Phase imaging based on modified transport of intensity equation using liquid crystal variable retarder with partial coherent illumination

Gupta, Alok; Fatima, Areeba; Nishchal, Naveen K.; Nomura, Takanori

doi:10.1007/s10043-020-00576-x

Cited by 17 publications

(14 citation statements)

References 33 publications

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“…It also automatically incorporates the effect of diffraction between successive intensity measurement planes. In a sense, this concept bears some resemblance with manipulating the refractive index in the path of the optical field near the focus plane as is achieved with liquid crystals [15] except that, in our case, the refractive index is transversely inhomogeneous, and intensity registrations around the defocused planes are still required. Simulations with simple phase objects are performed to give an understanding of the error analysis in the FFT-based TIE solution and the TIE + TPE method's improvement.…”

Section: Introductionmentioning

confidence: 97%

“…However, for more iterations, more intensity captures are needed, and solving the TPE with the Gaussian-Seidel iterative method increases the computational complexity and time for the phase retrieval. Recently, liquid crystal devices such as phase shifters and [14] variable retarders [15], have been developed to modify the TIE phase retrieval.…”

Section: Introductionmentioning

confidence: 99%

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Non-recursive transport of intensity phase retrieval with the transport of phase

2021

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The transport of intensity equation (TIE) is a non-interferometric phase retrieval method that originates from the imaginary part of the Helmholtz equation and is equivalent to the law of conservation of energy. From the real part of the Helmholtz equation, the transport of phase equation (TPE), which represents the Eikonal equation in the presence of diffraction, can be derived. The amplitude and phase for an arbitrary optical field should satisfy these coupled equations simultaneously during propagation. In this work, the coupling between the TIE and TPE is exploited to improve the phase retrieval solutions from the TIE. Specifically, a non-recursive fast Fourier transform (FFT)-based phase retrieval method using both the TIE and TPE is demonstrated. Based on the FFT-based TIE solution, a correction factor calculated by the TPE is introduced to improve the phase retrieval results.

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Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Non-recursive transport of intensity phase retrieval with the transport of phase

2021

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“…The disadvantage stems from the introduction of transverse misalignments among intensity images captured during CCD translation. To avoid this mechanical displacement, Gupta et al 17,18 proposed a method that does not need shifting the camera or the object, by instead invoking the use of electrooptic materials, such as liquid crystals (LCs), to create an optical phase difference or optical path length (OPL) through the application of a bias voltage. A similar approach viz., non-interferometric phase retrieval using refractive index manipulation was introduced by Chen et al 19 Incidentally, TIE can be used as an effective unwrapping tool during phase retrieval in DH by numerically calculating defocused intensity images during DH reconstruction and thus does not require any mechanical movement.…”

Section: Introductionmentioning

confidence: 99%

Retrieval of phase and three-dimensional topography using modified transport of intensity and phase equations with electrically programmable optical path lengths

Alanazi,

Banerjee

2023

Opt. Eng.

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.Transport of intensity (TI) is a well-known non-interferometric technique for phase retrieval. The TI and phase equations result from the Helmholtz equation and show the coupling of intensity and phase during optical propagation. TI is an alternative to digital holography, which requires a reference beam for a recording of the interference pattern. However, the conventional TI method has an experimental challenge in that mechanical displacement of the camera or object is needed to record the optical intensities at multiple defocused planes, which can cause errors from misalignments. This work expands on a modified TI technique that avoids mechanical displacements, instead invoking the use of electrooptic materials to create an optical phase difference and hence optical path length through the application of a bias voltage. We demonstrate the use of the modified TI equation (TIE) through simulation and experiment by selecting suitable objects and a biased nematic liquid crystal cell made from pentyl-4-cyanobiphenyl (5CB). The corresponding modified transport of phase equation is also derived and is used to enhance the accuracy of the modified TIE. After providing simulation results for imaged phase retrieval, we demonstrate the unwrapped image phase and hence height or profile extraction for an object with three-dimensional topography using this technique.

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“…In order to calculate the phase information, TIE requires two or more defocused intensity recordings. Of late, there are reports where phase-retrieval has been achieved from intensity patterns with partially coherent illumination [26]. In comparison to various methods of phase retrieval, TIE has been found as reliable and deterministic method and also cost effective [23,24].…”

Section: Introductionmentioning

confidence: 99%

“…The mechanical displacement should be precisely controlled and accurately measured for quantitative phase imaging applications. Gupta et al [26] demonstrated a technique in which instead of changing the propagating displacement, the variation in refractive index through liquid crystal variable retarder was achieved. Thus, the problem of mechanical translation of camera or sample was eliminated to capture the defocused image.…”

Section: Introductionmentioning

confidence: 99%

Combining digital holography and transport of intensity equation for quantitative phase imaging: a review

Kumar¹,

Nishchal²,

Singh³

2022

AJP

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Dedicated to Professor Partha Banerjee for his enormous contributions to the advancement of research and education in holography through his unique vision and outstanding dedicationRecent advances in the field of digital sensors and computational facilities have turned digital holography (DH) into a powerful tool for many applications such as quantitative phase imaging, optical metrology, evaluation of cell parameters, optical cryptography, and optical pattern recognition among others. The transport of intensity equation (TIE) is one of the deterministic phase-retrieval methods, which does not use interferometric geometry. In this method, the phase is calculated directly from a set of intensities rather than iteratively approximating a solution. Recently, use of the TIE in the DH reconstruction process has been reported as a phase-retrieval method. Combining both DH and TIE provides better solution to the phase-retrieval. Refocusing property of the DH helps exploit the translation issue of digital sensor along the optical axis while capturing the intensity distributions at different depths. The issue of phase unwrapping is solved through the use of TIE. Hence, both the methods complement each other. In this paper, we review briefly the applicability of the combination of DH with TIE.

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Phase imaging based on modified transport of intensity equation using liquid crystal variable retarder with partial coherent illumination

Cited by 17 publications

References 33 publications

Non-recursive transport of intensity phase retrieval with the transport of phase

Non-recursive transport of intensity phase retrieval with the transport of phase

Retrieval of phase and three-dimensional topography using modified transport of intensity and phase equations with electrically programmable optical path lengths

Combining digital holography and transport of intensity equation for quantitative phase imaging: a review

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