Fourier ptychographic microscopy (FPM) has its strength in tackling the trade-off between resolution and field-of-view of imaging systems by computational methods. Here, we present a time-efficient and physics-based algorithm for FPM image stack reconstruction using implicit neural representation and tensor low-rank approximation. The method is free of any pre-training process and can be easily adapted to various computational microscopes. Compared to the conventional FPM methods for image stack reconstruction, the proposed method can be several times faster than conventional FPM methods on the same graphics processing units (GPU) and significantly reduce data volume for storage. The proposed method has potential applications in digital pathology and its downstream data-driven tasks, and can be beneficial to data collaboration in biological sciences.
We design and implement a novel imaging technique that integrates bimodal phase and 3D fluorescence capabilities through aperture segmentation. This approach involves capturing four distinct fluorescence images, mirroring the principles of the Fourier light field microscope and the multi-view reflector microscope, enabling accurate 3D sample reconstruction. Additionally, four brightfield images are acquired for quantitative phase and amplitude reconstruction based on the Kramers-Kronig relations. By combining the strengths of phase imaging, such as digital refocusing, extended depth of field, and non-invasiveness, with the specificity of fluorescence imaging, this method offers a unique imaging solution. Imaging maize roots highlights its exceptional depth of field extension, while imaging a mixture of bacterial cells with and without fluorescent protein tags demonstrates its unique bimodal capabilities.
Digital refocusing is a key feature of Fourier ptychographic microscopy (FPM). It is currently performed by determining and removing the defocus aberration during the iterative phase retrieval process. We examine the feasibility of digitally refocusing an FPM image by numerically propagating the recovered complex FPM image after the phase retrieval process has been completed – in effect, disentangling the defocus correction process from the iterative phase retrieval process. If feasible, this type of postreconstruction digital refocusing can significantly reduce the FPM computational load and provide a quick and efficient way for refocusing microscopy images on the fly. We report that such an approach is infeasible for large defocus distances because the raw FPM dataset associated with a defocused sample is illconditioned for the FPM’s phase-retrieval process, and it will not output a complex-valued image that corresponds to any physically relevant image wavefront. When the defocus distance is small, the FPM can output an approximately correct image wavefront. However, this wavefront does not contain a global defocus phase term and, therefore, cannot be further focused using the digital refocusing application of a reverse global phase term. In totality, this means that postreconstruction digital refocusing does not serve a meaningful function for any defocus distance. To verify our analysis, we performed a series of experiments, and the results showed that the postreconstruction digital refocusing method is not a viable digital refocusing method.
We reported a novel non-interferometric and non-iterative computational imaging method, synthetic aperture imaging based on Kramers-Kronig relations (KKSAI), to reconstruct complex wave-field. By collecting images through a modified microscope system with pupil modulation capability, we show that the phase and amplitude profile of the sample at pupil limited resolution can be extracted from as few as two intensity images by exploiting Kramers-Kronig relations. KKSAI reconstruction is non-iterative, free of parameter tuning and applicable to a wider range of samples. Simulation and experiment results have proved that it has much lower computational burden and achieves the best reconstruction quality when compared with two existing phase imaging methods.
The transport of intensity equation (TIE) has been widely applied to phase imaging. A variety of methods for solving the TIE have been proposed. One of the most popular methods is an FFT-based method, which is simple and fast. However, this method has a strict restriction that the intensity of the object is assumed to be uniform. Otherwise, the accuracy of phase retrieval results may drop significantly. The transport of phase equation (TPE) is an equation coupled with the TIE, and both are derived from the Helmholtz equation. Few works have studied the role of the TPE in 3D imaging. In this work, a non-iterative FFT-based TIE with TPE correction is proposed. The phases at the object plane and four defocused planes are first calculated by the TIE. Ideally, the object intensity and computed phases are supposed to satisfy both the TIE and TPE. But the non-uniformity of object intensity, as well as the use of finite differences of intensities in the calculation of longitudinal derivatives for the FFT-based TIE method, introduce errors in phase retrieval result. We show that by using the TPE, the local refractive index during propagation can be updated and used as a correction in the TIE. The TIE is solved once again using the updated refractive index, and shows reduction of errors. This proposed technique can be extended to amplitude and phase imaging. It also offers the advantage of yielding the unwrapped phase with good accuracy performance and can be potentially applied to medical high-definition 3D imaging, for cells, micro bubbles, etc.
Correlation of two dimensional (2D) images using photorefractive materials are first reviewed. The performance of a joint transform correlator based on photorefractive beam coupling is analyzed by determining the dependence of typical figures of merit such as the discrimination ratio, peak-to-correlation plane energy ratio, peak-to-noise ratio, etc. on the photorefractive gain coefficient and beam power ratio using typical reference and signal images. Furthermore, correlation of three dimensional (3D) images is introduced as the correlation of their 2D digital holograms. Critical figures of merit used for assessment of 2D correlation of images are applied to the correlation of holograms.
In our previous work, digital holographic topography has been used to investigate the depth pattern of different surfaces. Two-wavelength digital holography has been used to resolve depth variations on surfaces, which are in the order of several microns to centimeters. These holograms are reconstructed numerically by Fresnel diffraction to retrieve phase and intensity information, which reveals the three-dimensional topographic surface details. To determine the similarity/difference between two 3D objects, we have recently proposed a novel technique involving 2D correlation of holograms, where holograms constructed from sets of point sources in 3D space were simulated to demonstrate the feasibility of this method. Crosscorrelation of holograms can also be used to authenticate the quality of holograms, and for 3D image encryption. In this work, correlation of holograms, both computer-generated, as well as optically recorded from diffuse objects, will be investigated. Computer generated holograms are also created to mimic surface roughness of real 3D objects. Correlation can be used to evaluate the quality of the surfaces, such as objects fabricated by 3D manufacturing techniques.
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