2010
DOI: 10.1364/josaa.27.002244
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Non-interferometric, non-iterative phase retrieval by Green’s functions

Abstract: In this paper a non-interferometric, non-iterative method for phase retrieval by Green's functions is presented. The theory is based on the parabolic wave equation that describes propagation of light in the Fresnel approximation in homogeneous media. Green's first identity will be used to derive an algorithm for phase retrieval considering different boundary conditions. Finally it will be shown that a commonly used solution of the transport-of-intensity equation can be obtained as a special case of the more ge… Show more

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Cited by 48 publications
(32 citation statements)
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“…The principle of NIQPM and its application to quantifying the spatial cellular density map in a cell has been established and described elsewhere. 15,17,[26][27][28][29][30] Briefly, NIQPM consists of an image acquisition step and a postprocessing procedure to determine the phase profile of optical waves transmitted through the specimen. Through-focus intensity measurements [ Fig.…”
Section: Noninterferometric Quantitative Phase Microscopymentioning
confidence: 99%
See 1 more Smart Citation
“…The principle of NIQPM and its application to quantifying the spatial cellular density map in a cell has been established and described elsewhere. 15,17,[26][27][28][29][30] Briefly, NIQPM consists of an image acquisition step and a postprocessing procedure to determine the phase profile of optical waves transmitted through the specimen. Through-focus intensity measurements [ Fig.…”
Section: Noninterferometric Quantitative Phase Microscopymentioning
confidence: 99%
“…2(a)] in different planes along the optical axis through the specimen are used to approximate the axial derivative of the intensity. A Green function technique, 17 carried out using a custom written program in MATLAB (The MathWorks, Inc., Natick, MA), is then utilized to solve for phase using the transport of intensity equation, which defines the relationship of axial intensity variations to phase 26 under the paraxial approximation. Last, phase is used to determine the axially integrated mass density, ϱ (pg∕μm 2 ), [31][32][33][34] from which the total cellular mass is determined by integration over the area of the cell [ Fig.…”
Section: Noninterferometric Quantitative Phase Microscopymentioning
confidence: 99%
“…2(b)] were taken using the NI-QPM technique, where measured intensity values were used to approximate the axial derivative of the intensity, followed by the application of a Green function technique to solve for phase numerically. 11,17 Lastly, projected sample mass density was determined using a custom MATLAB® program, followed by integration over the area of the sample to retrieve total sample mass. 2 Volume and mass calculations were used to calculate the mean density [ Fig.…”
Section: Methodsmentioning
confidence: 99%
“…Conversely, the phase image, which indicates the phase delay when light transmits through the sample and is independent of the absorption, can achieve a much better contrast, making the phase detection technique an important tool in the fields of material and biological science. [1][2][3][4][5] Phase contrast imaging can be achieved via a number of methods such as interferometry, 6 crystal analysis, 7 Transport of Intensity Equation (TIE) solution, 8,9 or lensless imaging. 10 Coherent diffractive imaging (CDI) is a lensless imaging technique that reconstructs the complex field from the recorded intensity via iterative approaches.…”
Section: Introductionmentioning
confidence: 99%