Non-Interferometric Phase Retrieval and Quantitative Phase Microscopy Based on Transport of Intensity Equation: A Review

Zuo Chao1,2 Chen Qian2 Sun Jiasong1,2 Anand Asundi3

(1.Smart Computational Imaging Laboratory, School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing, Jiangsu, China 210094)
(2.Jiangsu Provincial Key Laboratory of Spectral Imaging & Intelligent Sense, Nanjing University of Science and Technology, Nanjing, Jiangsu, China 210094)
(3.School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore 639798)

【Abstract】Phase retrieval and quantitative phase imaging are central subjects in optical measuring and imaging technologies. The most well-established method for obtaining quantitative phase is through interferometry. However, this class of methods relies heavily on the superposition of two beams with a high degree of coherence, and complex interferometric device, stringent requirement on the environmental stability, and associated laser speckle noise greatly limit its applications in the field of microscopic imaging. On a different note, as one of the typical phase retrieval approaches, the transport of intensity equation (TIE) provides a new non-interferometric way to access the quantitative phase information. In recent years, it has been extensively studied and remarkable advancements have been made in the fields of adaptive optics, X-ray diffraction imaging, electron microscopy, and optical microscopy. In this work, we will review the basic principles and some recent advances in TIE phase retrieval, including its solutions, axial intensity derivative estimation, partially coherent imaging and light field imaging, with emphasis on its applications in the field of quantitative phase microscopy. The challenging problems as well as future research directions will also be discussed.

【Keywords】 imaging systems; phase retrieval; transport of intensity equation; quantitative phase imaging; microscopy;

【Funds】 National Natural Science Foundation of China (11574152, 61505081) Project for Talents in Six Industries of Jiangsu Province (2015-DZXX-009) 333 Project in Jiangsu Province (BRA2015294) Open Fund of Jiangsu Provincial Key Laboratory of Spectral Imaging & Intelligent Sense (3092014012200417) Independent Research Fund of Nanjing University of Science and Technology (3092014012200417); Project for Outstanding Young Scholars in Nanjing University of Science and Technology

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(Translated by LIU Tao)


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This Article


CN: 31-1339/TN

Vol 43, No. 06, Pages 227-257

June 2016


Article Outline


  • 1 Introduction
  • 2Basic concepts
  • 3Solutions to TIE
  • 4 Difference estimation of axial intensity derivative
  • 5Partially coherent imaging
  • 6Applications of TIE in the field of phase microscopy
  • 7Conclusions
  • References