Transport-of-intensity phase imaging using Savitzky-Golay differentiation filter - theory and applications

Zuo, Chao; Qian, Chen; Yu, Yingjie; Asundi, Anand

doi:10.1364/oe.21.005346

Cited by 129 publications

(94 citation statements)

References 31 publications

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“…The authors have designed spectral weighting coefficients that minimize the pointwise variance in the frequency domain in [21]. In [22], multiple spectral bands are combined via the Savitzky-Golay differentiation filter. Similarly, bandpass filters that are specific to the defocus distance are used in the frequency domain for the calculation of the phase image [23].…”

Section: A Overview Of Previous Approachesmentioning

confidence: 99%

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Variational Phase Imaging Using the Transport-of-Intensity Equation

Bostan

Froustey

Nilchian

et al. 2016

IEEE Trans. on Image Process.

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Abstract-We introduce a variational phase retrieval algorithm for the imaging of transparent objects. Our formalism is based on the transport-of-intensity equation (TIE), which relates the phase of an optical field to the variation of its intensity along the direction of propagation. TIE practically requires one to record a set of defocus images to measure the variation of intensity. We first investigate the effect of the defocus distance on the retrieved phase map. Based on our analysis, we propose a weighted phase reconstruction algorithm yielding a phase map that minimizes a convex functional. The method is nonlinear and combines different ranges of spatial frequencies-depending on the defocus value of the measurements-in a regularized fashion. The minimization task is solved iteratively via the alternatingdirection method of multipliers. Our simulations outperform commonly used linear and nonlinear TIE solvers. We also illustrate and validate our method on real microscopy data of HeLa cells.

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Section: A Overview Of Previous Approachesmentioning

confidence: 99%

“…Note that (22) provides a smooth transition zone of width L around ω 0 . A graphical representation of our filters is seen in Figure 5.…”

Section: A Spectral Weighting Filtersmentioning

confidence: 99%

Variational Phase Imaging Using the Transport-of-Intensity Equation

Bostan

Froustey

Nilchian

et al. 2016

IEEE Trans. on Image Process.

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“…Its experimental simplicity makes it amenable to existing microscopes in optical [1][2][3][4][5][6], x-ray [7,8], and electron [9][10][11] imaging. Subwavelength phase accuracy and real-time processing [12] are routinely achieved and errors can be reduced with multiple images [5,13,14]. One particularly convenient advantage of the TIE method is that it is fairly robust under partially coherent illumination [15,16], making it suitable for lithography aerial imaging tools, which we use here.…”

Section: Introductionmentioning

confidence: 99%

Transport of intensity phase imaging in the presence of curl effects induced by strongly absorbing photomasks

et al. 2014

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We report theoretical and experimental results for imaging of electromagnetic phase edge effects in lithography photomasks. Our method starts from the transport of intensity equation (TIE), which solves for phase from through-focus intensity images. Traditional TIE algorithms make an implicit assumption that the underlying in-plane power flow is curl-free. Motivated by our current study, we describe a practical situation in which this assumption breaks down. Strong absorption gradients in mask features interact with phase edges to contribute a curl to the in-plane Poynting vector, causing severe artifacts in the phase recovered. We derive how curl effects are coupled into intensity measurements and propose an iterative algorithm that not only corrects the artifacts, but also recovers missing curl components.

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“…(7). In other words, a low-pass differentiator is wanted, i.e., a differentiator with a frequency response like H (1)L and that can be thought as a cascade of a low-pass filter H L and the ideal derivative H (1) (Luo et al, 2005;Zuo et al, 2013):…”

Section: Low-pass Filter and First Derivativementioning

confidence: 99%

Effective resolution concepts for lidar observations

et al. 2015

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Abstract. Since its establishment in 2000, EARLINET (European Aerosol Research Lidar NETwork) has provided, through its database, quantitative aerosol properties, such as aerosol backscatter and aerosol extinction coefficients, the latter only for stations able to retrieve it independently (from Raman or high-spectral-resolution lidars). These coefficients are stored in terms of vertical profiles, and the EARLINET database also includes the details of the range resolution of the vertical profiles. In fact, the algorithms used in the lidar data analysis often alter the spectral content of the data, mainly acting as low-pass filters to reduce the high-frequency noise. Data filtering is described by the digital signal processing (DSP) theory as a convolution sum: each filtered signal output at a given range is the result of a linear combination of several signal input data samples (relative to different ranges from the lidar receiver), and this could be seen as a loss of range resolution of the output signal. Low-pass filtering always introduces distortions in the lidar profile shape. Thus, both the removal of high frequency, i.e., the removal of details up to a certain spatial extension, and the spatial distortion produce a reduction of the range resolution.This paper discusses the determination of the effective resolution (ERes) of the vertical profiles of aerosol properties retrieved from lidar data. Large attention has been dedicated to providing an assessment of the impact of low-pass filtering on the effective range resolution in the retrieval procedure.

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Transport-of-intensity phase imaging using Savitzky-Golay differentiation filter - theory and applications

Cited by 129 publications

References 31 publications

Variational Phase Imaging Using the Transport-of-Intensity Equation

Variational Phase Imaging Using the Transport-of-Intensity Equation

Transport of intensity phase imaging in the presence of curl effects induced by strongly absorbing photomasks

Effective resolution concepts for lidar observations

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