We kindly request that you cite the following article [A1] and [A2] if you use wavePy.

[A1]Lahsen Assoufid, Xianbo Shi, Shashidhara Marathe, Erika Benda, Michael J. Wojcik, Keenan Lang, Ruqing Xu, Wenjun Liu, Albert T. Macrander, and Jon Z. Tischler. Development and implementation of a portable grating interferometer system as a standard tool for testing optics at the advanced photon source beamline 1-bm. Review of Scientific Instruments, 87(5):052004, 2016. URL:, doi:10.1063/1.4950775.
[A2]Shashidhara Marathe, Lahsen Assoufid, Xianghui Xiao, Kyungmin Ham, Warren W. Johnson, and Leslie G. Butler. Improved algorithm for processing grating-based phase contrast interferometry image sets. Review of Scientific Instruments, 85(1):, 2014. URL:, doi:


[B1]Amit Agrawal, Ramesh Raskar, and Rama Chellappa. What Is the Range of Surface Reconstructions from a Gradient Field?, pages 578–591. Springer Berlin Heidelberg, Berlin, Heidelberg, 2006. URL:, doi:10.1007/11744023_45.
[B2]F. Bayer, S. Zabler, C. Brendel, G. Pelzer, J. Rieger, A. Ritter, T. Weber, T. Michel, and G. Anton. ”projection angle dependence in grating-based x-ray dark-field imaging of ordered structures”. Optics Express, 21(17):19922–19933, 2013.
[B3]B. Betz, R. P. Harti, M. Strobl, J. Hovind, A. Kaestner, E. Lehmann, H. Van Swygenhoven, and C. Gruenzweig. ”quantification of the sensitivity range in neutron dark-field imaging”. Review of Scientific Instruments, 2015.
[B4]E. Eggl, S. Schleede, M. Bech, K. Achterhold, R. Loewen, R. D. Ruth, and F. Pfeiffer. ”x-ray phase-contrast tomography with a compact laser-driven synchrotron source”. Proceedings of the National Academy of Sciences of the United States of America, 112(18):5567–5572, 2015.
[B5]R. T. Frankot and R. Chellappa. A method for enforcing integrability in shape from shading algorithms. IEEE Transactions on Pattern Analysis and Machine Intelligence, 10(4):439–451, Jul 1988. doi:10.1109/34.3909.
[B6]S. M. Gruner, M. W. Tate, and E. F. Eikenberry. ”charge-coupled device area x-ray detectors”. Review of Scientific Instruments, 73(8):2815–2842, 2002.
[B7]C. Grünzweig, F. Pfeiffer, O. Bunk, T. Donath, G. Kühne, G. Frei, M. Dierolf, and C. David. Design, fabrication, and characterization of diffraction gratings for neutron phase contrast imaging. Review of Scientific Instruments, 79(5):, 2008. URL:, doi:
[B8]M. Harker and P. O’Leary. Least squares surface reconstruction from measured gradient fields. In 2008 IEEE Conference on Computer Vision and Pattern Recognition, volume, 1–7. June 2008. doi:10.1109/CVPR.2008.4587414.
[B9]Matthew Harker and Paul O’Leary. Matlab toolbox for the regularized surface reconstruction from gradients. Proc.SPIE, 9534:9534 – 9534 – 7, 2015. URL:, doi:10.1117/12.2182827.
[B10]Lei Huang, Mourad Idir, Chao Zuo, Konstantine Kaznatcheev, Lin Zhou, and Anand Asundi. Comparison of two-dimensional integration methods for shape reconstruction from gradient data. Optics and Lasers in Engineering, 64(Supplement C):1 – 11, 2015. URL:, doi:
[B11]T. Lauridsen, M. Willner, M. Bech, F. Pfeiffer, and R. Feidenhans’l. ”detection of sub-pixel fractures in x-ray dark-field tomography”. Applied Physics a-Materials Science & Processing, 121(3):1243–1250, 2015.
[B12]S. K. Lynch, V. Pai, J. Auxier, A. F. Stein, E. E. Bennett, C. K. Kemble, X. Xiao, W.-K. Lee, N. Y. Morgan, and H. H. Wen. ”interpretation of dark-field contrast and particle-size selectivity in grating interferometers”. Applied Optics, 50(22):4310–4319, 2011.
[B13]S. Marathe, L. Assoufid, X. Xiao, K. Ham, W. W. Johnson, and L. G. Butler. ”improved algorithm for processing grating-based phase contrast interferometry image sets”. Review of Scientific Instruments, 85(1):art. no. 013704, 2014.
[B14]S. Marathe, X. Xiao, M. J. Wojcik, R. Divan, L. G. Butler, K. Ham, K. Fezzaa, M. Erdmann, H. H. Wen, W.-K. Lee, A. T. Macrander, F. De Carlo, D. C. Mancini, and L. Assoufid. ”development of grating-based x-ray talbot interferometry at the advanced photon source”. AIP Conference Proceedings, 1466(1):249–254, 2012.
[B15]Shashidhara Marathe, Lahsen Assoufid, Xianghui Xiao, Kyungmin Ham, Warren W. Johnson, and Leslie G. Butler. Improved algorithm for processing grating-based phase contrast interferometry image sets. Review of Scientific Instruments, 85(1):, 2014. URL:, doi:
[B16]V. Revol, C. Kottler, R. Kaufmann, A. Neels, and A. Dommann. ”orientation-selective x-ray dark field imaging of ordered systems”. Journal of Applied Physics, 112(11):art. no. 114903, 2012.
[B17]Ioana S. Sevcenco, Peter J. Hampton, and Panajotis Agathoklis. A wavelet based method for image reconstruction from gradient data with applications. Multidimensional Systems and Signal Processing, 26(3):717–737, Jul 2015. URL:, doi:10.1007/s11045-013-0262-3.
[B18]M. Strobl. ”general solution for quantitative dark-field contrast imaging with grating interferometers”. Scientific Reports, 4:art. no. 7243, 2014.
[B19]A. Velroyen, A. Yaroshenko, D. Hahn, A. Fehringer, A. Tapfer, M. Muller, P. B. Noel, B. Pauwels, A. Sasov, A. O. Yildirim, O. Eickelberg, K. Hellbach, S. D. Auweter, F. G. Meinel, M. F. Reiser, M. Bech, and F. Pfeiffer. ”grating-based x-ray dark-field computed tomography of living mice”. EBioMedicine, 2(10):1500–6, 2015.
[B20]H. H. Wen, E. E. Bennett, R. Kopace, A. F. Stein, and V. Pai. ”single-shot x-ray differential phase-contrast and diffraction imaging using two-dimensional transmission gratings”. Optics Letters, 35(12):1932–1934, 2010.
[B21]M. Willner, G. Fior, M. Marschner, L. Birnbacher, J. Schock, C. Braun, A. A. Fingerle, P. B. Noel, E. J. Rummeny, F. Pfeiffer, and J. Herzen. ”phase-contrast hounsfield units of fixated and non-fixated soft-tissue samples”. Plos One, 10(8):art. no. e0137016, 2015.