The transport of intensity equation for optical path length recovery using partially coherent illumination

Petruccelli, Jonathan C.; Tian, Lei; Barbastathis, George

doi:10.1364/oe.21.014430

Cited by 118 publications

(69 citation statements)

References 25 publications

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“…53, No. 34 / 1 December 2014 sources [2,33] would require more sophisticated algorithms [34][35][36][37]. Images were captured with 10 nm defocus steps across a 200 nm range, building up a through-focus stack.…”

Section: J4mentioning

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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Section: J4mentioning

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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“…Within the context of phase retrieval from micrographs recorded under varying conditions, methods may be broadly categorized as iterative [6,[38][39][40][41][42][43][44] or deterministic [45][46][47][48][49][50][51][52][53]. Iterative methods account for the inherent nonlinearity of the image formation process; however, because the problem is nonconvex [54], they cannot be proven to converge, thus adding additional complexity and constraints.…”

Section: Introductionmentioning

confidence: 99%

Quantitative phase microscopy via optimized inversion of the phase optical transfer function

Jenkins

Gaylord

2015

Appl. Opt.

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Although the field of quantitative phase imaging (QPI) has wide-ranging biomedical applicability, many QPI methods are not well-suited for such applications due to their reliance on coherent illumination and specialized hardware. By contrast, methods utilizing partially coherent illumination have the potential to promote the widespread adoption of QPI due to their compatibility with microscopy, which is ubiquitous in the biomedical community. Described herein is a new defocus-based reconstruction method that utilizes a small number of efficiently sampled micrographs to optimally invert the partially coherent phase optical transfer function under assumptions of weak absorption and slowly varying phase. Simulation results are provided that compare the performance of this method with similar algorithms and demonstrate compatibility with large phase objects. The accuracy of the method is validated experimentally using a microlens array as a test phase object. Lastly, time-lapse images of live adherent cells are obtained with an off-the-shelf microscope, thus demonstrating the new method's potential for extending QPI capability widely in the biomedical community.

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“…Alternatively, iterative algorithms solve the nonlinear problem by propagating the field between the images and imposing constraints based on the measurements [5,[13][14][15][16][17]. These approaches generally assume coherent illumination, and partially coherent extensions [18][19][20] do not fully consider the interactions between Numerical Aperture (NA) and partial coherence.…”

Section: Introductionmentioning

confidence: 99%

Quantitative phase retrieval with arbitrary pupil and illumination

et al. 2015

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We present a general algorithm for combining measurements taken under various illumination and imaging conditions to quantitatively extract the amplitude and phase of an object wave. The algorithm uses the weak object transfer function, which incorporates arbitrary pupil functions and partially coherent illumination. The approach is extended beyond the weak object regime using an iterative algorithm. We demonstrate the method on measurements of Extreme Ultraviolet Lithography (EUV) multilayer mask defects taken in an EUV zone plate microscope with both a standard zone plate lens and a zone plate implementing Zernike phase contrast. Am. 73, 1434Am. 73, (1983. 5. J. R. Fienup, "Phase retrieval algorithms: a comparison," Appl. Opt. 21, 2758Opt. 21, -2769Opt. 21, (1982. 217, 408-432 (1953). 32. C. Chang, A. Sakdinawat, P. Fischer, E. Anderson, and D. Attwood, "Single-element objective lens for soft x-ray differential interference contrast microscopy," Opt. Lett. 31, 1564Lett. 31, -1566Lett. 31, (2006. 33. F. Zernike, "Phase contrast, a new method for the microscopic observation of transparent objects," Physica 9, 686-698 (1942

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The transport of intensity equation for optical path length recovery using partially coherent illumination

Cited by 118 publications

References 25 publications

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

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

Quantitative phase microscopy via optimized inversion of the phase optical transfer function

Quantitative phase retrieval with arbitrary pupil and illumination

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