New achievements in orbital angular momentum beam characterization using a Hartmann wavefront sensor and the Kirkpatrick-Baez active optical system KAOS.

Advances in physics have been significantly driven by state-of-the-art technology, and in photonics and X-ray science this calls for the ability to manipulate the characteristics of optical beams. Orbital angular momentum (OAM) beams hold substantial promise in various domains such as ultra-high-capacity optical communication, rotating body detection, optical tweezers, laser processing, super-resolution imaging etc. Hence, the advancement of OAM beam-generation technology and the enhancement of its technical proficiency and characterization capabilities are of paramount importance. These endeavours will not only facilitate the use of OAM beams in the aforementioned sectors but also extend the scope of applications in diverse fields related to OAM beams. At the FERMI Free-Electron Laser (Trieste, Italy), OAM beams are generated either by tailoring the emission process on the undulator side or, in most cases, by coupling a spiral zone plate (SZP) in tandem with the refocusing Kirkpatrick-Baez active optic system (KAOS). To provide a robust and reproducible workflow to users, a Hartmann wavefront sensor (WFS) is used for both optics tuning and beam characterization. KAOS is capable of delivering both tightly focused and broad spots, with independent control over vertical and horizontal magnification. This study explores a novel non-conventional `near collimation' operational mode aimed at generating beams with OAM that employs the use of a lithographically manufactured SZP to achieve this goal. The article evaluates the mirror's performance through Hartmann wavefront sensing, offers a discussion of data analysis methodologies, and provides a quantitative analysis of these results with ptychographic reconstructions.

Spexwavepy: an open-source Python package for X-ray wavefront sensing using speckle-based techniques.

In situ wavefront sensing plays a critical role in the delivery of high-quality beams for X-ray experiments. X-ray speckle-based techniques stand out among other in situ techniques for their easy experimental setup and various data acquisition modes. Although X-ray speckle-based techniques have been under development for more than a decade, there are still no user-friendly software packages for new researchers to begin with. Here, we present an open-source Python package, spexwavepy, for X-ray wavefront sensing using speckle-based techniques. This Python package covers a variety of X-ray speckle-based techniques, provides plenty of examples with real experimental data and offers detailed online documentation for users. We hope it can help new researchers learn and apply the speckle-based techniques for X-ray wavefront sensing to synchrotron radiation and X-ray free-electron laser beamlines.

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 Kα, 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 Kα), 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.

Large-Dynamic-Range Ocular Aberration Measurement Based on Deep Learning with a Shack-Hartmann Wavefront Sensor.

The Shack-Hartmann wavefront sensor (SHWFS) is widely utilized for ocular aberration measurement. However, large ocular aberrations caused by individual differences can easily make the spot move out of the range of the corresponding sub-aperture in SHWFS, rendering the traditional centroiding method ineffective. This study applied a novel convolutional neural network (CNN) model to wavefront sensing for large dynamic ocular aberration measurement. The simulation results demonstrate that, compared to the modal method, the dynamic range of our method for main low-order aberrations in ocular system is increased by 1.86 to 43.88 times in variety. Meanwhile, the proposed method also has the best measurement accuracy, and the statistical root mean square (RMS) of the residual wavefronts is 0.0082 ± 0.0185 λ (mean ± standard deviation). The proposed method generally has a higher accuracy while having a similar or even better dynamic range as compared to traditional large-dynamic schemes. On the other hand, compared with recently developed deep learning methods, the proposed method has a much larger dynamic range and better measurement accuracy.

Adaptive Optics Microscopy with Wavefront Sensing Based on Neighbor Correlation.

Complex structures in living cells and tissues induce wavefront errors when light waves pass through them, and images observed with optical microscopes are undesirably blurred. This problem is especially serious for living plant cells because images are strikingly degraded even within a single cell. Adaptive optics (AO) is expected to be a solution to this problem by correcting such wavefront errors, thus enabling high-resolution imaging. In particular, scene-based AO involves wavefront sensing based on the image correlation between subapertures in a Shack-Hartmann wavefront sensor and thus does not require an intense point light source. However, the complex 3D structures of living cells often cause low correlation between subimages, leading to loss of accuracy in wavefront sensing. This paper proposes a novel method for scene-based sensing using only image correlations between adjacent subapertures. The method can minimize changes between subimages to be correlated and thus prevent inaccuracy in phase estimation. Using an artificial test target mimicking the optical properties of a layer of living plant cells, an imaging performance with a Strehl ratio of approximately 0.5 was confirmed. Upon observation of chloroplast autofluorescence inside living leaf cells of the moss Physcomitrium patens, recovered resolution images were successfully obtained even with complex biological structures. Under bright-field illumination, the proposed method outperformed the conventional method, demonstrating the future potential of this method for label- and damage-free AO microscopy. Several points for improvement in terms of the effect of AO correction are discussed.

Atmospheric Turbulence Aberration Correction Based on Deep Learning Wavefront Sensing.

In this paper, research was conducted on Deep Learning Wavefront Sensing (DLWS) neural networks using simulated atmospheric turbulence datasets, and a novel DLWS was proposed based on attention mechanisms and Convolutional Neural Networks (CNNs). The study encompassed both indoor experiments and kilometer-range laser transmission experiments employing DLWS. In terms of indoor experiments, data were collected and training was performed on the platform built by us. Subsequent comparative experiments with the Shack-Hartmann Wavefront Sensing (SHWS) method revealed that our DLWS model achieved accuracy on par with SHWS. For the kilometer-scale experiments, we directly applied the DLWS model obtained from the indoor platform, eliminating the need for new data collection or additional training. The DLWS predicts the wavefront from the beacon light PSF in real time and then uses it for aberration correction of the emitted laser. The results demonstrate a substantial improvement in the average peak intensity of the light spot at the target position after closed-loop correction, with a remarkable increase of 5.35 times compared to the open-loop configuration.

At-wavelength characterization of X-ray wavefronts in Bragg diffraction from crystals.

The advent of next-generation synchrotron radiation sources and X-ray free-electron lasers calls for high-quality Bragg-diffraction crystal optics to preserve the X-ray beam coherence and wavefront. This requirement brings new challenges in characterizing crystals in Bragg diffraction in terms of Bragg-plane height errors and wavefront phase distortions. Here, a quantitative methodology to characterize crystal optics using a state-of-the-art at-wavelength wavefront sensing technique and statistical analysis is proposed. The method was tested at the 1-BM-B optics testing beamline at the Advanced Photon Source for measuring silicon and diamond crystals in a self-referencing single-crystal mode and an absolute double-crystal mode. The phase error sensitivity of the technique is demonstrated to be at the λ/100 level required by most applications, such as the characterization of diamond crystals for cavity-based X-ray free-electron lasers.

Real-Time Wavefront Sensing at High Resolution with an Electrically Tunable Lens.

We have designed, assembled, and evaluated a compact instrument capable of capturing the wavefront phase in real time, across various scenarios. Our approach simplifies the optical setup and configuration, which reduces the conventional capture and computation time when compared to other methods that use two defocused images. We evaluated the feasibility of using an electrically tunable lens in our camera by addressing its issues and optimizing its performance. Additionally, we conducted a comparison study between our approach and a Shack-Hartmann sensor. The camera was tested on multiple targets, such as deformable mirrors, lenses with aberrations, and a liquid lens in movement. Working at the highest resolution of the CMOS sensor with a small effective pixel size enables us to achieve the maximum level of detail in lateral resolution, leading to increased sensitivity to high-spatial-frequency signals.

Rapid quantification of 3D ultrasound fields with wavefront sensing and Schlieren tomography.

The rapid and precise characterization of three-dimensional (3D) pressure fields inside water is paramount for ultrasound (US) applications in fields as relevant as biomedicine and acoustic trapping. The most conventional way is to scan point-by-point a needle hydrophone across the field of interest, which is an intrinsically invasive and slow process. With typical acquisition times of hours and even days, this method remains impractical in many realistic scenarios. Alternatively, optical techniques can be used to non-invasively and rapidly measure the changes in light intensity or phase induced by pressure differences. However, these techniques remain largely qualitative: extracting precise pressure values can require extensive calibration, and complex processing, or can be limited to low-pressure ranges. Here, we report how combining wavefront sensing and Schlieren tomography enables rapid and direct quantification of 3D pressure fields while obviating any calibration steps. By simultaneously capturing optical phase and intensity information of the US-perturbed fluid using a Wavefront Sensor and Schlieren projections, respectively, 3D pressure fields over several millimeters cubic can be reconstructed after a few seconds. We present a detailed description of the approach and prove its feasibility by characterizing the US field after an acoustic lens, which is in excellent agreement with calibrated hydrophone measurements and simulations. These results are a significant step forward toward the precise and real-time characterization of ultrasound patterns.

Research on Optical Metrology for Complex Optical Surfaces with Focal Plane Wavefront Sensing.

Complex optical elements have the advantages of improving image quality and optical performance and expanding the field of view. Therefore, it is widely used in X-ray scientific devices, adaptive optical elements, high-energy laser systems, and other fields and is a hot research direction in precision optics. Especially for precision machining, there is a greater need for high-precision testing technology. However, how to measure complex surfaces efficiently and accurately is still an important research topic in optical metrology technology. In order to verify the ability of optical metrology for complex optical surfaces with wavefront sensing based on image information of the focal plane, some experiment platforms in different types of optical surfaces were set up. In order to validate the feasibility and validity of wavefront-sensing technology based on image information of focal planes, a large number of repetitive experiments were carried out. The measurement results with wavefront sensing based on image information of the focal plane were compared with the measurement results with the ZYGO interferometer. The experimental results demonstrate that good agreement is obtained among the error distribution, PV value, and RMS value of the ZYGO interferometer, which shows the feasibility and validity of wavefront sensing based on image information of focal plane technology in optical metrology for the complex optical surface.

Frequency Division Control of Line-of-Sight Tracking for Space Gravitational Wave Detector.

The space gravitational wave detector uses the inter-satellite laser interferometer to measure a change in distance with ultra-high precision at the picometer level. Its special differential wavefront sensing technology based on laser interference is used to obtain the ultra-high-precision relative attitude between spacecrafts. In order to acquire the measurement, it is necessary to maintain high-precision attitude pointing and alignment for the optical path line-of-sight of the detector. This paper proposes a frequency division control method. More specifically, we chose the telescope attitude control loop frequency division as it is the faster response part, mainly relative to the high-frequency band within the measurement bandwidth. The spacecraft attitude frequency division is mainly in the low-frequency band within the measurement bandwidth. Finally, a high-precision simulation analysis is carried out. The results show that compared with traditional methods, the use of frequency division control design can significantly improve the attitude and pointing stability of the system and provide control support for systems requiring high pointing coordination accuracy, such as space gravity wave detectors.

Advanced Optical Wavefront Technologies to Improve Patient Quality of Vision and Meet Clinical Requests.

Adaptive optics (AO) is employed for the continuous measurement and correction of ocular aberrations. Human eye refractive errors (lower-order aberrations such as myopia and astigmatism) are corrected with contact lenses and excimer laser surgery. Under twilight vision conditions, when the pupil of the human eye dilates to 5-7 mm in diameter, higher-order aberrations affect the visual acuity. The combined use of wavefront (WF) technology and AO systems allows the pre-operative evaluation of refractive surgical procedures to compensate for the higher-order optical aberrations of the human eye, guiding the surgeon in choosing the procedure parameters. Here, we report a brief history of AO, starting from the description of the Shack-Hartmann method, which allowed the first in vivo measurement of the eye's wave aberration, the wavefront sensing technologies (WSTs), and their principles. Then, the limitations of the ocular wavefront ascribed to the IOL polymeric materials and design, as well as future perspectives on improving patient vision quality and meeting clinical requests, are described.

Recent advances in optical imaging through deep tissue: imaging probes and techniques.

Optical imaging has been essential for scientific observations to date, however its biomedical applications has been restricted due to its poor penetration through tissues. In living tissue, signal attenuation and limited imaging depth caused by the wave distortion occur because of scattering and absorption of light by various molecules including hemoglobin, pigments, and water. To overcome this, methodologies have been proposed in the various fields, which can be mainly categorized into two stategies: developing new imaging probes and optical techniques. For example, imaging probes with long wavelength like NIR-II region are advantageous in tissue penetration. Bioluminescence and chemiluminescence can generate light without excitation, minimizing background signals. Afterglow imaging also has high a signal-to-background ratio because excitation light is off during imaging. Methodologies of adaptive optics (AO) and studies of complex media have been established and have produced various techniques such as direct wavefront sensing to rapidly measure and correct the wave distortion and indirect wavefront sensing involving modal and zonal methods to correct complex aberrations. Matrix-based approaches have been used to correct the high-order optical modes by numerical post-processing without any hardware feedback. These newly developed imaging probes and optical techniques enable successful optical imaging through deep tissue. In this review, we discuss recent advances for multi-scale optical imaging within deep tissue, which can provide reseachers multi-disciplinary understanding and broad perspectives in diverse fields including biophotonics for the purpose of translational medicine and convergence science. Methodologies for multi-scale optical imaging within deep tissues are discussed in diverse fields including biophotonics for the purpose of translational medicine and convergence science. Recent imaging probes have tried deep tissue imaging by NIR-II imaging, bioluminescence, chemiluminescence, and afterglow imaging. Optical techniques including direct/indirect and coherence-gated wavefront sensing also can increase imaging depth.

Jitter-Robust Phase Retrieval Wavefront Sensing Algorithms.

Phase retrieval wavefront sensing methods are now of importance for imaging quality maintenance of space telescopes. However, their accuracy is susceptible to line-of-sight jitter due to the micro-vibration of the platform, which changes the intensity distribution of the image. The effect of the jitter shows some stochastic properties and it is hard to present an analytic solution to this problem. This paper establishes a framework for jitter-robust image-based wavefront sensing algorithm, which utilizes two-dimensional Gaussian convolution to describe the effect of jitter on an image. On this basis, two classes of jitter-robust phase retrieval algorithms are proposed, which can be categorized into iterative-transform algorithms and parametric algorithms, respectively. Further discussions are presented for the cases where the magnitude of jitter is unknown to us. Detailed simulations and a real experiment are performed to demonstrate the effectiveness and practicality of the proposed approaches. This work improves the accuracy and practicality of the phase retrieval wavefront sensing methods in the space condition with non-ignorable micro-vibration.

Use of a Rotating Square Spatial-Frequency Filter to Map the Optical Path Length Variation in Microscopic Biological Samples.

Gradient images can be obtained using a rotating square mask to filter the angular spectra of the wavefront generated by a complex transmittance object. This method can be applied to measure the three-dimensional structure of microscopic biological samples through the relationship of the phase with the optical path length. This work describes the implementation of a system using an inverted optical microscope and shows the experimental results of phase maps generated by boar sperm cells.

Sensitivity of remote focusing microscopes to magnification mismatch.

Remote focusing (RF) is a technique that greatly extends the aberration-free axial scan range of an optical microscope. To maximise the diffraction limited depth range in an RF system, the magnification of the relay lenses should be such that the pupil planes of the objectives are accurately mapped on to each other. In this paper we study the tolerance of the RF system to magnification mismatch and quantify the amount of residual spherical aberration present at different focusing depths. We observe that small deviations from ideal magnification results in increased amounts of residual spherical aberration terms leading to a reduction in the diffracted limited range. For high-numerical aperture objectives, the simulation predicts a 50% decrease in the diffracted limited range for 1% magnification mismatch. The simulation has been verified against an experimental RF system with ideal and nonideal magnifications. Experimentally confirmed predictions also provide a valuable empirical method of determining when a system is close to the ideal phase matching condition, based on the sign of the spherical aberration on either side of focus.

Optimization of Virtual Shack-Hartmann Wavefront Sensing.

Virtual Shack-Hartmann wavefront sensing (vSHWS) can flexibly adjust parameters to meet different requirements without changing the system, and it is a promising means for aberration measurement. However, how to optimize its parameters to achieve the best performance is rarely discussed. In this work, the data processing procedure and methods of vSHWS were demonstrated by using a set of normal human ocular aberrations as an example. The shapes (round and square) of a virtual lenslet, the zero-padding of the sub-aperture electric field, sub-aperture number, as well as the sequences (before and after diffraction calculation), algorithms, and interval of data interpolation, were analyzed to find the optimal configuration. The effect of the above optimizations on its anti-noise performance was also studied. The Zernike coefficient errors and the root mean square of the wavefront error between the reconstructed and preset wavefronts were used for performance evaluation. The performance of the optimized vSHWS could be significantly improved compared to that of a non-optimized one, which was also verified with 20 sets of clinical human ocular aberrations. This work makes the vSHWS's implementation clearer, and the optimization methods and the obtained results are of great significance for its applications.

Polarization-Dependent All-Dielectric Metasurface for Single-Shot Quantitative Phase Imaging.

Phase retrieval is a noninterferometric quantitative phase imaging technique that has become an essential tool in optical metrology and label-free microscopy. Phase retrieval techniques require multiple intensity measurements traditionally recorded by camera or sample translation, which limits their applicability mostly to static objects. In this work, we propose the use of a single polarization-dependent all-dielectric metasurface to facilitate the simultaneous recording of two images, which are utilized in phase calculation based on the transport-of-intensity equation. The metasurface acts as a multifunctional device that splits two orthogonal polarization components and adds a propagation phase shift onto one of them. As a proof-of-principle, we demonstrate the technique in the wavefront sensing of technical samples using a standard imaging setup. Our metasurface-based approach fosters a fast and compact configuration that can be integrated into commercial imaging systems.

Shack-Hartmann Wavefront Sensing of Ultrashort Optical Vortices.

Light beams carrying Orbital Angular Momentum (OAM), also known as optical vortices (OV), have led to fascinating new developments in fields ranging from quantum communication to novel light-matter interaction aspects. Even though several techniques have emerged to synthesize these structured-beams, their detection, in particular, single-shot amplitude, wavefront, and modal content characterization, remains a challenging task. Here, we report the single-shot amplitude, wavefront, and modal content characterization of ultrashort OV using a Shack-Hartmann wavefront sensor. These vortex beams are obtained using spiral phase plates (SPPs) that are frequently used for high-intensity applications. The reconstructed wavefronts display a helical structure compatible with the topological charge induced by the SPPs. We affirm the accuracy of the optical field reconstruction by the wavefront sensor through an excellent agreement between the numerically backpropagated and experimentally obtained intensity distribution at the waist. Consequently, through Laguerre-Gauss (LG) decomposition of the reconstructed fields, we reveal the radial and azimuthal mode composition of vortex beams under different conditions. The potential of our method is further illustrated by characterizing asymmetric Gaussian vortices carrying fractional average OAM, and a realtime topological charge measurement at a 10Hz repetition rate. These results can promote Shack-Hartmann wavefront sensing as a single-shot OV characterization tool.

Imaging performance of microscopy adaptive-optics system using scene-based wavefront sensing.

SIGNIFICANCE: A scene-based adaptive-optics (AO) system is developed and a method for investigating its imaging performance is proposed. The system enables derivation of Strehl ratios from observed images via collaboration with computer simulations. The resultant Strehl ratios are comparable with those of other current AO systems. AIM: For versatile and noninvasive AO microscopy, a scene-based wavefront-sensing technique working on a Shack-Hartmann wavefront sensor is developed in a modal control system. The purpose of the research is to clarify the imaging performance of the AO system via the derivation of Strehl ratios from observed images toward applications in microscopy of living cells and tissues. APPROACH: Two imaging metrics that can be directly measured from observed images (i.e., an energy concentration ratio and unbiased maximum ratio) are defined and related to the Strehl ratio via computer simulations. Experiments are conducted using artificial targets to measure the imaging metrics, which are then converted to Strehl ratios. RESULTS: The resultant Strehl ratios are >0.7 and 0.5 in the cases of defocus and higher aberrations, respectively. The half-widths at half-maximum of the AO-corrected bead images are favorably comparable to those of on-focus images under simple defocus aberration, and the AO system works both under bright-field illumination and on fluorescent bead images. CONCLUSIONS: The proposed scene-based AO system is expected to work with a Strehl ratio of more than 0.5 when applied to high-resolution live imaging of cells and tissues under bright-field and fluorescence microscopies.