Wavefront Correction Research Articles

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.

Aberration Modulation Correlation Method for Dim and Small Space Target Detection

The significance of detecting faint and diminutive space targets cannot be overstated, as it underpins the preservation of Earth’s orbital environment’s safety and long-term sustainability. Founded by the different response characteristics between targets and backgrounds to aberrations, this paper proposes a novel aberration modulation correlation method (AMCM) for dim and small space target detection. By meticulously manipulating the light path using a wavefront corrector via a modulation signal, the target brightness will fluctuate periodically, while the background brightness remains essentially constant. Benefited by the strong correlation between targets’ characteristic changes and the modulation signal, dim and small targets can be effectively detected. Rigorous simulations and practical experiments have validated the remarkable efficacy of AMCM. Compared to conventional algorithms, AMCM boasts a substantial enhancement in the signal-to-noise ratio (SNR) detection limit from 5 to approximately 2, with an area under the precision–recall curve of 0.9396, underscoring its ability to accurately identify targets while minimizing false positives. In essence, AMCM offers an effective method for detecting dim and small space targets and is also conveniently integrated into other passive target detection systems.

Comparison of optimized surface ablation and combined customized plus optimized surface ablation in myopic eyes

Background Proscan treats errors of refraction without affecting asphericity, while customized treatment treats correction with high-order aberration (HOA). Recently, Zyoptix HD has been used in the treatment of preoperative HOA and lower-order aberrations without inducing spherical aberrations. Aim To compare the visual outcomes and HOAs after optimized surface ablation versus Zyoptix HD surface ablation for myopia. Patients and methods A prospective comparative clinically controlled study was conducted on patients who have myopia, 40 eyes of 20 patients divided into two groups. Group I: 20 eyes underwent optimized surface ablation. Group II: 20 eyes underwent customized plus optimized surface ablation. The selection of treatment was according to root mean square and spherical aberration corneal topography. All participants were examined by a slit lamp just after the operation, on the first, third, seventh postoperative day, weekly for 1 month, then biweekly for 3 months. The patients had full follow-up by best corrected visual acuity, slit lamp, Orbscan IIZ, and wavefront aberrometry using Zywave after 3 months of procedure. Results The comparison between preoperative uncorrected visual acuity and 3 months postoperative uncorrected visual acuity improved significantly in both groups but better in group II. The comparison between preoperative and 3 months postoperative root mean square in group I increased significantly, and in group II improved significantly, which is better in group II. Conclusion Zyoptix HD is superior to optimized surface ablation in the correction of low-order and high-order eye aberrations, correcting myopia and visual acuity.

Development of novel interferometric system for short and long gauge block calibration

Abstract This paper presents the development of a novel multiwavelength Twyman–Green interferometer for gauge block (GB) calibration. In this work, a novel gauge block interferometer (GBI) for both short- and long-gauge block calibration at the SASO-NMCC was designed, built, tested, and described. The interferometer features an optomechanical modulation-based proprietary evaluation system, and the final length value was determined by applying Edlén’s equation to the refractive index of air. The developed interferometric system comprises two setups: one for short GB calibration, and the other for long GB calibration. The first short (GBI) setup utilizes two stabilized lasers, green and red, in vertical-mode operation. Another long GBI utilizes three stabilized lasers in the horizontal mode of operation. The primary characteristics of the interferometric system are explained. An uncertainty analysis with a careful study of the main components, such as wavelength standards, fringe fraction, temperature corrections, refractive index correction, obliquity correction, phase correction, block geometry correction, wavefront correction, and wringing correction, is presented. With interferometry, measurement method (ISO 3650 and ASME B89.1), using our described highly-precision horizontal mode system (GBI), we could achieve uncertainty level of ‘Q[49;0,28 l]nm l (mm)’ (k = 2) in the measurement range ‘125–1000 (mm)’. For the other system(GBI) for short gauge blocks, the associated uncertainty is ‘Q[30;0,27 l]nm l(mm)’ (k = 2) in the range of ‘0.5–100 (mm)’.

Design and fabrication of polarization independent LCoS phase modulators with polymer waveplate and analog driving

Abstract Phase-only liquid crystal on silicon (LCoS) spatial light modulators are used in a variety of applications. Despite their wide use, current phase-only LCoS devices are hindered by their single-polarization modulation. We propose a polarization independent LCoS device which uses a polymer quarter-wave plate for polarization conversion. We designed a custom pixel circuit which enables high driving voltage and high pixel grayscale by utilizing an analog driving frame buffer pixel circuit. Our pixel circuit is optimized for small pixel size and the silicon backplanes can be fabricated at a traditional foundry. We demonstrate polarization independent phase modulation through optical beam steering tests for various input polarizations. Our fabricated device lays the foundation for commercial LCoS devices highly suitable for wavelength selective switches, holographic display, wavefront correction, and optical beam shaping.

Biometry study of foveal isoplanatic patch variation for adaptive optics retinal imaging.

The change in ocular wavefront aberrations with visual angle determines the isoplanatic patch, defined as the largest field of view over which diffraction-limited retinal imaging can be achieved. Here, we study how the isoplanatic patch at the foveal center varies across 32 schematic eyes, each individualized with optical biometry estimates of corneal and crystalline lens surface topography, assuming a homogeneous refractive index for the crystalline lens. The foveal isoplanatic patches were calculated using real ray tracing through 2, 4, 6 and 8 mm pupil diameters for wavelengths of 400-1200 nm, simulating five adaptive optics (AO) strategies. Three of these strategies, used in flood illumination, point-scanning, and line-scanning ophthalmoscopes, apply the same wavefront correction across the entire field of view, resulting in almost identical isoplanatic patches. Two time-division multiplexing (TDM) strategies are proposed to increase the isoplanatic patch of AO scanning ophthalmoscopes through field-varying wavefront correction. Results revealed substantial variation in isoplanatic patch size across eyes (40-500%), indicating that the field of view in AO ophthalmoscopes should be adjusted for each eye. The median isoplanatic patch size decreases with increasing pupil diameter, coarsely following a power law. No statistically significant correlations were found between isoplanatic patch size and axial length. The foveal isoplanatic patch increases linearly with wavelength, primarily due to its wavelength-dependent definition (wavefront root-mean-squared, RMS <λ/14), rather than aberration chromatism. Additionally, ray tracing reveals that in strongly ametropic eyes, induced aberrations can result in wavefront RMS errors as large as λ/3 for an 8-mm pupil, with implications for wavefront sensing, open-loop ophthalmic AO, spectacle prescription and refractive surgery.

Adaptive optics in an oblique plane microscope.

Adaptive optics (AO) can restore diffraction-limited performance when imaging beyond superficial cell layers in vivo and in vitro, and as such, is of interest for advanced 3D microscopy methods such as light-sheet fluorescence microscopy (LSFM). In a typical LSFM system, the illumination and detection paths are separate and subject to different optical aberrations. To achieve optimal microscope performance, it is necessary to sense and correct these aberrations in both light paths, resulting in a complex microscope system. Here, we show that in an oblique plane microscope (OPM), a type of LSFM with a single primary objective lens, the same deformable mirror can correct both illumination and fluorescence detection. Besides reducing the complexity, we show that AO in OPM also restores the relative alignment of the light-sheet and focal plane, and that a projection imaging mode can stabilize and improve the wavefront correction in a sensorless AO format. We demonstrate OPM with AO on fluorescent nanospheres and by imaging the vasculature and cancer cells in zebrafish embryos embedded in a glass capillary, restoring diffraction limited resolution and improving the signal strength twofold.

High precision wavefront correction method in interferometer testing.

A wavefront correction method is proposed for high-precision optic surfacing, addressing the discrepancy between wavefront and real surface errors in Fizeau interferometer testing. We believe this to be a proposed novel method that encompasses optical surface function parameters fitting, lateral distortion correction, misalignment error removal, and sag surface error calculation. The method's error has been thoroughly analyzed, including aspects of function parameters fitting, ray tracing, and interpolation. The effectiveness of the method was demonstrated by correcting the wavefront of an off-axis parabolic mirror in null testing configurations, significantly reducing artificially created annular errors and improving off-axis direction errors from 0.23λ to 0.05λ (λ=632.8 nm), with the PV of aspheric departures exceeding 8.5 mm.

Image-based wavefront correction using model-free reinforcement learning.

Optical aberrations prevent telescopes from reaching their theoretical diffraction limit. Once estimated, these aberrations can be compensated for using deformable mirrors in a closed loop. Focal plane wavefront sensing enables the estimation of the aberrations on the complete optical path, directly from the images taken by the scientific sensor. However, current focal plane wavefront sensing methods rely on physical models whose inaccuracies may limit the overall performance of the correction. The aim of this study is to develop a data-driven method using model-free reinforcement learning to automatically perform the estimation and correction of the aberrations, using only phase diversity images acquired around the focal plane as inputs. We formulate the correction problem within the framework of reinforcement learning and train an agent on simulated data. We show that the method is able to reliably learn an efficient control strategy for various realistic conditions. Our method also demonstrates robustness to a wide range of noise levels.

Soft X-ray wavefront sensing at an ellipsoidal mirror shell

A reliable `in situ' method for wavefront sensing in the soft X-ray domain is reported, developed for the characterization of rotationally symmetric optical elements, like an ellipsoidal mirror shell. In a laboratory setup, the mirror sample is irradiated by an electron-excited (4.4 keV), micrometre-sized (∼2 µm) fluorescence source (carbon K α, 277 eV). Substantially, the three-dimensional intensity distribution I(r) is recorded by a CCD camera (2048 × 512 pixels of 13.5 µm) at two positions along the optical axis, symmetrically displaced by ±21–25% from the focus. The transport-of-intensity equation is interpreted in a geometrical sense from plane to plane and implemented as a ray tracing code, to retrieve the phase Φ(r) from the radial intensity gradient on a sub-pixel scale. For reasons of statistical reliability, five intra-/extra-focal CCD image pairs are evaluated and averaged to an annular two-dimensional map of the wavefront error {\cal W}. In units of the test wavelength (C K α), an r.m.s. value \sigma_{\cal{W}} = ±10.9λ0 and a peak-to-valley amplitude of ±31.3λ0 are obtained. By means of the wavefront, the focus is first reconstructed with a result for its diameter of 38.4 µm, close to the direct experimental observation of 39.4 µm (FWHM). Secondly, figure and slope errors of the ellipsoid are characterized with an average of ±1.14 µm and ±8.8 arcsec (r.m.s.), respectively, the latter in reasonable agreement with the measured focal intensity distribution. The findings enable, amongst others, the precise alignment of axisymmetric X-ray mirrors or the design of a wavefront corrector for high-resolution X-ray science.

Turbulence image correction using focused light field camera

Under turbulent conditions, the images of objects may be severely blurred and become unrecognizable because of the complex aberrations introduced by turbulence. Using adaptive optics (AO) to compensate for these wavefront aberrations can theoretically solve the problem of image blurring under turbulent conditions. However, due to its small field of view and high cost, the AO system is difficult to widely use. In recent years, using the technology of light field photography to correct turbulence images has been proposed. However, the current studies are either based on the structure of the non-focused light field camera, which makes it hard to achieve good image quality, or on the need to redesign the core sensor of the non-focused light field camera, which greatly increases the cost and complexity. We believe that the structure of a focused light field camera has a good potential for turbulence image correction and propose a new method of achieving a corrected focused image using a focused light field camera in this paper. We propose to use phase estimation instead of depth estimation for a focused light field camera and phase maps instead of a depth map as the basis for achieving a focused image. By the proposed method, a corrected focused image with a large field of view under turbulent conditions is achieved without using independent wavefront correction devices or redesigning the light field camera. The experiments are given to verify the effectiveness of the proposed method under strong turbulent conditions in the laboratory and real turbulent conditions in the outdoors. The proposed method in this paper provides a new and low-cost solution for image correction for optical imaging systems under turbulent conditions, so it has a high application value.

Lensless fiber endomicroscopy in biomedicine

Lensless fiber endomicroscopy, an emergent paradigm shift for minimally-invasive microscopic optical imaging and targeted light delivery, holds transformative potential, especially in biomedicine. Leveraging holographic detection and physical or computational wavefront correction, it enables three-dimensional imaging in an unprecedentedly small footprint, which is crucial for various applications such as brain surgery. This perspective reviews the recent breakthroughs, highlighting potential emerging applications, and pinpointing gaps between innovation and real-world applications. As the research in this realm accelerates, the novel breakthroughs and existing frontiers highlighted in this perspective can be used as guidelines for researchers joining this exciting domain.

Reference optical turbulence characteristics at the Large Solar Vacuum Telescope site

Abstract Large ground-based solar telescopes are equipped with adaptive optics systems to correct wavefront distortions induced in the turbulent atmosphere. The design of the adaptive optics system strongly depends on the vertical profiles of the optical turbulence. In particular, the characteristics of the optical turbulence determine the design of tomographic adaptive optics systems, which provide image correction within a wide field of view. In the article, a new method to estimate reference optical turbulence characteristics from Era-5 reanalysis assimilated data is presented. This method is based on the dependence of the air refractive index structure constant $C_n^2$ on the vertical shears of wind speed as well as the outer scale of turbulence L0. The L0 parameter is estimated by minimization of the dispersion between the modeled and measured values of the refractive index structure constant $C_n^2$ within the surface layer. For the first time, parametrization coefficients and reference profiles of optical turbulence averaged for the period 1940–2022 are calculated for the Large Solar Vacuum Telescope (LSVT) site. The calculated optical turbulence profiles are representative; these profiles correspond to typical changes of the measured values of the Fried parameter, the isoplanatic angle, and the outer scale of turbulence at the LSVT site. The model turbulence profiles are verified taking into account the Shack–Hartmann wavefront sensor measurements at the LSVT. The higher accuracy of estimation of the optical turbulence characteristics makes it possible to refine parameters relevant to the LSVT adaptive optics system. The obtained results can be used in order to develop high-resolution solar adaptive optics technologies as applied to ground-based telescopes including those using the principles of atmospheric tomography.

Turbulence impacted wavefront corrections using beam modulation technique

New experimental technique have been proposed to discuss the turbulence impact reduction using beam shaping technique. In first phase of experiments, turbulence Impacted Vortex beam shaping technique has been introduced for a propagating beam which is effected by Kolmogorov type lab based turbulence simulator using Pseudo Random Phase Plate (PRPP). The new technique is executed with a spatially filtered collimated Gaussian beam that is propagated through computer controlled rotating PRPP to introduce the lab based turbulence on the beam profile. The turbulence impacted beam is then propagated through Vortex Phase Plate (VPP) to shape that beam into different topological charged Laguerre Gaussian modes and further collimated using two lens based configuration. We have measured the scintillation index of the spatial intensity profile collected from CCD. Comparative studies have been done by placing the image plane in five different positions on the propagation path of the beam so that we can detect Collimated, diverging and converging outputs. Four topological charges of LG beams and Gaussian beam have been used to envisage results.

Experimental demonstration of wavefront reconstruction and correction techniques for variable targets based on distorted grating and deep learning

This research presents a practical approach for wavefront reconstruction and correction adaptable to variable targets, with the aim of constructing a high-precision, general extended target adaptive optical system. Firstly, we delve into the detailed design of a crucial component, the distorted grating, simplifying the optical system implementation while circumventing potential issues in traditional phase difference-based collection methods. Subsequently, normalized fine features (NFFs) and structure focus features (SFFs) which both are independent of the imaging target but corresponded precisely to the wavefront aberration are proposed. The two features provide a more accurate and robust characterization of the wavefront aberrations. Then, a Noise-to-Denoised Generative Adversarial Network (N2D-GAN) is employed for denoising real images. And a lightweight network, Attention Mechanism-based Efficient Network (AM-EffNet), is applied to achieve efficient and high-precision mapping between features and wavefronts. A prototype of object-independent adaptive optics system is demonstrated by experimental setup, and the effectiveness of this method in wavefront reconstruction for different imaging targets has been verified. This research holds significant relevance for engineering applications of adaptive optics, providing robust support for addressing challenges within practical systems.

Wavefront analysis and phase correctors design using SHADOW.

Knife-edge imaging is a successful method for determining the wavefront distortion of focusing optics such as Kirkpatrick-Baez mirrors or compound refractive lenses. In this study, the wavefront error of an imperfect elliptical mirror is predicted by developing a knife-edge program using the SHADOW/OASYS platform. It is shown that the focusing optics can be aligned perfectly by minimizing the parabolic and cubic coefficients of the wavefront error. The residual wavefront error provides precise information about the figure/height errors of the focusing optics suggesting it as an accurate method for in situ optical metrology. A Python program is developed to design a customized wavefront refractive corrector to minimize the residual wavefront error. Uniform beam at and out of focus and higher peak intensity are achieved by the wavefront correction in comparison with ideal focusing. The developed code provides a quick way for wavefront error analysis and corrector design for non-ideal optics especially for the new-generation diffraction-limited sources, and saves considerable experimental time and effort.

X-ray focusing below 3 nm with aberration-corrected multilayer Laue lenses

Multilayer Laue lenses are volume diffractive optical elements for hard X-rays with the potential to focus beams to sizes as small as 1 nm. This ability is limited by the precision of the manufacturing process, whereby systematic errors that arise during fabrication contribute to wavefront aberrations even after calibration of the deposition process based on wavefront metrology. Such aberrations can be compensated by using a phase plate. However, current high numerical aperture lenses for nanometer resolution exhibit errors that exceed those that can be corrected by a single phase plate. To address this, we accumulate a large wavefront correction by propagation through a linear array of 3D-printed phase correcting elements. With such a compound refractive corrector, we report on a point spread function with a full-width at half maximum area of 2.9 × 2.8 nm2 at a photon energy of 17.5 keV.

Integrated Wavefront Sensing and Processing Method Utilizing Optical Neural Network

Wavefront sensors and processors are vital components of adaptive optical (AO) systems, directly impacting the operating bandwidth. As application scenarios become increasingly complex, AO systems are confronted with more extreme atmospheric turbulence. Additionally, as optical systems scale up, the data processing demands of AO systems increase exponentially. These challenges necessitate advancements in wavefront sensing and processing capabilities. To address this, this paper proposes an integrated wavefront sensing and processing method based on the optical neural network architecture, capable of directly providing control coefficients for the wavefront corrector. Through simulation and experimentation, this method demonstrates high sensing precision and processing speed, promising to realize large-scale, high-bandwidth AO systems.

Heimdallr, Baldr, and Solarstein: designing the next generation of VLTI instruments in the Asgard suite

High angular resolution imaging is an increasingly important capability in contemporary astrophysics. Of particular relevance to emerging fields such as the characterization of exoplanetary systems, imaging at the required spatial scales and contrast levels results in forbidding challenges in the correction of atmospheric phase errors, which in turn drives demanding requirements for precise wavefront sensing. Asgard is the next-generation instrument suite at the European Southern Observatory’s Very Large Telescope Interferometer (VLTI), targeting advances in sensitivity, spectral resolution, and nulling interferometry. In this paper, we describe the requirements and designs of three core modules: Heimdallr, a beam combiner for fringe tracking, low order wavefront correction, and visibility science; Baldr, a Zernike wavefront sensor to correct high order atmospheric aberrations; and Solarstein, an alignment and calibration unit. In addition, we draw generalizable insights for designing such system and discuss integration plans.

Daytime HyWFS approach for daylight adaptive optics wavefront sensing.

Bright daylight photon noise and the saturation of wavefront sensors pose challenges to high-resolution daytime imaging. In this paper, a daytime hybrid wavefront sensor (HyWFS) approach for real-time wavefront sensing in daylight adaptive optics (AO) is described. The Shack-Hartmann wavefront sensor (SHWFS) algorithm is used to efficiently compensate large-scale wavefronts, while the pyramid wavefront sensor (PyWFS) algorithm offers highly sensitive correction of small wavefronts. Daylight closed-loop AO experiments were performed using the daytime HyWFS approach with both algorithms, respectively. The experiment results indicate that the proposed approach provides accurate daylight AO correction and allows for a simple switch between the two algorithms without increasing system complexity. The daytime HyWFS approach can serve as an alternative for daylight natural guide star AO, enabling high-resolution observation of resident space objects no longer limited to dawn and dusk.