Analytical target-agnostic piston sensing for segmented telescopes using sparse redundant baseline pairs.

Piston correction is the key to achieving high resolution of segmented telescopes. Phasing with extended objects is still challenging. In this Letter, we propose an analytical target-agnostic phasing approach using redundant baseline pairs. It is derived that the mixed phase distribution caused by redundant sampling can be decoupled via phase modulation. Then the pistons can be resolved by performing phase cross-correlation to remove the object phase. We validate this theory through simulations and experiments. It does not require additional optical paths and is relatively robust against noise, thus providing a simple, fast, and low-system-complexity solution for piston monitoring of the segmented telescope over the period of imaging complex scenes.

Fast and high-precision tracking technology for image-based closed-loop cascaded control system with a Risley prism and fast steering mirror.

The Risley prism's compact structure, dynamic responsiveness, and high tracking accuracy make it ideal for photoelectric image tracking. To realize fast and high-precision tracking of the target, we propose an image-based closed-loop tracking cascade control (IBCLTCR-F) system using a single image detector that integrates the Risley prism and fast steering mirror (FSM). Firstly, We propose a cascade control input-decoupling method (CCIDM) for the IBCLTCR-F system to solve the complex problem of coarse-fine control input decoupling in traditional single detector cascaded control systems. Moreover, the CCIDM method ensures that the FSM deflection angle is small and does not exceed its range during the fine tracking process, by using the Risley prism to compensate for the FSM deflection angle. Next, we design the image-based closed-loop tracking controllers of the Risley prism system and FSM system and analyze the stability of the IBCLTCR-F system. Finally, we track static and moving targets through experiments. The experimental results verify the feasibility of the IBCLTCR-F system, the effectiveness of the decoupling method, and the fast and high-precision tracking of the targets.

Weak non-line-of-sight target echoes extraction without accumulation.

Non-line-of-sight (NLOS) technology has been rapidly developed in recent years, allowing us to visualize or localize hidden objects by analyzing the returned photons, which is expected to be applied to autonomous driving, field rescue, etc. Due to the laser attenuation and multiple reflections, it is inevitable for future applications to separate the returned extremely weak signal from noise. However, current methods find signals by direct accumulation, causing noise to be accumulated simultaneously and inability of extracting weak targets. Herein, we explore two denoising methods without accumulation to detect the weak target echoes, relying on the temporal correlation feature. In one aspect, we propose a dual-detector method based on software operations to improve the detection ability for weak signals. In the other aspect, we introduce the pipeline method for NLOS target tracking in sequential histograms. Ultimately, we experimentally demonstrated these two methods and extracted the motion trajectory of the hidden object. The results may be useful for practical applications in the future.

Accuracy and reproducibility analysis of different reference axes for femoral prosthesis rotation alignment in TKA based on 3D CT femoral model.

BACKGROUND: There are many reference axes to determine the rotational positioning of the femoral prosthesis in total knee arthroplasty (TKA), mainly including the surgical transepicondylar axis (sTEA), anatomical transepicondylar axis (aTEA), Whiteside line, and the posterior condylar line (PCL), etc., but there is still no definite conclusion on which is the most accurate reference axis. OBJECTIVE: To explore the reproducibility of each reference axis of femoral external osteotomy based on the 3D CT femoral model, compare the deviation of the simulated femoral prosthesis rotation alignment, positioned based on each reference axis, with the gold standard sTEA, and analyze the accuracy of each reference axis. METHODS: The imaging data of 120 patients with knee osteoarthritis who underwent a 3D CT examination of the knee in our hospital from June 2018 to December 2021 were retrospectively collected. The 3D model of the femur was established by Mimics software. The line relative to PCL externally rotated 3° (PCL + 3°), aTEA, and the vertical line of the Whiteside line were constructed and compared with the gold standard sTEA. Intra-observer, as well as inter-observer reproducibility analysis, was performed by the intra-group correlation coefficient (ICC) and Bland-Altman method. RESULTS: The angle ∠WS, between the vertical line of Whiteside and sTEA, was 2.54 ± 2.30°, with an outlier of 54.2%; the angle ∠aTEA, between aTEA and sTEA, was 4.21 ± 1.01°, with an outlier of 99.1%; the angle ∠PCL, between PCL + 3° external rotation and sTEA, was 0.50 ± 1.06°, with the highest accuracy and an outlier of 5.8%, and the differences among all three were statistically significant, P < 0.05. The intra-observer ICC values of ∠WS, ∠aTEA, and ∠PCL were 0.975 (0.964-0.982), 0.926 (0.896-0.948), and 0.924(0.892,0.946), respectively, and the reproducibility levels were excellent; the inter-observer ICC values of ∠WS, ∠aTEA, and ∠PCL were 0.968(0.955-0.978), 0.906 (0.868-0.934) and 0.970 (0.957,0.979), respectively, with excellent reproducibility levels; Bland-Altman plots suggested that the scatter points of intra-observer and inter-observer measurement differences more than 95% were within the limits of agreement. CONCLUSION: The reference axis for locating the distal femoral external rotation osteotomy based on the 3D CT femoral model has good reproducibility. The PCL is easy to operate, has the highest precision, and the lowest outliers among the reference axes is therefore recommended.

Pointing-error correction of optical communication terminals on motion platforms using a parameter model and kernel weight function estimation.

Optical communication terminals (OCTs) with high pointing accuracy on motion platforms are highly important for establishing a global communication network. The pointing accuracy of such OCTs is seriously affected by linear and nonlinear errors generated by various sources. A method based on a parameter model and kernel weight function estimation (KWFE) is proposed to correct the pointing errors of an OCT on a motion platform. Initially, a parameter model, which has a physical meaning, is established to reduce the linear pointing errors. Then, the nonlinear pointing errors are corrected using the proposed KWFE method. Tracking star experiments are conducted to verify the efficiency of the proposed method. The parameter model reduces the initial pointing error associated with the stars used for calibration from 1311.5 µrad to 87.0 µrad. After applying parameter model correction, the KWFE method is applied to further reduce the modified pointing error associated with the stars used for calibration from 87.0 µrad to 70.5 µrad. Additionally, based on the parameter model, the KWFE method reduces the actual open-loop pointing error associated with the target stars from 93.7 µrad to 73.3 µrad. The sequential correction using the parameter model and KWFE can gradually and effectively improve the pointing accuracy of an OCT on a motion platform.

Demonstration of a Fizeau Directly-Imaging Sparse-Aperture Telescope with Pointing and Tracking Capabilities.

At present, the majority of sparse-aperture telescopes (SATs) are unable to observe moving targets. In this paper, we describe the construction of and present the results obtained using a Fizeau directly-imaging sparse-aperture telescope (FDISAT) that permits pointing and the tracking of moving targets. The telescope comprises three sub-apertures, each of which is equipped with a Risley prism system that permits a maximum tracking range of 5° and has independent boresight adjustment capability. On targets in various positions, experiments with pointing and tracking are conducted. The maximum root-mean-square error (RMSE) of pointing in the sub-apertures was found to be 8.22 arcsec. When considering a target moving at 0.01°/s for approximately 320 s, the maximum RMSE of tracking in the sub-apertures was found to be 4.23 arcsec. The images obtained from the focal plane detector exhibit clear interference fringes while tracking. The experimental results demonstrate that the system can effectively track moving targets, providing a method for SAT observation of moving targets.

Multivariable Decoupling and Nonlinear Correction Method for Image-Based Closed-Loop Tracking of the Risley Prisms System.

Image-based closed-loop tracking (IBCLT) is an important part of the process of target tracking. The Risley prism system has a unique advantage in improving the target tracking ability because of its compact and lightweight structure. Compared with traditional target tracking equipment, the Risley prism system has two difficulties in the process of IBCLT. First, the Risley prism is a complex coupling system of double input and double output. Second, the Risley prism itself is a nonlinear system. These problems lead to decrease in dynamic response and inconsistent target tracking capabilities. Thus, this paper proposes a method to implement multivariable decoupling and reduce the nonlinear effect. First, the boresight error of IBCLT is decoupled to the azimuth and elevation directions by the rotation matrix error-decoupling (RMED) method. Second, the gains of IBCLT in azimuth and elevation directions are independent variables that comes from two functions of the target elevation angle. The experimental results show that the IBCLT error deviation of different static targets in the field of view is within 0.025 arcsec, which is 70% lower compared with the fixed gain method. Furthermore, the steady-state error deviation of moving targets is controlled within 2.5 arcsec. These experimental results prove the feasibility and effectiveness of the proposed method.

Piston error correction of sparse aperture systems using the metaheuristic stochastic parallel gradient descent algorithm.

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.

Wide-band high-resolution synthetic imaging of a segmented large-scaled lightweight diffractive telescope.

In this Letter, we report a segmented large-scaled lightweight diffractive telescope testbed newly built in our laboratory. The telescope, consisting of one 710-mm-diameter element in the center surrounded by eight 352-mm-diameter elements and a smaller eyepiece of achromatic lenses, can realize wide-band high-resolution imaging of 0.55-0.65 µm. The stitching errors are coarsely corrected by adjusting the motion stage mounted on each element. In particular, an optical synthesis system inserted behind the eyepiece is designed to compensate the residual tip-tilt-piston errors. We present the experimental imaging result of two stitched elements, which is the first successful experimental verification obtained by a practical segmented diffractive telescope to enhance the resolution. Moreover, spatial modulation diversity technology is used to restore the synthetic image so as to improve its quality and contrast.

Hypertelescope with multiplexed fields of view.

Hypertelescope interferometers having many highly diluted sub-apertures are capable of directly imaging, within a narrow field of view, celestial objects at a high resolution thanks to pupil densification. This Letter verifies with OpticStudio modeling the possibility of simultaneously imaging multiple such fields. A strategy of multi-field sampling uses a microlens array to generate multiplexed field channels, where independent active corrections of the tip-tilt and piston are applied for compensating for the off-axis aberrations. Adopting this strategy, we have designed a model of a multi-field hypertelescope with OpticStudio. The reported design expands the observing performance of hypertelescopes for directly imaging multiple sources with very high angular resolution.

Piston sensing of sparse aperture systems with a single broadband image via deep learning.

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.

Research on high-resolution imaging technology based on light field manipulation for a lenslet-based plenoptic camera.

In this paper, an aberration correction method for an extended target is proposed to solve the problem of the lenslet-based plenoptic camera not imaging clearly under the influence of aberrations. We propose a light field manipulation method to improve performance of the light field imaging system. The principle of this method is that the sub-aperture images extracted from the raw light field image are offset when the light field imaging system is affected by aberrations, and the symmetrical arrangement of the sub-aperture image array is destroyed. By repairing the symmetrical arrangement of the sub-aperture image array, the influence of phase aberrations on the imaging system can be eliminated, and the resolution of the plenoptic camera can be improved. We use an image correlation algorithm to process the sub-aperture images of the plenoptic camera, calculate and compensate each sub-aperture image's displacement caused by aberrations, and restore the symmetrical arrangement of the sub-aperture image array; then, a corrected high-resolution refocused image can be generated. In particular, this method uses only the raw light field information obtained by the plenoptic camera in a single exposure, without adding other hardware devices. Furthermore, it takes the extended target itself as the reference image, so the ideal position need not be calibrated in advance. Also, the parallax information of the sub-aperture images is retained, and the method is simple and easy to use. Numerical simulation and experimental results show that the technology proposed in this paper can work well for high-resolution imaging of a plenoptic camera with phase aberrations. This method can be potentially applied to analyze lens aberration, media-induced image distortion such as water turbulence in underwater imaging, and atmospheric turbulence in remote imaging. It may have important application prospects in the fields of astronomical object detection, remote sensing, etc.

Adaptive piston correction of sparse aperture systems with stochastic parallel gradient descent algorithm.

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.

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.

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.

Synthetic aperture imaging by using spatial modulation diversity technology with stochastic parallel gradient descent algorithm.

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.

Ultra-directional forward scattering by individual core-shell nanoparticles.

We study the angular scattering properties of individual core-shell nanoparticles that support simultaneously both electric and optically-induced magnetic resonances of different orders. In contrast to the approach to suppress the backward scattering and enhance the forward scattering relying on overlapping electric and magnetic dipoles, we reveal that the directionality of the forward scattering can be further improved through the interferences of higher order electric and magnetic modes. Since the major contributing electric and magnetic responses can be tuned to close magnitudes, ultra-directional forward scattering can be achieved by single nanoparticles without compromising the feature of backward scattering suppression, which may offer new opportunities for nanoantennas, photovoltaic devices, bio-sensing and many other interdisciplinary researches.

Simultaneous adaptive control of dual deformable mirrors for full-field beam shaping with the improved stochastic parallel gradient descent algorithm.

We propose and demonstrate the simultaneous adaptive control of a dual deformable mirror system for full-field beam shaping based on an improved stochastic parallel gradient descent (SPGD) algorithm and dual-phase-only liquid crystal spatial light modulators (LC-SLMs). One LC-SLM adaptively redistributes the intensity of the input beam and the other adaptively compensates the wavefront of the output beam. However, the intensity redistribution and wavefront compensation closed loops run simultaneously. In addition, the intensity redistribution and wavefront compensation closed loops adopt their respective metric functions independently. Experimental results show that the improved SPGD algorithm can not only be used for controlling dual deformable mirror configuration to adaptively generate near diffraction-limited flattop beams with desired intensity distributions, but also can greatly improve the control bandwidth.

Full-field unsymmetrical beam shaping for decreasing and homogenizing the thermal deformation of optical element in a beam control system.

We propose and demonstrate the full-field unsymmetrical beam shaping for decreasing and homogenizing the thermal deformation of optical element in a beam control system. The transformation of square dark hollow beam with unsymmetrical and inhomogeneous intensity distribution into square dark hollow beam with homogeneous intensity distribution is chosen to prove the validity of the technique. Dual deformable mirrors (DMs) based on the stochastic parallel gradient descent (SPGD) controller are used to redistribute the intensity of input beam and generate homogeneous square dark hollow beam with near-diffraction-limited performance. The SPGD algorithm adaptively optimizes the coefficients of Lukosz-Zernike polynomials to form the phase distributions for dual DMs. Based on the finite element method, the thermal deformations of CaF(2) half transparent and half reflecting mirror irradiated by high power laser beam before and after beam shaping are numerically simulated and compared. The thermal deformations of the mirror irradiated by the laser beam with different powers and the influences of thermal deformation on beam quality are also numerically studied. Results show that full-field beam shaping can greatly decrease and homogenize the thermal deformation of the mirror in the beam control system. The strehl ratios of the high power laser beams passing through the beam control system can be greatly improved by the full-field beam shaping. The technique presented in this paper can provide effective guidance for optimum design of high power laser cavity and beam shaping system.

Adaptive conversion of a high-order mode beam into a near-diffraction-limited beam.

We present a new method for efficiently transforming a high-order mode beam into a nearly Gaussian beam with much higher beam quality. The method is based on modulation of phases of different lobes by stochastic parallel gradient descent algorithm and coherent addition after phase flattening. We demonstrate the method by transforming an LP11 mode into a nearly Gaussian beam. The experimental results reveal that the power in the diffraction-limited bucket in the far field is increased by more than a factor of 1.5.