N. Pandey, D. Kelly, T. Naughton, and B. Hennelly, “Speed up of Fresnel transforms for digital holography using pre-computed chirp and GPU processing,” Proc. SPIE 7442, 744205 (2009).

[Crossref]

F. Zhang, G. Pedrini, and W. Osten, “Phase retrieval of arbitrary complex-valued fields through aperture-plane modulation,” Phys. Rev. A 75, 043805 (2007).

[Crossref]

G. Pedrini, W. Osten, and Y. Zhang, “Wavefront reconstruction from a sequence of interferograms recorded at different planes,” Opt. Lett. 30, 833–835 (2005).

[Crossref]
[PubMed]

L. Seifert, H. J. Tiziani, and W. Osten, “Wavefront reconstruction with the adaptive Shack–Hartmann sensor,” Opt. Commun. 245, 255–269 (2005).

[Crossref]

J. Primot, “Theoretical description of Shack–Hartmann sensor,” Opt. Commun. 222, 81–92 (2003).

[Crossref]

R. Vincent, “Phase retrieval in TEM using Fresnel images,” Ultramicroscopy 90, 135–151 (2002).

[Crossref]
[PubMed]

L. J. Allen and M. P. Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun. 199, 65–75 (2001).

[Crossref]

F. Wu, H. Zhang, M. J. Lalor, and D. R. Barton, “A novel design for fiber optic interferometric fringe projection phase-shifting 3-D profilometry,” Opt. Commun. 187, 347–357 (2001).

[Crossref]

G.-C Jin and N.-K Bao, “Surface detection and 3D profilometry for microstructure using optical metrology,” Opt. Lasers Eng. 36, 1–9 (2001).

[Crossref]

C. Siegel, F. Loewenthal, and J. E. Balmer, “A wavefront sensor based on the fractional Talbot effect,” Opt. Commun. 194, 265–275 (2001).

[Crossref]

M. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198, 82–87 (2000).

[Crossref]
[PubMed]

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164, 233–245 (1999).

[Crossref]

T. Kotzer, N. Cohen, and J. Shamir, “Generalized projection algorithms with applications to optics and signal restoration,” Opt. Commun. 156, 77–91 (1998).

[Crossref]

J. Primot, L. Sogno, B. Fracasso, and K. Heggarty, “Wavefront sensor prototype for industrial applications based on three-level phase grating,” Opt. Eng. 36, 901–904 (1997).

[Crossref]

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[Crossref]

H. Kuck, W. Doleschal, A. Gehner, W. Grundke, R. Melcher, J. Paufler, R. Seltmann, and G. Zimmer, “Deformable micromirror devices as phase-modulating high-resolution light valves,” Sens. Actuators A 54, 536–541 (1996).

[Crossref]

M. Suzuki and M. Kanaya, “Applications of moiré topography measurement methods in industry,” Opt. Lasers Eng. 8, 171–188 (1988).

[Crossref]

K. Patorski, “Moiré methods in interferometry,” Opt. Lasers Eng. 8, 147–170 (1988).

[Crossref]

P. E. Gill and W. Murray, “Algorithms for the solution of the nonlinear least-squares problem,” SIAM J. Numer. Anal. 15, 977–992 (1978).

[Crossref]

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

G. E. P. Box and M. E. Muller, “A note on the generation of random normal deviates,” Ann. Math. Stat. 29, 610–611(1958).

[Crossref]

L. J. Allen and M. P. Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun. 199, 65–75 (2001).

[Crossref]

C. Siegel, F. Loewenthal, and J. E. Balmer, “A wavefront sensor based on the fractional Talbot effect,” Opt. Commun. 194, 265–275 (2001).

[Crossref]

G.-C Jin and N.-K Bao, “Surface detection and 3D profilometry for microstructure using optical metrology,” Opt. Lasers Eng. 36, 1–9 (2001).

[Crossref]

F. Wu, H. Zhang, M. J. Lalor, and D. R. Barton, “A novel design for fiber optic interferometric fringe projection phase-shifting 3-D profilometry,” Opt. Commun. 187, 347–357 (2001).

[Crossref]

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164, 233–245 (1999).

[Crossref]

G. E. P. Box and M. E. Muller, “A note on the generation of random normal deviates,” Ann. Math. Stat. 29, 610–611(1958).

[Crossref]

T. Kotzer, N. Cohen, and J. Shamir, “Generalized projection algorithms with applications to optics and signal restoration,” Opt. Commun. 156, 77–91 (1998).

[Crossref]

H. Kuck, W. Doleschal, A. Gehner, W. Grundke, R. Melcher, J. Paufler, R. Seltmann, and G. Zimmer, “Deformable micromirror devices as phase-modulating high-resolution light valves,” Sens. Actuators A 54, 536–541 (1996).

[Crossref]

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164, 233–245 (1999).

[Crossref]

J. Primot, L. Sogno, B. Fracasso, and K. Heggarty, “Wavefront sensor prototype for industrial applications based on three-level phase grating,” Opt. Eng. 36, 901–904 (1997).

[Crossref]

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164, 233–245 (1999).

[Crossref]

H. Kuck, W. Doleschal, A. Gehner, W. Grundke, R. Melcher, J. Paufler, R. Seltmann, and G. Zimmer, “Deformable micromirror devices as phase-modulating high-resolution light valves,” Sens. Actuators A 54, 536–541 (1996).

[Crossref]

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

P. E. Gill and W. Murray, “Algorithms for the solution of the nonlinear least-squares problem,” SIAM J. Numer. Anal. 15, 977–992 (1978).

[Crossref]

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

H. Kuck, W. Doleschal, A. Gehner, W. Grundke, R. Melcher, J. Paufler, R. Seltmann, and G. Zimmer, “Deformable micromirror devices as phase-modulating high-resolution light valves,” Sens. Actuators A 54, 536–541 (1996).

[Crossref]

M. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198, 82–87 (2000).

[Crossref]
[PubMed]

J. Primot, L. Sogno, B. Fracasso, and K. Heggarty, “Wavefront sensor prototype for industrial applications based on three-level phase grating,” Opt. Eng. 36, 901–904 (1997).

[Crossref]

N. Pandey, D. Kelly, T. Naughton, and B. Hennelly, “Speed up of Fresnel transforms for digital holography using pre-computed chirp and GPU processing,” Proc. SPIE 7442, 744205 (2009).

[Crossref]

J. L. Hornbeck, “Current status of the digital micromirror device (DMD) for projection television applications,” in International Electron Devices Meeting IEDM ’93 Technical Digest (IEEE, 1993), pp. 381–384.

G.-C Jin and N.-K Bao, “Surface detection and 3D profilometry for microstructure using optical metrology,” Opt. Lasers Eng. 36, 1–9 (2001).

[Crossref]

M. Suzuki and M. Kanaya, “Applications of moiré topography measurement methods in industry,” Opt. Lasers Eng. 8, 171–188 (1988).

[Crossref]

N. Pandey, D. Kelly, T. Naughton, and B. Hennelly, “Speed up of Fresnel transforms for digital holography using pre-computed chirp and GPU processing,” Proc. SPIE 7442, 744205 (2009).

[Crossref]

T. Kotzer, N. Cohen, and J. Shamir, “Generalized projection algorithms with applications to optics and signal restoration,” Opt. Commun. 156, 77–91 (1998).

[Crossref]

H. Kuck, W. Doleschal, A. Gehner, W. Grundke, R. Melcher, J. Paufler, R. Seltmann, and G. Zimmer, “Deformable micromirror devices as phase-modulating high-resolution light valves,” Sens. Actuators A 54, 536–541 (1996).

[Crossref]

F. Wu, H. Zhang, M. J. Lalor, and D. R. Barton, “A novel design for fiber optic interferometric fringe projection phase-shifting 3-D profilometry,” Opt. Commun. 187, 347–357 (2001).

[Crossref]

C. Siegel, F. Loewenthal, and J. E. Balmer, “A wavefront sensor based on the fractional Talbot effect,” Opt. Commun. 194, 265–275 (2001).

[Crossref]

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164, 233–245 (1999).

[Crossref]

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164, 233–245 (1999).

[Crossref]

A. Mazine, “La caractérisation de front d’onde dans un système de propagation à multi-illumination gérée par un SLM,” doctoral thesis (Ecole Nationale Supérieure des Télécommunications Paris, 2006), pp. 1–126.

H. Kuck, W. Doleschal, A. Gehner, W. Grundke, R. Melcher, J. Paufler, R. Seltmann, and G. Zimmer, “Deformable micromirror devices as phase-modulating high-resolution light valves,” Sens. Actuators A 54, 536–541 (1996).

[Crossref]

G. E. P. Box and M. E. Muller, “A note on the generation of random normal deviates,” Ann. Math. Stat. 29, 610–611(1958).

[Crossref]

P. E. Gill and W. Murray, “Algorithms for the solution of the nonlinear least-squares problem,” SIAM J. Numer. Anal. 15, 977–992 (1978).

[Crossref]

N. Pandey, D. Kelly, T. Naughton, and B. Hennelly, “Speed up of Fresnel transforms for digital holography using pre-computed chirp and GPU processing,” Proc. SPIE 7442, 744205 (2009).

[Crossref]

F. Zhang, G. Pedrini, and W. Osten, “Phase retrieval of arbitrary complex-valued fields through aperture-plane modulation,” Phys. Rev. A 75, 043805 (2007).

[Crossref]

L. Seifert, H. J. Tiziani, and W. Osten, “Wavefront reconstruction with the adaptive Shack–Hartmann sensor,” Opt. Commun. 245, 255–269 (2005).

[Crossref]

G. Pedrini, W. Osten, and Y. Zhang, “Wavefront reconstruction from a sequence of interferograms recorded at different planes,” Opt. Lett. 30, 833–835 (2005).

[Crossref]
[PubMed]

L. J. Allen and M. P. Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun. 199, 65–75 (2001).

[Crossref]

N. Pandey, D. Kelly, T. Naughton, and B. Hennelly, “Speed up of Fresnel transforms for digital holography using pre-computed chirp and GPU processing,” Proc. SPIE 7442, 744205 (2009).

[Crossref]

K. Patorski, “Moiré methods in interferometry,” Opt. Lasers Eng. 8, 147–170 (1988).

[Crossref]

K. Patorski, The Self-Imaging Phenomenon and Its Applications, Vol. 27 of Progress in Optics (Elsevier, 1989) pp. 1–110.

H. Kuck, W. Doleschal, A. Gehner, W. Grundke, R. Melcher, J. Paufler, R. Seltmann, and G. Zimmer, “Deformable micromirror devices as phase-modulating high-resolution light valves,” Sens. Actuators A 54, 536–541 (1996).

[Crossref]

F. Zhang, G. Pedrini, and W. Osten, “Phase retrieval of arbitrary complex-valued fields through aperture-plane modulation,” Phys. Rev. A 75, 043805 (2007).

[Crossref]

G. Pedrini, W. Osten, and Y. Zhang, “Wavefront reconstruction from a sequence of interferograms recorded at different planes,” Opt. Lett. 30, 833–835 (2005).

[Crossref]
[PubMed]

J. Primot, “Theoretical description of Shack–Hartmann sensor,” Opt. Commun. 222, 81–92 (2003).

[Crossref]

J. Primot, L. Sogno, B. Fracasso, and K. Heggarty, “Wavefront sensor prototype for industrial applications based on three-level phase grating,” Opt. Eng. 36, 901–904 (1997).

[Crossref]

P. K. Rastogi, Optical Measurements Techniques and Applications (Artech, 1997).

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

L. Seifert, H. J. Tiziani, and W. Osten, “Wavefront reconstruction with the adaptive Shack–Hartmann sensor,” Opt. Commun. 245, 255–269 (2005).

[Crossref]

H. Kuck, W. Doleschal, A. Gehner, W. Grundke, R. Melcher, J. Paufler, R. Seltmann, and G. Zimmer, “Deformable micromirror devices as phase-modulating high-resolution light valves,” Sens. Actuators A 54, 536–541 (1996).

[Crossref]

T. Kotzer, N. Cohen, and J. Shamir, “Generalized projection algorithms with applications to optics and signal restoration,” Opt. Commun. 156, 77–91 (1998).

[Crossref]

C. Siegel, F. Loewenthal, and J. E. Balmer, “A wavefront sensor based on the fractional Talbot effect,” Opt. Commun. 194, 265–275 (2001).

[Crossref]

J. Primot, L. Sogno, B. Fracasso, and K. Heggarty, “Wavefront sensor prototype for industrial applications based on three-level phase grating,” Opt. Eng. 36, 901–904 (1997).

[Crossref]

M. Suzuki and M. Kanaya, “Applications of moiré topography measurement methods in industry,” Opt. Lasers Eng. 8, 171–188 (1988).

[Crossref]

L. Seifert, H. J. Tiziani, and W. Osten, “Wavefront reconstruction with the adaptive Shack–Hartmann sensor,” Opt. Commun. 245, 255–269 (2005).

[Crossref]

R. Vincent, “Phase retrieval in TEM using Fresnel images,” Ultramicroscopy 90, 135–151 (2002).

[Crossref]
[PubMed]

F. Wu, H. Zhang, M. J. Lalor, and D. R. Barton, “A novel design for fiber optic interferometric fringe projection phase-shifting 3-D profilometry,” Opt. Commun. 187, 347–357 (2001).

[Crossref]

F. Zhang, G. Pedrini, and W. Osten, “Phase retrieval of arbitrary complex-valued fields through aperture-plane modulation,” Phys. Rev. A 75, 043805 (2007).

[Crossref]

F. Wu, H. Zhang, M. J. Lalor, and D. R. Barton, “A novel design for fiber optic interferometric fringe projection phase-shifting 3-D profilometry,” Opt. Commun. 187, 347–357 (2001).

[Crossref]

H. Kuck, W. Doleschal, A. Gehner, W. Grundke, R. Melcher, J. Paufler, R. Seltmann, and G. Zimmer, “Deformable micromirror devices as phase-modulating high-resolution light valves,” Sens. Actuators A 54, 536–541 (1996).

[Crossref]

G. E. P. Box and M. E. Muller, “A note on the generation of random normal deviates,” Ann. Math. Stat. 29, 610–611(1958).

[Crossref]

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[Crossref]
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[Crossref]
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[Crossref]
[PubMed]

M. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198, 82–87 (2000).

[Crossref]
[PubMed]

L. J. Allen and M. P. Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun. 199, 65–75 (2001).

[Crossref]

J. Primot, “Theoretical description of Shack–Hartmann sensor,” Opt. Commun. 222, 81–92 (2003).

[Crossref]

L. Seifert, H. J. Tiziani, and W. Osten, “Wavefront reconstruction with the adaptive Shack–Hartmann sensor,” Opt. Commun. 245, 255–269 (2005).

[Crossref]

F. Wu, H. Zhang, M. J. Lalor, and D. R. Barton, “A novel design for fiber optic interferometric fringe projection phase-shifting 3-D profilometry,” Opt. Commun. 187, 347–357 (2001).

[Crossref]

C. Siegel, F. Loewenthal, and J. E. Balmer, “A wavefront sensor based on the fractional Talbot effect,” Opt. Commun. 194, 265–275 (2001).

[Crossref]

T. Kotzer, N. Cohen, and J. Shamir, “Generalized projection algorithms with applications to optics and signal restoration,” Opt. Commun. 156, 77–91 (1998).

[Crossref]

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164, 233–245 (1999).

[Crossref]

J. Primot, L. Sogno, B. Fracasso, and K. Heggarty, “Wavefront sensor prototype for industrial applications based on three-level phase grating,” Opt. Eng. 36, 901–904 (1997).

[Crossref]

G.-C Jin and N.-K Bao, “Surface detection and 3D profilometry for microstructure using optical metrology,” Opt. Lasers Eng. 36, 1–9 (2001).

[Crossref]

M. Suzuki and M. Kanaya, “Applications of moiré topography measurement methods in industry,” Opt. Lasers Eng. 8, 171–188 (1988).

[Crossref]

K. Patorski, “Moiré methods in interferometry,” Opt. Lasers Eng. 8, 147–170 (1988).

[Crossref]

S. Wolfling, N. Ben-Yosef, and Y. Arieli, “Generalized method for wave-front analysis,” Opt. Lett. 29, 462–464 (2004).

[Crossref]
[PubMed]

G. Pedrini, W. Osten, and Y. Zhang, “Wavefront reconstruction from a sequence of interferograms recorded at different planes,” Opt. Lett. 30, 833–835 (2005).

[Crossref]
[PubMed]

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

F. Zhang, G. Pedrini, and W. Osten, “Phase retrieval of arbitrary complex-valued fields through aperture-plane modulation,” Phys. Rev. A 75, 043805 (2007).

[Crossref]

N. Pandey, D. Kelly, T. Naughton, and B. Hennelly, “Speed up of Fresnel transforms for digital holography using pre-computed chirp and GPU processing,” Proc. SPIE 7442, 744205 (2009).

[Crossref]

H. Kuck, W. Doleschal, A. Gehner, W. Grundke, R. Melcher, J. Paufler, R. Seltmann, and G. Zimmer, “Deformable micromirror devices as phase-modulating high-resolution light valves,” Sens. Actuators A 54, 536–541 (1996).

[Crossref]

P. E. Gill and W. Murray, “Algorithms for the solution of the nonlinear least-squares problem,” SIAM J. Numer. Anal. 15, 977–992 (1978).

[Crossref]

R. Vincent, “Phase retrieval in TEM using Fresnel images,” Ultramicroscopy 90, 135–151 (2002).

[Crossref]
[PubMed]

P. K. Rastogi, Optical Measurements Techniques and Applications (Artech, 1997).

K. Patorski, The Self-Imaging Phenomenon and Its Applications, Vol. 27 of Progress in Optics (Elsevier, 1989) pp. 1–110.

A. Mazine, “La caractérisation de front d’onde dans un système de propagation à multi-illumination gérée par un SLM,” doctoral thesis (Ecole Nationale Supérieure des Télécommunications Paris, 2006), pp. 1–126.

J. L. Hornbeck, “Current status of the digital micromirror device (DMD) for projection television applications,” in International Electron Devices Meeting IEDM ’93 Technical Digest (IEEE, 1993), pp. 381–384.

Holoeye systems, http∶//www.holoeyesystems.com/.

Texas Instruments, http∶//www.dlp.com/.

Boston Micromachines, http∶//www.bostonmicromachines.com.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

Forward and backward DFrT calculations are generally computed with the help of fast Fourier transform algorithms designed in an optimal manner for both speed and accuracy.