Fourier Ptychographic Wigner Distribution Deconvolution

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FOURIER PTYCHOGRAPHIC WIGNER DISTRIBUTION DECONVOLUTION Justin Lee1, George Barbastathis2,3 1. Department of Health Sciences and Technology, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA 2. Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA 3. Singapore–MIT Alliance for Research and Technology (SMART) Centre Singapore 138602, Singapore Email: [email protected] KEY WORDS: Computational Imaging, phase retrieval, ptychography, Fourier ptychography Ptychography was first proposed as a method for phase retrieval by Hoppe in the late 1960s [1]. A typical ptychographic setup involves generation of illumination diversity via lateral translation of an object relative to its illumination (often called the probe) and measurement of the intensity of the far-field diffraction pattern/Fourier transform of the illuminated object. In the decades following Hoppes initial work, several important extensions to ptychography were developed, including an ability to simultaneously retrieve the amplitude and phase of both the probe and the object via application of an extended ptychographic iterative engine (ePIE) [2] and a non-iterative technique for phase retrieval using ptychographic information called Wigner Distribution Deconvolution (WDD) [3,4]. Most recently, the Fourier dual to ptychography was introduced by the authors in [5] as an experimentally simple technique for phase retrieval using an LED array as the illumination source in a standard microscope setup. In Fourier ptychography, lateral translation of the object relative to the probe occurs in frequency space and is obtained by tilting the angle of illumination (while holding the pupil function of the imaging system constant). In the past few years, several improvements to Fourier ptychography have been introduced, including an ePIE-like technique for simultaneous pupil function and object retrieval [6]. Here, we demonstrate the Fourier dual of WDD, Fourier Wigner Distribution Deconvolution (FWDD) and show in model calculations and experiments that our technique outperforms traditional Fourier ptychography in the presence of significant levels of noise. Our technique utilizes an LED array for illumination in a standard desktop microscope setup. Notably, the camera used in our experimental setup has an 8-bit bit depth and is not cooled (similar to what pathologists might expect to have on hand in their office). Development of algorithms and techniques for noise-robust ptychographic imaging and quantitative phase retrieval using low-cost equipment accessible to users in non-research settings (e.g., in the clinic) is essential if the technique is to be utilized by clinicians to aid in medical diagnostics. REFERENCES: [1] W. Hoppe, Acta Crystallogr. A 25 (1969) 495–501. [2] A.M. Maiden, J.M. Rodenburg, Ultramicroscopy 109 (2009) 1256–1262. [3] J.M.Rodenburg and R.H.T.Bates, Phil. Trans. R. Soc. Lond. A 339, 521–553 (1992). [4] G. Zhang, R. Horstmeyer, C. Yang, Nature Photonics 7, 739–745 (2013). [5] P. Li, T.B. Edo, J.M. Rodenburg, Ultramicroscopy 147, 106–113 (2014). [6] X. Ou, G. Zheng, and C. Yang, Optics Express, Vol. 22, Issue 5, pp. 4960-4972 (2014) .

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