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

Two improved defocus quantitative phase imaging methods: discussion

Multifilter phase imaging with partially coherent light (MFPI-PC) and phase optical transfer function recovery (POTFR) are two viable defocus-based, two-dimensional quantitative phase imaging (QPI) methods. While both methods use transfer function inversion, MFPI-PC is based on the in-focus intensity derivative, while POTFR is based on the intensity difference between symmetrically defocused images. This paper compares and contrasts MFPI-PC and POTFR. Six disadvantages (five in MFPI-PC and one in POTFR) are identified. Improvement strategies to overcome each of the six shortcomings are identified and implemented, and both methods are shown to be clearly improved. The revised MFPI-PC is shown to be more accurate than the original MFPI-PC and generally more accurate than the revised POTFR. The revised POTFR is shown to be inherently faster than the original POTFR and also slightly faster than the revised MFPI-PC.

Measurements on ATP induced cellular fluctuations using real-time dual view transport of intensity phase microscopy

Dual view transport of intensity phase microscopy is adopted to quantitatively study the regulation of adenosine triphosphate (ATP) on cellular mechanics. It extracts cell phases in real time from simultaneously captured under- and over-focus images. By computing the root-mean-square phase and correlation time, it is found that the cellular fluctuation amplitude and speed increased with ATP compared to those with ATP depletion. Besides, when adenylyl-imidodiphosphate (AMP-PNP) was introduced, it competed with ATP to bind to the ATP binding site, and the cellular fluctuation amplitude and speed decreased. The results prove that ATP is a factor in the regulation of cellular mechanics. To our best knowledge, it is the first time that the dual view transport of intensity phase microscopy was used for live cell phase imaging and analysis. Our work not only provides direct measurements on cellular fluctuations to study ATP regulation on cellular mechanics, but it also proves that our proposed dual view transport of intensity phase microscopy can be well used, especially in quantitative phase imaging of live cells in biological and medical applications.

Accelerating wavefront-sensing-based autofocusing using pixel reduction in spatial and frequency domains

The wavefront-sensing-based autofocus method can precisely determine the focal plane only with few captured images; however, the required phase retrieval, numerical wavefront propagation, and in-focus determination are often time consuming, inevitably limiting its high-speed applications. To accelerate its processing speed, the pixel-reduced wavefront-sensing-based autofocus (PRWSA) method is proposed: with field of interest selection as pixel reduction in the spatial domain and image compression as pixel reduction in the frequency domain, the wavefront with fewer pixels can be used for autofocusing, significantly decreasing the processing time. With simulations, pixel reduction criteria in both the spatial and frequency domains are first determined and tested; next certificated by experiments, the PRWSA method is proved to be well implemented for different specimens. Considering it can precisely locate the focal plane with simple setup, and accelerate the processing speed, this PRWSA method can be a potential tool for high-speed autofocusing.

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.

Field of view scanning based quantitative interferometric microscopic cytometers for cellular imaging and analysis

Microimaging is of great significance in the biological and medical fields, since it can realize observations acting as important references for cellular research and disease diagnosis. However, traditional microscopy only offers qualitative sample contours; moreover, it is difficult to reach large-amount sample observations limited by the fixed field of view (FoV). To realize massive cellular measurements quantitatively, three designed quantitative interferometric microscopic cytometers based on the FoV scanning are introduced and compared in details in this article. These devices not only retrieve the quantitative sample phase distributions in the extended FoV, but also provide the detailed information of massive cells, such as cellular volume, area, and roundness. Considering their capabilities as quantitative imaging and large-amount sampling, it is believed that these quantitative interferometric microscopic cytometers (QIMCs) can be potentially adopted in high-throughput cell imaging and statistical analysis for both the biological and medical applications.

Evaluation of finite difference and FFT-based solutions of the transport of intensity equation

A finite difference method is proposed for solving the transport of intensity equation. Simulation results show that although slower than fast Fourier transform (FFT)-based methods, finite difference methods are able to reconstruct the phase with better accuracy due to relaxed assumptions for solving the transport of intensity equation relative to FFT methods. Finite difference methods are also more flexible than FFT methods in dealing with different boundary conditions.

Source diversity for transport of intensity phase imaging

The transport of intensity equation (TIE) is a phase retrieval method that relies on measurements of the intensity of a paraxial field under propagation between two or more closely spaced planes. A limitation of TIE is its susceptibility to low frequency noise artifacts in the reconstructed phase. Under Köhler illumination, when both illumination power and exposure time are limited, the use of larger sources can improve low-frequency performance although it introduces blurring. Appropriately combining intensity measurements taken with a diversity of source sizes can improve both low- and high-frequency performance in phase reconstruction.

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

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.

Multi-filter transport of intensity equation solver with equalized noise sensitivity

Phase retrieval based on the Transport of Intensity Equation (TIE) has shown to be a powerful tool to obtain the phase of complex fields. Recently, it has been proven that the performance of TIE techniques can be improved when using unequally spaced measurement planes. In this paper, an algorithm is presented that recovers accurately the phase of a complex objects from a set of intensity measurements obtained at unequal plane separations. This technique employs multiple band-pass filters in the frequency domain of the axial derivative and uses these specific frequency bands for the calculation of the final phase. This provides highest accuracy for TIE based phase recovery giving minimal phase error for a given set of measurement planes. Moreover, because each of these band-pass filters has a distinct sensitivity to noise, a new plane selection strategy is derived that equalizes the error contribution of all frequency bands. It is shown that this new separation strategy allows controlling the final error of the retrieved phase without using a priori information of the object. This is an advantage compared to previous optimum phase retrieval techniques. In order to show the stability and robustness of this new technique, we present the numerical simulations.

Lensless phase microscopy and diffraction tomography with multi-angle and multi-wavelength illuminations using a LED matrix

We demonstrate lensless quantitative phase microscopy and diffraction tomography based on a compact on-chip platform, using only a CMOS image sensor and a programmable color LED matrix. Based on the multi-wavelength phase retrieval and multi-angle illumination diffraction tomography, this platform offers high quality, depth resolved images with a lateral resolution of 3.72μm and an axial resolution of 5μm, across a wide field-of-view of 24mm². We experimentally demonstrate the success of our method by imaging cheek cells, micro-beads, and fertilized eggs of Parascaris equorum. Such high-throughput and miniaturized imaging device can provide a cost-effective tool for telemedicine applications and point-of-care diagnostics in resource-limited environments.

Partially coherent phase imaging with simultaneous source recovery

We propose a new method for phase retrieval that uses partially coherent illumination created by any arbitrary source shape in Köhler geometry. Using a stack of defocused intensity images, we recover not only the phase and amplitude of the sample, but also an estimate of the unknown source shape, which describes the spatial coherence of the illumination. Our algorithm uses a Kalman filtering approach which is fast, accurate and robust to noise. The method is experimentally simple and flexible, so should find use in optical, electron, X-ray and other phase imaging systems which employ partially coherent light. We provide an experimental demonstration in an optical microscope with various condenser apertures.

Phase imaging for absorptive phase objects using hybrid uniform and structured illumination transport of intensity equation

Transport of intensity equation (TIE) has been a popular and convenient phase imaging method that retrieves phase profile from the measurement of intensity differentials. Conventional 2-shot uniform illumination TIE can give reliable inversion of the phase from intensity in many situations of practical interest; however, it has a null space consisting of fields with non-zero circulation of the Poynting vector. Here, we propose the hybrid illumination TIE method to disambiguate such objects. By comparing the diffraction signals using uniform and structured (sinusoidal) illumination patterns, we obtain a modulation-induced signal that depends solely on the phase gradient. In this way, we also increase signal sensitivity in the low spatial frequency region.