Three-dimensional phase optical transfer function in axially symmetric microscopic quantitative phase imaging

Partially coherent broadband 3D optical transfer functions with arbitrary temporal and angular power spectra

Optical diffraction tomography is a powerful technique to produce 3D volumetric images of biological samples using contrast produced by variations in the index of refraction in an unlabeled specimen. While this is typically performed with coherent illumination from a variety of angles, interest has grown in partially coherent methods due to the simplicity of the illumination and the computation-free axial sectioning provided by the coherence window of the source. However, such methods rely on the symmetry or discretization of a source to facilitate quantitative analysis and are unable to efficiently handle arbitrary illumination that may vary asymmetrically in angle and continuously in the spectrum, such as diffusely scattered or thermal sources. A general broadband theory may expand the scope of illumination methods available for quantitative analysis, as partially coherent sources are commonly available and may benefit from the effects of spatial and temporal incoherence. In this work, we investigate partially coherent tomographic phase microscopy from arbitrary sources regardless of angular distribution and spectrum by unifying the effects of spatial and temporal coherence into a single formulation. This approach further yields a method for efficient computation of the overall systems' optical transfer function, which scales with O(n ³), down from O(mn ⁴) for existing convolutional methods, where n ³ is the number of spatial voxels in 3D space and m is the number of discrete wavelengths in the illumination spectrum. This work has important implications for enabling partially coherent 3D quantitative phase microscopy and refractive index tomography in virtually any transmission or epi-illumination microscope.

Research on partially coherent spatial light interference microscopy

Based on partial coherence theory, this study rigorously deduces the principle of spatial light interference microscopy (SLIM) and improves the calculation method of SLIM. The main problem we found with SLIM is that it simply defaults the phase of the direct light to 0. To address this problem, we propose and experimentally demonstrate a double four-step phase shift method. Simulation results show that this method can reduce the relative error of oil-immersed microsphere reconstruction to about 3.7%, and for red blood cell reconstruction, the relative error can be reduced to about 13%.

Nonparaxial optical transfer function for arbitrary illumination in partially coherent imaging systems and the oblique source application

Recent research in quantitative phase and refractive index microscopy showed promising results with methods using a partially coherent imaging setup, such as partially coherent optical diffraction tomography. For these methods, the phase optical transfer function (POTF), which describes the transmission of spatial frequencies by the imaging system, is crucial. Here, a one-dimensional integral representation of the POTF for imaging systems with arbitrary illumination is derived. It generalizes the existing expression, which is limited to axially symmetric setups. From the general integral form, an analytical solution is derived for the case of oblique homogeneous disk-shaped illumination. This demonstrates the potential of the general representation by offering an additional approach for illumination design in quantitative phase and refractive index microscopy.

Accelerated Fourier ptychographic diffraction tomography with sparse annular LED illuminations

Fourier ptychographic diffraction tomography (FPDT) is a recently developed label-free computational microscopy technique that retrieves high-resolution and large-field three-dimensional (3D) tomograms by synthesizing a set of low-resolution intensity images obtained with a low numerical aperture (NA) objective. However, in order to ensure sufficient overlap of Ewald spheres in 3D Fourier space, conventional FPDT requires thousands of intensity measurements and consumes a significant amount of time for stable convergence of the iterative algorithm. Herein, we present accelerated Fourier ptychographic diffraction tomography (aFPDT), which combines sparse annular light-emitting diode (LED) illuminations and multiplexing illumination to significantly decrease data amount and achieve computational acceleration of 3D refractive index (RI) tomography. Compared with existing FPDT technique, the equivalent high-resolution 3D RI results are obtained using aFPDT with reducing data requirement by more than 40 times. The validity of the proposed method is experimentally demonstrated on control samples and various biological cells, including polystyrene beads, unicellular algae and clustered HeLa cells in a large field of view. With the capability of high-resolution and high-throughput 3D imaging using small amounts of data, aFPDT has the potential to further advance its widespread applications in biomedicine.

Roadmap on Digital Holography-Based Quantitative Phase Imaging

Quantitative Phase Imaging (QPI) provides unique means for the imaging of biological or technical microstructures, merging beneficial features identified with microscopy, interferometry, holography, and numerical computations. This roadmap article reviews several digital holography-based QPI approaches developed by prominent research groups. It also briefly discusses the present and future perspectives of 2D and 3D QPI research based on digital holographic microscopy, holographic tomography, and their applications.

Analytical phase optical transfer function for Gaussian illumination and the optimized illumination profiles

The imaging performance of tomographic deconvolution phase microscopy can be described in terms of the phase optical transfer function (POTF) which, in turn, depends on the illumination profile. To facilitate the optimization of the illumination profile, an analytical calculation method based on polynomial fitting is developed to describe the POTF for general nonuniform axially symmetric illumination. This is then applied to Gaussian and related profiles. Compared to numerical integration methods that integrate over a series of annuli, the present analytical method is much faster and is equally accurate. Further, a "balanced distribution" criterion for the POTF and a least-squares minimization are presented to optimize the uniformity of the POTF. An optimum general profile is found analytically by relaxed optimal search, and an optimum Gaussian profile is found through a tree search. Numerical simulations confirm the performance of these optimum profiles and support the balanced distribution criterion introduced.