Abstract

The accuracy of measuring optical aberrations in the random phase field by the Talbot wavefront sensor is theoretically investigated. The possibilities of a grating self-imaging phenomenon in the random phase field are investigated based on the simulation results. Random fields of two different types are considered: amplitude and phase Gaussian fields. Simulation results show that the cosine grating is more stable for phase noise in comparison with gratings that have Gaussian and square binary profiles on each cell unit. It is found that phase noise gives increments of high-order aberrations for wavefront reconstruction.

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References

  • View by:

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    [Crossref]
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2021 (4)

A. A. Goloborodko, “Talbot image formation in random phase field,” Opt. Quantum Electron. 53, 614 (2021).
[Crossref]

M. M. Kotov, V. P. Danko, and A. A. Goloborodko, “Simulation of Talbot effect from a binary phase grating using Fresnel integral approach,” Opt. Laser Eng. 137, 106400 (2021).
[Crossref]

K. Munechika, S. Cabrini, W. Chao, I. Lacey, C. Pina-Hernandez, S. Rochester, and V. V. Yashchuk, “Binary pseudo-random array test standard optimized for characterization of interferometric microscopes,” Proc. SPIE 11817, 1181704 (2021).
[Crossref]

G. Zhou, Z. H. Lim, Y. Qi, F. S. Chau, and G. Zhou, “MEMS gratings and their applications,” Int. J. Optomechatron. 15, 61–86 (2021).
[Crossref]

2019 (2)

S. Rasouli and D. Hebri, “Theory of diffraction of vortex beams from 2D orthogonal periodic structures and Talbot self-healing under vortex beam illumination,” J. Opt. Soc. Am. A 36, 800–808 (2019).
[Crossref]

G. Calogero, N. R. Papior, B. Kretz, A. Garcia-Lekue, T. Frederiksen, and M. Brandbyge, “Electron transport in nanoporous graphene: probing the Talbot effect,” Nano Lett. 19, 576–581 (2019).
[Crossref]

2017 (5)

K. Li, F. Xia, M. Wang, P. Sun, T. Liu, W. Hu, W. Kong, M. Yun, and L. Dong, “Discrete Talbot effect in dielectric graphene plasmonic waveguide arrays,” Carbon 118, 192–199 (2017).
[Crossref]

W. Grizolli, X. Shi, T. Kolodziej, Y. Shvyd’ko, and L. Assoufid, “Single-grating Talbot imaging for wavefront sensing and x-ray metrology,” Proc. SPIE 10385, 1038502 (2017).
[Crossref]

S. Marathe, M.-C. Zdora, I. Zanette, S. Cipiccia, and C. Rau, “Comparison of data processing techniques for single-grating x-ray Talbot interferometer data,” Proc. SPIE 10391, 103910S (2017).
[Crossref]

M. M. Kotov and A. A. Goloborodko, “Measurement range of Talbot wavefront sensor,” Opt. Eng. 56, 014101 (2017).
[Crossref]

D. Podanchuk, V. Danko, A. Goloborodko, and N. Goloborodko, “Shack–Hartmann wavefront sensor with the precorrected holographic lenslet array,” Optik 131, 520–526 (2017).
[Crossref]

2016 (2)

2015 (2)

D. Podanchuk, A. Goloborodko, M. Kotov, and D. Petriv, “Talbot sensor with diffraction grating adaptation to wavefront aberrations,” Ukr. J. Phys. 60, 10–14 (2015).
[Crossref]

W. Zhang, J. Wang, Y. Cui, and S. Teng, “Talbot effect of curved grating,” Opt. Commun. 341, 245–251 (2015).
[Crossref]

2014 (3)

D. P. Kelly, “Numerical calculation of the Fresnel transform,” J. Opt. Soc. Am. A 31, 755–764 (2014).
[Crossref]

M. Yuanhua, H. Bingliang, L. Ran, S. Lang, S. Nian, and W. Zhengjie, “Talbot effect and noise reduction in image processing based on Gyrator transform,” Infrared Laser Eng. 43, 665–670 (2014).

V. P. Lukin, L. A. Bol’basova, and V. V. Nosov, “Comparison of Kolmogorov’s and coherent turbulence,” Appl. Opt. 53, B231–B236 (2014).
[Crossref]

2013 (4)

M. Yeganeh, S. Rasouli, M. Dashti, S. Slussarenko, E. Santamato, and E. Karimi, “Reconstructing the Poynting vector skew angle and wavefront of optical vortex beams via two-channel Moiré deflectometery,” Opt. Lett. 38, 887–889 (2013).
[Crossref]

J. Wen, Y. Zhang, and M. Xiao, “The Talbot effect: recent advances in classical optics, nonlinear optics, and quantum optics,” Adv. Opt. Photon. 5, 83–130 (2013).
[Crossref]

A. Kovalenko, M. Kotov, V. Kurashov, and M. Movchan, “Role of diffraction grating profile in the wavefront sensor based on the Talbot effect,” Proc. SPIE 9066, 90660R (2013).
[Crossref]

D. V. Podanchuk, M. M. Kotov, A. A. Goloborodko, V. N. Kurashov, V. P. Dan’ko, and A. V. Kurashov, “Influence of aperture size on wavefront sensor based on the Talbot effect,” Proc. SPIE 9066, 90660S (2013).
[Crossref]

2012 (1)

M. Dashti and S. Rasouli, “Measurement and statistical analysis of the wavefront distortions induced by atmospheric turbulence using two-channel Moiré deflectometry,” J. Opt. 14, 095704 (2012).
[Crossref]

2010 (4)

Y. Zhang, J. Wen, S. N. Zhu, and M. Xiao, “Nonlinear Talbot effect,” Phys. Rev. Lett. 104, 183901 (2010).
[Crossref]

Y. Wang, K. Zhou, X. Zhang, K. Yang, Y. Wang, Y. Song, and S. Liu, “Discrete plasmonic Talbot effect in subwavelength metal waveguide arrays,” Opt. Lett. 35, 685–687 (2010).
[Crossref]

Z. Wang and Z. Ding, “Influence of phase modulation on Talbot effect,” Phys. Lett. A 374, 1550–1554 (2010).
[Crossref]

F. J. Torcal-Milla, L. M. Sanchez-Brea, F. J. Salgado-Remacha, and E. Bernabeu, “Self-imaging with curved gratings,” Opt. Commun. 283, 3869–3873 (2010).
[Crossref]

2009 (1)

B. J. McMorran and A. D. Cronin, “An electron Talbot interferometer,” New J. Phys. 11, 033021 (2009).
[Crossref]

2008 (1)

D. V. Podanchuk, V. N. Kurashov, V. P. Dan’ko, M. M. Kotov, and N. S. Sutyagina, “Shack–Hartmann wavefront sensor with holographic lenslet array for the aberration measurements in a speckle field,” Semicond. Phys. Quantum Electron. Optoelectron. 11, 29–33 (2008).
[Crossref]

2007 (1)

2005 (1)

S. Mirza and C. Shakher, “Surface profiling using phase shifting Talbot interferometric technique,” Opt. Eng. 44, 013601 (2005).
[Crossref]

2003 (1)

J.-Y. Son, D. Podanchuk, V. Dan’ko, and K.-D. Kwak, “Shack–Hartmann wavefront sensor with holographic memory,” Opt. Eng. 42, 3326–3398 (2003).
[Crossref]

1997 (1)

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1294 (1997).
[Crossref]

1996 (1)

D. F. James and G. S. Agarwal, “The generalized Fresnel transform and its application to optics,” Opt. Commun. 126, 207–212 (1996).
[Crossref]

1995 (1)

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: the atomic Talbot effect,” Phys. Rev. A 51, R14–R17 (1995).
[Crossref]

1993 (1)

L. V. Bourimborde, A. O. Tonso, C. M. Colautti, and E. E. Sicre, “Real-time measurement of the meniscus shape using the Talbot effect,” Opt. Commun. 102, 397–400 (1993).
[Crossref]

1992 (1)

A. V. Kovalenko and V. N. Kurashov, “Depolarization of inhomogeneously polarized radiation by a random phase diffuser,” Opt. Spectrosc. 72, 345–348 (1992).

1990 (1)

Y. Nakano, R. Ohmura, and K. Murata, “Refractive power mapping of progressive power lenses using Talbot interferometry and digital image processing,” Opt. Laser Technol. 22, 195–198 (1990).
[Crossref]

1984 (1)

1976 (1)

1881 (1)

L. Rayleigh, “XXV. On copying diffraction-gratings, and on some phenomena connected therewith,” Phil. Mag. Ser. 11(67), 196–205 (1881).
[Crossref]

1836 (1)

H. F. Talbot, “LXXVI. Facts relating to optical science. No. IV,” Phil. Mag. Ser. 9(56), 401–407 (1836).
[Crossref]

Agarwal, G. S.

D. F. James and G. S. Agarwal, “The generalized Fresnel transform and its application to optics,” Opt. Commun. 126, 207–212 (1996).
[Crossref]

Assoufid, L.

W. Grizolli, X. Shi, T. Kolodziej, Y. Shvyd’ko, and L. Assoufid, “Single-grating Talbot imaging for wavefront sensing and x-ray metrology,” Proc. SPIE 10385, 1038502 (2017).
[Crossref]

Bernabeu, E.

F. J. Torcal-Milla, L. M. Sanchez-Brea, F. J. Salgado-Remacha, and E. Bernabeu, “Self-imaging with curved gratings,” Opt. Commun. 283, 3869–3873 (2010).
[Crossref]

Bingliang, H.

M. Yuanhua, H. Bingliang, L. Ran, S. Lang, S. Nian, and W. Zhengjie, “Talbot effect and noise reduction in image processing based on Gyrator transform,” Infrared Laser Eng. 43, 665–670 (2014).

Bol’basova, L. A.

Bourimborde, L. V.

L. V. Bourimborde, A. O. Tonso, C. M. Colautti, and E. E. Sicre, “Real-time measurement of the meniscus shape using the Talbot effect,” Opt. Commun. 102, 397–400 (1993).
[Crossref]

Brandbyge, M.

G. Calogero, N. R. Papior, B. Kretz, A. Garcia-Lekue, T. Frederiksen, and M. Brandbyge, “Electron transport in nanoporous graphene: probing the Talbot effect,” Nano Lett. 19, 576–581 (2019).
[Crossref]

Cabrini, S.

K. Munechika, S. Cabrini, W. Chao, I. Lacey, C. Pina-Hernandez, S. Rochester, and V. V. Yashchuk, “Binary pseudo-random array test standard optimized for characterization of interferometric microscopes,” Proc. SPIE 11817, 1181704 (2021).
[Crossref]

Calogero, G.

G. Calogero, N. R. Papior, B. Kretz, A. Garcia-Lekue, T. Frederiksen, and M. Brandbyge, “Electron transport in nanoporous graphene: probing the Talbot effect,” Nano Lett. 19, 576–581 (2019).
[Crossref]

Chao, W.

K. Munechika, S. Cabrini, W. Chao, I. Lacey, C. Pina-Hernandez, S. Rochester, and V. V. Yashchuk, “Binary pseudo-random array test standard optimized for characterization of interferometric microscopes,” Proc. SPIE 11817, 1181704 (2021).
[Crossref]

Chapman, M. S.

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: the atomic Talbot effect,” Phys. Rev. A 51, R14–R17 (1995).
[Crossref]

Chau, F. S.

G. Zhou, Z. H. Lim, Y. Qi, F. S. Chau, and G. Zhou, “MEMS gratings and their applications,” Int. J. Optomechatron. 15, 61–86 (2021).
[Crossref]

Chavel, P.

Cipiccia, S.

S. Marathe, M.-C. Zdora, I. Zanette, S. Cipiccia, and C. Rau, “Comparison of data processing techniques for single-grating x-ray Talbot interferometer data,” Proc. SPIE 10391, 103910S (2017).
[Crossref]

Colautti, C. M.

L. V. Bourimborde, A. O. Tonso, C. M. Colautti, and E. E. Sicre, “Real-time measurement of the meniscus shape using the Talbot effect,” Opt. Commun. 102, 397–400 (1993).
[Crossref]

Cronin, A. D.

B. J. McMorran and A. D. Cronin, “An electron Talbot interferometer,” New J. Phys. 11, 033021 (2009).
[Crossref]

Cui, Y.

W. Zhang, J. Wang, Y. Cui, and S. Teng, “Talbot effect of curved grating,” Opt. Commun. 341, 245–251 (2015).
[Crossref]

Dan’ko, V.

J.-Y. Son, D. Podanchuk, V. Dan’ko, and K.-D. Kwak, “Shack–Hartmann wavefront sensor with holographic memory,” Opt. Eng. 42, 3326–3398 (2003).
[Crossref]

Dan’ko, V. P.

D. V. Podanchuk, A. A. Goloborodko, M. M. Kotov, A. V. Kovalenko, V. N. Kurashov, and V. P. Dan’ko, “Adaptive wavefront sensor based on the Talbot phenomenon,” Appl. Opt. 55, B150–B157 (2016).
[Crossref]

D. V. Podanchuk, M. M. Kotov, A. A. Goloborodko, V. N. Kurashov, V. P. Dan’ko, and A. V. Kurashov, “Influence of aperture size on wavefront sensor based on the Talbot effect,” Proc. SPIE 9066, 90660S (2013).
[Crossref]

D. V. Podanchuk, V. N. Kurashov, V. P. Dan’ko, M. M. Kotov, and N. S. Sutyagina, “Shack–Hartmann wavefront sensor with holographic lenslet array for the aberration measurements in a speckle field,” Semicond. Phys. Quantum Electron. Optoelectron. 11, 29–33 (2008).
[Crossref]

Danko, V.

D. Podanchuk, V. Danko, A. Goloborodko, and N. Goloborodko, “Shack–Hartmann wavefront sensor with the precorrected holographic lenslet array,” Optik 131, 520–526 (2017).
[Crossref]

Danko, V. P.

M. M. Kotov, V. P. Danko, and A. A. Goloborodko, “Simulation of Talbot effect from a binary phase grating using Fresnel integral approach,” Opt. Laser Eng. 137, 106400 (2021).
[Crossref]

Dashti, M.

M. Yeganeh, S. Rasouli, M. Dashti, S. Slussarenko, E. Santamato, and E. Karimi, “Reconstructing the Poynting vector skew angle and wavefront of optical vortex beams via two-channel Moiré deflectometery,” Opt. Lett. 38, 887–889 (2013).
[Crossref]

M. Dashti and S. Rasouli, “Measurement and statistical analysis of the wavefront distortions induced by atmospheric turbulence using two-channel Moiré deflectometry,” J. Opt. 14, 095704 (2012).
[Crossref]

Ding, Z.

Z. Wang and Z. Ding, “Influence of phase modulation on Talbot effect,” Phys. Lett. A 374, 1550–1554 (2010).
[Crossref]

Dong, L.

K. Li, F. Xia, M. Wang, P. Sun, T. Liu, W. Hu, W. Kong, M. Yun, and L. Dong, “Discrete Talbot effect in dielectric graphene plasmonic waveguide arrays,” Carbon 118, 192–199 (2017).
[Crossref]

Ekstrom, C. R.

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: the atomic Talbot effect,” Phys. Rev. A 51, R14–R17 (1995).
[Crossref]

Erdogan, T.

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1294 (1997).
[Crossref]

Francon, M.

M. Francon, Laser Speckle and Applications in Optics (Elsevier, 2012).

Frederiksen, T.

G. Calogero, N. R. Papior, B. Kretz, A. Garcia-Lekue, T. Frederiksen, and M. Brandbyge, “Electron transport in nanoporous graphene: probing the Talbot effect,” Nano Lett. 19, 576–581 (2019).
[Crossref]

Garcia-Lekue, A.

G. Calogero, N. R. Papior, B. Kretz, A. Garcia-Lekue, T. Frederiksen, and M. Brandbyge, “Electron transport in nanoporous graphene: probing the Talbot effect,” Nano Lett. 19, 576–581 (2019).
[Crossref]

Goloborodko, A.

D. Podanchuk, V. Danko, A. Goloborodko, and N. Goloborodko, “Shack–Hartmann wavefront sensor with the precorrected holographic lenslet array,” Optik 131, 520–526 (2017).
[Crossref]

D. Podanchuk, A. Goloborodko, M. Kotov, and D. Petriv, “Talbot sensor with diffraction grating adaptation to wavefront aberrations,” Ukr. J. Phys. 60, 10–14 (2015).
[Crossref]

Goloborodko, A. A.

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M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: the atomic Talbot effect,” Phys. Rev. A 51, R14–R17 (1995).
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K. Li, F. Xia, M. Wang, P. Sun, T. Liu, W. Hu, W. Kong, M. Yun, and L. Dong, “Discrete Talbot effect in dielectric graphene plasmonic waveguide arrays,” Carbon 118, 192–199 (2017).
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M. M. Kotov, V. P. Danko, and A. A. Goloborodko, “Simulation of Talbot effect from a binary phase grating using Fresnel integral approach,” Opt. Laser Eng. 137, 106400 (2021).
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D. V. Podanchuk, A. A. Goloborodko, M. M. Kotov, A. V. Kovalenko, V. N. Kurashov, and V. P. Dan’ko, “Adaptive wavefront sensor based on the Talbot phenomenon,” Appl. Opt. 55, B150–B157 (2016).
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G. Calogero, N. R. Papior, B. Kretz, A. Garcia-Lekue, T. Frederiksen, and M. Brandbyge, “Electron transport in nanoporous graphene: probing the Talbot effect,” Nano Lett. 19, 576–581 (2019).
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D. V. Podanchuk, M. M. Kotov, A. A. Goloborodko, V. N. Kurashov, V. P. Dan’ko, and A. V. Kurashov, “Influence of aperture size on wavefront sensor based on the Talbot effect,” Proc. SPIE 9066, 90660S (2013).
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D. V. Podanchuk, A. A. Goloborodko, M. M. Kotov, A. V. Kovalenko, V. N. Kurashov, and V. P. Dan’ko, “Adaptive wavefront sensor based on the Talbot phenomenon,” Appl. Opt. 55, B150–B157 (2016).
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D. V. Podanchuk, V. N. Kurashov, V. P. Dan’ko, M. M. Kotov, and N. S. Sutyagina, “Shack–Hartmann wavefront sensor with holographic lenslet array for the aberration measurements in a speckle field,” Semicond. Phys. Quantum Electron. Optoelectron. 11, 29–33 (2008).
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A. V. Kovalenko and V. N. Kurashov, “Depolarization of inhomogeneously polarized radiation by a random phase diffuser,” Opt. Spectrosc. 72, 345–348 (1992).

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J.-Y. Son, D. Podanchuk, V. Dan’ko, and K.-D. Kwak, “Shack–Hartmann wavefront sensor with holographic memory,” Opt. Eng. 42, 3326–3398 (2003).
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K. Munechika, S. Cabrini, W. Chao, I. Lacey, C. Pina-Hernandez, S. Rochester, and V. V. Yashchuk, “Binary pseudo-random array test standard optimized for characterization of interferometric microscopes,” Proc. SPIE 11817, 1181704 (2021).
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M. Yuanhua, H. Bingliang, L. Ran, S. Lang, S. Nian, and W. Zhengjie, “Talbot effect and noise reduction in image processing based on Gyrator transform,” Infrared Laser Eng. 43, 665–670 (2014).

Li, K.

K. Li, F. Xia, M. Wang, P. Sun, T. Liu, W. Hu, W. Kong, M. Yun, and L. Dong, “Discrete Talbot effect in dielectric graphene plasmonic waveguide arrays,” Carbon 118, 192–199 (2017).
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G. Zhou, Z. H. Lim, Y. Qi, F. S. Chau, and G. Zhou, “MEMS gratings and their applications,” Int. J. Optomechatron. 15, 61–86 (2021).
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Liu, T.

K. Li, F. Xia, M. Wang, P. Sun, T. Liu, W. Hu, W. Kong, M. Yun, and L. Dong, “Discrete Talbot effect in dielectric graphene plasmonic waveguide arrays,” Carbon 118, 192–199 (2017).
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S. Marathe, M.-C. Zdora, I. Zanette, S. Cipiccia, and C. Rau, “Comparison of data processing techniques for single-grating x-ray Talbot interferometer data,” Proc. SPIE 10391, 103910S (2017).
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B. J. McMorran and A. D. Cronin, “An electron Talbot interferometer,” New J. Phys. 11, 033021 (2009).
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S. Mirza and C. Shakher, “Surface profiling using phase shifting Talbot interferometric technique,” Opt. Eng. 44, 013601 (2005).
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A. Kovalenko, M. Kotov, V. Kurashov, and M. Movchan, “Role of diffraction grating profile in the wavefront sensor based on the Talbot effect,” Proc. SPIE 9066, 90660R (2013).
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K. Munechika, S. Cabrini, W. Chao, I. Lacey, C. Pina-Hernandez, S. Rochester, and V. V. Yashchuk, “Binary pseudo-random array test standard optimized for characterization of interferometric microscopes,” Proc. SPIE 11817, 1181704 (2021).
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Y. Nakano, R. Ohmura, and K. Murata, “Refractive power mapping of progressive power lenses using Talbot interferometry and digital image processing,” Opt. Laser Technol. 22, 195–198 (1990).
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Y. Nakano, R. Ohmura, and K. Murata, “Refractive power mapping of progressive power lenses using Talbot interferometry and digital image processing,” Opt. Laser Technol. 22, 195–198 (1990).
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M. Yuanhua, H. Bingliang, L. Ran, S. Lang, S. Nian, and W. Zhengjie, “Talbot effect and noise reduction in image processing based on Gyrator transform,” Infrared Laser Eng. 43, 665–670 (2014).

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Nosov, V. V.

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Y. Nakano, R. Ohmura, and K. Murata, “Refractive power mapping of progressive power lenses using Talbot interferometry and digital image processing,” Opt. Laser Technol. 22, 195–198 (1990).
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G. Calogero, N. R. Papior, B. Kretz, A. Garcia-Lekue, T. Frederiksen, and M. Brandbyge, “Electron transport in nanoporous graphene: probing the Talbot effect,” Nano Lett. 19, 576–581 (2019).
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D. Podanchuk, A. Goloborodko, M. Kotov, and D. Petriv, “Talbot sensor with diffraction grating adaptation to wavefront aberrations,” Ukr. J. Phys. 60, 10–14 (2015).
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K. Munechika, S. Cabrini, W. Chao, I. Lacey, C. Pina-Hernandez, S. Rochester, and V. V. Yashchuk, “Binary pseudo-random array test standard optimized for characterization of interferometric microscopes,” Proc. SPIE 11817, 1181704 (2021).
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D. Podanchuk, V. Danko, A. Goloborodko, and N. Goloborodko, “Shack–Hartmann wavefront sensor with the precorrected holographic lenslet array,” Optik 131, 520–526 (2017).
[Crossref]

D. Podanchuk, A. Goloborodko, M. Kotov, and D. Petriv, “Talbot sensor with diffraction grating adaptation to wavefront aberrations,” Ukr. J. Phys. 60, 10–14 (2015).
[Crossref]

J.-Y. Son, D. Podanchuk, V. Dan’ko, and K.-D. Kwak, “Shack–Hartmann wavefront sensor with holographic memory,” Opt. Eng. 42, 3326–3398 (2003).
[Crossref]

Podanchuk, D. V.

D. V. Podanchuk, A. A. Goloborodko, M. M. Kotov, A. V. Kovalenko, V. N. Kurashov, and V. P. Dan’ko, “Adaptive wavefront sensor based on the Talbot phenomenon,” Appl. Opt. 55, B150–B157 (2016).
[Crossref]

D. V. Podanchuk, M. M. Kotov, A. A. Goloborodko, V. N. Kurashov, V. P. Dan’ko, and A. V. Kurashov, “Influence of aperture size on wavefront sensor based on the Talbot effect,” Proc. SPIE 9066, 90660S (2013).
[Crossref]

D. V. Podanchuk, V. N. Kurashov, V. P. Dan’ko, M. M. Kotov, and N. S. Sutyagina, “Shack–Hartmann wavefront sensor with holographic lenslet array for the aberration measurements in a speckle field,” Semicond. Phys. Quantum Electron. Optoelectron. 11, 29–33 (2008).
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M. Yuanhua, H. Bingliang, L. Ran, S. Lang, S. Nian, and W. Zhengjie, “Talbot effect and noise reduction in image processing based on Gyrator transform,” Infrared Laser Eng. 43, 665–670 (2014).

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S. Marathe, M.-C. Zdora, I. Zanette, S. Cipiccia, and C. Rau, “Comparison of data processing techniques for single-grating x-ray Talbot interferometer data,” Proc. SPIE 10391, 103910S (2017).
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S. Mirza and C. Shakher, “Surface profiling using phase shifting Talbot interferometric technique,” Opt. Eng. 44, 013601 (2005).
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W. Grizolli, X. Shi, T. Kolodziej, Y. Shvyd’ko, and L. Assoufid, “Single-grating Talbot imaging for wavefront sensing and x-ray metrology,” Proc. SPIE 10385, 1038502 (2017).
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W. Grizolli, X. Shi, T. Kolodziej, Y. Shvyd’ko, and L. Assoufid, “Single-grating Talbot imaging for wavefront sensing and x-ray metrology,” Proc. SPIE 10385, 1038502 (2017).
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L. V. Bourimborde, A. O. Tonso, C. M. Colautti, and E. E. Sicre, “Real-time measurement of the meniscus shape using the Talbot effect,” Opt. Commun. 102, 397–400 (1993).
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J.-Y. Son, D. Podanchuk, V. Dan’ko, and K.-D. Kwak, “Shack–Hartmann wavefront sensor with holographic memory,” Opt. Eng. 42, 3326–3398 (2003).
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K. Li, F. Xia, M. Wang, P. Sun, T. Liu, W. Hu, W. Kong, M. Yun, and L. Dong, “Discrete Talbot effect in dielectric graphene plasmonic waveguide arrays,” Carbon 118, 192–199 (2017).
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D. V. Podanchuk, V. N. Kurashov, V. P. Dan’ko, M. M. Kotov, and N. S. Sutyagina, “Shack–Hartmann wavefront sensor with holographic lenslet array for the aberration measurements in a speckle field,” Semicond. Phys. Quantum Electron. Optoelectron. 11, 29–33 (2008).
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L. V. Bourimborde, A. O. Tonso, C. M. Colautti, and E. E. Sicre, “Real-time measurement of the meniscus shape using the Talbot effect,” Opt. Commun. 102, 397–400 (1993).
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F. J. Torcal-Milla, L. M. Sanchez-Brea, F. J. Salgado-Remacha, and E. Bernabeu, “Self-imaging with curved gratings,” Opt. Commun. 283, 3869–3873 (2010).
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W. Zhang, J. Wang, Y. Cui, and S. Teng, “Talbot effect of curved grating,” Opt. Commun. 341, 245–251 (2015).
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K. Li, F. Xia, M. Wang, P. Sun, T. Liu, W. Hu, W. Kong, M. Yun, and L. Dong, “Discrete Talbot effect in dielectric graphene plasmonic waveguide arrays,” Carbon 118, 192–199 (2017).
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K. Li, F. Xia, M. Wang, P. Sun, T. Liu, W. Hu, W. Kong, M. Yun, and L. Dong, “Discrete Talbot effect in dielectric graphene plasmonic waveguide arrays,” Carbon 118, 192–199 (2017).
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K. Munechika, S. Cabrini, W. Chao, I. Lacey, C. Pina-Hernandez, S. Rochester, and V. V. Yashchuk, “Binary pseudo-random array test standard optimized for characterization of interferometric microscopes,” Proc. SPIE 11817, 1181704 (2021).
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M. Yuanhua, H. Bingliang, L. Ran, S. Lang, S. Nian, and W. Zhengjie, “Talbot effect and noise reduction in image processing based on Gyrator transform,” Infrared Laser Eng. 43, 665–670 (2014).

Yun, M.

K. Li, F. Xia, M. Wang, P. Sun, T. Liu, W. Hu, W. Kong, M. Yun, and L. Dong, “Discrete Talbot effect in dielectric graphene plasmonic waveguide arrays,” Carbon 118, 192–199 (2017).
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S. Marathe, M.-C. Zdora, I. Zanette, S. Cipiccia, and C. Rau, “Comparison of data processing techniques for single-grating x-ray Talbot interferometer data,” Proc. SPIE 10391, 103910S (2017).
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S. Marathe, M.-C. Zdora, I. Zanette, S. Cipiccia, and C. Rau, “Comparison of data processing techniques for single-grating x-ray Talbot interferometer data,” Proc. SPIE 10391, 103910S (2017).
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M. Yuanhua, H. Bingliang, L. Ran, S. Lang, S. Nian, and W. Zhengjie, “Talbot effect and noise reduction in image processing based on Gyrator transform,” Infrared Laser Eng. 43, 665–670 (2014).

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Adv. Opt. Photon. (1)

Appl. Opt. (3)

Carbon (1)

K. Li, F. Xia, M. Wang, P. Sun, T. Liu, W. Hu, W. Kong, M. Yun, and L. Dong, “Discrete Talbot effect in dielectric graphene plasmonic waveguide arrays,” Carbon 118, 192–199 (2017).
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Infrared Laser Eng. (1)

M. Yuanhua, H. Bingliang, L. Ran, S. Lang, S. Nian, and W. Zhengjie, “Talbot effect and noise reduction in image processing based on Gyrator transform,” Infrared Laser Eng. 43, 665–670 (2014).

Int. J. Optomechatron. (1)

G. Zhou, Z. H. Lim, Y. Qi, F. S. Chau, and G. Zhou, “MEMS gratings and their applications,” Int. J. Optomechatron. 15, 61–86 (2021).
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J. Lightwave Technol. (1)

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1294 (1997).
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J. Opt. (1)

M. Dashti and S. Rasouli, “Measurement and statistical analysis of the wavefront distortions induced by atmospheric turbulence using two-channel Moiré deflectometry,” J. Opt. 14, 095704 (2012).
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J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

Nano Lett. (1)

G. Calogero, N. R. Papior, B. Kretz, A. Garcia-Lekue, T. Frederiksen, and M. Brandbyge, “Electron transport in nanoporous graphene: probing the Talbot effect,” Nano Lett. 19, 576–581 (2019).
[Crossref]

New J. Phys. (1)

B. J. McMorran and A. D. Cronin, “An electron Talbot interferometer,” New J. Phys. 11, 033021 (2009).
[Crossref]

Opt. Commun. (4)

L. V. Bourimborde, A. O. Tonso, C. M. Colautti, and E. E. Sicre, “Real-time measurement of the meniscus shape using the Talbot effect,” Opt. Commun. 102, 397–400 (1993).
[Crossref]

F. J. Torcal-Milla, L. M. Sanchez-Brea, F. J. Salgado-Remacha, and E. Bernabeu, “Self-imaging with curved gratings,” Opt. Commun. 283, 3869–3873 (2010).
[Crossref]

W. Zhang, J. Wang, Y. Cui, and S. Teng, “Talbot effect of curved grating,” Opt. Commun. 341, 245–251 (2015).
[Crossref]

D. F. James and G. S. Agarwal, “The generalized Fresnel transform and its application to optics,” Opt. Commun. 126, 207–212 (1996).
[Crossref]

Opt. Eng. (3)

J.-Y. Son, D. Podanchuk, V. Dan’ko, and K.-D. Kwak, “Shack–Hartmann wavefront sensor with holographic memory,” Opt. Eng. 42, 3326–3398 (2003).
[Crossref]

M. M. Kotov and A. A. Goloborodko, “Measurement range of Talbot wavefront sensor,” Opt. Eng. 56, 014101 (2017).
[Crossref]

S. Mirza and C. Shakher, “Surface profiling using phase shifting Talbot interferometric technique,” Opt. Eng. 44, 013601 (2005).
[Crossref]

Opt. Laser Eng. (1)

M. M. Kotov, V. P. Danko, and A. A. Goloborodko, “Simulation of Talbot effect from a binary phase grating using Fresnel integral approach,” Opt. Laser Eng. 137, 106400 (2021).
[Crossref]

Opt. Laser Technol. (1)

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Data Availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (5)

Fig. 1.
Fig. 1. Schematic diagram of Talbot image formation in a speckle field.
Fig. 2.
Fig. 2. Dependence of pit RMS error $\Delta x$ on the correlation radius.
Fig. 3.
Fig. 3. Dependence of pit RMS error $\Delta x$ on the correlation radius for different phase dispersion.
Fig. 4.
Fig. 4. Pit image evolution in the Talbot plane for gratings having a period of $D = 100\,\,\unicode{x00B5}{\rm m}$ illuminated by the random field with different parameters.
Fig. 5.
Fig. 5. Zernike coefficient of the first to third orders for the reconstructed wavefront with the initial Zernike value of 5 for aberration curvature, astigmatism, and coma for the different random field parameters.

Tables (1)

Tables Icon

Table 1. Results of Pit Root-Mean-Square Error Δ x Measuring Based on the Images from Fig. 4

Equations (32)

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E ( ξ , η | 0 ) = E 0 A ( ξ , η ) e j ( φ ( ξ , η ) + Z ( ξ , η ) ) ,
Z ( ξ , η ) = n , m α n m Z n m ( ξ , η ) ,
E ( x , y | z ) = E 0 + E ( ξ , η | 0 ) T ( ξ , η ) × P S F ( x ξ , y η | z ) d ξ d η ,
P S F ( x ξ , y η | z ) = 1 j λ z e j 2 π z λ e j π ( x ξ ) 2 + ( y η ) 2 λ z ,
T ( ξ , η ) = T 0 n , m C n , m e j 2 π D ( n ξ + m η ) ,
C n , m = 1 S S T ( x , y ) e j 2 π n x + m y D d x d y = s i n c ( π d D n ) s i n c ( π d D m ) ,
E ( x , y | z ) = E 0 T 0 j λ z e j 2 π z λ n , m C n , m + E ( ξ , η | 0 ) × e j π ( ( x ξ ) 2 + ( y η ) 2 λ z + 2 ( n ξ + m η ) D ) d ξ d η = E 0 T 0 j λ z e j 2 π z λ n , m C n , m e j π ( λ z D 2 ( n 2 + m 2 ) 2 x n + y m D ) × F S ^ { E ( ξ n , η m | 0 ) } ,
F S ^ { E ( ξ n , η m | 0 ) } = + E ( ξ , η | 0 ) e j π ( x λ z D n ξ ) 2 λ z × e j π ( y λ z D m η ) 2 λ z d ξ d η .
I ( x , y | z ) = E ( x , y | z ) E ( x , y | z ) = ( E 0 T 0 λ z ) 2 n , m C n , m e j π ( λ z D 2 ( n 2 + m 2 ) 2 x n + y m D ) × n , m C n , m e j π ( λ z D 2 ( n 2 + m 2 ) 2 x n + y m D ) × F S ^ { F S ^ { G ( ξ n , ξ n ; η m , η m ) } } ,
I ( x , y | z ) n , m C n , m e j π ( λ z D 2 ( n 2 + m 2 ) 2 x n + y m D ) × n , m C n , m e j π ( λ z D 2 ( n 2 + m 2 ) 2 x n + y m D ) × + G ( ξ , ξ ; η , η ) e j π ( x λ z D n ξ ) 2 + ( y λ z D m η ) 2 λ z × e j π ( x λ z D n ξ ) 2 + ( y λ z D m η ) 2 λ z d ξ d η d ξ d η ,
G ( ξ , ξ ; η , η ) = G ( ξ ξ 1 ; η η 1 ) = + S ( f x , f y ) × e j 2 π f x ( ξ ξ ) e j 2 π f y ( η η ) d f x d f y ,
I ( x , y | z ) n , m C n , m e j π ( 2 λ z D 2 ( n 2 + m 2 ) 2 x n + y m D ) × n , m C n , m e j π ( 2 λ z D 2 ( n 2 + m 2 ) 2 x n + y m D ) × + S ( f x , f y ) T ^ n ( f x ) T ^ m ( f y ) T ^ n ( f x ) × T ^ m ( f y ) d f x d f y ,
T ^ n ( f ) = + e j π ( 2 ( f n D ) ξ + ξ 2 λ z ) ,
T ^ n ( f ) = + e j π ( 2 ( f + n D ) ξ ξ 2 λ z ) .
+ e j π ( 2 f ξ + ξ 2 λ z ) d ξ = ( 1 + j ) λ z 2 e j π λ z f 2 ,
+ e j π ( 2 f ξ ξ 2 λ z ) d ξ = ( 1 j ) λ z 2 e j π λ z f 2 ,
T ^ n ( f ) e j π λ z ( f n D ) 2 ,
T ^ n ( f ) e j π λ z ( f + n D ) 2 .
I ( x , y | z ) n , m C n , m e j π ( λ z D 2 ( n 2 + m 2 ) 2 x n + y m D ) × n , m C n , m e j π ( λ z D 2 ( n 2 + m 2 ) 2 x n + y m D ) × + S ( f x , f y ) e j 2 π λ z D ( f x ( n n ) + f y ( m m ) ) × e j π λ z ( f x 2 + f y 2 ) d f x d f y .
I ( x , y | z T ) n , m , n , m C n , m C n , m e j 2 π x n + y m x n y m D × + S ( f x , f y ) e j 4 π D ( f x ( n n ) + f y ( m m ) ) × e j 2 π D 2 ( f x 2 + f y 2 ) d f x d f y .
( x , y ) = ( x , y ) I ( x , y | z T ) d x d y I ( x , y | z T ) d x d y ,
( Δ x 2 , Δ y 2 ) = ( ( x x ) 2 , ( y y ) 2 ) I ( x , y | z T ) d x d y I ( x , y | z T ) d x d y .
G ( ξ , ξ ; η , η ) e ( ξ ξ ) 2 + ( η η ) 2 2 ρ A 2 ,
S ( f x , f y ) e 2 π 2 ( f x 2 + f y 2 ) ρ A 2 ,
I ( x , y | z T ) n , m , n , m C n , m C n , m e j 2 π x n x n + y m y m D × e j 2 π D 4 ( n n ) 2 + ( m m ) 2 D 4 π 4 ρ A 4 × e 2 π 2 D 2 ρ A 2 ( n n ) 2 + ( m m ) 2 D 4 π 4 ρ A 4 .
G ( ξ x ) e σ P 2 + ( 1 e σ P 2 ) e ( ξ ξ ) 2 + ( η η ) 2 2 ρ P 2 ,
S ( f x , f y ) e σ P 2 δ ( f x , f y ) + π 2 ρ P 2 ( 1 e σ P 2 ) e 2 π 2 ( f x 2 + f y 2 ) ρ P 2 ,
δ ( f x , f y ) = { , f x = 0 , f y = 0 0 , f x 0 , f y 0 .
I ( x , y | z T ) n , m , n , m C n , m C n , m e j 2 π x ( n n ) + y ( m m ) D × ( e σ P 2 + 4 D 4 ρ P 4 ( 1 e σ P 2 ) e j 2 π D 4 ( n n ) 2 + ( m m ) 2 D 4 π 4 ρ P 4 × e 2 π 2 D 2 ρ P m 2 ( n n ) 2 + ( m m ) 2 D 4 π 4 ρ P 4 ) .
T ( x , y ) = n = 0 N 1 r e c t ( x n D d ) × m = 0 N 1 r e c t ( y m D d ) ,
T ( x , y ) = 1 4 ( cos ( 2 π x D ) + 1 ) × ( cos ( 2 π y D ) + 1 ) ;
T ( x , y ) = n = 0 N 1 m = 0 N 1 e ( x n D ) 2 + ( y m D ) 2 2 a 2 ,

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