Interferogram demodulation is a fundamental problem in optical interferometry. It is still challenging to obtain high-accuracy phases from a single-frame interferogram that contains closed fringes. In this paper, we propose a neural network architecture for single-frame interferogram demodulation. Furthermore, instead of using real experimental data, an interferogram generation model is constructed to generate the dataset for the network's training. A four-stage training strategy adopting appropriate optimizers and loss functions is developed to guarantee the high-accuracy training of the network. The experimental results indicate that the proposed method can achieve a phase demodulation accuracy of 0.01 λ (root mean square error) for actual interferograms containing closed fringes.

Non-null interferometry is a prospective method for aspheric and freeform surface measurements because of its potential versatility over null interferometry. Due to the existence of the retrace error, non-null testing usually has the drawbacks of low accuracy and inconvenient alignment of the surface under test (SUT). In this paper, a calibration method for freeform SUT in a non-null interferometer is introduced. This method calibrates the position and attitude of the SUT in a virtual interferometer with an optimization algorithm, and no accurate adjustment mechanism is required to adjust the SUT in the real interferometer. An application of this method in the digital moiré interferometric technique (DMIT) is presented. The retrace error and the influence of the alignment error can be removed after calibration. Experimental results indicate that with this calibration method, the DMIT can achieve a measurement repeatability of $\lambda /20$ (PV) when the freeform SUT has obvious alignment error. This is adequate for most aspheric and freeform surface measurements, especially when the vibration cannot be isolated completely and the freeform SUT is not easy to align.

Fourier ptychography microscopy(FPM) is a recently developed computational imaging approach for microscopic super-resolution imaging. By turning on each light-emitting-diode (LED) located on different position on the LED array sequentially and acquiring the corresponding images that contain different spatial frequency components, high spatial resolution and quantitative phase imaging can be achieved in the case of large field-of-view. Nevertheless, FPM has high requirements for the system construction and data acquisition processes, such as precise LEDs position, accurate focusing and appropriate exposure time, which brings many limitations to its practical applications. In this paper, inspired by artificial neural network, we propose a Fourier ptychography multi-parameter neural network (FPMN) with composite physical prior optimization. A hybrid parameter determination strategy combining physical imaging model and data-driven network training is proposed to recover the multi layers of the network corresponding to different physical parameters, including sample complex function, system pupil function, defocus distance, LED array position deviation and illumination intensity fluctuation, etc. Among these parameters, LED array position deviation is recovered based on the features of brightfield to darkfield transition low-resolution images while the others are recovered in the process of training of the neural network. The feasibility and effectiveness of FPMN are verified through simulations and actual experiments. Therefore FPMN can evidently reduce the requirement for practical applications of FPM.

Fourier ptychography microscopy (FPM) shares its roots with the synthetic aperture technique and phase retrieval method, and is a recently developed computational microscopic super-resolution technique. By turning on the light-emitting diode (LED) elements sequentially and acquiring the corresponding images that contain different spatial frequencies, FPM can achieve a wide field-of-view (FOV), high-spatial-resolution imaging and phase recovery simultaneously. Conventional FPM assumes that the sample is sufficiently thin and strictly in focus. Nevertheless, even for a relatively thin sample, the non-planar distribution characteristics and the non-ideal position/posture of the sample will cause all or part of FOV to be defocused. In this paper, we proposed a fast digital refocusing and depth-of-field (DOF) extended FPM strategy by taking the advantages of image lateral shift caused by sample defocusing and varied-angle illuminations. The lateral shift amount is proportional to the defocus distance and the tangent of the illumination angle. Instead of searching the optimal defocus distance with the optimization search strategy, which is time consuming, the defocus distance of each subregion of the sample can be precisely and quickly obtained by calculating the relative lateral shift amounts corresponding to different oblique illuminations. And then, digital refocusing strategy rooting in the angular spectrum (AS) method is integrated into FPM framework to achieve the high-resolution and phase information reconstruction for each part of the sample, which means the DOF of the FPM can be effectively extended. The feasibility of the proposed method in fast digital refocusing and DOF extending is verified in the actual experiments with the USAF chart and biological samples.

Deep learning has been proven to provide solutions for computational ghost imaging (CGI). However, in current CGI techniques, the quality of the reconstructed image is adversely affected by the position and intensity of the scattering medium. In this study, the feasibility of using a deep neural network (DNN) by using the hybrid simulated data to facilitate CGI through a scattering medium is demonstrated, particularly when the scattering medium is in front of an object. Under a specific order of the measurement matrix, the CGI measurement equation is introduced along with a disturbance factor of the scattering effect to generate simulation data, thereby representing imaging situations with the scattering medium at different positions. The selection of disturbance parameters is determined by the correlation between the simulation signal and the experimental signal. Then an end-to-end DNN is trained using experimentally obtained light intensity signals, and it shows that the quality of the reconstruction results is improved when there is a scattering medium in the emission path. The reported technique effectively solves the problem of CGI reconstruction under different scattering paths with a common DNN, and may have broad applications in fast adaptive CGI for new and uncertain scenarios.

Owing to preferable anti-interference and anti-cumulative-error capabilities, polarized skylight navigation technology has been developed. However, in urban environments with extensive demand, the sky is usually partially obscured by buildings and trees. Urban landscape obscurations with polarization patterns that have not been sufficiently studied can greatly influence navigation accuracy. In this paper, we study the polarization patterns generated by obscurations and summarize the impacts of obscured urban sky scenes on the navigation results. We also propose a full-sky polarization imaging navigation method adapted to urban environments. A compact full-sky polarimeter is established, and a specific pattern inpainting algorithm based on convolution operation is proposed to amend the navigation errors caused by obscurations. Among 174 sets of comparative experiments, 90.2% of the extraction results are improved after inpainting, which verifies the effectiveness and robustness of the method. Discussions on the optimization of parameters in the algorithm and the recommended values are also provided. This work offers a novel approach to overcome the impacts of obscurations for urban polarization navigation.