Wavefront Measurements Research Articles

Simulation of X-ray Hartmann wavefront sensing with the Synchrotron Radiation Workshop.

X-ray wavefront measurement is an important beam diagnostic tool, especially for the diffraction-limited X-ray beam. These in situ diagnostics give a better understanding of beam imperfections, and they enable feedback for possible corrections and/or optical alignment improvements. Hartmann wavefront sensing is one of the promising techniques to perform in situ X-ray wavefront measurements. In this work, a simulation tool of the X-ray Hartmann Wavefront Sensor (HWS) is developed under the Synchrotron Radiation Workshop (SRW) framework. Using this new simulation capability, one can take advantage of the full SRW package to simulate Hartmann wavefront sensing with the beam traveling from the X-ray source to the sample through different X-ray optical components. This SRW HWS simulation tool can help to optimize the wavefront sensor parameters for a specific X-ray energy range. It can also simulate an in situ wavefront measurement experiment with a particular beamline optical layout and predict the expected results of the wavefront measurement under different beamline configurations.

Two-dimensional speckle technique for slope error measurements of weakly focusing reflective X-ray optics.

Speckle-based at-wavelength metrology techniques now play an important role in X-ray wavefront measurements. However, for reflective X-ray optics, the majority of existing speckle-based methods fail to provide reliable 2D information about the optical surface being characterized. Compared with the 1D information typically output from speckled-based methods, a 2D map is more informative for understanding the overall quality of the optic being tested. In this paper, we propose a method for in situ 2D absolute metrology of weakly focusing X-ray mirrors. Importantly, the angular misalignment of the mirror can be easily corrected with the proposed 2D processing procedure. We hope the speckle pattern data processing method presented here will help to extend this technique to wider applications in the synchrotron radiation and X-ray free-electron laser communities.

Evaluating Optical Quality of a New Hydrophilic Enhanced Monofocal Intraocular Lens and Comparison to the Monofocal Counterpart: An Optical Bench Analysis.

The aim of the study was to analyze the optical properties of a new hydrophilic enhanced monofocal intraocular lens (IOL) using optical bench analysis and compare it with its monofocal counterpart. This laboratory study investigates the enhanced monofocal intraocular lens (L-333) and the monofocal counterpart (L-313) IOL by Teleon Surgical, Spankeren, Netherlands on the optical bench, using OptiSpheric IOL PRO2 (Trioptics, Germany) in order to assess the optical quality according to ISO11979 with ISO-2 Cornea. IOLs (power 22.0D) were evaluated regarding through frequency modulation transfer function (MTF), Strehl ratio (SR), and through focus MTF at 50lp/mm using a 3.0-mm and a 4.5-mm aperture. Tilt and decentration were applied. In addition, wavefront measurements were obtained using WaveMaster® IOL2 device (Trioptics, Germany) and analyzed. Centered: The MTF (mean) at 50lp/mm (L-333/L-313) with 3.0mm aperture was 0.606/0.724 and with 4.5mm aperture 0.330/0.409. The SR (mean) with 3.0mm aperture was 0.586/0.809 and with 4.5mm aperture 0.330/0.348. Decentered by 1mm: The MTF (mean) at 50lp/mm (L-333/L-313) with 3.0mm aperture was 0.485/0.705 and with 4.5mm aperture 0.255/0.374. The SR (mean) with 3.0mm aperture was 0.457/0.739 and with 4.5mm aperture 0.185/0.268. Tilted by 5degrees: The MTF (mean) at 50lp/mm (L-333/L-313) with 3.0mm aperture was 0.577/0.657 and with 4.5mm aperture 0.345/0.336. The SR (mean) with 3.0mm aperture was 0.583/0.702 and with 4.5mm aperture 0.269/0.237. In through focus MTF and aperture of 3.0mm, the L-333 showed a peak of 0.41 with some enlarged depth of power of about 2D. For the aperture of 4.5mm, the MTF values of L-313 and L-333 were slightly reduced; L-333 showed an MTF peak of 0.23 and some reduced depth of power of about 1.5D. Wavefront measurements showed no major aberrations for the L-313, while a combination of moderate increase in Z 4-0 and Z 6-0 with opposite sign was revealed for the L-333. The enhanced monofocal Lentis Quantum (L-333) produces some enlarged depth of focus by combining spherical aberration of different order and opposite sign. The Lentis Quantum performs very well in comparison to the aspherical monofocal counterpart owing to its optical design. Results with large apertures were sufficient too, suggesting that the lens isa good option in eyes with a wide pupil and thus in refractive surgeries of young patients.

Stress and wavefront measurement of large-aperture optical components with a ptychographical iterative engine.

The clamping stress of large-aperture optical elements has a significant influence on the optical quality of the system. In this study, a comprehensive measurement system combined with ptychographical iterative engine (PIE) wavefront sensors and polarization components is developed to determine the stress distribution of the optical elements and its effect on the transmitted and reflected wavefronts. This system avoids the use of multiple measuring instruments and has low cost and strong anti-interference ability. The experimental results demonstrate that the stress distributions measured at different resolutions are consistent with the finite element analysis, and the wavefront measurement accuracy is 0.1λ. This test configuration is very flexible and provides a useful means for online installation and quality control of large-aperture optical systems.

Measuring transmitted wavefronts for general optical systems in a broad bandwidth range

Although laser interferometers have emerged as the main tool for the measurement of transmitted wavefronts, their application is greatly limited as they are typically designed for operations at specific wavelengths. In a previous study [Q. Zhang, H. Wang, P. Wu, Y. Fu, X. Li, Q. Wang, and S. Han, “Estimating transmitted wavefronts in a broad bandwidth based on Zernike coefficients,” J. Opt. 21(9), 095601 (2019)], we proposed a method for determining the wavefront transmitted by an optical system at any wavelength in a certain band. Although this method works well for most monochromatic systems where the image plane is at the focal point for the transmission wavelength, for general multi-color systems, it is more practical to measure the wavefront at the defocused image plane. Hence, in this paper, we have developed a complete method for determining transmitted wavefronts in a broad bandwidth at any defocused position, thereby enabling wavefront measurements for multi-color systems. We also conducted experiments to verify these assumptions, validating the method. The experimental setup has been improved so that it can handle multi-color systems, and a detailed experimental process is summarized. With this technique, application of broadband transmission wavefront measurement can be extended to most general optical systems, which is of great significance for the characterization of achromatic and apochromatic optical lenses.

Turbulent parameters at different heights in the atmosphere. Shack–Hartmann wavefront sensor data

The paper presents the results of studies of wavefront distortions at different heights in the atmosphere. We have used measurement wavefront data to determine optical turbulence parameters along the line of sight of the Large Solar Vacuum Telescope. Through cross-correlation analysis of differential motions of sunspots at spaced wavefront sensor subapertures, we determined turbulent parameters at different heights at the Large Solar Vacuum Telescope site. The differential motions of sunspots characterize the small-scale structure of turbulent phase distortions in the atmosphere. Synchronous temporal changes in the amplitude of these distortions at certain regions of the telescope aperture are conditioned by turbulent layers at different heights. We have estimated the contribution of optical turbulence to integral distortions at the telescope aperture for layers 0–0.6, 0.6–1.1, 1.1–1.7 km. The contribution of optical turbulence concentrated in a 1.7 km atmospheric layer to the wavefront distortions at the aperture telescope is shown to be ~43 %.

Формирование искажений волнового фронта на разных высотах в атмосфере. Измерения, выполненные с помощью датчика Шэка–Гартмана

The paper presents the results of studies of wavefront distortions at different heights in the atmosphere. We have used measurement wavefront data to determine optical turbulence parameters along the line of sight of the Large Solar Vacuum Telescope. Through cross-correlation analysis of differential motions of sunspots at spaced wavefront sensor subapertures, we determined turbulent parameters at different heights at the Large Solar Vacuum Telescope site. The differential motions of sunspots characterize the small-scale structure of turbulent phase distortions in the atmosphere. Synchronous temporal changes in the amplitude of these distortions at certain regions of the telescope aperture are conditioned by turbulent layers at different heights. We have estimated the contribution of optical turbulence to integral distortions at the telescope aperture for layers 0–0.6, 0.6–1.1, 1.1–1.7 km. The contribution of optical turbulence concentrated in a 1.7 km atmospheric layer to the wavefront distortions at the aperture telescope is shown to be ~43 %.

(3N+1)-frame phase retrieval for double-grating Ronchi lateral shearing interferometry

Accurate wavefront measurement using double-grating Ronchi lateral shearing interferometry significantly relies on the accuracy of shear-phase retrieval. Traditional methods cannot effectively suppress the interferences of unwanted diffractions generated by the Ronchi grating at the image plane. In this paper, we propose a method that uses 3N+1 shear interferograms to retrieve the shear phase, where N is a positive integer. The selection of N depends on the number of the diffraction orders existing in the shearogram. According to the numerical aperture of the optical system under test and the period of image grating, the interferograms corresponding to the specific 3N+1 phase shifts are obtained, from which the shear phase is calculated. For validation, the frequency response of the proposed algorithm is characterized, and the improved accuracy of wavefront measurement is demonstrated by comparisons with the existing 8-frame, 10-frame and 13-frame methods.

Toward practical weak measurement wavefront sensing: spatial resolution and achromatism.

The weak measurement wavefront sensor detects the phase gradient of light like the Shack-Hartmann sensor does. However, the use of one thin birefringent crystal to displace light beams results in a wavelength-dependent phase difference between the two polarization components, which limits the practical application. Use of a Savart plate, which consists of two such crystals, can compensate for the phase difference and realize achromatic wavefront sensing when combined with an achromatic retarder. We discuss the spatial resolution of the sensor and experimentally reconstruct a wavefront modulated by a pattern. Then we obtain the Zernike coefficients with three different wavelengths before and after modulation. Our work makes this new wavefront sensor more applicable to actual tasks like biomedical imaging.

Single-shot phase retrieval for aspheric surface testing based on the transport of intensity equation and a prism-mirror module

Transport of intensity equation (TIE) relates the longitudinal intensity derivative of propagating light wave to the transverse phase gradient. The phase is retrieved by measuring the intensity of propagating light wave at two or more longitudinally displaced planes by moving the detector and then solving the TIE. We present a single-shot transport of intensity equation-based phase retrieval using a prism-mirror based module to capture the two defocused intensity images simultaneously. The results obtained by single-shot transport of intensity equation-based phase retrieval have been compared with interferometry and profilometer-based measurements. We highlight an important aspect of the TIE-based approach that this formulation decouples the intensity and the unwrapped phase of the unknown field. Intensity and phase are individually low-bandwidth functions when compared to the complex field associated with the unknown wavefront. When compared to interferometry, the TIE-based approach therefore inherently has many reduced sampling requirements. For a given array sensor, TIE can therefore measure large phase deviations for which an interferometer would produce very high density fringes that are impossible to sample as per the Nyquist criterion. The prism-mirror module shown in this work is easy to fabricate, align, and can be easily integrated with an experimental setup. The applications of the proposed method for the wavefront measurement of spherical and aspheric lenses are demonstrated.

Single-shot quantitative aberration and scattering length measurements in mouse brain tissues using an extended-source Shack-Hartmann wavefront sensor.

Deep fluorescence imaging in mammalian brain tissues remains challenging due to scattering and optical aberration-induced loss in signal and resolution. Correction of aberrations using adaptive optics (AO) requires their reliable measurement in the tissues. Here, we show that an extended-source Shack-Hartmann wavefront sensor (ESSH) allows quantitative aberration measurements through fixed brain slices with a thickness up to four times their scattering length. We demonstrate in particular that this wavefront measurement method based on image correlation is more robust to scattering compared to the standard centroid-based approach. Finally, we obtain a measurement of the tissue scattering length taking advantage of the geometry of a Shack-Hartmann sensor.

Influence of Photon Beam and Motor Vibrations on At-Wavelength X-Ray Speckle Scanning Metrology

Speckle scanning metrology is an effective tool to determine the X-ray wave front error in synchrotron radiation. By measuring wave front radii of curvature, X-ray optics can be high-precision aligned and adaptive optics can be used for compensating these wave front errors to pursue an aberration-free wave front. Photon beam and motor vibrations are the major limitations in characterizing the beam performances. An analytical model is presented in this article to reveal the influences of photon beams and motor vibrations on the measurements of the wave front radii of curvature. It is worth noting that the influence of low-frequency vibration is oscillatory and thus the selection of sampling frequency is strongly related. The experimental results verify the model and reveal the main dependency of the experimental deviations on the amplitude and frequency of vibrations.

Wavefront detection method for orbital angular momentum modes based on conformal mapping–spatial phase-shifting interferometry

The orbital angular momentum (OAM) of light has garnered significant interest in recent years owing to its various applications, and extensive creative research has been conducted to generate OAM. However, the particular helical phase structure of an optical vortex leads to nonsmooth and discontinuous phase profiles and hinders the accurate recovery of the phase distribution of the vortex beam. Significantly, the existence of a wavefront dislocation leads to the failure of the traditional phase unwrapping algorithm. At the same time, it is essential to detect the wavefront of OAM modes in real-time for free-space optical communication and optical precision measurement. Therefore, we designed conformal mapping–spatial phase-shifting interferometry and achieved rapid and high-precision wavefront measurements for the OAM modes. The wavefront of the OAM modes with a topological charge of 1, 2, 4 and 6 were measured, respectively. The results were significantly consistent with the anticipated results based on simulations. This study reveals the mathematical mechanism behind the forked fringe patterns and presents a method for demodulating the helical wavefront from the forked fringe patterns.

Alternative Interpretation of Speckle Autocorrelation Imaging Through Scattering Media

High-resolution optical imaging through or within thick scattering media is a long sought after yet unreached goal. In the past decade, the thriving technique developments in wavefront measurement and manipulation do not significantly push the boundary forward. The optical diffusion limit is still a ceiling. In this work, we propose that a scattering medium can be conceptualized as an assembly of randomly packed pinhole cameras and the corresponding speckle pattern as a superposition of randomly shifted pinhole images. The concept is demonstrated through both simulation and experiments, confirming the new perspective to interpret the mechanism of information transmission through scattering media under incoherent illumination. We also analyze the efficiency of single-pinhole and dual-pinhole channels. While in infancy, the proposed method reveals a new perspective to understand imaging and information transmission through scattering media.

Shock wave diagnostics with an ultra-short optical fiber probe

We report a highly localized, rapid-response pressure measurement of a shock wave front in a solid by utilizing a miniature fiber-optic-based probe. The probe used was a 100 μm-long fiber Bragg grating (FBG) inscribed on a standard silica communication fiber, 125 μm in diameter. The optical fiber was embedded within a ceramic zirconia ferrule and was shocked axially by a polycarbonate impactor fired from a gas gun. In a second ferrule, included in the same experiment, a 1 mm long FBG was embedded for comparison. Both FBGs were positioned at the front face of their respective ferrules, in order to sense the region where the shock wave is pristine, with no release waves, and where the stress conditions were expected to be constant for a few hundreds of nanoseconds. A simulation has been performed using LS-DYNA software describing the temporal dependence of the axial stress operating on the zirconia target and the embedded fiber gratings. The reflected spectra of both fiber grating probes were interrogated by an array of wavelength division demultiplexers and 200 MHz InGaAs detectors. Both probes exhibited a wavelength shift that corresponded to the pressure profile of the shock wave that traveled through the fiber, agreeing quite well with the predictions of the simulation. The wavelength blueshift was about 3.5 nm under a calculated shock pressure in the silica of 320 MPa, induced by a shock pressure of 700 MPa in the host zirconia target. Overall, the 100 μm probe demonstrated superior measurement capabilities to the 1 mm probe, both in time response and localization, as well as better agreement with the simulation. Multiple probes can be applied to provide high resolution mapping of shock phenomena in space and time, thus assisting in establishing the dynamic properties of materials under impact loading.

Terahertz referenceless wavefront sensing by means of computational shear-interferometry.

In this contribution, we demonstrate the first referenceless measurement of a THz wavefront by means of shear-interferometry. The technique makes use of a transmissive Ronchi phase grating to generate the shear. We fabricated the grating by mechanical machining of high-density polyethylene. At the camera plane, the +1 and -1 diffraction orders are coherently superimposed, generating an interferogram. We can adjust the shear by selecting the period of the grating and the focal length of the imaging system. We can also alter the direction of the shear by rotating the grating. A gradient-based iterative algorithm is used to reconstruct the wavefront from a set of shear interferograms. The results presented in this study demonstrate the first step towards wavefield sensing in the terahertz band without using a reference wave.

Characterizing turbulence profile layers through celestial single-source observations.

Future spacecraft missions aim to communicate with the Earth using near-infrared lasers. The possible bit rate of free-space optical communication (FSOC) is orders of magnitude greater when compared to current radio frequency transmissions. The challenge of ground-space FSOC is that atmospheric turbulence perturbs optical wavefront propagation. These wavefront aberrations can be measured using a Shack-Hartmann wavefront sensor (SHWFS). A ground-based adaptive optics (AO) system can mitigate these aberrations along the optical path by translating wavefront measurements into deformable mirror commands. However, errors result from atmospheric turbulence continuously evolving, and there are unavoidable delays during AO wavefront correction. The length of an acceptable delay is referred to as the coherence time-a parameter dependent on the strength of turbulence profile layers and their corresponding wind-driven velocity. This study introduces a novel technique, to the best of our knowledge, for using SHWFS single-source observations, e.g., the downlink signal from a geostationary satellite, to measure the strength and velocity of turbulence profile layers. This work builds upon previous research and demonstrates that single-source observations can disentangle turbulence profile layers through studying the cross-covariance of temporally offset SHWFS centroid measurements. Simulated data are used to verify that the technique can recover the coherence time. The expected and measured results have a correlation coefficient of 0.95.

Scanning Measurement of Large Aperture Collimated Wavefront with Pentaprism Array Based on Nonuniform Sampling

Scanning Measurement of Large Aperture Collimated Wavefront with Pentaprism Array Based on Nonuniform Sampling

Thermal effects reduction in a diode side-pumped rod-like bonded α-quartz||Nd:glass||α-quartz amplifying medium

We present a numerical study of a square-shape rod-like bonded laser gain medium operating at 1053 nm. The sample is composed of a 5-mm thick Nd-doped phosphate glass bonded to two α-quartz crystals. Owing to this face cooling scheme, the heat generated in the gain medium is effectively reduced, hence resulting in less optical distortions. The simulation of the thermomechanical effects was conducted using COMSOL MultiPhysics® software. Transverse wavefront distortion and birefringence profiles were computed for a given pump mean power. Wavefront and birefringence measurements will be conducted on the bonded sample using a pump-probe setup which is discussed in this paper. These measurements will be presented and weighed with the numerical results.

Ultra-compact post-compressor on-shot wavefront measurement for beam correction at PHELIX

Abstract In order to reach the highest intensities, modern laser systems use adaptive optics to control their beam quality. Ideally, the focal spot is optimized after the compression stage of the system in order to avoid spatio-temporal couplings. This also requires a wavefront sensor after the compressor, which should be able to measure the wavefront on-shot. At PHELIX, we have developed an ultra-compact post-compressor beam diagnostic due to strict space constraints, measuring the wavefront over the full aperture of 28 cm. This system features all-reflective imaging beam transport and a high dynamic range in order to measure the wavefront in alignment mode as well as on shot.