Wavefront Distortion Research Articles

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.

Study on the Difference in Wavefront Distortion on Beams Caused by Wavelength Differences in the Strong Turbulence Region

Study on the Difference in Wavefront Distortion on Beams Caused by Wavelength Differences in the Strong Turbulence Region

Ptychographic lensless coherent endomicroscopy through a flexible fiber bundle

Conventional fiber-bundle-based endoscopes allow minimally invasive imaging through flexible multi-core fiber (MCF) bundles by placing a miniature lens at the distal tip and using each core as an imaging pixel. In recent years, lensless imaging through MCFs was made possible by correcting the core-to-core phase distortions pre-measured in a calibration procedure. However, temporally varying wavefront distortions, for instance, due to dynamic fiber bending, pose a challenge for such approaches. Here, we demonstrate a coherent lensless imaging technique based on intensity-only measurements insensitive to core-to-core phase distortions. We leverage a ptychographic reconstruction algorithm to retrieve the phase and amplitude profiles of reflective objects placed at a distance from the fiber tip, using as input a set of diffracted intensity patterns reflected from the object when the illumination is scanned over the MCF cores. Our approach thus utilizes an acquisition process equivalent to confocal microendoscopy, only replacing the single detector with a camera.

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.

Wavefront distortion correction in scanning tunneling microscope image.

We report an algorithm to identify and correct distorted wavefronts in atomic resolution scanning tunneling microscope images. This algorithm can be used to correct nonlinear in-plane distortions without prior knowledge of the physical scanning parameters, the characteristics of the piezoelectric actuator, or individual atom positions. The 2D image is first defined as a sum of sinusoidal plane waves, where a nonlinear distortion renders a curve for an otherwise ideal linear wavefront. Using the Fourier transforms of local areas of the image, the algorithm generates a wavefront vector field. The identified wavefronts are subsequently linearized for each plane wave without changing lattice orders, giving rise to distortion corrections. Our algorithm is complementary to conventional post-processing algorithms that require prior detection of real space features, which can also be used to correct nonlinear distortions in 2D images acquired by other microscopy techniques.

Quantitative phase imaging by gradient retardance optical microscopy

Quantitative phase imaging (QPI) has become a vital tool in bioimaging, offering precise measurements of wavefront distortion and, thus, of key cellular metabolism metrics, such as dry mass and density. However, only a few QPI applications have been demonstrated in optically thick specimens, where scattering increases background and reduces contrast. Building upon the concept of structured illumination interferometry, we introduce Gradient Retardance Optical Microscopy (GROM) for QPI of both thin and thick samples. GROM transforms any standard Differential Interference Contrast (DIC) microscope into a QPI platform by incorporating a liquid crystal retarder into the illumination path, enabling independent phase-shifting of the DIC microscope's sheared beams. GROM greatly simplifies related configurations, reduces costs, and eradicates energy losses in parallel imaging modalities, such as fluorescence. We successfully tested GROM on a diverse range of specimens, from microbes and red blood cells to optically thick (~ 300 μm) plant roots without fixation or clearing.

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.

Observation of dynamic nanoscale thermal expansion in mirrors and graphene-aided heat dissipation by an advanced chromatic confocal microscopy

In this Letter, dynamic nano-thermal expansion images of reflective mirrors from high-intensity incident laser beams were observed in situ. The inspections are based on rapid 3D surface morphology changes on the reflective surfaces, captured by a Chromatic Confocal Microscope with Nanoscale Sensitivity (CCMNS). Nano-expansions of two types of coatings were studied: the E02 dielectric coating (coating 1) and the graphene-on-E02 complex film (coating 2), both applied to the same fused silica substrate. The superior thermal dissipation properties of coating 2, including enhanced heat dissipation, suppressed wavefront distortion, and its unique negative expansion coefficient, were observed. In addition to studying the effects of graphene coating, the CCMNS demonstrates an accurate and efficient approach for evaluating reflective mirrors. Moreover, the proposed methodology possesses enormous potential across various fields, ranging from estimating photonic elements dealing with high-intensity beams to physical thermal conductivity measurements.