We propose and demonstrate the improvement of conventional Galilean refractive beam shaping system for accurately generating near-diffraction-limited flattop beam with arbitrary beam size. Based on the detailed study of the refractive beam shaping system, we found that the conventional Galilean beam shaper can only work well for the magnifying beam shaping. Taking the transformation of input beam with Gaussian irradiance distribution into target beam with high order Fermi-Dirac flattop profile as an example, the shaper can only work well at the condition that the size of input and target beam meets R ₀≥1.3w ₀. For the improvement, the shaper is regarded as the combination of magnifying and demagnifying beam shaping system. The surface and phase distributions of the improved Galilean beam shaping system are derived based on Geometric and Fourier Optics. By using the improved Galilean beam shaper, the accurate transformation of input beam with Gaussian irradiance distribution into target beam with flattop irradiance distribution is realized. The irradiance distribution of the output beam is coincident with that of the target beam and the corresponding phase distribution is maintained. The propagation performance of the output beam is greatly improved. Studies of the influences of beam size and beam order on the improved Galilean beam shaping system show that restriction of beam size has been greatly reduced. This improvement can also be used to redistribute the input beam with complicated irradiance distribution into output beam with complicated irradiance distribution.

A phased sparse aperture system provides an economic solution to get high resolution images with less volume and weight. The crucial point of such systems is adaptive correction of piston, that is, a close-loop control aiming at stabilizing the optical path differences within a fraction of the wavelength. In this paper, we present an autonomous phasing approach using stochastic parallel gradient descent algorithm through optimization of image quality. The synthetic system can be phased by iteratively commanding piston actuators without any additional optics. Simulations are first performed to test the validity. Then experimental results based on a binocular telescope testbed are presented, showing that our proposed close-loop control of piston correction doesn’t only work with both laser and white-light point sources, but also with an extended object.

The pistons of sparse aperture systems need to be controlled within a fraction of a wavelength for the system’s optimal imaging performance. In this paper, we demonstrate that deep learning is capable of performing piston sensing with a single wide-band image after appropriate training. Taking the sensing issue as a fitting task, the deep learning-based method utilizes a deep convolutional neural network to learn complex input-output mapping relations between the broadband intensity distributions and corresponding piston values. Given a trained network and one broadband focal intensity image as the input, the piston can be obtained directly and the capture range achieving the coherence length of the broadband light is available. Simulations and experiments demonstrate the validity of the proposed method. Using only in-focused broadband images as the inputs without defocus division and wavelength dispersion, obviously relaxes the optics complexity. In view of the efficiency and superiority, it’s expected that the method proposed in this paper may be widely applied in multi-aperture imaging.

The next generation of optical telescopes will provide high-resolution imaging of celestial objects by using the aperture synthesis technique. To preserve the quality of the image, fast corrections of the pistons among subapertures have to be applied, namely, the co-phasing of the array. The image-based co-phasing method via an optimization procedure has been newly developed. Despite simplicity and strong commonality, when dealing with large piston errors, this correction method is also faced with a problem in which the metric function easily falls into the local convergence, especially in the case of broadband imaging with many subapertures. In this study, an improved stochastic parallel gradient descent (SPGD) algorithm based on heuristic search is proposed for co-phasing, termed the metaheuristic SPGD algorithm. The heuristic research scheme assists the original SPGD algorithm in getting rid of local extrema. By iterations of this algorithm, the synthetic system can be co-phased without any additional instruments and operations. The effectiveness of the proposed algorithm is verified by means of simulation. Given the efficiency and superiority, it is expected that the method proposed in this study may find wide applications in multi-aperture imaging.

In free-space optical (FSO) communication, high-precision pointing is a critical technology required for rapid acquisition to reduce link establishment time and increase communication time. FSO communication on a motion platform is necessary to expand the communication area and to promote the establishment of a global communication network. However, the pointing accuracy of an optical communication terminal on a motion platform is low due to numerous error sources and error coupling. This paper evaluates the error sources and proposes a pointing model to avoid problems resulting from error coupling. This proposed pointing model was designed to improve the pointing accuracy of a gimbals-type optical communication terminal (GOCT) on a motion platform. The effectiveness of the proposed pointing model was verified by tracking star experiments. The modified residual error of the proposed point model was 94.8 μrad compared to 1324.2 μrad without correction. Additionally, the modified residual error was 94.8 μrad of the proposed pointing model compared to 140.2 μrad of the existing model. The actual open-loop pointing error was reduced from 150.4 μrad of the existing model to 101.3 μrad of the proposed model. Thus, the pointing accuracy of a GOCT on a motion platform was significantly improved after correction by the proposed pointing model.

In this paper, we propose and demonstrate the synthetic aperture imaging by using spatial modulation diversity technology with stochastic parallel gradient descent (SPGD) algorithm. Instead of creating diversity images by means of focus adjustments, the technology, proposed in this paper, creates diversity images by modulating the transmittance of individual sub-aperture of multi-aperture system, respectively. Specifically, spatial modulation is realized by switching off the transmittance of each sub-aperture with electrical shutters, alternately. Based on these multi diversity images, SPGD algorithm is used for adaptively optimizing the coefficients of Zernike polynomials to reconstruct the real phase distortions of multi-aperture system and to restore the near-diffraction-limited image of object. Numerical simulation and experimental results show that this technology can be used for joint estimation of both pupil aberrations and an high resolution image of the object, successfully. The technology proposed in this paper can have wide applications in segmented and multi-aperture imaging systems.