Wavefront Metrology Research Articles

Double-edge scan wavefront metrology and its application in crystal diffraction wavefront measurements.

Achieving diffraction-limited performance in fourth-generation synchrotron radiation sources demands monochromator crystals that can preserve the wavefront across an unprecedented extensive range. There is an urgent need for techniques of absolute crystal diffraction wavefront measurement. At the Beijing Synchrotron Radiation Facility (BSRF), a novel edge scan wavefront metrology technique has been developed. This technique employs a double-edge tracking method, making diffraction-limited level absolute crystal diffraction wavefront measurement a reality. The results demonstrate an equivalent diffraction surface slope error below 70 nrad (corresponding to a wavefront phase error of 4.57% λ) r.m.s. within a nearly 6 mm range for a flat crystal in the crystal surface coordinate. The double-edge structure contributes to exceptional measurement precision for slope error reproducibility, achieving levels below 15 nrad (phase error reproducibility < λ/100) even at a first-generation synchrotron radiation source. Currently, the measurement termed double-edge scan (DES) has already been regarded as a critical feedback mechanism in the fabrication of next-generation crystals.

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.

Characterization of the error of the speckle-based wavefront metrology device at Shanghai Synchrotron Radiation Facility.

A metrology device based on the near-field speckle technique was developed in the x-ray test beamline at the Shanghai Synchrotron Radiation Facility to meet the at-wavelength detection requirements of ultra-high-precision optical elements. Different sources of error that limit the uncertainty of the instrument were characterized. Two main factors that contribute to the uncertainty of the measurements were investigated: (1) noise errors introduced by the electronics and the errors introduced by the algorithm and (2) stability errors owing to environmental conditions. The results show that the high measurement stability of the device is realized because it is insensitive to the effect of the external environment. The repetition accuracy of the device achieved 9 nrad (rms) when measuring the planar mirror that produces weak phase curvature.

Robust ptychographic X-ray speckle tracking with multilayer Laue lenses.

In recent years, X-ray speckle tracking techniques have emerged as viable tools for wavefront metrology and sample imaging applications, and have been actively developed for use at synchrotron light sources. Speckle techniques can recover an image free of aberrations and can be used to measure wavefronts with a high angular sensitivity. Since they are compatible with low-coherence sources they can be also used with laboratory X-ray sources. A new implementation of the ptychographic X-ray speckle tracking method, suitable for the metrology of highly divergent wavefields, such as those created by multilayer Laue lenses, is presented here. This new program incorporates machine learning techniques such as Huber and non-parametric regression and enables robust and quick wavefield measurements and data evaluation even for low brilliance X-ray beams, and the imaging of low-contrast samples. To realize this, a software suite was written in Python 3, with a C back-end capable of concurrent calculations for high performance. It is accessible as a Python module and is available as source code under Version 3 or later of the GNU General Public License.

ALTECH 2021 – Analytical Techniques for Precise Characterization of Nano Materials

ALTECH 2021 – Analytical Techniques for Precise Characterization of Nano Materials

Adaptive and active X-ray optics

This review describes the principles and capabilities of X-ray adaptive and active optics. The main executive mechanisms of bending mirrors used at synchrotron radiation sources and in X-ray telescopes are considered. Particular attention is paid to wavefront metrology using Shack-Hartmann sensors, as well as sensors based on grating interferometers, X-ray speckle and ptychography. Keywords: X-rays, adaptive optics, active optics, bimorph mirror, wavefront metrology.

Present Research Status of X-Ray Near-Field Speckle Based Wavefront Metrology

Present Research Status of X-Ray Near-Field Speckle Based Wavefront Metrology

Optical Wavefront Sensing with Picometer Sensitivity

Precision optical wavefront metrology is crucial in a range of areas, including direct imaging of exoplanets. Although ground-based systems have reached high sensitivities, systems that are suitable for space use using stellar photons for sensing are lacking. In work published this year, we have developed a robust phase reconstruction expression that allows very accurate measurement of small phase changes at the highest spatial frequencies possible, targeting very small signals to demonstrate its applicability for space-based high-contrast missions

Quantitative X-ray Channel-Cut Crystal Diffraction Wavefront Metrology Using the Speckle Scanning Technique.

A speckle-based method for the X-ray crystal diffraction wavefront measurement is implemented, and the slope errors of channel-cut crystals with different surface characteristics are measured. The method uses a speckle scanning technique generated by a scattering membrane translated using a piezo motor to infer the deflection of X-rays from the crystals. The method provides a high angular sensitivity of the channel-cut crystal slopes in both the tangential and sagittal directions. The experimental results show that the slope error of different cutting and etching processes ranges from 0.25 to 2.98 μrad. Furthermore, the results of wavefront deformation are brought into the beamline for simulation. This method opens up possibilities for new high-resolution applications for X-ray crystal diffraction wavefront measurement and provides feedback to crystal manufacturers to improve channel-cut fabrication.

Speckle-tracking: a software suite for ptychographic X-ray speckle tracking.

In recent years, X-ray speckle-tracking techniques have emerged as viable tools for wavefront metrology and sample imaging applications. These methods are based on the measurement of near-field images. Thanks to their simple experimental setup, high angular sensitivity and compatibility with low-coherence sources, these methods have been actively developed for use with synchrotron and laboratory light sources. Not only do speckle-tracking techniques give the potential for high-resolution imaging, but they also provide rapid and robust characterization of aberrations of X-ray optical elements, focal spot profiles, and sample position and transmission properties. In order to realize these capabilities, software implementations are required that are equally rapid and robust. To address this need, a software suite has been developed for the ptychographic X-ray speckle-tracking technique, an X-ray speckle-based method suitable for highly divergent wavefields. The software suite is written in Python 3, with an OpenCL back end for GPU and multi-CPU core processing. It is accessible as a Python module, through the command line or through a graphical user interface, and is available as source code under Version 3 or later of the GNU General Public License.

A Toolbox for Isophase-Curvature Guided Computation of Metrology Hologram.

We describe the algorithmic foundations of an open-source numerical toolbox, written in the Octave language, for the creation of computer-generated binary and multi-level holograms used in interferometric form error measurements of complex aspheric and free-form precision surfaces and wavefronts. In a typical measurement setup for this type of surface, a hologram is used to generate a test wavefront that has the design shape of the surface, which is then compared to a fabricated part using an imaging laser interferometer. The optical function of the hologram in the measurement is generally modeled with optical ray-tracing software and it can be encapsulated by a scalar optical phase function φ : R2 →R. The toolbox converts phase functions into equivalent binary holograms that generate the desired test wavefronts for an interferometric form error measurement. The algorithms in this toolbox take advantage of the relationship between the local properties of phase functions and the local geometry (curvature) of isophase lines. It forms the core of an effcient algorithm for the computation of optical holograms. Holograms are created in a format that can be processed by most laser-or e-beam lithography systems. While the toolbox is chiefy aimed at the creation of hologram layouts needed for measurements of precision surfaces and wavefronts, we show that the isophase-following algorithm is easily extended to phase functions with singularities and discontinuities. Such phase functions result in holograms with zone bifurcation and they can be used to generate helical wavefronts. Light beams with helical wavefronts have applications beyond surface and wavefront metrology. The toolbox also includes a family of functions for the effcient estimation and evaluation of Zernike polynomials, which are widely used in optical applications.

Ptychographic X-ray speckle tracking with multi-layer Laue lens systems.

The ever-increasing brightness of synchrotron radiation sources demands improved X-ray optics to utilize their capability for imaging and probing biological cells, nano-devices and functional matter on the nanometre scale with chemical sensitivity. Hard X-rays are ideal for high-resolution imaging and spectroscopic applications owing to their short wavelength, high penetrating power and chemical sensitivity. The penetrating power that makes X-rays useful for imaging also makes focusing them technologically challenging. Recent developments in layer deposition techniques have enabled the fabrication of a series of highly focusing X-ray lenses, known as wedged multi-layer Laue lenses. Improvements to the lens design and fabrication technique demand an accurate, robust, in situ and at-wavelength characterization method. To this end, a modified form of the speckle tracking wavefront metrology method has been developed. The ptychographic X-ray speckle tracking method is capable of operating with highly divergent wavefields. A useful by-product of this method is that it also provides high-resolution and aberration-free projection images of extended specimens. Three separate experiments using this method are reported, where the ray path angles have been resolved to within 4 nrad with an imaging resolution of 45 nm (full period). This method does not require a high degree of coherence, making it suitable for laboratory-based X-ray sources. Likewise, it is robust to errors in the registered sample positions, making it suitable for X-ray free-electron laser facilities, where beam-pointing fluctuations can be problematic for wavefront metrology.

Ptychographic X-ray speckle tracking.

A method is presented for the measurement of the phase gradient of a wavefront by tracking the relative motion of speckles in projection holograms as a sample is scanned across the wavefront. By removing the need to obtain an undistorted reference image of the sample, this method is suitable for the metrology of highly divergent wavefields. Such wavefields allow for large magnification factors that, according to current imaging capabilities, will allow for nanoradian angular sensitivity and nanoscale sample projection imaging. Both the reconstruction algorithm and the imaging geometry are nearly identical to that of ptychography, except that the sample is placed downstream of the beam focus and that no coherent propagation is explicitly accounted for. Like other X-ray speckle tracking methods, it is robust to low-coherence X-ray sources, making it suitable for laboratory-based X-ray sources. Likewise, it is robust to errors in the registered sample positions, making it suitable for X-ray free-electron laser facilities, where beam-pointing fluctuations can be problematic for wavefront metrology. A modified form of the speckle tracking approximation is also presented, based on a second-order local expansion of the Fresnel integral. This result extends the validity of the speckle tracking approximation and may be useful for similar approaches in the field.

Measuring laser beam quality, wavefronts, and lens aberrations using ptychography.

We report on an approach for quantitative characterization of laser beam quality, wavefronts, and lens aberrations using ptychography with a near-infrared supercontinuum laser. Ptychography is shown to offer a powerful alternative for both beam propagation ratio M2 and wavefront measurements compared with existing techniques. In addition, ptychography is used to recover the transmission function of a microlens array for aberration analysis. The results demonstrate ptychography's flexibility in wavefront metrology and optical shop testing.

Phase measurement of a segmented wave front using PISton and TILt interferometry (PISTIL).

New architectures for telescopes or powerful lasers require segmented wave front metrology. This paper deals with a new interferometric wave front sensing technique called PISTIL (PISton and TILt), able to recover both piston and tilts of segment beams. The main advantages of the PISTIL technique are the absence of a reference arm and an access to the tilt information. An explanation of the principle, as well as an experimental implementation and the use of a segmented active mirror, are presented. Measurement errors of λ/200 for piston and 40 µrad for tilts have been achieved, well beyond performances requested for the above mentioned applications.

X-ray grating interferometer for insitu and at-wavelength wavefront metrology.

A wavefront metrology setup based on the X-ray grating interferometry technique for spatially resolved, quantitative, insitu and at-wavelength measurements of the wavefront at synchrotron radiation and hard X-ray free-electron laser beamlines is reported. Indeed, the ever-increasing demands on the optical components to preserve the wavefront shape and the coherence of the delivered X-ray beam call for more and more sensitive diagnostic instruments. Thanks to its angular sensitivity, X-ray grating interferometry has been established in recent years as an adequate wavefront-sensing technique for quantitatively assessing the quality of the X-ray wavefront under working conditions and hence for the insitu investigation of X-ray optical elements. In order to characterize the optical elements at any given beamline by measuring the aberrations introduced in the wavefront, a transportable X-ray grating interferometry setup was realised at the Swiss Light Source (SLS). The instrument, which is expected to be a valuable tool for investigating the quality of the X-ray beam delivered at an endstation, will be described hereafter in terms of the hardware setup and the related data analysis procedure. Several exemplary experiments performed at the X05DA Optics beamline of the SLS will be presented.

Wavefront metrology for coherent hard X-rays by scanning a microsphere.

Characterization of the wavefront of an X-ray beam is of primary importance for all applications where coherence plays a major role. Imaging techniques based on numerically retrieving the phase from interference patterns are often relying on an a-priori assumption of the wavefront shape. In Coherent X-ray Diffraction Imaging (CXDI) a planar incoming wave field is often assumed for the inversion of the measured diffraction pattern, which allows retrieving the real space image via simple Fourier transformation. It is therefore important to know how reliable the plane wave approximation is to describe the real wavefront. Here, we demonstrate that the quantitative wavefront shape and flux distribution of an X-ray beam used for CXDI can be measured by using a micrometer size metal-coated polymer sphere serving in a similar way as the hole array in a Hartmann wavefront sensor. The method relies on monitoring the shape and center of the scattered intensity distribution in the far field using a 2D area detector while raster-scanning the microsphere with respect to the incoming beam. The reconstructed X-ray wavefront was found to have a well-defined central region of approximately 16 µm diameter and a weaker, asymmetric, intensity distribution extending 30 µm from the beam center. The phase front distortion was primarily spherical with an effective radius of 0.55 m which matches the distance to the last upstream beam-defining slit, and could be accurately represented by Zernike polynomials.

Optimized mirror shape tuning using beam weightings based on distance, angle of incidence, reflectivity, and power.

For glancing-incidence optical systems, such as short-wavelength optics used for nano-focusing, incorporating physical factors in the calculations used for shape optimization can improve performance. Wavefront metrology, including the measurement of a mirror's shape or slope, is routinely used as input for mirror figure optimization on mirrors that can be bent, actuated, positioned, or aligned. Modeling shows that when the incident power distribution, distance from focus, angle of incidence, and the spatially varying reflectivity are included in the optimization, higher Strehl ratios can be achieved. Following the works of Maréchal and Mahajan, optimization of the Strehl ratio (for peak intensity with a coherently illuminated system) occurs when the expectation value of the phase error's variance is minimized. We describe an optimization procedure based on regression analysis that incorporates these physical parameters. This approach is suitable for coherently illuminated systems of nearly diffraction-limited quality. Mathematically, this work is an enhancement of the methods commonly applied for ex situ alignment based on uniform weighting of all points on the surface (or a sub-region of the surface). It follows a similar approach to the optimization of apodized and non-uniformly illuminated optical systems. Significantly, it reaches a different conclusion than a more recent approach based on minimization of focal plane ray errors.

基于光学相干层析成像的视网膜图像自动分层方法

Ptychography, a phase retrieval technology based on scanning coherent diffractive imaging, shows such advantages as simple experimental setup and strong anti-noise ability. Ptychography is used in the field of wavefront metrology for projection lens. The formulas of optical field propagation, the conditions of discretion, and the experimental configurations are analyzed in detail for projection lenses with different numerical apertures. Numerical simulations and experimental results show that to achieve reasonable convergence and measurement accuracy, the transmittance of the object should be set between 45% and 80%. Increasing the complexity of the object pattern and adding registration process of probe and object into the iterative algorithm can also improve the convergence speed and the recovery accuracy. The wavefront aberration measurement accuracy can reach 10~(-3)lambda or less. It is feasible to use ptychography in wavefront aberration measurement for extreme ultraviolet lithographic projection lenses.

X-ray pulse wavefront metrology using speckle tracking

An instrument allowing the quantitative analysis of X-ray pulsed wavefronts is presented and its processing method explained. The system relies on the X-ray speckle tracking principle to accurately measure the phase gradient of the X-ray beam from which beam optical aberrations can be deduced. The key component of this instrument, a semi-transparent scintillator emitting visible light while transmitting X-rays, allows simultaneous recording of two speckle images at two different propagation distances from the X-ray source. The speckle tracking procedure for a reference-less metrology mode is described with a detailed account on the advanced processing schemes used. A method to characterize and compensate for the imaging detector distortion, whose principle is also based on speckle, is included. The presented instrument is expected to find interest at synchrotrons and at the new X-ray free-electron laser sources under development worldwide where successful exploitation of beams relies on the availability of an accurate wavefront metrology.