J. A. Ferrari, G. A. Ayubi, J. L. Flores, and C. D. Perciante, “Transport of intensity equation: Validity limits of the usually accepted solution,” Opt. Commun. 318, 133–136 (2014).

[Crossref]

A. Shanker, L. Tian, M. Sczyrba, B. Connolly, A. Neureuther, and L. Waller, “Transport of intensity phase imaging in the presence of curl effects induced by strongly absorbing photomasks,” Appl. Opt. 53, J1–J6 (2014).

[Crossref]

Z. Jingshan, R. A. Claus, J. Dauwels, L. Tian, and L. Waller, “Transport of intensity phase imaging by intensity spectrum fitting of exponentially spaced defocus planes,” Opt. Express 22, 10661–10674 (2014).

[Crossref]
[PubMed]

C. Zuo, Q. Chen, Y. Yu, and A. Asundi, “Transport-of-intensity phase imaging using savitzky-golay differentiation filter-theory and applications,” Opt. Express 21, 5346–5362 (2013).

[Crossref]
[PubMed]

A. Kostenko, K. J. Batenburg, A. King, S. E. Offerman, and L. J. van Vliet, “Total variation minimization approach in in-line x-ray phase-contrast tomography,” Opt. Express 21, 12185–12196 (2013).

[Crossref]
[PubMed]

J. C. Petruccelli, L. Tian, and G. Barbastathis, “The transport of intensity equation for optical path length recovery using partially coherent illumination,” Opt. Express 21, 14430–14441 (2013).

[Crossref]
[PubMed]

L. Tian, J. C. Petruccelli, and G. Barbastathis, “Nonlinear diffusion regularization for transport of intensity phase imaging,” Opt. Lett. 37, 4131 (2012).

[Crossref]
[PubMed]

R. Bie, X.-H. Yuan, M. Zhao, and L. Zhang, “Method for estimating the axial intensity derivative in the tie with higher order intensity derivatives and noise suppression,” Opt. Express 20, 8186–8191 (2012).

[Crossref]
[PubMed]

S. Zheng, B. Xue, W. Xue, X. Bai, and F. Zhou, “Transport of intensity phase imaging from multiple noisy intensities measured in unequally-spaced planes,” Opt. Express 20, 972–985 (2012).

[Crossref]
[PubMed]

J. A. Schmalz, T. E. Gureyev, D. M. Paganin, and K. M. Pavlov, “Phase retrieval using radiation and matter-wave fields: Validity of Teague’s method for solution of the transport-of-intensity equation,” Phys. Rev. A 84, 023808 (2011).

[Crossref]

J. M. Bardsley, S. Knepper, and J. Nagy, “Structured linear algebra problems in adaptive optics imaging,” Advances in Computational Mathematics 35, 103–117 (2011).

[Crossref]

S. S. Kou, L. Waller, G. Barbastathis, and C. J. R. Sheppard, “Transport-of-intensity approach to differential interference contrast (ti-dic) microscopy for quantitative phase imaging,” Opt. Lett. 35, 447–449 (2010).

[Crossref]
[PubMed]

L. Waller, L. Tian, and G. Barbastathis, “Transport of intensity phase-amplitude imaging with higher order intensity derivatives,” Opt. Express 18, 12552–12561 (2010).

[Crossref]
[PubMed]

G. R. Brady and J. R. Fienup, “Nonlinear optimization algorithm for retrieving the full complex pupil function,” Opt. Express 14, 474–486 (2006).

[Crossref]
[PubMed]

T. Gureyev, Y. I. Nesterets, D. Paganin, A. Pogany, and S. Wilkins, “Linear algorithms for phase retrieval in the fresnel region. 2. partially coherent illumination,” Opt. Commun. 259, 569–580 (2006).

[Crossref]

K. Ishizuka and B. Allman, “Phase measurement of atomic resolution image using transport of intensity equation,” J. Electron Microsc. 54, 191–197 (2005).

[Crossref]

M. Beleggia, M. Schofield, V. V. Volkov, and Y. Zhu, “On the transport of intensity technique for phase retrieval,” Ultramicroscopy 102, 37–49 (2004).

[Crossref]
[PubMed]

D. Paganin, A. Barty, P. J. McMahon, and K. A. Nugent, “Quantitative phase-amplitude microscopy. III. The effects of noise,” J. Microsc. 214, 51–61 (2004).

[Crossref]
[PubMed]

B. E. Allan, P. J. McMahon, K. A. Nugent, D. Paganin, D. L. Jacobson, M. Arif, and S. A. Werner, “Phase radiography with neutrons,” Nature 408, 158–159 (2000).

[Crossref]

T. E. Gureyev and S. W. Wilkins, “On x-ray phase imaging with a point source,” J. Opt. Soc. Am. A 15, 579–585 (1998).

[Crossref]

A. Barty, K. Nugent, D. Paganin, and A. Roberts, “Quantitative optical phase microscopy,” Opt. Lett. 23, 817–819 (1998).

[Crossref]

D. Paganin and K. A. Nugent, “Noninterferometric phase imaging with partially coherent light,” Phys. Rev. Lett. 80, 2586–2589 (1998).

[Crossref]

K. Scheerschmidt, “Retrieval of object information by inverse problems in electron diffraction,” J. Microsc. 190, 238–248 (1998).

[Crossref]

T. E. Gureyev and K. A. Nugent, “Rapid quantitative phase imaging using the transport of intensity equation,” Opt. Commun. 133, 339–346 (1997).

[Crossref]

K. A. Nugent, T. E. Gureyev, D. J. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard X rays,” Phys. Rev. Lett. 77, 2961–2964 (1996).

[Crossref]
[PubMed]

N. Streibl, “Phase imaging by the transport equation of intensity,” Opt. Commun. 49, 6–10 (1984).

[Crossref]

R. Henderson and P. N. T. Unwin, “Three-dimensional model of purple membrane obtained by electron microscopy,” Nature 257, 28–32 (1975).

[Crossref]
[PubMed]

B. E. Allan, P. J. McMahon, K. A. Nugent, D. Paganin, D. L. Jacobson, M. Arif, and S. A. Werner, “Phase radiography with neutrons,” Nature 408, 158–159 (2000).

[Crossref]

K. Ishizuka and B. Allman, “Phase measurement of atomic resolution image using transport of intensity equation,” J. Electron Microsc. 54, 191–197 (2005).

[Crossref]

B. E. Allan, P. J. McMahon, K. A. Nugent, D. Paganin, D. L. Jacobson, M. Arif, and S. A. Werner, “Phase radiography with neutrons,” Nature 408, 158–159 (2000).

[Crossref]

J. A. Ferrari, G. A. Ayubi, J. L. Flores, and C. D. Perciante, “Transport of intensity equation: Validity limits of the usually accepted solution,” Opt. Commun. 318, 133–136 (2014).

[Crossref]

J. C. Petruccelli, L. Tian, and G. Barbastathis, “The transport of intensity equation for optical path length recovery using partially coherent illumination,” Opt. Express 21, 14430–14441 (2013).

[Crossref]
[PubMed]

L. Tian, J. C. Petruccelli, and G. Barbastathis, “Nonlinear diffusion regularization for transport of intensity phase imaging,” Opt. Lett. 37, 4131 (2012).

[Crossref]
[PubMed]

L. Waller, L. Tian, and G. Barbastathis, “Transport of intensity phase-amplitude imaging with higher order intensity derivatives,” Opt. Express 18, 12552–12561 (2010).

[Crossref]
[PubMed]

S. S. Kou, L. Waller, G. Barbastathis, and C. J. R. Sheppard, “Transport-of-intensity approach to differential interference contrast (ti-dic) microscopy for quantitative phase imaging,” Opt. Lett. 35, 447–449 (2010).

[Crossref]
[PubMed]

J. M. Bardsley, S. Knepper, and J. Nagy, “Structured linear algebra problems in adaptive optics imaging,” Advances in Computational Mathematics 35, 103–117 (2011).

[Crossref]

K. A. Nugent, T. E. Gureyev, D. J. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard X rays,” Phys. Rev. Lett. 77, 2961–2964 (1996).

[Crossref]
[PubMed]

D. Paganin, A. Barty, P. J. McMahon, and K. A. Nugent, “Quantitative phase-amplitude microscopy. III. The effects of noise,” J. Microsc. 214, 51–61 (2004).

[Crossref]
[PubMed]

A. Barty, K. Nugent, D. Paganin, and A. Roberts, “Quantitative optical phase microscopy,” Opt. Lett. 23, 817–819 (1998).

[Crossref]

L. N. Trefethen and D. Bau, Numerical Linear Algebra, vol. 50 (Siam, 1997), pp. 77–82.

M. Beleggia, M. Schofield, V. V. Volkov, and Y. Zhu, “On the transport of intensity technique for phase retrieval,” Ultramicroscopy 102, 37–49 (2004).

[Crossref]
[PubMed]

E. Froustey, E. Bostan, S. Lefkimmiatis, and M. Unser, “Digital phase reconstruction via iterative solutions of transport-of-intensity equation,” in the 2014 13th Workshop on Information Optics, WIO (2014) pp. 1–3.

J. Cheng and S. Han, “X-ray phase imaging with a finite size source,” in “International Symposium on Biomedical Optics,” (International Society for Optics and Photonics, 1999), pp. 119–123.

K. A. Nugent, T. E. Gureyev, D. J. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard X rays,” Phys. Rev. Lett. 77, 2961–2964 (1996).

[Crossref]
[PubMed]

J. A. Ferrari, G. A. Ayubi, J. L. Flores, and C. D. Perciante, “Transport of intensity equation: Validity limits of the usually accepted solution,” Opt. Commun. 318, 133–136 (2014).

[Crossref]

J. A. Ferrari, G. A. Ayubi, J. L. Flores, and C. D. Perciante, “Transport of intensity equation: Validity limits of the usually accepted solution,” Opt. Commun. 318, 133–136 (2014).

[Crossref]

E. Froustey, E. Bostan, S. Lefkimmiatis, and M. Unser, “Digital phase reconstruction via iterative solutions of transport-of-intensity equation,” in the 2014 13th Workshop on Information Optics, WIO (2014) pp. 1–3.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (Roberts and Company Publishers, 1996), Sec. 6.6.

T. Gureyev, Y. I. Nesterets, D. Paganin, A. Pogany, and S. Wilkins, “Linear algorithms for phase retrieval in the fresnel region. 2. partially coherent illumination,” Opt. Commun. 259, 569–580 (2006).

[Crossref]

Y. I. Nesterets and T. E. Gureyev, “Partially coherent contrast-transfer-function approximation,” J. Opt. Soc. Am. A 33, 464–474 (2016).

[Crossref]

J. A. Schmalz, T. E. Gureyev, D. M. Paganin, and K. M. Pavlov, “Phase retrieval using radiation and matter-wave fields: Validity of Teague’s method for solution of the transport-of-intensity equation,” Phys. Rev. A 84, 023808 (2011).

[Crossref]

T. E. Gureyev and S. W. Wilkins, “On x-ray phase imaging with a point source,” J. Opt. Soc. Am. A 15, 579–585 (1998).

[Crossref]

T. E. Gureyev and K. A. Nugent, “Rapid quantitative phase imaging using the transport of intensity equation,” Opt. Commun. 133, 339–346 (1997).

[Crossref]

K. A. Nugent, T. E. Gureyev, D. J. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard X rays,” Phys. Rev. Lett. 77, 2961–2964 (1996).

[Crossref]
[PubMed]

J. Cheng and S. Han, “X-ray phase imaging with a finite size source,” in “International Symposium on Biomedical Optics,” (International Society for Optics and Photonics, 1999), pp. 119–123.

R. Henderson and P. N. T. Unwin, “Three-dimensional model of purple membrane obtained by electron microscopy,” Nature 257, 28–32 (1975).

[Crossref]
[PubMed]

K. Ishizuka and B. Allman, “Phase measurement of atomic resolution image using transport of intensity equation,” J. Electron Microsc. 54, 191–197 (2005).

[Crossref]

B. E. Allan, P. J. McMahon, K. A. Nugent, D. Paganin, D. L. Jacobson, M. Arif, and S. A. Werner, “Phase radiography with neutrons,” Nature 408, 158–159 (2000).

[Crossref]

J. M. Bardsley, S. Knepper, and J. Nagy, “Structured linear algebra problems in adaptive optics imaging,” Advances in Computational Mathematics 35, 103–117 (2011).

[Crossref]

E. Froustey, E. Bostan, S. Lefkimmiatis, and M. Unser, “Digital phase reconstruction via iterative solutions of transport-of-intensity equation,” in the 2014 13th Workshop on Information Optics, WIO (2014) pp. 1–3.

D. Paganin, A. Barty, P. J. McMahon, and K. A. Nugent, “Quantitative phase-amplitude microscopy. III. The effects of noise,” J. Microsc. 214, 51–61 (2004).

[Crossref]
[PubMed]

B. E. Allan, P. J. McMahon, K. A. Nugent, D. Paganin, D. L. Jacobson, M. Arif, and S. A. Werner, “Phase radiography with neutrons,” Nature 408, 158–159 (2000).

[Crossref]

J. M. Bardsley, S. Knepper, and J. Nagy, “Structured linear algebra problems in adaptive optics imaging,” Advances in Computational Mathematics 35, 103–117 (2011).

[Crossref]

Y. I. Nesterets and T. E. Gureyev, “Partially coherent contrast-transfer-function approximation,” J. Opt. Soc. Am. A 33, 464–474 (2016).

[Crossref]

T. Gureyev, Y. I. Nesterets, D. Paganin, A. Pogany, and S. Wilkins, “Linear algorithms for phase retrieval in the fresnel region. 2. partially coherent illumination,” Opt. Commun. 259, 569–580 (2006).

[Crossref]

D. Paganin, A. Barty, P. J. McMahon, and K. A. Nugent, “Quantitative phase-amplitude microscopy. III. The effects of noise,” J. Microsc. 214, 51–61 (2004).

[Crossref]
[PubMed]

B. E. Allan, P. J. McMahon, K. A. Nugent, D. Paganin, D. L. Jacobson, M. Arif, and S. A. Werner, “Phase radiography with neutrons,” Nature 408, 158–159 (2000).

[Crossref]

D. Paganin and K. A. Nugent, “Noninterferometric phase imaging with partially coherent light,” Phys. Rev. Lett. 80, 2586–2589 (1998).

[Crossref]

T. E. Gureyev and K. A. Nugent, “Rapid quantitative phase imaging using the transport of intensity equation,” Opt. Commun. 133, 339–346 (1997).

[Crossref]

K. A. Nugent, T. E. Gureyev, D. J. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard X rays,” Phys. Rev. Lett. 77, 2961–2964 (1996).

[Crossref]
[PubMed]

T. Gureyev, Y. I. Nesterets, D. Paganin, A. Pogany, and S. Wilkins, “Linear algorithms for phase retrieval in the fresnel region. 2. partially coherent illumination,” Opt. Commun. 259, 569–580 (2006).

[Crossref]

D. Paganin, A. Barty, P. J. McMahon, and K. A. Nugent, “Quantitative phase-amplitude microscopy. III. The effects of noise,” J. Microsc. 214, 51–61 (2004).

[Crossref]
[PubMed]

B. E. Allan, P. J. McMahon, K. A. Nugent, D. Paganin, D. L. Jacobson, M. Arif, and S. A. Werner, “Phase radiography with neutrons,” Nature 408, 158–159 (2000).

[Crossref]

A. Barty, K. Nugent, D. Paganin, and A. Roberts, “Quantitative optical phase microscopy,” Opt. Lett. 23, 817–819 (1998).

[Crossref]

D. Paganin and K. A. Nugent, “Noninterferometric phase imaging with partially coherent light,” Phys. Rev. Lett. 80, 2586–2589 (1998).

[Crossref]

K. A. Nugent, T. E. Gureyev, D. J. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard X rays,” Phys. Rev. Lett. 77, 2961–2964 (1996).

[Crossref]
[PubMed]

J. A. Schmalz, T. E. Gureyev, D. M. Paganin, and K. M. Pavlov, “Phase retrieval using radiation and matter-wave fields: Validity of Teague’s method for solution of the transport-of-intensity equation,” Phys. Rev. A 84, 023808 (2011).

[Crossref]

J. A. Schmalz, T. E. Gureyev, D. M. Paganin, and K. M. Pavlov, “Phase retrieval using radiation and matter-wave fields: Validity of Teague’s method for solution of the transport-of-intensity equation,” Phys. Rev. A 84, 023808 (2011).

[Crossref]

J. A. Ferrari, G. A. Ayubi, J. L. Flores, and C. D. Perciante, “Transport of intensity equation: Validity limits of the usually accepted solution,” Opt. Commun. 318, 133–136 (2014).

[Crossref]

J. C. Petruccelli, L. Tian, and G. Barbastathis, “The transport of intensity equation for optical path length recovery using partially coherent illumination,” Opt. Express 21, 14430–14441 (2013).

[Crossref]
[PubMed]

L. Tian, J. C. Petruccelli, and G. Barbastathis, “Nonlinear diffusion regularization for transport of intensity phase imaging,” Opt. Lett. 37, 4131 (2012).

[Crossref]
[PubMed]

T. Gureyev, Y. I. Nesterets, D. Paganin, A. Pogany, and S. Wilkins, “Linear algorithms for phase retrieval in the fresnel region. 2. partially coherent illumination,” Opt. Commun. 259, 569–580 (2006).

[Crossref]

K. Scheerschmidt, “Retrieval of object information by inverse problems in electron diffraction,” J. Microsc. 190, 238–248 (1998).

[Crossref]

J. A. Schmalz, T. E. Gureyev, D. M. Paganin, and K. M. Pavlov, “Phase retrieval using radiation and matter-wave fields: Validity of Teague’s method for solution of the transport-of-intensity equation,” Phys. Rev. A 84, 023808 (2011).

[Crossref]

M. Beleggia, M. Schofield, V. V. Volkov, and Y. Zhu, “On the transport of intensity technique for phase retrieval,” Ultramicroscopy 102, 37–49 (2004).

[Crossref]
[PubMed]

N. Streibl, “Phase imaging by the transport equation of intensity,” Opt. Commun. 49, 6–10 (1984).

[Crossref]

Z. Jingshan, R. A. Claus, J. Dauwels, L. Tian, and L. Waller, “Transport of intensity phase imaging by intensity spectrum fitting of exponentially spaced defocus planes,” Opt. Express 22, 10661–10674 (2014).

[Crossref]
[PubMed]

A. Shanker, L. Tian, M. Sczyrba, B. Connolly, A. Neureuther, and L. Waller, “Transport of intensity phase imaging in the presence of curl effects induced by strongly absorbing photomasks,” Appl. Opt. 53, J1–J6 (2014).

[Crossref]

J. C. Petruccelli, L. Tian, and G. Barbastathis, “The transport of intensity equation for optical path length recovery using partially coherent illumination,” Opt. Express 21, 14430–14441 (2013).

[Crossref]
[PubMed]

L. Tian, J. C. Petruccelli, and G. Barbastathis, “Nonlinear diffusion regularization for transport of intensity phase imaging,” Opt. Lett. 37, 4131 (2012).

[Crossref]
[PubMed]

L. Waller, L. Tian, and G. Barbastathis, “Transport of intensity phase-amplitude imaging with higher order intensity derivatives,” Opt. Express 18, 12552–12561 (2010).

[Crossref]
[PubMed]

L. N. Trefethen and D. Bau, Numerical Linear Algebra, vol. 50 (Siam, 1997), pp. 77–82.

E. Froustey, E. Bostan, S. Lefkimmiatis, and M. Unser, “Digital phase reconstruction via iterative solutions of transport-of-intensity equation,” in the 2014 13th Workshop on Information Optics, WIO (2014) pp. 1–3.

R. Henderson and P. N. T. Unwin, “Three-dimensional model of purple membrane obtained by electron microscopy,” Nature 257, 28–32 (1975).

[Crossref]
[PubMed]

M. Beleggia, M. Schofield, V. V. Volkov, and Y. Zhu, “On the transport of intensity technique for phase retrieval,” Ultramicroscopy 102, 37–49 (2004).

[Crossref]
[PubMed]

Z. Jingshan, R. A. Claus, J. Dauwels, L. Tian, and L. Waller, “Transport of intensity phase imaging by intensity spectrum fitting of exponentially spaced defocus planes,” Opt. Express 22, 10661–10674 (2014).

[Crossref]
[PubMed]

A. Shanker, L. Tian, M. Sczyrba, B. Connolly, A. Neureuther, and L. Waller, “Transport of intensity phase imaging in the presence of curl effects induced by strongly absorbing photomasks,” Appl. Opt. 53, J1–J6 (2014).

[Crossref]

S. S. Kou, L. Waller, G. Barbastathis, and C. J. R. Sheppard, “Transport-of-intensity approach to differential interference contrast (ti-dic) microscopy for quantitative phase imaging,” Opt. Lett. 35, 447–449 (2010).

[Crossref]
[PubMed]

L. Waller, L. Tian, and G. Barbastathis, “Transport of intensity phase-amplitude imaging with higher order intensity derivatives,” Opt. Express 18, 12552–12561 (2010).

[Crossref]
[PubMed]

B. E. Allan, P. J. McMahon, K. A. Nugent, D. Paganin, D. L. Jacobson, M. Arif, and S. A. Werner, “Phase radiography with neutrons,” Nature 408, 158–159 (2000).

[Crossref]

T. Gureyev, Y. I. Nesterets, D. Paganin, A. Pogany, and S. Wilkins, “Linear algorithms for phase retrieval in the fresnel region. 2. partially coherent illumination,” Opt. Commun. 259, 569–580 (2006).

[Crossref]

M. Beleggia, M. Schofield, V. V. Volkov, and Y. Zhu, “On the transport of intensity technique for phase retrieval,” Ultramicroscopy 102, 37–49 (2004).

[Crossref]
[PubMed]

J. M. Bardsley, S. Knepper, and J. Nagy, “Structured linear algebra problems in adaptive optics imaging,” Advances in Computational Mathematics 35, 103–117 (2011).

[Crossref]

A. Shanker, L. Tian, M. Sczyrba, B. Connolly, A. Neureuther, and L. Waller, “Transport of intensity phase imaging in the presence of curl effects induced by strongly absorbing photomasks,” Appl. Opt. 53, J1–J6 (2014).

[Crossref]

J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982).

[Crossref]
[PubMed]

K. Ishizuka and B. Allman, “Phase measurement of atomic resolution image using transport of intensity equation,” J. Electron Microsc. 54, 191–197 (2005).

[Crossref]

D. Paganin, A. Barty, P. J. McMahon, and K. A. Nugent, “Quantitative phase-amplitude microscopy. III. The effects of noise,” J. Microsc. 214, 51–61 (2004).

[Crossref]
[PubMed]

K. Scheerschmidt, “Retrieval of object information by inverse problems in electron diffraction,” J. Microsc. 190, 238–248 (1998).

[Crossref]

R. Henderson and P. N. T. Unwin, “Three-dimensional model of purple membrane obtained by electron microscopy,” Nature 257, 28–32 (1975).

[Crossref]
[PubMed]

B. E. Allan, P. J. McMahon, K. A. Nugent, D. Paganin, D. L. Jacobson, M. Arif, and S. A. Werner, “Phase radiography with neutrons,” Nature 408, 158–159 (2000).

[Crossref]

N. Streibl, “Phase imaging by the transport equation of intensity,” Opt. Commun. 49, 6–10 (1984).

[Crossref]

J. A. Ferrari, G. A. Ayubi, J. L. Flores, and C. D. Perciante, “Transport of intensity equation: Validity limits of the usually accepted solution,” Opt. Commun. 318, 133–136 (2014).

[Crossref]

T. E. Gureyev and K. A. Nugent, “Rapid quantitative phase imaging using the transport of intensity equation,” Opt. Commun. 133, 339–346 (1997).

[Crossref]

T. Gureyev, Y. I. Nesterets, D. Paganin, A. Pogany, and S. Wilkins, “Linear algorithms for phase retrieval in the fresnel region. 2. partially coherent illumination,” Opt. Commun. 259, 569–580 (2006).

[Crossref]

J. C. Petruccelli, L. Tian, and G. Barbastathis, “The transport of intensity equation for optical path length recovery using partially coherent illumination,” Opt. Express 21, 14430–14441 (2013).

[Crossref]
[PubMed]

S. Zheng, B. Xue, W. Xue, X. Bai, and F. Zhou, “Transport of intensity phase imaging from multiple noisy intensities measured in unequally-spaced planes,” Opt. Express 20, 972–985 (2012).

[Crossref]
[PubMed]

R. Bie, X.-H. Yuan, M. Zhao, and L. Zhang, “Method for estimating the axial intensity derivative in the tie with higher order intensity derivatives and noise suppression,” Opt. Express 20, 8186–8191 (2012).

[Crossref]
[PubMed]

C. Zuo, Q. Chen, Y. Yu, and A. Asundi, “Transport-of-intensity phase imaging using savitzky-golay differentiation filter-theory and applications,” Opt. Express 21, 5346–5362 (2013).

[Crossref]
[PubMed]

G. R. Brady and J. R. Fienup, “Nonlinear optimization algorithm for retrieving the full complex pupil function,” Opt. Express 14, 474–486 (2006).

[Crossref]
[PubMed]

A. Kostenko, K. J. Batenburg, A. King, S. E. Offerman, and L. J. van Vliet, “Total variation minimization approach in in-line x-ray phase-contrast tomography,” Opt. Express 21, 12185–12196 (2013).

[Crossref]
[PubMed]

L. Waller, L. Tian, and G. Barbastathis, “Transport of intensity phase-amplitude imaging with higher order intensity derivatives,” Opt. Express 18, 12552–12561 (2010).

[Crossref]
[PubMed]

Z. Jingshan, R. A. Claus, J. Dauwels, L. Tian, and L. Waller, “Transport of intensity phase imaging by intensity spectrum fitting of exponentially spaced defocus planes,” Opt. Express 22, 10661–10674 (2014).

[Crossref]
[PubMed]

L. Tian, J. C. Petruccelli, and G. Barbastathis, “Nonlinear diffusion regularization for transport of intensity phase imaging,” Opt. Lett. 37, 4131 (2012).

[Crossref]
[PubMed]

S. S. Kou, L. Waller, G. Barbastathis, and C. J. R. Sheppard, “Transport-of-intensity approach to differential interference contrast (ti-dic) microscopy for quantitative phase imaging,” Opt. Lett. 35, 447–449 (2010).

[Crossref]
[PubMed]

J. Guigay, M. Langer, and R. Boistel, “Mixed transfer function and transport of intensity approach for phase retrieval in the Fresnel region,” Opt. Lett. 32, 1617–1619 (2007).

[Crossref]
[PubMed]

A. Barty, K. Nugent, D. Paganin, and A. Roberts, “Quantitative optical phase microscopy,” Opt. Lett. 23, 817–819 (1998).

[Crossref]

J. A. Schmalz, T. E. Gureyev, D. M. Paganin, and K. M. Pavlov, “Phase retrieval using radiation and matter-wave fields: Validity of Teague’s method for solution of the transport-of-intensity equation,” Phys. Rev. A 84, 023808 (2011).

[Crossref]

D. Paganin and K. A. Nugent, “Noninterferometric phase imaging with partially coherent light,” Phys. Rev. Lett. 80, 2586–2589 (1998).

[Crossref]

K. A. Nugent, T. E. Gureyev, D. J. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard X rays,” Phys. Rev. Lett. 77, 2961–2964 (1996).

[Crossref]
[PubMed]

M. Beleggia, M. Schofield, V. V. Volkov, and Y. Zhu, “On the transport of intensity technique for phase retrieval,” Ultramicroscopy 102, 37–49 (2004).

[Crossref]
[PubMed]

E. Froustey, E. Bostan, S. Lefkimmiatis, and M. Unser, “Digital phase reconstruction via iterative solutions of transport-of-intensity equation,” in the 2014 13th Workshop on Information Optics, WIO (2014) pp. 1–3.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (Roberts and Company Publishers, 1996), Sec. 6.6.

J. Cheng and S. Han, “X-ray phase imaging with a finite size source,” in “International Symposium on Biomedical Optics,” (International Society for Optics and Photonics, 1999), pp. 119–123.

L. N. Trefethen and D. Bau, Numerical Linear Algebra, vol. 50 (Siam, 1997), pp. 77–82.