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Principles Of Optics Electromagnetic Theory Of Propagation Interference And Diffraction Of Light

We present SLIM, a new optical method measuring optical pathlength changes of 0.3 nm spatially and 0.03nm temporally. SLIM combines two classic ideas in light imaging: Zernike’s phase contrast microscopyand Gabor’s holography.

Spatial light interference microscopy (SLIM)

Realizing high resolution across large volumes is challenging for 3D imaging techniques with high-speed acquisition. Here, we describe a new method for 3D intensity and phase recovery from 4D light field measurements, achieving enhanced resolution via Fourier ptychography. Starting from geometric optics light field refocusing, we incorporate phase retrieval and correct diffraction artifacts. Further, we incorporate dark-field images to achieve lateral resolution beyond the diffraction limit of the objective (5× larger NA) and axial resolution better than the depth of field, using a low-magnification objective with a large field of view. Our iterative reconstruction algorithm uses a multislice coherent model to estimate the 3D complex transmittance function of the sample at multiple depths, without any weak or single-scattering approximations. Data are captured by an LED array microscope with computational illumination, which enables rapid scanning of angles for fast acquisition. We demonstrate the method with thick biological samples in a modified commercial microscope, indicating the technique’s versatility for a wide range of applications.

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3D intensity and phase imaging from light field measurements in an LED array microscope

For quantitative phase imaging (QPI) based on transport-of-intensity equation (TIE), partially coherent illumination provides speckle-free imaging, compatibility with brightfield microscopy, and transverse resolution beyond coherent diffraction limit. Unfortunately, in a conventional microscope with circular illumination aperture, partial coherence tends to diminish the phase contrast, exacerbating the inherent noise-to-resolution tradeoff in TIE imaging, resulting in strong low-frequency artifacts and compromised imaging resolution. Here, we demonstrate how these issues can be effectively addressed by replacing the conventional circular illumination aperture with an annular one. The matched annular illumination not only strongly boosts the phase contrast for low spatial frequencies, but significantly improves the practical imaging resolution to near the incoherent diffraction limit. By incorporating high-numerical aperture (NA) illumination as well as high-NA objective, it is shown, for the first time, that TIE phase imaging can achieve a transverse resolution up to 208 nm, corresponding to an effective NA of 2.66. Time-lapse imaging of in vitro Hela cells revealing cellular morphology and subcellular dynamics during cells mitosis and apoptosis is exemplified. Given its capability for high-resolution QPI as well as the compatibility with widely available brightfield microscopy hardware, the proposed approach is expected to be adopted by the wider biology and medicine community.

High-resolution transport-of-intensity quantitative phase microscopy with annular illumination

Transport of intensity equation: a tutorial

The field of three-dimensional quantitative phase imaging (3D QPI) is expanding rapidly with applications in biological, medical, and industrial research, development, diagnostics, and metrology. Much of this research has centered on developing optical diffraction tomography (ODT) for biomedical applications. In addition to technical difficulties associated with coherent noise, ODT is not congruous with optical microscopy utilizing partially coherent light, which is used in most biomedical laboratories. Thus, ODT solutions have, for the most part, been limited to customized optomechanical systems which would be relatively expensive to implement on a wide scale. In the present work, a new phase reconstruction method, called tomographic deconvolution phase microscopy (TDPM), is described which makes use of commercial microscopy hardware in realizing 3D QPI. TDPM is analogous to methods used in deconvolution microscopy which improve spatial resolution and 3D-localization accuracy of fluorescence micrographs by combining multiple through-focal scans which are deconvolved by the system point spread function. TDPM is based on the 3D weak object transfer function theory which is shown here to be capable of imaging “nonweak” phase objects with large phase excursions. TDPM requires no phase unwrapping and recovers the entire object spectrum via object rotation, mitigating the need to fill in the “missing cone” of spatial frequencies algorithmically as in limited-angle ODT. In the present work, TDPM is demonstrated using optical fibers, including single-mode, polarization-maintaining, and photonic-crystal fibers as well as an azimuthally varying CO2-laser-induced long-period fiber grating period as test phase objects.

Three-dimensional quantitative phase imaging via tomographic deconvolution phase microscopy

A type of integrated hollow core waveguide with low intrinsic photoluminescence fabricated with Ta2O5 and SiO2 films is demonstrated. Hollow core waveguides made with a combination of plasma-enhanced chemical vapor deposition SiO2 and sputtered Ta2O5 provide a nearly optimal structure for optofluidic biofluorescence measurements with low optical loss, high fabrication yield, and low background photoluminescence. Compared to earlier structures made using Si3N4, the photoluminescence background of Ta2O5 based hollow core waveguides is decreased by a factor of 10 and the signal-to-noise ratio for fluorescent nanobead detection is improved by a factor of 12.

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Hollow waveguides with low intrinsic photoluminescence fabricated with Ta2O5 and SiO2 films

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.

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

A novel quantitative phase imaging method is shown to estimate phase accurately over a wide range of length scales using Kohler illumination from an extended incoherent source. The method is based on estimating the longitudinal intensity derivative in the transport-of-intensity equation via convolution with multiple Savitzky-Golay differentiation filters and generalizes methods previously developed for coherent imaging to the practical scenario of partially coherent imaging. The resulting noise and resolution performance are evaluated via numerical simulation and demonstrated experimentally using a blazed transmission grating as well as a single-mode fiber as test objects.

Multifilter phase imaging with partially coherent light

Integrated silicon microwave photonics offers great potential in microwave phase shifter elements, and promises compact and scalable multi-element chips that are free from electromagnetic interference. Stimulated Brillouin scattering, which was recently demonstrated in silicon, is a particularly powerful approach to induce a phase shift due to its inherent flexibility, offering an optically controllable and selective phase shift. However, to date, only moderate amounts of Brillouin gain have been achieved and theoretically this would restrict the phase shift to a few tens of degrees, significantly less than the required 360°. Here, we overcome this limitation with a phase enhancement method using RF interference, showing a 360° broadband phase shifter based on Brillouin scattering in a suspended silicon waveguide. We achieve a full 360° phase shift over a bandwidth of 15 GHz using a phase enhancement factor of 25, thereby enabling a practical broadband Brillouin phase shifter for beam forming and other applications.

Micah H. Jenkins

Papers

Three-dimensional quantitative phase imaging via tomographic deconvolution phase microscopy

Hollow waveguides with low intrinsic photoluminescence fabricated with Ta2O5 and SiO2 films

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

Multifilter phase imaging with partially coherent light

Brillouin-based phase shifter in a silicon waveguide