Simultaneous measurement and reconstruction tailoring for quantitative phase imaging.

We propose simultaneous measurement and reconstruction tailoring (SMaRT) for quantitative phase imaging; it is a joint optimization approach to inverse problems wherein minimizing the expected end-to-end error yields optimal design parameters for both the measurement and reconstruction processes. Using simulated and experimentally-collected data for a specific scenario, we demonstrate that optimizing the design of the two processes together reduces phase reconstruction error over past techniques that consider these two design problems separately. Our results suggest at times surprising design principles, and our approach can potentially inspire improved solution methods for other inverse problems in optics as well as the natural sciences.

[1]  J. Petruccelli,et al.  Source diversity for transport of intensity phase imaging. , 2017, Optics express.

[2]  Rene A. Claus,et al.  Transport of Intensity phase imaging by intensity spectrum fitting of exponentially spaced defocus planes. , 2014, Optics express.

[3]  Zuowei Shen,et al.  Coherence Retrieval Using Trace Regularization , 2017, SIAM J. Imaging Sci..

[4]  Y. C. Pati,et al.  Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition , 1993, Proceedings of 27th Asilomar Conference on Signals, Systems and Computers.

[5]  N. Streibl.  Phase imaging by the transport equation of intensity , 1984 .

[6]  David Mumford,et al.  Occlusion Models for Natural Images: A Statistical Study of a Scale-Invariant Dead Leaves Model , 2004, International Journal of Computer Vision.

[7]  K. Nugent,et al.  Quantitative optical phase microscopy. , 1998, Optics letters.

[8]  Edward R. Dowski,et al.  A New Paradigm for Imaging Systems , 2002, PICS.

[9]  D. Tolhurst,et al.  Amplitude spectra of natural images , 1992 .

[10]  X. Bai,et al.  Transport of intensity phase imaging from multiple noisy intensities measured in unequally-spaced planes. , 2011, Optics express.

[11]  J R Fienup,et al.  Phase retrieval algorithms: a comparison. , 1982, Applied optics.

[12]  Emmanuel J. Candès,et al.  Adaptive Restart for Accelerated Gradient Schemes , 2012, Foundations of Computational Mathematics.

[13]  G. J. Burton,et al.  Color and spatial structure in natural scenes. , 1987, Applied optics.

[14]  Chao Zuo,et al.  Iterative optimum frequency combination method for high efficiency phase imaging of absorptive objects based on phase transfer function. , 2015, Optics express.

[15]  Yakov I Nesterets,et al.  Partially coherent contrast-transfer-function approximation. , 2016, Journal of the Optical Society of America. A, Optics, image science, and vision.

[16]  R. Gerchberg.  A practical algorithm for the determination of phase from image and diffraction plane pictures , 1972 .

[17]  L. M. Voortman,et al.  When to use the projection assumption and the weak-phase object approximation in phase contrast cryo-EM. , 2014, Ultramicroscopy.

[18]  L. Tian,et al.  Nonlinear diffusion regularization for transport of intensity phase imaging. , 2012, Optics letters.

[19]  E. Wolf.  New theory of partial coherence in the space–frequency domain. Part I: spectra and cross spectra of steady-state sources , 1982 .

[20]  D J Field,et al.  Relations between the statistics of natural images and the response properties of cortical cells. , 1987, Journal of the Optical Society of America. A, Optics and image science.

[21]  L. Tian,et al.  The transport of intensity equation for optical path length recovery using partially coherent illumination. , 2013, Optics express.

[22]  L. Tian,et al.  Transport of Intensity phase-amplitude imaging with higher order intensity derivatives. , 2010, Optics express.

[23]  W. Cathey,et al.  Extended depth of field through wave-front coding. , 1995, Applied optics.

[24]  M. Teague.  Deterministic phase retrieval: a Green’s function solution , 1983 .

[25]  Yonina C. Eldar,et al.  Phase Retrieval via Matrix Completion , 2013, SIAM J. Imaging Sci..

[26]  Mark A Neifeld,et al.  Relaxing the alignment and fabrication tolerances of thin annular folded imaging systems using wavefront coding. , 2007, Applied optics.

[27]  Marc Teboulle,et al.  A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems , 2009, SIAM J. Imaging Sci..

[28]  Lei Tian,et al.  Compressive x-ray phase tomography based on the transport of intensity equation. , 2013, Optics letters.

[29]  L. Mandel,et al.  Spectral coherence and the concept of cross-spectral purity , 1976 .