Optical Sparse Aperture Research Articles

Multiplexed terahertz multifocal metalens based on stretchable single-, dual-, and quad-axis synthetic rectangular optical sparse aperture

As ultrathin optical elements with subwavelength structures densely arranged, planar lens or called metalens can effectively focus incident wave. Due to the compact design and wide operating frequency of metalens, it becomes promising in applications like information encryption, imaging, and wireless communication fields. However, the fabrication of large-aperture metalens is still time-consuming and costly while the focusing performances are commonly tuned by introducing active materials requiring extra stimuli, such as laser and electrical pulses. In this study, five designs of metalenses with synthetic rectangular aperture are proposed and demonstrated with excellent focusing performances. By reconfiguring the synthetic aperture, focusing properties like focusing lengths, full width at half maximum values, and modulation transfer function can be tuned with great flexibility. With a polarization-dependent phase-shifting structure, the proposed metalens shows different focusing performances with incident wave under transverse magnetic field and transverse electric field modes. By utilizing spatial multiplexing, terahertz variable foci metalenses based on a stretchable single-, dual- and quad-axis synthetic rectangular optical sparse aperture are investigated to achieve tunable multifocal performances. These designs provide a novel strategy that can reconfigure the synthetic aperture with stretchable substrate to make metalens with multifunction and active tunability, which show promising applications in imaging, information encryption, and space telescope areas.

Super-resolution macroscopic imaging via unknown speckle illumination using sparse aperture transmitter

Optical sparse aperture imaging technology has promising applications in the next generation of high-resolution imaging systems, but the phasing errors correction of sparse aperture is an urgent problem to be addressed. In this paper, we propose a blind structured-illumination super-resolution imaging system using a sparse aperture as the transmitter to overcome phasing errors and obtain higher resolution. In our scheme, an unknown pattern is projected onto the object by a sparse aperture system. By translating the unknown pattern, a sequence of modulated raw images is obtained. Based on these low-resolution raw images, the super-resolution object and the unknown illumination pattern are jointly estimated by the Adam algorithm. Here we show, both in the simulation and experiment, the resolution of reconstructions using sparse aperture as transmitter are similar to those using monolithic lens. Furthermore, we validate that the proposed method can protect the reconstruction effect from piston error and widen the tolerance range of tip/tilt error (peak-valley values) up to 0.5λ. At the same time, our proposed system can also alleviate to some extent the problem of mid-frequency modulation transfer function (MTF) attenuation that exists in sparse aperture imaging. Our approach not only simplifies the process of constructing synthetic aperture system, but also provides a novel application for synthetic aperture systems.

Single-shot image restoration via a model-enhanced network with unpaired supervision in an optical sparse aperture system.

We propose a model-enhanced network with unpaired single-shot data for solving the imaging blur problem of an optical sparse aperture (OSA) system. With only one degraded image captured from the system and one "arbitrarily" selected unpaired clear image, the cascaded neural network is iteratively trained for denoising and restoration. With the computational image degradation model enhancement, our method is able to improve contrast, restore blur, and suppress noise of degraded images in simulation and experiment. It can achieve better restoration performance with fewer priors than other algorithms. The easy selectivity of unpaired clear images and the non-strict requirement of a custom kernel make it suitable and applicable for single-shot image restoration of any OSA system.

Piston Detection of Optical Sparse Aperture Systems Based on an Improved Phase Diversity Method

The piston error has a significant effect on the imaging resolution of the optical sparse aperture system. In this paper, an improved phase diversity method based on particle swarm optimization and the sequential quadratic programming algorithm is proposed, which can overcome the drawbacks of the traditional phase diversity method and particle swarm optimization, such as the instability that results from polychromatic light conditions and premature convergence. The method introduces factor β in the stage of calculating the objective function, and combines the advantages of a heuristic algorithm and a nonlinear programming algorithm in the optimization stage, thus enhancing the accuracy and stability of piston detection. Simulations based on a dual-aperture optical sparse aperture system verified that the root mean square error obtained by the method can be guaranteed to be within 0.001λ (wavelength), which satisfies the requirement of practical imaging. An experimental test was also conducted to demonstrate the performance of the method, and the test results showed that the quality of the image after piston detection and correction improved significantly compared to images with the co-phase error.

Lossless imaging based on a donut-like optical sparse aperture metalens

The optical sparse aperture approach has been shown to have significant potential in enlarging the aperture size and enhancing the imaging resolution of metalenses. However, because of frequency loss caused by the sparsity and dispersion of sparse aperture arrays, the stitch method for conventional optical sparse aperture metalenses has a non-uniform imaging resolution at different azimuth angles and cannot achieve the same resolution as the corresponding full-aperture metalens. Here, we design and demonstrate the application of a donut-like optical sparse aperture metalens with a lossless imaging property using a shear design method. This metalens has a diffraction-limited resolution of 153 lp/mm for all azimuth angles, which allows us to circumvent the non-uniform imaging resolution of the conventional optical sparse aperture metalens at different azimuth angles and enables us to achieve full resolution. Furthermore, noise resistance in practical images is achieved because of the improved modulation transfer function in the high-frequency region. Such a metalens without frequency loss has significant application potential in the fields of integrated optical systems, lightweight imaging devices, and wearable optics.

End-to-end aperture layout optimization and image restoration for optical sparse aperture systems.

The optical sparse aperture (OSA) imaging technique is capable of improving the spatial resolution of a telescope while maintaining lower size, weight, and cost. The majority of OSA system researches separately focus on the design optimization of aperture layout and the method for image restoration, which have great design redundancy. In this Letter, an end-to-end design framework that simultaneously optimizes the aperture layout parameters of the OSA system and neural network parameters of image restoration is proposed, which achieves excellent imaging quality. The results show that adequate image mid-frequency information captured by the OSA system benefits network processing more than incomplete high-frequency information in a few directions. Based on this framework, we design a simplified OSA system on geostationary orbit. The simulation results show that our simplified OSA system with six sub-apertures measuring 1.2m each has a comparable imaging performance to a single-aperture system measuring 12 m.

Piston Sensing for Golay-6 Sparse Aperture System with Double-Defocused Sharpness Metrics via ResNet-34

In pursuit of high imaging quality, optical sparse aperture systems must correct piston errors quickly within a small range. In this paper, we modified the existing deep-learning piston detection method for the Golay-6 array, by using a more powerful single convolutional neural network based on ResNet-34 for feature extraction; another fully connected layer was added, on the basis of this network, to obtain the best results. The Double-defocused Sharpness Metric (DSM) was selected first, as a feature vector to enhance the model performance; the average RMSE of the five sub-apertures for valid detection in our study was only 0.015λ (9 nm). This modified method has higher detecting precision, and requires fewer training datasets with less training time. Compared to the conventional approach, this technique is more suitable for the piston sensing of complex configurations.

An unconventional optical sparse aperture metalens

Metalens consisting of arrays of subwavelength nanostructures with ultrathin, lightweight, and tailorable characteristics have been in the spotlight to develop next-generation optical elements beyond existing refractive or diffractive optics. However, billions of subwavelength nanostructures of the metalens pose a serious challenge for fabrication, especially for the large-area ones. Herein, we designed and fabricated an unconventional optical sparse aperture (UOSA) metalens that consists of four identical and concentric annular sectors sub-aperture metalens, and it has the larger nonzero domain of modulation transfer function compared with the OSA metalens. The numerical simulation and experiments jointly show that the UOSA metalens has a limited diffraction resolution (0.91 µm) as the conventional full aperture metalens. The UOSA method can not only enlarge the effective aperture of the metalens with lower cost and less processing time but also extend a new degree of freedom for the design of the OSA metalens.

Object-independent tilt detection for optical sparse aperture system with large-scale piston error via deep convolution neural network

The optical sparse aperture technique can improve the imaging resolution significantly under the ideal co-phase condition. However, the position deviation between different sub-apertures leads to notorious co-phase errors, seriously impacting the image quality. While the position deviation arises in practical applications, it is difficult to detect the errors in real-time for traditional iterative algorithms because of their narrow detection range and long-time iteration process. The deep neural network has shown its potential in optical information process, and it has some attempts in the detection of piston error. However, all existing deep learning-based methods just focus on the detection of piston error with the weak or corrected tilt error, which is not in line with reality. Here we implement the deep convolutional neural network to detect tilt error with large-scale piston error, and compare the detection performance of two kinds of network, one takes the point spread function as input while the other takes the phase diversity features as the input. The detection ability and generalization capability of network are verified under single wavelength, broadband light and turbulence aberration in simulation. The object-independent of tilt error detection ability is offered because the phase diversity features and point spread function are all unrelated to the object. In addition, the cyclic correction strategy is carried out to improve the generalization performance facing the larger errors. As a result, the deep learning-based method can detect the tilt error accurately with fast calculation, and the trained network is hopeful for the real-time correction with cyclic correction strategy.

Optimized Golay-9 array configurations for mid-frequency compensation in optical sparse aperture systems.

Optical sparse aperture (OSA) imaging systems show great potential to generate higher resolution images than those of equivalent single filled aperture systems. However, due to the sparsity and dispersion of sparse aperture arrays, pupil function is no longer a connected domain, which further attenuates or loses the mid-frequency modulation transfer function (MTF), resulting in lower mid-frequency contrast and blurred images. Therefore, an improved traversal algorithm is proposed to optimize Golay-9 array configurations for compensating the mid-frequency MTF. Its structural parameters include diameters of sub-apertures, relative rotation angles between individual sub-apertures, and radius of concentric circles. Then, these parameters are traversed successively in order. Finally, the influences of the obtained optimized array configurations on the mid-frequency MTF are analyzed in detail, and the image performances are evaluated. The experimental results prove the contrast enhancement. Compared with a Golay-9 array at F=36.5%, the maximum MTF increases from 0.1503 to 0.307, and the mid-frequency MTF is boosted from 0.0565 to 0.0767. In addition, the peak signal to noise ratio of the degraded image is promoted from 19.75 dB to 20.63 dB. Both quantitative and qualitative evaluations demonstrate the validity of the proposed method.

Image restoration of optical sparse aperture systems based on a dual target network

Optical sparse aperture (OSA) systems show great potential for the next generation astronomical telescope system due to its excellent high resolution with low volume and weight. However, the sparse arrangement causes its mid-frequency modulation transfer function to be lower compared with a single fully-filled aperture system, which further leads to blurred images and reduced contrast. Therefore, image restoration becomes an indispensable part for OSA systems. In this paper, a dual target network (DTN) is proposed for the image restoration of OSA systems. The noise in a raw image is estimated with interpolation and difference calculation. A block matching 3D filter is used as a denoiser. A denoised image is regarded as a degraded image which cannot be accurately modeled. To cope with the restoration problem, a dual target (negative structural similarity and the sum of fidelity and regularization term) network is trained. A function determined by the filling factor and the aperture distribution is trained as a correction term of the network. The trained network is used to deconvolve the denoised image. Simulation and experiment results show that the proposed method has good peak signal-to-noise ratio and structure similarity. For a Golay-6 system with a filling factor of 0.3245, when the signal-to-noise ratio is 30 dB, the DTN method increases the average peak signal to noise ratio from 22.6 dB to 31.7 dB and improves the average structural similarity from 0.77 to 0.90.

The optimal design of a binaural sparse-aperture system

Optical sparse-aperture (OSA) can greatly improve the spatial resolution of optical system. However, its optical designs are complex. This paper proposes a binaural sparse-aperture system with a simple and symmetrical structure, which is composed of three apertures. Apertures are rotated to obtain rich frequency information. The scheme of rotating apertures is analyzed by taking the ratios of sub-apertures and the number of rotations as variables. The image artifacts are suppressed through processing in the frequency domain. Simulation results analyze the effects on OTFs and imaging quality with different rotation numbers and ratios of sub-apertures. Experimental results show that this system can reach almost the same cut-off frequency as what the equivalent multi-aperture system can reach.

Large effective aperture metalens based on optical sparse aperture system

We present a kind of large effective aperture metalens based on an optical sparse aperture (OSA) system. Each subaperture of the system is a metalens, which is comprised of just a thin Au film with patterned subwavelength rectangular annular arrays on a SiO2 substrate and has a numerical aperture of 0.46 with a diameter of 21.6 μm. Ring6 design was selected to enlarge the effective aperture and enhance the spatial resolution. Compared with the absent mid-frequency and high-frequency modulation transfer function of individual metalens, Ring6 can offer a full-frequency band and show a better restored image quality by using Tikhonov regularization.

Mid-frequency MTF compensation of optical sparse aperture system.

Optical sparse aperture (OSA) can greatly improve the spatial resolution of optical system. However, because of its aperture dispersion and sparse, its mid-frequency modulation transfer function (MTF) are significantly lower than that of a single aperture system. The main focus of this paper is on the mid-frequency MTF compensation of the optical sparse aperture system. Firstly, the principle of the mid-frequency MTF decreasing and missing of optical sparse aperture are analyzed. This paper takes the filling factor as a clue. The method of processing the mid-frequency MTF decreasing with large filling factor and method of compensation mid-frequency MTF with small filling factor are given respectively. For the MTF mid-frequency decreasing, the image spatial-variant restoration method is proposed to restore the mid-frequency information in the image; for the mid-frequency MTF missing, two images obtained by two system respectively are fused to compensate the mid-frequency information in optical sparse aperture image. The feasibility of the two method are analyzed in this paper. The numerical simulation of the system and algorithm of the two cases are presented using Zemax and Matlab. The results demonstrate that by these two methods the mid-frequency MTF of OSA system can be compensated effectively.

Optical sparse aperture imaging with faint objects using improved spatial modulation diversity

The next generation of optical sparse aperture systems will provide high angular resolution for astronomical observations. Spatial modulation diversity (SMD) is a newly developed post-processing technique for such telescopes, faced with challenges of imaging faint objects, which are very attractive for astronomers but always make raw diversity images suffer serious photon noise. In this paper, we propose an improved SMD with denoising reprocessing embedded to address the problem. The blocking-matching and 3D filtering algorithm, a state-of-the-art denoising technique, is first employed to process the diversity images with low photon intensities generated by spatial modulation, specifically switching off each sub-aperture sequentially. SMD algorithm then can be applied to estimate wavefront and digitally restore images. It is demonstrated by both simulations and experiments that the proposed method outperforms the previous SMD in terms of reconstructions of wavefront and imagery from the raw images of faint objects corrupted seriously by photon noise. The reported method may provide an alternative approach to acquire high-quality images of faint objects for astronomical observations of the future segmented mirrors or telescope arrays.

Image restoration via improved Wiener filter applied to optical sparse aperture systems

Image deconvolution problem is a challenging task in the field of image process. In this paper, an improved wiener filtering algorithm is proposed to accurately restore the degraded image of optical sparse aperture systems (OSAS). Differing from Wiener filter which needs to estimate the ratio of power spectrum of noise to power spectrum of original image, our algorithm analyzes the relationship between restored image and original image with the change of this ratio. Based on our algorithm, an optimum restored image in which the ring effect and smoothing effect are able to achieve a perfect balance can be gotten without additional estimation. Moreover, in the case of application to OSAS, several main factors which affect the restored image are expounded. Thus, applying this algorithm to image restoration of OSAS would be of great convenience.

Active sparse aperture imaging using independent transmitter modulation with improved incoherent Fourier ptychographic algorithm.

Optical sparse aperture imaging shows great promise for the next generation of high resolution systems. In this paper, we propose and demonstrate an active sparse aperture imaging approach using independent transmitter modulation to digitally overcome phasing errors, correct aberrations, and further improve resolution. The reported imaging scheme consists of a general sparse aperture system and an active illumination unit, specifically an independent pattern projector. A series of raw images are captured with the projector scanned to illuminate the object. Based on the acquired data set, the improved incoherent Fourier ptychographic algorithm is utilized to reconstruct sparse aperture images with distortions removed and contrast enhanced. Furthermore, thanks to illumination pattern modulation, higher resolution beyond the diffraction limit of the synthetic aperture system is gained as a benefit. Good-quality and higher-resolution sparse aperture imagery obtained by employing our proposed technique in both simulation and experiment demonstrates the effectiveness. The reported approach may provide new insights to address the phasing and image restoration problems of sparse aperture systems in the transmitting path rather than only in the receiving path.

Single exposure superresolution restoration for optical sparse aperture based on random convolution

A single exposure superresolution (SR) restoration algorithm for an optical sparse aperture (OSA) imaging system based on random convolution is proposed. The low-resolution image from the OSA system is restored by adding a set of incoherent measurements taken using random convolution architecture, in which there is a random phase mask in the Fourier plane and a random amplitude mask in the image plane in the conventional optical 4f system. Both masks are generated by chaotic maps. The simulation results show that this algorithm can effectively recover the images degraded by both optical diffraction effect and geometrical limited resolution under noisy and aberrated conditions. The spatial resolution gain factor is above 2.82 without subsampling and 1.26 with subsampling. Moreover, it can obtain a better restoration quality than traditional algorithms by optimizing the initial conditions of chaotic maps.

Genetic apertures: an improved sparse aperture design framework.

The majority of optical sparse aperture imaging research in the remote sensing field has been confined to a small set of aperture layouts. While these layouts possess some desirable properties for imaging, they may not be ideal for all applications. This work introduces an optimization framework for sparse aperture layouts based on genetic algorithms as well as a small set of fitness functions for incoherent sparse aperture image quality. The optimization results demonstrate the merits of existing designs and the opportunity for creating new sparse aperture layouts.

Wavefront Sensing by Digital Holography in Optical Sparse Aperture Imaging System

The optical sparse aperture imaging system consists of several small apertures for high resolution imaging. The incoherent light from each small aperture will form an image together strictly at the same focal plane, while the phase error will destroy such co-phase condition. The phase error is caused by deployment of small aperture and should be diminished. We applied digital holography technology to detect the wavefront of this system. The theoretical analysis and experiment are presented to demonstrate successful reconstruction of phase error.