Wavefront Distortion Research Articles

Physics-driven untrained neural network for vortex beam compensation in adaptive optics aided underwater wireless optical communications

Orbital angular momentum (OAM) multiplexing is emerging as a critical technique for achieving high data capacity in underwater wireless optical communications (UWOC). Nonetheless, wavefront distortions induced by underwater turbulence compromise the orthogonality of OAM modes. In this paper, we introduce a physics-driven untrained learning approach for adaptive optics that operates independently of extensive amplitude datasets. Without iterative processing and pre-trained datasets, the underwater turbulence characteristics can be retrieved accurately by only relying on a one-shot distorted probe beam and a priori known amplitude of the probe beam. By leveraging a single distorted diffraction pattern and a priori known amplitude of the probe beam, the characteristics of underwater turbulence can be accurately retrieved without iterative processing or pre-trained datasets. Furthermore, by implementing a hybrid input/output alternating projection algorithm with a square constraint area, the retrieved underwater turbulence phase screen beyond the [0, 2π] range aligns with the target pattern. This consistency indicates that the proposed wavefront recovery technology is validated across a broad range of turbulence strengths. As a demonstration of feasibility, numerical simulations, and optical experiments were conducted to validate the compensation of OAM beams. Furthermore, the theoretical bit error rate (BER) and channel capacity were inferred based on the purity of OAM modes and the level of crosstalk.

Aberration correction in complex media over multiple isoplanatic patches by exploiting their spatial correlation

Optical imaging in complex media, such as biological tissues, poses significant challenges due to the presence of aberrations and scattering that distort wavefronts and degrade image quality. Wavefront correction has emerged as a crucial technique for mitigating these effects. Recent advances, such as adaptive optics, wavefront shaping, and matrix-based methods, have made significant strides in correcting for wavefront distortions to achieve high-resolution imaging. However, current approaches face challenges when addressing spatially varying distortions and small isoplanatic patches, where the corrections lose reliability due to the rapid spatial variation of distortions. To address this limitation, we introduce a method that exploits the spatial correlation of wavefront distortions across neighboring isoplanatic patches. This approach, termed "inward-outward progression", enables a more reliable wavefront correction across multiple small patches. The process involves two key steps: (1) the inward progression, where a small zone surrounding a pixel is optimized while progressively shrinking the optimized region, and (2) the outward progression, where the wavefront correction phases of the corrected zone serve as the initial guess to optimize adjacent areas, extending the correction from the small zone at the inward progression until the entire field of view is covered. We validate this method by imaging a USAF resolution target under 700-µm-thick chicken breast. Our approach shows a significant improvement in image quality and superior performance over existing techniques, paving the way for noninvasive imaging where conventional methods face substantial limitations due to the spatially varying aberrations and scattering.

Large angle and high uniform diffractive laser beam splitter with divergent spherical wave illumination

Splitting angle, generally limited by the feature size of diffractive optical element (DOE), is one of the significant metrics of the diffractive laser beam splitter. In this study, we realize large angle and high uniform split beams by using a divergent spherical wave front incidence. For designing this diffractive beam splitter, the Gerchberg-Saxton (GS) optimization algorithm which is known as a widely used method in DOE design is modified. Meanwhile, a negative feedback method is proposed to further improve the uniformity in experiment to compensate the incident wavefront distortion. Finally, a phase-only spatial light modulator (SLM) was used to test the feasibility and adaptiveness of our design strategy. In the experiment, we achieved several kinds of beam splitters and the uniformities are all better than 3.0% which the uniformity is measured by the peak-to-valley (PV) ratio.

Experimental Research on the Correction of Vortex Light Wavefront Distortion

Wavefront distortion occurs when vortex beams are transmitted in the atmosphere. The turbulence effect greatly affects the transmission of information, so it is necessary to use adaptive optical correction technology to correct the wavefront distortion of the vortex beam at the receiving end. In this paper, a method of vortex wavefront distortion correction based on the deep deterministic policy gradient algorithm is proposed; this is a new correction method that can effectively handle high-dimensional state and action spaces and is especially suitable for correction problems in continuous action spaces. The entire system uses adaptive wavefront correction technology without a wavefront sensor. The simulation results show that the deep deterministic policy gradient algorithm can effectively correct the distorted vortex beams and improve the mode purity, and the intensity correlation coefficient of single-mode vortex light can be increased to about 0.88 and 0.69, respectively, under weak turbulence and strong turbulence, and the intensity coefficient of weak-turbulence multi-mode vortex light can be increased to about 0.96. The experimental results also show that the adaptive correction technology based on the deep deterministic policy gradient algorithm can effectively correct the wavefront distortion of vortex light.

Wavefront sensing based on large guide region in solar ground layer adaptive optics

In ground-based high-resolution solar observation, ground-layer adaptive optics (GLAO) offers a significant advancement by compensating for wavefront aberrations caused by near-ground atmospheric turbulence. GLAO overcomes the field-of-view limitations of conventional adaptive optics (AO), which is constrained by turbulence anisoplanatism. In conventional solar AO, wavefront sensing requires correlation calculations across an extended guide region to extract wavefront information. However, the cross correlation algorithm with a larger guide region size smooths the wavefront distortions caused by high-altitude turbulence, reducing the accuracy of single-line wavefront detection. This effect is particularly pronounced in GLAO systems that utilize large guide regions for ground layer wavefront sensing. This paper proposed a theoretical model for GLAO wavefront sensing using correlating Shack-Hartmann wavefront sensors targeting extended objects. We quantitatively analyze the impact of the guide region size on wavefront detection accuracy and validate our findings through simulation experiments. Simulation results indicate that for a 1-meter telescope, the difference between the root mean square (RMS) of detected aberrations differs from the RMS of ground-layer aberrations by less than 1/30 wavelength when using the CP7 model at 60" and the MK8 model at 140". Results also indicate that increasing the guide region effectively enables the detection of ground-layer wavefront aberrations. This finding not only provides valuable guidance for achieving accurate ground-layer wavefront sensing in GLAO systems, but also offers what we believe to be new solutions for optimizing GLAO system performance.

Influence of exposure time on the aero-optical effects of a high-speed aircraft optical window

Under high-speed conditions (Mach number > 3), the turbulent shear layer formed on the optical window causes phase changes in the light, resulting in the aero-optical effects, which significantly affect the imaging quality at different exposure times, τ. In this study, imaging data of an optical window were collected in a Mach 3.8 supersonic low-noise wind tunnel for a facula and a USAF 1951 resolution board, as well as distorted wavefront data of visible light. As τ increases from 0.2 ms to 5 ms, the centroid jitter of the facula shows an overall decreasing trend and the increase of τ mainly inhibits the jitter in the spanwise direction. While τ varies from 0.2 ms to 28 ms, structural analysis indicated that the structural similarity and stability of imaging improves and this improvement has an upper limit of τ0 = 22 ms, coined as the saturation exposure time. Normalized modulation transfer function curves derived from USAF 1951 images show a decrease in the imaging resolution as τ increases. The average wavefront distortion can be reduced by up to 71.7% as τ increases from 5 ms to 30 ms, while the standard deviation of wavefront distortion initially decreases and then stabilizes at 0.0025λ.

Model for restoring obstructed beam transmission in atmospheric turbulence based on BP neural network

Atmospheric turbulence and obstacles can distort rays during transmission, resulting in significant wavefront distortion and loss of optical field information. This paper employs the phase screen method to simulate the transmission characteristics of a Gaussian plane wave in turbulent conditions, establishing an obstacle grid at the receiver to represent beam obstruction. A dataset of unobstructed transmissions is used to train a Backpropagation Neural Network, constructing neurons and connection weights. By scanning optical field data systematically, the model compensates for the obstructed portions of the optical field distribution. The results are compared to unobstructed transmissions, focusing on image similarity, and demonstrate the entire process from compensation to distortion correction. Simulation results indicate that the Backpropagation Neural Network effectively compensates for optical field information loss, showcasing strong performance within a certain time scale.

Effect of wavefront distortion on focusing performance of long-focal-depth mirror

Abstract A long-focal-depth mirror can produce a quasi-Bessel beam, which has the advantages of a long focal depth, a small spot, independence of wavelength, and a uniform longitudinal intensity. The laser beam emitted by a laser has a certain wavefront distortion, and real optical elements will also produce extra aberrations in the process of processing and assembling, which will then introduce new wavefront distortion to the optical system. Wavefront distortion will affect the phase and then affect the coherence and beam quality of the laser beam, ultimately affecting the beam focusing performance. To accurately study the effect of wavefront distortion on the focusing performances of long-focal-depth mirrors, an aberration model based on Zernike polynomials was established. Based on scalar diffraction theory, the effects of three typical aberrations on the focusing performances of long-focal-depth mirrors were calculated. The focusing performances were comprehensively evaluated by using various evaluation manners, including the power in the bucket. The calculation results showed that, compared with the ideal state, for an astigmatism or coma with a root mean square (RMS) more than 0.25 μm, the focusing performance of the long-focal-depth mirror dropped abruptly. The focused spot calculated with a 0.10 μm aberration shows a distribution identical to that when the component is properly clamped, exhibiting no significant aberration features, indicating that a RMS of 0.10 μm is acceptable.

Improving SMF coupling efficiency in aberrated optical system through optical system aberration correction method based on MPLC

In spatial laser communication terminals, the distortion of wavefront caused by the aberrations due to optical system processing and installation errors reduces the coupling efficiency of single-mode fiber (SMF). A method based on Multi-Plane Light Conversion (MPLC) is proposed to correct optical system aberrations and improve the coupling efficiency by converting the distorted light into Gaussian beam which matches SMF through a succession of phase planes. The Gaussian beam to SMF coupling efficiency model is firstly established and demonstrates that the SMF coupling efficiency can be effectively improved to 100% by converting the incident light into Gaussian beam which matches the SMF mode. The optical system aberration correction comparison simulation and experiment is conducted, and the results show after correcting aberrations using MPLC, the coupling efficiency increases from less than 0.1%–58.61% compared to distorted light directly coupling into SMF. Results show that the optical system aberrations are effectively corrected by this method, which has a certain reference value for the study of improving the coupling efficiency.

Development of piezo-actuated x-ray deformable mirror for vertical focusing of synchrotron radiation at Indus-2

Piezo-actuated x-ray deformable mirrors (PXDMs) can effectively control the surface profile with sub-nanometre accuracy for adaptive focusing and correct the wavefront distortion generated due to imperfections in optical components or other extraneous effects like heat load, minor misalignments of synchrotron radiation beamline. Generating and controlling the desired shape of PXDMs with sub-nanometre accuracy is very challenging due to the presence of a large number of actuators and constraints related to nonlinearity of piezoactuator, boundary conditions, fabrication related limitations and the requirement for ex-situ as well as in-situ characterization of PXDM. To accomplish this, a PXDM of zerodur with multiple electrodes on a piezoactuator has been developed for vertical focusing of synchrotron x-rays for the first time in India. The PXDM has been fabricated and characterized by in-house developed technologies. The iterative piezo response function-based optimization technique is used to optimize the electric fields of individual piezoactuators in order to achieve the desired parabolic shape of the PXDM. The ex-situ characterization showed that the PXDM can achieve the target parabolic profile with 42 nm root-mean-square error. Furthermore, in-situ characterization at a beamline, BL-12, of Indus-2 synchrotron radiation source using PXDM has confirmed the focusing of collimated x-ray beam in the vertical direction from FWHM 235 μm to FWHM 83 μm.

Innozag amplifier: optimizing the Innoslab platform to improve beam quality and gain

This study presents an innovative zigzag-type Innoslab amplifier platform, termed ‘Innozag,’ that merges the essential attributes of both Innoslab and zigzag slab amplifiers. A thorough theoretical and experimental examination has been performed to analyze and compare the gain and amplified beam wavefront distortion of the Innoslab and Innozag amplifiers. Our investigation includes detailed optical path difference computation coupled with examination of the far-field amplified beam profile. The results confirm that the Innozag amplifier reduces the thermally induced wave distortion by up to 40%. Geometric features, particularly the overlapping zones in the zigzag path, increase the gain of the Innozag amplifier. The Innozag design achieves an amplification factor 1.4 times greater than that of the Innoslab amplifier in a five-pass structure.

Measurement precision bounds on aberrated single-molecule emission patterns.

Single-molecule localization microscopy (SMLM) has revolutionized the study of biological phenomena by providing exquisite nanoscale spatial resolution. However, optical aberrations induced by sample and system imperfections distort the single-molecule emission patterns (i.e. PSFs), leading to reduced precision and resolution of SMLM, particularly in three-dimensional (3D) applications. While various methods, both analytical and instrumental, have been employed to mitigate these aberrations, a comprehensive analysis of how different types of commonly encountered aberrations affect single-molecule experiments and their image formation remains missing. In this study, we addressed this gap by conducting a quantitative study of the theoretical precision limit for position and wavefront distortion measurements in the presence of aberrations. Leveraging Fisher information and Cramér-Rao lower bound (CRLB), we quantitively analyzed and compared the effects of different aberration types, including index mismatch aberrations, on localization precision in both biplane and astigmatism 3D modalities as well as 2D SMLM imaging. Furthermore, we studied the achievable wavefront estimation precision from aberrated single-molecule emission patterns, a pivot step for successful adaptive optics in SMLM through thick specimens. This analysis lays a quantitative foundation for the development and application of SMLM in whole-cells, tissues and with a large field of view, providing in-depth insights into the behavior of different aberration types in single-molecule imaging and thus generating theoretical guidelines for developing highly efficient aberration correction strategies and enhancing the precision and reliability of 3D SMLM.

Suppression of vortex electromagnetic wave divergence by modulating the wave front dislocation line

Abstract When the beam is transmitted in the atmosphere, under the influence of atmospheric turbulence, the beam will occur energy attenuation, wavefront distortion and other phenomena, which will seriously affect the transmission and reception of information. Based on the PB phase principle enhances the focusing capability of the auto-focusing Airy Gaussian vortex beam by regulating the wavefront error curvature of the vortex beam, and then enhances the resistance of the beam against atmospheric turbulence. The results reveal the curvature of the wavefront error curve and the peak intensity of the light field of the beam can be changed by changing the beam polarization state parameters n and m in the focal plane. The auto-focusing Airy Gaussian vortex beam with the polarization state parameters m=1, n=4 increases the peak magnitude of the light field intensity in the focal plane of the auto-focusing Airy Gaussian vortex beam with the polarization state parameters m=0, n=0 to 1.99 times. Demonstrate that geometric phase tuning the auto-focusing Airy Gaussian vortex beams can enhance resistance to atmospheric turbulence. Furthermore, this paper extends this method to the field of millimeter wave. Under the transmission distance of 1km, the peak intensity of the initial vortex electromagnetic wave after the geometric phase adjustment is increased to 3.33 times, and the receiving radius of the target surface is reduced to 0.24 of the initial vortex electromagnetic wave. It shows that geometric phase-regulated vortex electromagnetic wave can suppress vortex electromagnetic wave divergence and have potential applications in wireless communication.

Correction of Aero-Optical Effect with Blow–Suction Control for Hypersonic Vehicles

High-speed turbulence induces significant aero-optical effects that severely disrupt the functionality of imaging systems of hypersonic vehicles. In this study, the aero-optical correction of various jet cooling modes is investigated using a Terminal High Altitude Area Defense (THAAD)-like seeker model and the imaging impact of high-speed flow field and flow control on the optical window is analyzed by the Delayed Detached Eddy Simulation (DDES) method. The findings reveal that a jet mode parallel to the window exhibits better cooling effectiveness compared to a perpendicular jet mode along the body axis; however, it introduces additional wavefront distortion, leading to degraded imaging quality. Although micro-vortex generators (MVGs) can reduce density fluctuations near the window from a refractive index perspective, they do not effectively mitigate wavefront distortion or improve window cooling efficiency. Finally, incorporating suction control, a comprehensive flow control solution, significantly improves the flow field structure near the window, resulting in a more uniform temperature distribution and reduced wavefront distortion. Applying this flow control method results in a 14.7% reduction in wavefront distortion at 3 Ma and an approximately 20% maximum value reduction at 5 Ma. This study proposes a novel and comprehensive flow control method to effectively mitigate the aero-optical effect in hypersonic flows, providing a new avenue for subsequent researchers in this field.

Performance analysis of free space optical communications with FOA-WFS.

Adaptive optics (AO) technology can correct wavefront distortion in coherent free space optical communication (FSOC), with wavefront sensors playing a vital role in this process. However, traditional wavefront sensors are large and expensive. Therefore, we propose using the inexpensive and easy-to-deploy flat optics angle-based wavefront sensor (FOA-WFS) to measure the wavefront aberration. It aims to meet the needs of various FSOC applications. We first establish the relationship between the energy ratio and the Zernike coefficient through theoretical studies and analyze the feasibility of applying the FOA-WFS to the FSOC. We then generate experimental datasets based on the relevant principles. Through numerical simulation, we verify that it can reconstruct wavefront aberration accurately and improve system performance. Finally, we analyze the mixing efficiency and bit error rate based on the collected aberration data by the experimental platform. The results indicate that the AO system based on the FOA-WFS can efficiently improve the performance of the FSOC. This study provides a novel wavefront aberration detection method for designing the AO systems in the FSOC.

Continuous-wave degenerate cavity laser for optical imaging in scattering media.

Lasers play a significant role in optical communication, medical, and scientific research, owing to their high brightness and high coherence. However, the high spatial coherence will lead to specific challenges, such as speckle noise in imaging and wavefront distortion during propagation through scattering media. Here, a continuous-wave (cw) degenerate cavity laser (DCL) with low spatial coherence is demonstrated with efficient suppression of the thermal lensing effect from the gain crystal. Experimentally, a cw degenerate laser output with about 2000 transverse modes corresponding to a speckle contrast of about 0.0224 is achieved. This laser can be used for speckle reduction and is robust against atmospheric turbulence, which may find applications in the field of laser imaging technology and illumination.

Research on Distortion Control in Off-Axis Three-Mirror Astronomical Telescope Systems

With off-axis reflection systems with specific distortion values serving as objectives or collimators, it is possible to compensate and correct for spectral line bending in spectroscopic instruments. However, there is limited research on the precise control of distortion, which poses particular challenges in large field-of-view optical systems. This paper presents a method for controlling distortion in off-axis reflection systems. Based on Seidel aberration theory and the relationship between distortion wavefront error and primary ray error, we construct objective functions with structural constraints and aberration constraints. The initial structure with specific distortion values is then solved using a differential evolution algorithm. The effectiveness and reliability of this method are verified through the design of an off-axis three-reflection system. The method provided in this study facilitates the design of remote sensing instruments.

Active-compensation of systematic error for the 1000 mm aperture flat interferometer.

Large-aperture elements would induce unnegligible systematic errors due to material inhomogeneity, manufacturing or gravity, that are difficult to correct in an extreme large aperture flat interferometer and result in reference wavefront distortion. We propose an active-compensation method for systematic errors by employing a deformable mirror into the interferometer to modulate reference wavefront. A mapping relationship between sag of the deformable mirror and reference wavefront error is derived by theory of matrix optics, and two interferometer optical paths are designed for whether the deformable mirror is located at the pupil or not. The algorithm for calculating and controlling the sag of a deformable mirror can eliminate the need for the deformable mirror to be positioned at the pupil in order to achieve controllable modulation of the wavefront. This algorithm has been validated through the intentional introduction of systematic errors into the 1000 mm aperture flat interferometer for effective compensation. Moreover, the optimization algorithm in Ansys Zemax is utilized to calculate the optimal solution for surface shape of the deformable mirror, treating it as a nominal value. The algorithm error is on the order of 10-6 mm, falling within the acceptable tolerance range for the deformable mirror's surface shape.

All-optical phase conjugation using diffractive wavefront processing

Optical phase conjugation (OPC) is a nonlinear technique used for counteracting wavefront distortions, with applications ranging from imaging to beam focusing. Here, we present a diffractive wavefront processor to approximate all-optical phase conjugation. Leveraging deep learning, a set of diffractive layers was optimized to all-optically process an arbitrary phase-aberrated input field, producing an output field with a phase distribution that is the conjugate of the input wave. We experimentally validated this wavefront processor by 3D-fabricating diffractive layers and performing OPC on phase distortions never seen during training. Employing terahertz radiation, our diffractive processor successfully performed OPC through a shallow volume that axially spans tens of wavelengths. We also created a diffractive phase-conjugate mirror by combining deep learning-optimized diffractive layers with a standard mirror. Given its compact, passive and multi-wavelength nature, this diffractive wavefront processor can be used for various applications, e.g., turbidity suppression and aberration correction across different spectral bands.

Phase-diversity-based wavefront sensing for fluorescence microscopy

Fluorescence microscopy is an invaluable tool in biology, yet its performance is compromised when the wavefront of light is distorted due to optical imperfections or the refractile nature of the sample. Such optical aberrations can dramatically lower the information content of images by degrading the image contrast, resolution, and signal. Adaptive optics (AO) methods can sense and subsequently cancel the aberrated wavefront, but they are too complex, inefficient, slow, or expensive for routine adoption by most labs. Here, we introduce a rapid, sensitive, and robust wavefront sensing scheme based on phase diversity, a method successfully deployed in astronomy but underused in microscopy. Our method enables accurate wavefront sensing to less than λ/35 root mean square (RMS) error with few measurements, and AO with no additional hardware besides a corrective element. After validating the method with simulations, we demonstrate the calibration of a deformable mirror >hundredfold faster than comparable methods (corresponding to wavefront sensing on the ∼100ms scale), and sensing and subsequent correction of severe aberrations (RMS wavefront distortion exceeding λ/2), restoring diffraction-limited imaging on extended biological samples.