Solving ptychography with a convex relaxation

Horstmeyer, Roarke; Chen, Richard Y.; Ou, Xiaoze; Ames, Brendan; Tropp, Joel A.; Yang, Changhuei

doi:10.1088/1367-2630/17/5/053044

Cited by 89 publications

(87 citation statements)

References 48 publications

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“…This class of phase retrieval algorithms, called PhaseLift, re-frames the problem in higher dimensions such that it becomes convex, then aims to minimize the cost function between actual and predicted intensity via semidefinite programming. These algorithms come with the significant advantage of rigorous mathematical guarantees [28] and were successfully applied to FPM data [27]. The actual implementations of these algorithms, however, deviate from the provable case due to computational limitations.…”

Section: Introductionmentioning

confidence: 99%

Experimental robustness of Fourier ptychography phase retrieval algorithms

et al. 2015

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Fourier ptychography is a new computational microscopy technique that provides gigapixel-scale intensity and phase images with both wide field-of-view and high resolution. By capturing a stack of low-resolution images under different illumination angles, an inverse algorithm can be used to computationally reconstruct the high-resolution complex field. Here, we compare and classify multiple proposed inverse algorithms in terms of experimental robustness. We find that the main sources of error are noise, aberrations and mis-calibration (i.e. model mis-match). Using simulations and experiments, we demonstrate that the choice of cost function plays a critical role, with amplitude-based cost functions performing better than intensity-based ones. The reason for this is that Fourier ptychography datasets consist of images from both brightfield and darkfield illumination, representing a large range of measured intensities. Both noise (e.g. Poisson noise) and model mis-match errors are shown to scale with intensity. Hence, algorithms that use an appropriate cost function will be more tolerant to both noise and model mis-match. Given these insights, we propose a global Newton's method algorithm which is robust and accurate. Finally, we discuss the impact of procedures for algorithmic correction of aberrations and mis-calibration.

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Section: Introductionmentioning

confidence: 99%

Experimental robustness of Fourier ptychography phase retrieval algorithms

et al. 2015

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“…We used the well-known alternating projections phase retrieval update. Other solvers based upon convex optimization [55] or alternative gradient descent techniques [56,57] may perform better in the presence of noise. Alternative approximations besides first Born approximation (e.g., Rytov [15]) are also available to simplify the Born series.…”

Section: Discussionmentioning

confidence: 99%

Diffraction tomography with Fourier ptychography

Horstmeyer

Chung

et al. 2016

Optica

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128

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This paper presents a technique to image the complex index of refraction of a sample across three dimensions. The only required hardware is a standard microscope and an array of LEDs. The method, termed Fourier ptychographic tomography (FPT), first captures a sequence of intensity-only images of a sample under angularly varying illumination. Then, using principles from ptychography and diffraction tomography, it computationally solves for the sample structure in three dimensions. The experimental microscope demonstrates a lateral spatial resolution of 0.39 μm and an axial resolution of 3.7 μm at the Nyquist–Shannon sampling limit (0.54 and 5.0 μm at the Sparrow limit, respectively) across a total imaging depth of 110 μm. Unlike competing methods, this technique quantitatively measures the volumetric refractive index of primarily transparent and contiguous sample features without the need for interferometry or any moving parts. Wide field-of-view reconstructions of thick biological specimens suggest potential applications in pathology and developmental biology.

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“…Better pupil characterization via a global-minimum search method similar to the convex optimization approach by Ref. [16] will make the system's performance more uniform throughout its FOV.…”

Section: Discussionmentioning

confidence: 99%

“…Insights from FPM carried over to incoherent imaging to improve the resolution of fluorescence images [14]. There also have been numerous efforts in improving the Fourier ptychographic (FP) reconstruction by adopting more noise-robust algorithms [15][16][17][18]. Alternative FPM modalities involving aperture scanning instead of angular illuminations were demonstrated, which allowed for imaging the complex field of a thick specimen [19,20] and estimating optical aberrations [21].…”

Section: Introductionmentioning

confidence: 99%

Wide-field Fourier ptychographic microscopy using laser illumination source

Chung¹,

Lu²,

Ou³

et al. 2016

Biomed. Opt. Express

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Fourier ptychographic (FP) microscopy is a coherent imaging method that can synthesize an image with a higher bandwidth using multiple low-bandwidth images captured at different spatial frequency regions. The method's demand for multiple images drives the need for a brighter illumination scheme and a high-frame-rate camera for a faster acquisition. We report the use of a guided laser beam as an illumination source for an FP microscope. It uses a mirror array and a 2-dimensional scanning Galvo mirror system to provide a sample with plane-wave illuminations at diverse incidence angles. The use of a laser presents speckles in the image capturing process due to reflections between glass surfaces in the system. They appear as slowly varying background fluctuations in the final reconstructed image. We are able to mitigate these artifacts by including a phase image obtained by differential phase contrast (DPC) deconvolution in the FP algorithm. We use a 1-Watt laser configured to provide a collimated beam with 150 mW of power and beam diameter of 1 cm to allow for the total capturing time of 0.96 seconds for 96 raw FPM input images in our system, with the camera sensor's frame rate being the bottleneck for speed. We demonstrate a factor of 4 resolution improvement using a 0.1 NA objective lens over the full camera field-of-view of 2.7 mm by 1.5 mm. References and links1. G. Zheng, R. Horstmeyer, and C. Yang, "Wide-field, high-resolution Fourier ptychographic microscopy," Nat. Photonics 7(9), 739-745 (2013). 2. X. Ou, R. Horstmeyer, C. Yang, and G. Zheng, "Quantitative phase imaging via Fourier ptychographic microscopy,"Opt. Lett. 38(22), 4845-4848 (2013). 3. R. Hegerl, W. Hoppe, "Dynamic theory of crystal structure analysis by electron diffraction in the inhomogeneous primary radiation wave field," Ber. Bunsenges. Phys. Chem. 74(11), 1148-1154 (1970). 4. X. Ou, R. Horstmeyer, G. Zheng, and C. Yang, "High numerical aperture Fourier ptychography: principle, implementation and characterization," Opt. Express 23(3), 3472-3491 (2015). 5. J. Chung, X. Ou, R. P. Kulkarni, and C. Yang, "Counting White Blood Cells from a Blood Smear Using Fourier Ptychographic Microscopy," PloS ONE 10(7), e0133489 (2015). 6. S. Dong, K. Guo, P. Nanda, R. Shiradkar, and G. Zheng, "FPscope: a field-portable high-resolution microscope using a cellphone lens," Biomed. Opt. Express 5(10), 3305-3310 (2014). 7. K. Guo, Z. Bian, S. Dong, P. Nanda, Y. M. Wang, and G. Zheng, "Microscopy illumination engineering using a low-cost liquid crystal display," Biomed. Ultramicroscopy 109(10), 1256-1262 (2009). 11. X. Ou, G. Zheng, and C. Yang, "Embedded pupil function recovery for Fourier ptychographic microscopy," Opt.Express 22(5), 4960-4972 (2014). 12. A. Williams, J. Chung, X. Ou, G. Zheng, S. Rawal, Z. Ao, R. Datar, C. Yang, and R. Cote, "Fourier ptychographic microscopy for filtration-based circulating tumor cell enumeration and analysis," J.

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Solving ptychography with a convex relaxation

Cited by 89 publications

References 48 publications

Experimental robustness of Fourier ptychography phase retrieval algorithms

Experimental robustness of Fourier ptychography phase retrieval algorithms

Diffraction tomography with Fourier ptychography

Wide-field Fourier ptychographic microscopy using laser illumination source

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