Lateral shearing interferometry method based on double-checkerboard grating by suppressing aliasing effect

Ronchi lateral shearing interferometry is a promising wavefront sensing technology with the advantages of simple structure and no reference light, which can realize a high-precision wavefront aberration measurement. To obtain shear information in both directions, the conventional double-Ronchi interferometer sequentially applies two orthogonal one-dimensional Ronchi gratings as the object-plane splitting element of the optics under test. Simultaneously, another Ronchi grating is positioned on the image plane in the same orientation to capture two sets of interferograms, thereby enabling two-dimensional wavefront reconstruction. Mechanical errors will inevitably be introduced during grating conversion, affecting reconstruction accuracy. Based on this, we propose a lateral shearing interferometry applying double-checkerboard grating. Only unidirectional phase shift is needed to obtain shear information in two directions while evading the grating conversion step, aiming to streamline operational processes and mitigate the potential for avoidable errors. We employ scalar diffraction theory to analyze the full optical path propagation process of the double-checkerboard shearing interferometry and introduce a new reconstruction algorithm to effectively extract the two-dimensional shear phase by changing the grating morphology, suppressing the aliasing effect of irrelevant diffraction orders. We reduce the fitting error through iterative optimization to realize high-precision wavefront reconstruction. Compared with conventional Ronchi lateral shearing interferometry, the proposed method exhibits better robustness and stability in noisy environments.

Pseudo-gray-scale halftone gratings for shearing and Hartmann wavefront sensors

Now in use on x-ray beamlines worldwide, shearing interferometry and Hartmann wavefront sensing provide effective feedback for measuring and optimizing high-quality beams. Conventionally, both approaches spatially modulate the beam properties (amplitude or phase) using two-tone, binary patterns, leading to deleterious diffraction effects that must be mitigated. In shearing, the presence of multiple diffraction orders affects measurement near boundaries. In Hartmann, diffraction limits the measurement point density. We demonstrate that the use of pseudo-gray-scale halftone patterns in the diffracting elements can improve the performance of both techniques.

Binary Amplitude Reflection Gratings for X-ray Shearing and Hartmann Wavefront Sensors

New, high-coherent-flux X-ray beamlines at synchrotron and free-electron laser light sources rely on wavefront sensors to achieve and maintain optimal alignment under dynamic operating conditions. This includes feedback to adaptive X-ray optics. We describe the design and modeling of a new class of binary-amplitude reflective gratings for shearing interferometry and Hartmann wavefront sensing. Compact arrays of deeply etched gratings illuminated at glancing incidence can withstand higher power densities than transmission membranes and can be designed to operate across a broad range of photon energies with a fixed grating-to-detector distance. Coherent wave-propagation is used to study the energy bandwidth of individual elements in an array and to set the design parameters. We observe that shearing operates well over a ±10% bandwidth, while Hartmann can be extended to ±30% or more, in our configuration. We apply this methodology to the design of a wavefront sensor for a soft X-ray beamline operating from 230 eV to 1400 eV and model shearing and Hartmann tests in the presence of varying wavefront aberration types and magnitudes.

X-Ray Single-Grating Interferometry for Wavefront Measurement and Correction of Hard X-Ray Nanofocusing Mirrors

X-ray single-grating interferometry was applied to conduct accurate wavefront corrections for hard X-ray nanofocusing mirrors. Systematic errors in the interferometer, originating from a grating, a detector, and alignment errors of the components, were carefully examined. Based on the measured wavefront errors, the mirror shapes were directly corrected using a differential deposition technique. The corrected X-ray focusing mirrors with a numerical aperture of 0.01 attained two-dimensionally diffraction-limited performance. The results of the correction indicate that the uncertainty of the wavefront measurement was less than λ/72 in root-mean-square value.

Reflective binary amplitude grating for soft x-ray shearing and Hartmann wavefront sensing

We demonstrate a reflective wavefront sensor grating suitable for the characterization of high-quality x-ray beamlines and optical systems with high power densities. Operating at glancing incidence angles, the optical element is deeply etched with a two-level pattern of shearing interferometry gratings and Hartmann wavefront sensor grids. Transverse features block unwanted light, enabling binary amplitude in reflection with high pattern contrast. We present surface characterization and soft x-ray reflectometry of a prototype grating array to demonstrate function prior to wavefront measurement applications. A simulation of device performance is shown.

Wavefront sensing at X-ray free-electron lasers

Here a direct comparison is made between various X-ray wavefront sensing methods with application to optics alignment and focus characterization at X-ray free-electron lasers (XFELs). Focus optimization at XFEL beamlines presents unique challenges due to high peak powers as well as beam pointing instability, meaning that techniques capable of single-shot measurement and that probe the wavefront at an out-of-focus location are desirable. The techniques chosen for the comparison include single-phase-grating Talbot interferometry (shearing interferometry), dual-grating Talbot interferometry (moiré deflectometry) and speckle tracking. All three methods were implemented during a single beam time at the Linac Coherent Light Source, at the X-ray Pump Probe beamline, in order to make a direct comparison. Each method was used to characterize the wavefront resulting from a stack of beryllium compound refractive lenses followed by a corrective phase plate. In addition, difference wavefront measurements with and without the phase plate agreed with its design to within λ/20, which enabled a direct quantitative comparison between methods. Finally, a path toward automated alignment at XFEL beamlines using a wavefront sensor to close the loop is presented.

General measurement of optical system aberrations with a continuously variable lateral shear ratio by a randomly encoded hybrid grating

A general lateral shearing interferometry method to measure the wavefront aberrations with a continuously variable shear ratio by the randomly encoded hybrid grating (REHG) is proposed. The REHG consists of a randomly encoded binary amplitude grating and a phase chessboard. Its Fraunhofer diffractions contain only four orders which are the ±1 orders in two orthogonal directions due to the combined modulation of the amplitude and phase. As a result, no orders selection mask is needed for the REHG and the shear ratio is continuously variable, which is beneficial to the variation of sensitivity and testing range for different requirements. To determine the fabrication tolerance of this hybrid grating, the analysis of the effects of different errors on the diffraction intensity distributions is carried out. Experiments have shown that the testing method can achieve a continuously variable shear ratio with the same REHG, and the comparison with a ZYGO GPI interferometer exhibits that the aberration testing method by the REHG is highly precise and also has a good repeatability. This testing method by the REHG is available for general use in testing the aberrations of different optical systems in situ.

Fourier fringe analysis and its application to metrology of extreme physical phenomena: a review [Invited]

The paper reviews a technique for fringe analysis referred to as Fourier fringe analysis (FFA) or the Fourier transform method, with a particular focus on its application to metrology of extreme physical phenomena. Examples include the measurement of extremely small magnetic fields with subfluxon sensitivity by electron wave interferometry, subnanometer wavefront evaluation of projection optics for extreme UV lithography, the detection of sub-Ångstrom distortion of a crystal lattice, and the measurement of ultrashort optical pulses in the femotsecond to attosecond range, which show how the advantages of FFA are exploited in these cutting edge applications.

In situ optical testing of infrared lenses for high-performance cameras

We propose to evaluate infrared lenses with a dedicated analyzer having the same mechanical interface as the usual cameras. The proposed analysis is based on a wavefront measurement and allows a diagnostic of possible internal defects of the analyzed lens. The infrared lens analyzer described is constituted with a quadriwave lateral shearing interferometer and works with a blackbody light. We describe the response of this interferometer and an innovative method to obtain the wavefront under test. We finally present the experimental analysis of long-wavelength infrared lenses and the particular case of a modified lens that generates a large spherical aberration.

Wave-front reconstruction from multidirectional phase derivatives generated by multilateral shearing interferometers

To increase the accuracy of wave-front evaluation, we propose to exploit the natural capability of multiple lateral shearing interferometers to measure simultaneously more than two orthogonal phase derivatives. We also describe a method, based on Fourier-transform analysis, that uses this multiple information to reconstruct the wave-front under study.