front reconstruction from two lateral shearing interferograms,” J. Opt. Soc. Am. A 16(9), 2281–2285 (1999).
[Crossref]

Meas. Sci. Technol. (1)

D. Francis, R. P. Tatam, and R. M. Groves, “Shearography technology and applications: a review,” Meas. Sci. Technol. 21(10), 102001 (2010).
[Crossref]

Opt. Commun. (2)

J. Villa, G. García, and G. Gómez, “Wavefront recovery in shearing interferometry with variable magnitude and direction shear,” Opt. Commun. 195(1-4), 85–91 (2001).
[Crossref]

G. García-Torales, G. Paez, M. Strojnik, J. Villa, J. L. Flores, and A. González Alvarez, “Experimental intensity patterns obtained from a 2D shearing interferometer with adaptable sensitivity,” Opt. Commun. 257(1), 16–26 (2006).
[Crossref]

Opt. Express (5)

P. Bon, G. Maucort, B. Wattellier, and S. Monneret, “Quadriwave lateral shearing interferometry for quantitative phase microscopy of living cells,” Opt. Express 17(15), 13080–13094 (2009).
[Crossref] [PubMed]

P. Bon, G. Maucort, B. Wattellier, and S. Monneret, “Quadriwave lateral shearing interferometry for quantitative phase microscopy of living cells,” Opt. Express 17(15), 13080–13094 (2009).
[Crossref] [PubMed]

P. Liang, J. Ding, Z. Jin, C. S. Guo, and H. T. Wang, “Two-dimensional wave-front reconstruction from lateral shearing interferograms,” Opt. Express 14(2), 625–634 (2006).
[Crossref] [PubMed]

Y. F. Guo, H. Chen, J. Xu, and J. Ding, “Two-dimensional wavefront reconstruction from lateral multi-shear interferograms,” Opt. Express 20(14), 15723–15733 (2012).
[Crossref] [PubMed]

S. H. Zhai, J. Ding, J. Chen, Y. X. Fan, and H. T. Wang, “Three-wave shearing interferometer based on spatial light modulator,” Opt. Express 17(2), 970–977 (2009).
[Crossref] [PubMed]

Opt. Lasers Eng. (1)

X. Liu, Y. Gao, and M. Chang, “A new lateral shearing interferometer for precision surface measurement,” Opt. Lasers Eng. 47(9), 926–934 (2009).
[Crossref]

Proc. SPIE (2)

B. Bravo-Medina, G. Garcia-Torales, R. Legarda-Sáenz, and J. L. Flores, “Wavefront recovery Fourier-based algorithm used in a vectorial shearing interferometer,” Proc. SPIE 8867, 88670Z (2013).
[Crossref]

H. Schreiber, “Measuring wavefront tilt using shearing interferometry,” Proc. SPIE 5965, 59659Y (2005).
[Crossref]

Other (1)

X. Chen, Y. Li, G. Ding, and L. Lei, “Wavefront reconstruction with tilt from two shearing interferograms,” in Proceedings of IEEE Conference on Cross Strait Quad-Regional Radio Science and Wireless Technology (Harbin, 2011), pp. 202–205.
[Crossref]

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Figures (4)

Fig. 1
Fig. 1 Simulation results for a shear combination s = 1, 2, 3, 4, 5 and N = 420 × 420. (a) Original phase; (b) x-directional phase difference (4-pixel shear); (c) y-directional phase difference (4-pixel shear); (d) phase reconstructed with the old algorithm; (e) phase reconstructed with the new improved algorithm; (f) difference between the original and recovered phases in the 200-th row using the two algorithms.
Fig. 2
Fig. 2 Simulation results for the shear combination s = 1, 2, 3, 4, 5 and N = 420 × 420. (a) Original phase map; (b) deviation between the original phase and phase reconstructed with the old algorithm; (c) deviation between the original phase and phase reconstructed with the new improved algorithm; (d) difference between the original and recovered phases in the 200-th row using the two algorithms.
Fig. 3
Fig. 3 Three-wave lateral shearing interferometer based on an SLM with four lenses (L1, L2, L3 and L4) and a rotating ground glass that lowers the spatial coherence of light to reduce speckle noise.
Fig. 4
Fig. 4 Optic surface testing with the old and improved algorithms: (a) 2D phase map reconstructed using the old algorithm; (b) 2D phase map reconstructed using the new improved algorithm; (c) 1D relief profile: dotted line obtained using the old algorithm, dashed line obtained using the new algorithm.

Equations (20)

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D j x (m,n)={ φ(m,n)φ(m s j ,n) m[ s j ,N1]; n[0,N1] l=1 N/ s j 1 D j x (m+l s j ,n) m[0, s j 1]; n[0,N1]
D j y (m,n)={ φ(m,n)φ(m,n s j ) n[ s j ,N1]; m[0,N1] l=1 N/ s j 1 D j y (m,n+l s j ) n[0, s j 1]; m[0,N1]
ε 2 = m,n [ j=1 K | Δ j x (m,n) D j x (m,n) | 2 + j=1 K | Δ j x (m,n) D j y (m,n) | 2 ] .
Φ(p,q)= j=1 K (1 e i2πp s j /N ) Ζ j x (p,q)+ j=1 K (1 e i2πq s j /N ) Z j y (p,q) j=1 K [ 4 sin 2 ( πp s j N )+4 sin 2 ( πq s j N ) ] ,
Δ j x (m,n)= D j x (m,n)+ a j s j ,
Δ j y (m,n)= D j y (m,n)+ b j s j
Z j x (p,q)= m,n=0 N1 Δ j x (m,n)exp[ i2π N ( mp+nq ) ] 1exp( i2π s j p N ) ,
Z j y (m,q)= m,n=0 N1 Δ j y (m,n)exp[ i2π N ( mp+nq ) ] 1exp( i2π s j q N ) .
Z j x (p,q)= [ n=0 N1 exp( i2πnq N ) { m= s j N1 [ D j x (m,n)+ a j s j ]exp( i2πmp N ) m=0 s j 1 [ l=1 N/ s j 1 [ D j x (m+l s j ,n)+ a j s j ] ]exp( i2πmp N ) } ] / [ 1exp( i2π s j p N ) ] ,
Z j y (p,q)= [ m=0 N1 exp( i2πmp N ) { n= s j N1 [ D j y (m,n)+ b j s j ]exp( i2πnq N ) n=0 s j 1 [ l=1 N/ s j 1 [ D j y ( m j ,n+ls)+ b j s j ] ]exp( i2πnq N ) } ] / [ 1exp( i2π s j q N ) ] .
Z j x (p,q)= m,n=0 N1 D j x (m,n)exp( i2πmp N ) 1exp( i2π s j p N ) + a j s j m=0 N1 mexp( i2πmp N ) ,
Z j y (p,q)= m,n=0 N1 D j y (m,n)exp( i2πnq N ) 1exp( i2π s j q N ) + b j s j n=0 N1 nexp( i2πnq N ) .
Z j x (p,q)= W j x (p,q)+ a j s j Y(p),
Z j y (p,q)= W j y (p,q)+ b j s j Y(q).
Z j x ( p,q ) Z 1 x ( p,q ) Y(p) = α j ,
Z j y ( p,q ) Z 1 y ( p,q ) Y(p) = β j ,
Z j x ( p,q )= W j x ( p,q )+ α j Y(p),
Z j y ( p,q )= W j y ( p,q )+ β j Y(q).
Φ(p,q)= j=1 K (1 e i2πp s j N )[ W j x (p,q)+ α j Y(p)]+ j=1 K (1 e i2πq s j N )[ W j y (p,q)+ β j Y(q)] j=1 K [4 sin 2 ( πp s j N )+4 sin 2 ( πq s j N )] .
φ ( x , y ) = 2 π [ 0.15 ( x 2 + y 2 2 ) ( x 2 + y 2 + 1 ) 0.6 ( x 2 y 2 ) ( x 2 + y 2 1.25 ) ] ,

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