Phase retrieval based on transport of intensity and digital holography

2π ambiguity-free digital holography method for stepped phase imaging

It is known that phase ambiguity is always an inherent problem in digital holography. In this paper, a 2π ambiguity-free digital holography method is proposed. The method naturally avoids phase ambiguity by a quasianalytic method. This quasianalytic method accurately calculates the true phase by constructing an equation and solving the solution of the equation. Thus, the inherent wrapping problem in digital holography is eliminated. For example, our experimental result shows that the true phase of the stepped specimen with the phase distributed in [0, 16π] can be obtained unambiguously. Since the proposed method naturally avoids the phase ambiguity problem, it may be beneficial to enlarge the application potential of the digital holography. The effectiveness and accuracy of the proposed method are verified by both numerical simulations and experimental results.

Resolution and Contrast Enhancement for Lensless Digital Holographic Microscopy and Its Application in Biomedicine

An important imaging technique in biomedicine, the conventional optical microscopy relies on relatively complicated and bulky lens and alignment mechanics. Based on the Gabor holography, the lensless digital holographic microscopy has the advantages of light weight and low cost. It has developed rapidly and received attention in many fields. However, the finite pixel size at the sensor plane limits the spatial resolution. In this study, we first review the principle of lensless digital holography, then go over some methods to improve image contrast and discuss the methods to enhance the image resolution of the lensless holographic image. Moreover, the applications of lensless digital holographic microscopy in biomedicine are reviewed. Finally, we look forward to the future development and prospect of lensless digital holographic technology.

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

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.

Optical module for single-shot quantitative phase imaging based on the transport of intensity equation with field of view multiplexing

We present a cost-effective, simple, and robust method that enables single-shot quantitative phase imaging (QPI) based on the transport of intensity equation (TIE) using an add-on optical module that can be assembled into the exit port of any regular microscope. The module integrates a beamsplitter (BS) cube (placed in a non-conventional way) for duplicating the output image onto the digital sensor (field of view - FOV - multiplexing), a Stokes lens (SL) for astigmatism compensation (introduced by the BS cube), and an optical quality glass plate over one of the FOV halves for defocusing generation (needed for single-shot TIE algorithm). Altogether, the system provides two laterally separated intensity images that are simultaneously recorded and slightly defocused one to each other, thus enabling accurate QPI by conventional TIE-based algorithms in a single snapshot. The proposed optical module is first calibrated for defining the configuration providing best QPI performance and, second, experimentally validated by using different phase samples (static and dynamic ones). The proposed configuration might be integrated in a compact three-dimensional (3D) printed module and coupled to any conventional microscope for QPI of dynamic transparent samples.

Single-plane and multiplane quantitative phase imaging by self-reference on-axis holography with a phase-shifting method

A new quantitative phase imaging approach is proposed based on self-reference holography. Three on-axis interferograms with different values of the phase filter are superposed. The superposition yields a more accurate phase map of the wavefront emerging from the object, compared with standard off-axis interferometry. Reduced temporal noise levels in the measured phase map and efficient phase recovery process for optically thin and thick transmissive phase objects highlight the applicability of the suggested framework for various fields ranging from metrology to bio-imaging. Qualitative phase imaging is also done online without altering the optical configuration. Qualitative phase detections of multiple planes of interest are converted to quantitative phase maps of the multiplane scene by a rapid phase contrast-based phase retrieval algorithm, from a single camera exposure and with no moving parts in the system.

Single-shot higher-order transport-of-intensity quantitative phase imaging based on computer-generated holography

The imaging quality of quantitative phase imaging (QPI) based on the transport of intensity equation (TIE) can be improved using a higher-order approximation for defocused intensity distributions. However, this requires mechanically scanning an image sensor or object along the optical axis, which in turn requires a precisely aligned optical setup. To overcome this problem, a computer-generated hologram (CGH) technique is introduced to TIE-based QPI. A CGH generating defocused point spread function is inserted in the Fourier plane of an object. The CGH acts as a lens and grating with various focal lengths and orientations, allowing multiple defocused intensity distributions to be simultaneously detected on an image sensor plane. The results of a numerical simulation and optical experiment demonstrated the feasibility of the proposed method.

Performance analysis of phase retrieval using transport of intensity with digital holography [Invited]

The performance of direct and unwrapped phase retrieval, which combines digital holography with the transport of intensity, is examined in detail in this paper. In this technique, digital holography is used to numerically reconstruct the intensities at different planes around the image plane, and phase retrieval is achieved by the transport of intensity. Digital holography with transport of intensity is examined for inline and off-axis geometries. The effect of twin images in the inline case is evaluated. Phase-shifting digital holography with transport of intensity is introduced. The performance of digital holography with transport of intensity is compared with traditional off-axis single- and dual-wavelength techniques, which employ standard phase unwrapping algorithms. Simulations and experiments are performed to determine and compare the accuracy of phase retrieval through a mean-squared-error figure of merit as well as the computational speeds of the various methods.

Acoustofluidic phase microscopy in a tilted segmentation-free configuration

A low-cost device for registration-free quantitative phase microscopy (QPM) based on the transport of intensity equation of cells in continuous flow is presented. The method uses acoustic focusing to align cells into a single plane where all cells move at a constant speed. The acoustic focusing plane is tilted with respect to the microscope's focal plane in order to obtain cell images at multiple focal positions. As the cells are displaced at constant speed, phase maps can be generated without the need to segment and register individual objects. The proposed inclined geometry allows for the acquisition of a vertical stack without the need for any moving part, and it enables a cost-effective and robust implementation of QPM. The suitability of the solution for biological imaging is tested on blood samples, demonstrating the ability to recover the phase map of single red blood cells flowing through the microchip.

Phase contrast-based phase retrieval: a bridge between qualitative phase contrast and quantitative phase imaging by phase retrieval algorithms

In the last five decades, iterative phase retrieval methods have drawn a lot of interest across the research community as a non-interferometric approach to recover quantitative phase distributions from one (or more) intensity measurement. However, in cases where a unique solution does exist, these methods often require oversampling and high computational resources, which limit the use of this approach in important applications. On the other hand, phase contrast methods are based on a single camera exposure, but provide only a qualitative description of the phase; thus, they are not useful for applications in which the quantitative phase description is needed. In this Letter, we establish a combined approach based on the two above-mentioned methods to overcome their respective drawbacks. We show that a modified phase retrieval algorithm easily converges to the correct solution by initializing the algorithm with a phase-induced intensity measurement, namely with a phase contrast image of the examined object. Accurate quantitative phase measurements for both binary and continuously varying phase objects are demonstrated to support the suggested system as a single-shot quantitative phase contrast microscope.

Propagation properties of radially and azimuthally polarized chirped Airy-Gaussian vortex beams through slabs of right-handed materials and left-handed materials

By using Huygens-Fresnel diffraction integral formula and the transfer matrix method, the analytical expression of radially and azimuthally polarized chirped Airy-Gaussian vortex beams through left-handed materials and right-handed materials can be obtained. We study the effects of the chirp factor and the distribution factor on the radially and azimuthally polarized chirped Airy-Gaussian vortex beams in the propagation process, including the light intensity, the phase distribution, the propagation path, the peak intensity, and the radiation force. The focal position of the beams can be adjusted by the chirp parameter.

Detection method for the complex amplitude of a signal beam with intensity and phase modulation using the transport of intensity equation for holographic data storage

Holographic data storage (HDS), in which both the amplitude and the phase of a signal beam are modulated, has been extensively studied with the goal of increasing its storage capacity. To detect such modulation during data retrieval, it is necessary to acquire the complex amplitude of the signal beam. In this study, we focus on the transport of intensity equation (TIE) method, which allows us to detect the phase distribution of the light wave quantitatively without using interferometry, contributing to miniaturization of the optical system and improvement of the vibration tolerance of HDS. We discuss the conditions of the modulation phase distribution of the signal beam required for accurate phase detection and propose a method to estimate and eliminate the noise that frequently appears in the phase distribution detected by the TIE method.

Fourier-based solving approach for the transport-of-intensity equation with reduced restrictions

The transport-of-intensity equation (TIE) has been proven as a standard approach for phase retrieval. Some high efficiency solving methods for the TIE, extensively used in many works, is based on a Fourier transform (FT). However, several assumptions have to be made to solve the TIE by these methods. A common assumption is that there are no zero values for the intensity distribution allowed. The two most widespread Fourier-based approaches have further restrictions. One of these requires the uniformity of the intensity distribution and the other assumes the parallelism of the intensity and phase gradients. In this paper, we present an approach, which does not need any of these assumptions and consequently extends the application domain of the TIE.