Wavefront Distortion Research Articles

Expansion of the Laser Beam Wavefront in Terms of Zernike Polynomials in the Problem of Turbulence Testing

The results of a study of the wavefront distortions of laser radiation caused by artificial turbulence obtained in laboratory conditions using a fan heater are presented. Decomposition of the wavefront in terms of Zernike polynomials is a standard procedure that traditionally is used to investigate the set of existing aberrations. In addition, the spectral analysis of the wavefront dynamics makes it possible to estimate the fraction of the energy distributed between different Zernike modes. It is shown that the fraction of energy related to the low-order polynomials is higher compared to the high-order polynomials. Also, one of the consequences of Taylor’s hypothesis is confirmed—low-order aberrations are slower compared to the higher-order ones.

Electrically variable liquid crystal lens with spiral electrode

Spiral shaped transparent electrode is used to replace the weakly conductive layer traditionally used to build an electrically tunable liquid crystal lens (TLCL) of modal control geometry. This replacement simplifies the manufacturing process and the operation control of the TLCL thanks to its lower temperature dependence. We present a theoretical analysis of its optical performance and propose an optimized structure that helps to decrease wavefront distortions. TLCLs with 2.2 mm clear apertures were fabricated and characterized in view of their use in miniature cameras. These lenses demonstrate relatively low RMS spherical aberrations (less than 0.25 um) for optical powers ranging from 0 D to 10 D.

Measurement of the magnification and distortion of high-precision imaging system using dual-fiber point diffraction interferometer

Magnification and distortion are two important parameters for high-precision imaging systems. Point diffraction interferometers (PDIs) can measure the magnification, distortion, and wavefront aberration of imaging systems with high precision. However, determining the precise pinhole alignment of the classical PDI is difficult. A new method for measurement of the magnification and distortion based on a dual-fiber point diffraction interferometer (DFPDI) is proposed. The end faces of two fibers are placed on the object plane of the optics under test and imaged to the image plane. The distance between the image points in the x and y directions are proportional to the Z2 and Z3 Zernike coefficients of the wavefront measurement result, respectively. The measurements of the image placement shift and precise alignment of the point diffraction pinhole are realized rapidly with high accuracy. The feasibility of the method is verified experimentally. The wavefront aberration, magnification, and distortion of a 5 × reduction lens with numerical aperture (NA) of 0.3 is measured jointly. The measurement uncertainties (3σ) of the magnification in the x and y directions and distortion are 756 ppm, 793 ppm, and 0.233 μm, respectively. Error analysis shows that the position error of the object- and image-plane stages is the main error source. An improved measurement scheme with a pinhole–pinhole pairs array in the object plane and a pinhole–window pairs array in the image plane is proposed. The influence of the position errors of the stages is eliminated with optimized measurement procedure. The DFPDI’s measurement repeatability (3σ) of the Z2 and Z3 coefficients is 0.65 and 0.33 nm, respectively, corresponding measurement uncertainties (3σ) of the magnification (in the x and y directions) and distortion can reach 1.88 ppm, 1.69 ppm, and 0.812 nm, respectively.

Dynamic wavefront distortion in resonant scanners.

Dynamic mirror deformation can substantially degrade the performance of optical instruments using resonant scanners. Here, we evaluate two scanners with resonant frequencies >12kHz with low dynamic distortion. First, we tested an existing galvanometric motor with a novel, to the best of our knowledge, mirror substrate material, silicon carbide, which resonates at 13.8 kHz. This material is stiffer than conventional optical glasses and has lower manufacturing toxicity than beryllium, the stiffest material currently used for this application. Then, we tested a biaxial microelectromechanical (MEMS) scanner with the resonant axis operating at 29.4 kHz. Dynamic deformation measurements show that wavefront aberrations in the galvanometric scanner are dominated by linear oblique astigmatism (90%), while wavefront aberrations in the MEMS scanner are dominated by horizontal coma (30%) and oblique trefoil (27%). In both scanners, distortion amplitude increases linearly with deflection angle, yielding diffraction-limited performance over half of the maximum possible deflection for wavelengths longer than 450 nm and over the full deflection range for wavelengths above 850 nm. Diffraction-limited performance for shorter wavelengths or over larger fractions of the deflection range can be achieved by reducing the beam diameter at the mirror surface. The small dynamic distortion of the MEMS scanner offers a promising alternative to galvanometric resonant scanners with desirable but currently unattainably high resonant frequencies.

Adaptive optics technology and urban horizontal link laser communication system

The wavefront distortion caused by atmospheric turbulence seriously affects the performance of free-space optical communication (FSOC) system. Adaptive optics (AO) technology has been proven to be an effective method to suppress atmospheric turbulence. Two laser communication terminals equipped with AO system are designed and manufactured, which are used in the horizontal link near the ground. In the laboratory simulation, 100-Gbps data transmission can be realized under moderate turbulence (D / r0 < 10), the bit error rate (BER) is better than 1 × 10 − 6, and the measured single-mode fiber coupling efficiency is 42% to 48%. 10-Gbps data transmission can be realized under strong turbulence (D / r0 > 10), and the BER is better than 1 × 10 − 6. The BER is high in the practical communication test under the urban horizontal link of 1 km (D / r0 = 10), the BER is 1 × 10 − 3, and the coupling efficiency is 12% to 20%. Finally, to achieve the goal of 100-Gbps FSOC for near ground and long distance, based on the experimental performance of the existing two sets of laser communication system, the solution of laser communication system is proposed, which provides a reference for relevant researchers.

Dynamic aerosol and dynamic air-water interface curvature effects on a 2-Gbit/s free-space optical link using orbital-angular-momentum multiplexing

Abstract When an orbital-angular-momentum (OAM) beam propagates through the dynamic air–water interface, the aerosol above the water and the water surface curvature could induce various degradations (e.g., wavefront distortion, beam wandering, scattering, and absorption). Such time-varying degradations could affect the received intensity and phase profiles of the OAM beams, resulting in dynamic modal power loss and modal power coupling. We experimentally investigate the degradation for a single OAM beam under dynamic aerosol, dynamic curvature, and their comprehensive effects. Our results show the following: (i) with the increase of the aerosol strength (characterized by the attenuation coefficient) from ∼0 to ∼0.7–1.3 dB/cm over ∼7 cm, the power coupling ratio from OAM −1 to +2 increases by 4 dB, which might be due to the amplitude and phase distortion caused by spatially dependent scattering and absorption. (ii) With the increase of the curvature strength (characterized by the variance of curvature slope over time) from ∼0 to ∼2 × 10−5 rad2, the power coupling ratio from OAM −1 to +2 increases by 11 dB. This could be caused by both the wavefront distortion and the beam wandering. (iii) Under the comprehensive effect of aerosol (∼0.1–0.6 dB/cm) and curvature (∼6 × 10−7 rad2), there is an up to 2 dB higher modal power loss as compared with the single-effect cases. (iv) The received power on OAM −1 fluctuates in a range of ∼6 dB within a 220 ms measurement time under aerosol (∼0.1–0.6 dB/cm) and curvature (∼6 × 10−7 rad2) effects due to the dynamic degradations. We also demonstrate an OAM −1 and +2 multiplexed 2-Gbit/s on–off-keying link under dynamic aerosol and curvature effects. The results show a power penalty of ∼3 dB for the bit-error-rate at the 7% forward-error-correction limit under the comprehensive effect of aerosol (∼0.1–0.6 dB/cm) and curvature (∼6 × 10−7 rad2), compared with the no-effect case.

Phase conjugation of twisted Gaussian Schell model beams in stimulated down-conversion

AbstractStimulated parametric down-conversion is a nonlinear optical process that can be used for phase conjugation and frequency conversion of an optical field. A precise description of the outgoing stimulated field has been developed for the case where the input pump and seed fields are coherent. However, partially coherent beams can have interesting and important characteristics that are absent in coherent beams. One example is the twist phase, a novel optical phase that can appear in partially coherent Gaussian beams and gives rise to a nonzero orbital angular momentum. Here, we consider stimulated down-conversion for partially coherent input fields. As a case study, we use twisted Gaussian Schell-Model beams as the seed and pump beams in stimulated parametric down-conversion. It is shown both theoretically and experimentally that the stimulated idler beam can be written as a twisted Gaussian Schell-Model beam, where the beam parameters are determined entirely by the seed and pump. When the pump beam is coherent, the twist phase of the idler is the conjugate of that of the seed. These results could be useful for the correction of wavefront distortion such as in atmospheric turbulence in optical communication channels, and synthesis of partially coherent beams.

A time-division correction method for adaptive optics system

An adaptive optics system can measure and compensate the wavefront distortion caused by dynamic disturbance in real time. It is usually used for astronomical observation and other occasions. According to the current technology, it is only suitable for small field of view optical system or point target, but not for ground extended target detection. In order to solve this problem, a correction method is proposed: firstly, the sub aperture image of wavefront sensor is divided into several sub regions, each sub region corresponds to a certain light direction or field angle range; secondly, calculate the offset of the image feature points in each sub region, and an image with good correction effect in a field of view in this direction is obtained; the last step is to measure each sub region one by one and combine these images into a full frame image. Through comparison, it is found that the method proposed in this paper is essentially to divide the extended target into multiple point light sources for correction.

Effects of adaptive optics on bit error rate of M-ary PPM oceanic optical wireless communication systems with aperture averaging in strong turbulence

Scintillation is the result of oceanic turbulence reducing the bit error rate (BER) performance of oceanic optical wireless communication (OWC) systems. The scintillation, also known as intensity fluctuations, occurs due to the turbulence-induced wavefront deformations. The correction of deformations by adaptive optics (AO) reduces the scintillation effect of turbulence and results in improved BER performance. In this paper, an oceanic OWC (OOWC) system that has a Gaussian laser beam at the transmitter, finite-sized circular aperture at the receiver, employing M-ary pulse position modulation (PPM) and operating in strong oceanic turbulence, is considered. Improvement in the BER performance of the OOWC system is examined with the implementation of AO correction. Comparison of BER performances between the AO and non-adaptive optics OOWC systems is shown by calculating the metric defined. BER of M-ary PPM OOWC links is evaluated over gamma–gamma fading channels. The modified Rytov theory together with the Zernike filter functions is used to find the AO corrected aperture averaged scintillation index where extended Huygens–Fresnel technique is used to obtain the average received signal power.

Wavefront Detection and Compensation Technology Based on Signal Light Nutation Under Atmospheric Turbulence

The Shack-Hartmann wavefront sensor restricts the dynamic range and detection accuracy of wavefront detection due to the limitation of the lens array aperture. This study proposes a system using signal light nutation to detect wavefront distortion, providing high spatial resolution and detection dynamic range. Simulations show that the root mean square (RMS) and mixing efficiency of the compensated wavefront are optimized. In the case of strong turbulence, the mixing efficiency is increased by nearly 105 times, and the RMS is reduced to the original value of 0.048.

Wavefront Coherent Compensation Technology Under Direct Sunlight in Free Space Optical Communication System

The charge-coupled device-based Shaker–Hartmann wavefront sensor has been widely used to compensate for wavefront distortion in coherent optical communication. However, the influence of strong background light causes large errors when restoring the signal light wavefront. This study proposes a wavefront recovery method by combining a detector array with an optical nutation of the local oscillator. By adding a small rotation angle to the local oscillator, the wavefront slope is estimated according to the output of the change law of the mixed signal and the local oscillator light, and the multi-order Zernike mode is used to reconstruct the signal light wavefront. Simulation studies show that the root-mean-square value (RMS) and the coherence efficiency of the signal light wavefront were significantly optimized. Under direct sunlight, the estimation compensation error of the wavefront slope reached 0.008. Under strong turbulence, the mixing efficiency was increased by nearly 97.5 times, and the RMS was reduced to the original value of 0.048 The designed system has good background light compensation and wavefront recovery capabilities and is suitable for coherent optical communication under direct sunlight.

Performance Evaluation of Solid-State Laser Gain Module by Measurement of Thermal Effect and Energy Storage

The optimization of solid-state laser cavities requires a deep understanding of the gain module, the most critical laser component. This study proposes a procedure for evaluating the performance of the solid-state laser gain module. The thermal effect and energy storage characteristics are the performance criteria. A normalized heating parameter was calculated as a quantitative indicator of the performance criteria. We proposed a method to quantify the heat dissipated into the gain medium using the wavefront distortion, thermal deformation theory of the gain medium, and the ray transfer matrix method. The suggested procedure was verified by evaluating the flashlamp type Nd:YAG rod gain module, but it can also even be extended to other solid-state laser gain modules by applying the appropriate thermal deformation theory.

Influence of jet components on the aero-optical effects of a 3D supersonic mixing layer.

Aero-optical effects in the mixing layer have caused significant concern due to the negative influence of high-speed vehicles with infrared imaging guidance systems. Here, we study the influence of different cooling mediums on the aero-optical effects. Four different cooling components are considered: helium (He), nitrogen (N2), air, and argon (Ar). The large eddy simulation method and ray-tracing method are used, respectively, to simulate the 3D mixing layer and to calculate the optical path difference (OPD). The numerical results show that, as the molecular weight of the cooling mediums increases, the mixing layer transition advances and the 3D effect of the flow field is enhanced. The local minimum OPD values of the wavefront distortion are significantly correlated with the large-scale vortex structure of the mixing layer. The compression effect plays a dominant role in aero-optics before the large-scale structure forms. Once the large-scale vortex structure generates, the aero-optical effect is conducted by the density and compression effect. The cooling medium helium delays the development of the mixing layer and subsequently reduces the aero-optical effects. However, once the large-scale vortex structure forms, the aero-optical effect becomes serious due to the largest density difference between air and He.

Laboratory Simulation of Atmospheric Turbulence in the Problem of Correcting Laser Radiation Wavefront Distortions by Using a Fast Adaptive Optical System

Laboratory Simulation of Atmospheric Turbulence in the Problem of Correcting Laser Radiation Wavefront Distortions by Using a Fast Adaptive Optical System

Analysis on the coupling effect of wavefront distortion and pointing misalignment in space laser interferometry

Space-based gravitational wave detection aims to measure gravitational waves with strains of down to 10−20 in 10−4 Hz ∼ 1 Hz frequency band. In order to achieve this measurement sensitivity, inter-satellite laser interferometry with picometer precision for an armlength of 108 ∼ 109 m is required. However, the coupling of the transmitting-beam misalignment and the wavefront distortion results in a non-negligible measurement error of intersatellite laser interferometry. Considering a wavefront distortion model composed of the first 55 terms of Zernike polynomials, we analyze the coupling effect of beam misalignment and wavefront distortion in both analytical and numerical methods. Calculation results show that the position of the stationary point is mainly determined by defocus, astigmatism and coma of the wavefront distortion of the transmitting beam. Moreover, a large defocus and small coma are preferred to achieve a better alignment of the stationary pointing direction with the inter-satellite line-of-sight, such that the coupling noise and received laser power can be optimized.

Adaptive optics with spatio-temporal lock-in detection for temporal focusing microscopy.

Wavefront distortion in temporal focusing microscopy (TFM) results in a distorted temporal profile of the excitation pulses owing to spatio-temporal coupling. Since the pulse duration is dramatically changed in the excitation volume, it is difficult to correct the temporal profile for a thick sample. Here, we demonstrate adaptive optics (AO) correction in a thick sample. We apply structured illumination microscopy (SIM) to an AO correction in wide-field TFM to decrease the change in the pulse duration in the signal detection volume. The AO correction with SIM was very successful in a thick sample for which AO correction with TFM failed.

Multiscale optimization of the geometric wavefront sensor.

Since wavefront distortions cannot be directly measured from an image, a wavefront sensor (WFS) can use intensity variations from a point source to estimate slope or curvature of a wavefront. However, processing of measured aberration data from WFSs is computationally intensive, and this is a challenge for real-time image restoration or correction. A multi-resolutional method, known as the ridgelet transform, is explored to estimate wavefront distortions from astronomical images of natural source beacons (stars). Like the curvature sensor, the geometric WFS is relatively simple to implement but computationally more complex. The geometric WFS is extended by incorporating the sparse and multi-scale geometry of ridgelets, which are analyzed to optimize the performance of the geometric WFS. Ridgelets provide lower wavefront errors, in terms of root mean square error, specifically over low photon flux levels. The simulation results further show that by replacing the Radon transform of the geometric WFS with the ridgelet transform, computational complexity is reduced.

Nesterov-accelerated adaptive momentum estimation-based wavefront distortion correction algorithm

In order to improve the wavefront distortion correction performance of the classical stochastic parallel gradient descent (SPGD) algorithm, an optimized algorithm based on Nesterov-accelerated adaptive momentum estimation is proposed. It adopts a modified second-order momentum and a linearly varying gain coefficient to improve iterative stability. It integrates the Nesterov momentum term and the modified Adam optimizer to further improve the convergence speed, correct the direction of gradient descent in a timely fashion, and avoid falling into local extremum. Besides, to demonstrate the algorithm's performance, a wavefront sensorless adaptive optics system model is established using a 6×6 element deformable mirror as wavefront corrector. Simulation results show that, compared with the SPGD algorithm, the proposed algorithm converges faster, and its Strehl ratio after convergence is nearly 6.25 times that of the SPGD algorithm. Also, the effectiveness and superiority of the proposed algorithm are verified by comparing with two existing optimization algorithms.

High-spatial resolution stacked-actuator deformable mirror for correction of atmospheric wavefront aberrations.

Deformable mirrors are vital components of any adaptive optical system. Considering such a crucial role in compensation of incident wavefront distortions, the main requirements are imposed on these elements that determine performance of the entire system. To correct for phase distortions in high-power laser complexes a stacked-actuator deformable mirror with water cooling was developed. The main characteristics of the mirror, such as the initial surface profile (flatness), response functions of the actuators, maximal stroke, and amplitude-frequency characteristics are presented in this paper. Experimental investigations of the proposed cooling method of the mirror surface through actuators were performed.

Dynamic mode decomposition based predictive model performance on supersonic and transonic aero-optical wavefront measurements.

Air density variations around an airborne directed energy system distort a beam's wavefront, resulting in degraded performance after propagation into the far field. Adaptive optics (AO) can be used to correct for these rapidly evolving aero-optical aberrations; however, in some conditions, the inherent latency between measurement and correction in state-of-the-art AO systems results in significantly reduced performance. Predictive AO control methods utilize future state predictions to compensate for rapidly evolving distortions and are promising techniques for mitigating this limitation. This paper demonstrates an application of the dynamic mode decomposition (DMD) method on turbulent boundary layer wavefront data from supersonic and transonic wind tunnel flow from the Air Force Research Laboratory's Aero-Effects Laboratory. DMD is a lightweight algorithm used to isolate spatiotemporal patterns in a dataset into physically meaningful modes with associated dynamics, which were used to predict future states from a given wavefront. This method showed notable improvements in simulated wavefront correction, providing a reduction of residual wavefront distortion, measured as root mean square over the aperture, by up to 25.4% over a simulated latency model, which could accordingly result in higher laser system performance.