Diffraction Wavefront Research Articles

Separation detection and correction of mosaic errors in mosaic gratings based on two detection lights with the same diffraction order and different incident angles

Grating tiling is an important fabrication technology for large-size gratings. However, when using grating tiling technology to form large-size echelle gratings, the interferometer cannot detect the grating's zero-order diffraction wavefront because the zero-order diffraction light of the echelle grating is weak. This prevents use of the zero-order and non-zero-order diffraction light of the grating to realize separation detection and correction of mosaic errors. To solve this problem, a new method for separation detection and correction of mosaic errors in mosaic gratings based on two detection lights with the same diffraction order but different incident angles is proposed and a mosaic error detection system is designed. Then, the correction steps for mosaic errors are summarized and the error in mosaic error detection system is analyzed. Finally, the measurement uncertainty in detecting the wavefront of the mosaic grating and the mosaic accuracy of the grating wavefront are analyzed. The uncertainty is 0.008λ (λ=632.8 nm) and the mosaic accuracy of the peak-to-valley wavefront is 0.069λ, which shows that high-precision measurements of the wavefront and high-precision mosaic of the wavefront were successfully achieved. The proposed method can be used for the mosaic of all blazed gratings.

Limiting Spectral Resolution of a Reflection Grating Made via Electron-beam Lithography

Abstract Gratings enable dispersive spectroscopy from the X-ray to the optical, and feature prominently in proposed flagships and SmallSats alike. The exacting performance requirements of these future missions necessitate assessing whether the present state-of-the-art in grating manufacture will limit spectrometer performance. In this work, we manufacture a 1.5 mm thick, 1000 nm period (1000 gr mm−1) flat grating using electron-beam lithography (EBL), a promising lithographic technique for patterning gratings for future astronomical observatories. We assess the limiting spectral resolution of this grating by interferometrically measuring the diffracted wavefronts produced in ± first order. Our measurements show this grating has a performance of at least R ∼ 14,600, and that our assessment is bounded by the error of our interferometric measurement. The impact of EBL stitching error on grating performance is quantified, and a path to measuring the period error of customized, curved gratings is presented.

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.

PyNX: high-performance computing toolkit for coherent X-ray imaging based on operators

The open-source PyNX toolkit has been extended to provide tools for coherent X-ray imaging data analysis and simulation. All calculations can be executed on graphical processing units (GPUs) to achieve high-performance computing speeds. The toolkit can be used for coherent diffraction imaging (CDI), ptychography and wavefront propagation, in the far- or near-field regime. Moreover, all imaging operations (propagation, projections, algorithm cycles…) can be implemented in Python as simple mathematical operators, an approach which can be used to easily combine basic algorithms in a tailored chain. Calculations can also be distributed to multiple GPUs, e.g. for large ptychography data sets. Command-line scripts are available for on-line CDI and ptychography analysis, either from raw beamline data sets or using the coherent X-ray imaging data format.

Effect of the measuring mirror surface shape error on ruled groove straightness and the grating diffraction wavefront

Measuring mirror requirements and their impact on groove errors are related to the error compensation strategy for a ruling engine. We analyze why the measuring mirror of the CIOMP-6 engine affects the groove straightness and the grating diffraction wavefront. We study a theoretical model of the relationship between the measuring mirror's surface shape error and the grating wavefront, propose a requirement for the measuring mirror surface shape error, and reprocess the measuring mirror. Comparative ruling experiments prove that the grating's wavefront quality at the diffraction order along the groove direction improved significantly after reprocessing of the measuring mirror.

In-house beam-splitting pulse compressor for high-energy petawatt lasers.

One of the most significant bottlenecks in achieving kilojoule-level high-energy petawatt (PW) to hundreds-petawatt (100PW) lasers is the requirement of as large as meter-sized gratings so as to avoid the laser-induced damage in the compressor. High-quality meter-sized gratings have so far been difficult to manufacture. This paper proposes a new in-house (intra-) beam-splitting compressor based on the property that the damage threshold of gratings depends on the pulse duration. The proposed scheme will simultaneously improve the stability, save on expensive gratings, and simplify compressor size because the split beams share the first two parallel gratings. Furthermore, as the transmitted wavefront of a glass plate can be better and more precisely controlled than the diffraction wavefront of a large grating, we propose glass plates with designed transmitted wavefront to compensate for the wavefront distortion introduced by the second and third gratings, and other in-house optics, such as the beam splitter. This simple and economical method can compensate for the space-time distortion in the compressor, and thus improve focal intensity, which otherwise cannot be compensated by a deformable mirror outside the compressor. Together with a multi-beam tiled-aperture combining scheme, the proposed novel compressor provides a new scheme for achieving high-energy PW-100PW lasers or even exawatt lasers with relatively small gratings in the future.

Numerical calculation of the mosaic error between mosaic gratings.

The theoretical calculation model for a mosaic error was established based on the plane equation for a grating surface and the relationship equation for a mosaic grating surface. A mosaic grating was obtained based on this model. In the experiment, the mosaic error was calculated based on the diffraction wavefronts of two groups of mosaic gratings that were obtained simultaneously with a Zygo interferometer. The difference between the wavefront of the mosaic grating and the average wavefront of the mosaic grating element was 0.031λ. The maximum far-field intensity of the mosaic grating was 90% of that without an error. This model provides a theoretical basis for the numerical mosaic between gratings. In addition, the mosaic error can be calculated with this model, and the quality of the mosaic grating can be evaluated.

Testing the mid-spatial frequency error of a large aperture long-focal-length lens with CGH.

We present the use of a computer-generated hologram (CGH) to test the mid-spatial frequency error of a large aperture long-focal-length lens. In order to verify this test approach, a 450 mm × 450 mm reflective CGH is designed and fabricated for testing the 440 mm × 440 mm spatial filter lens. Both 0th and 1st order diffraction wavefront of CGH are measured, and the 0th order diffraction wavefront is used to calibrate the substrate error. The mid-spatial frequency wavefront error caused by the CGH fabrication errors are evaluated using the binary linear grating model and power spectral density (PSD) theory. Experimental results and error analysis show that the CGH test approach is also feasible for the measurement of mid-spatial frequency error, and the measurement accuracy of PSD1 can reach 0.8832 nm RMS.

Conception of diffractive wavefront correction for XUV and soft x-ray spectroscopy.

We present a simple and precise method to minimize aberrations of mirror-based, wavelength-dispersive spectrometers for the extreme ultraviolet (XUV) and soft x-ray domain. The concept enables an enhanced resolving power $ E/\Delta E $E/ΔE, in particular, close to the diffraction limit over a spectral band of a few percent around the design energy of the instrument. Our optical element, the "diffractive wavefront corrector" (DWC), is individually shaped to the form and figure error of the mirror profile and might be written directly with a laser on a plane and even strongly curved substrates. Theory and simulations of various configurations, like Hettrick-Underwood or compact, highly efficient all-in-one setups for $ {{\rm TiO}_2} $TiO2 spectroscopy with $ E/\Delta E \mathbin{\lower.3ex\hbox{$\buildrel{\displaystyle{\lt}}\over{\smash{\displaystyle\sim}\vphantom{_x}}$}} 4.5 \times {10^4} $E/ΔE∼x<4.5×104, are addressed, as well as aspects of their experimental realization.

Wave-Blocking Characteristics of Corrugated Plates under Explosion

Corrugated-board explosion-proof wall is the main means to prevent explosion shock wave damage, and it is important to study the effect of different corrugated plates on the shock wave. Using a high-speed schlieren experimental system and an air overpressure test system, the wave-blocking characteristics of different forms of corrugated plates are comprehensively studied. The schlieren images were used to analyze the influence that the corrugation shape of a corrugated plate has on the shock wave propagation characteristics. The results show that the reflection process of the triangular-, trapezoidal-, and half-cylindrical-shaped corrugated plates exhibit differences. The number of reflected waves from the triangular corrugated plate is much greater than that from the other corrugated plates, and it will consume more energy. The diffraction wave-front velocity has a trend of initially decreasing and then increasing and is also reduced by different degrees by the reflection. Comparative analysis of the schlieren images and the air shock wave overpressure test shows that plates corrugated with different corrugation shapes decrease the diffraction overpressure peak and exhibit a hysteresis.

Method to enhance the single mode fiber coupling efficiency for obscured receiver by beam shaping

Since the aperture obstruction contributes to an energy leak from the core to the sidelobe of the far field spot, the Gaussian mode of the single-mode fiber (SMF) will receive less energy leading to the coupling efficiency (CE) degradation. A method based on diffraction optical element (DOE) and wavefront corrector is introduced to reshape the plane wave with hollow uniform intensity into the plane wave with uniform intensity to improve the core energy of spot. The SMF CE with and without DOE for different central obscuration ratio is studied by numerical simulation. The DOE is effective to improve the SMF CE. Without the DOE, the CE decreases from 81% to 54% when the central obscuration ratio increases from 0 to 0.4. Compared with 54% CE at the of 0.4, the CE can increase to 72%, 78% and 80% with 4 level, 8 level and 16 level quantized DOE, respectively. It is not necessary to use the DOE beam shaper when the central obscuration ratio is small. The 4 level, 8 level and 16 level quantized DOE can obtain benefits of the CE when the central obscuration ratio is above 21.6%, 11.5% and 7%, respectively.

Diffraction of cellular detonation wave over a cylindrical convex wall

Numerical simulations were performed to study diffraction of a cellular detonation wave over a 90∘ cylindrical convex wall. The dynamics of this diffraction phenomenon was described by the two-dimensional reactive Euler equations with a detailed hydrogen/oxygen chemistry model and solved numerically by using the adaptive mesh refinement code AMROC. The present numerical observations indicate that the continuous variation trend of area divergence ratio caused by the curved convex wall can make detonation transverse wave reflect on the wall and sustain the coupling of the diffracted detonation wave for a certain distance. The reflection of the transverse waves can also enhance the energy to promote the re-intiation of the diffracted detonation. As the wall curvature radius increases to a certain value, the detonation wave can even propagate stably without decoupling in the expansion area. The critical wall curvature radius for re-initiation is found to have negative correlation with the contained detonation cell number in the exit, while the critical radius for stable propagation is mainly determined by the initial pressure. The critical re-initiation criterion for the detonation diffraction is further explored by introducing two different re-initiation mechanisms and considering the width of an “equivalent exit” calculated by the Chester-Chisnell-Whitham theory to satisfy the re-initiation condition. Meanwhile the critical criterion of stable propagation is described quantitatively by applying the Dn−κ theory to confirm the relation between the propagation velocity and the curvature of the diffracted detonation wave front, and calculating the minimum curvature radius of the curved detonation wave front theoretically. The accuracy of the criterions are verified by compared with the numerical results.

Full-field analysis of wavefront errors in point diffraction interferometer with misaligned Gaussian incidence.

The precision and accuracy of profile measurement achieved by a point diffraction interferometer (PDI) is determined by a spherical diffraction reference wavefront whose quality is mainly controlled by the pinhole's alignment. In consideration of a Gaussian beam incidence, different diffraction wavefront errors stemming from misalignment of pinhole including lateral shift, defocus, and tilt are analyzed with the help of a proposed systematic model and a new evaluation criterion established under spherical coordinates. The full-field distributions of various diffraction wavefront errors are obtained through simulation. The predicted accuracy of an actual PDI makes a good agreement with the experiment results. The achieved results will be beneficial to the accuracy evaluation of a PDI before and after its design.

Effect of the changes in refractive index of air on grating diffraction wavefront

Reduction of groove errors on the grating wavefront caused by the refractive index of air is a critical issue in ruling grating fabrication when using an interferometer to provide position feedback. We establish a mathematical model of the relationship between the grating wavefront and the refractive index of air. We then introduce two methods to measure the air’s refractive index, analyze the effects of temperature, pressure and humidity on the grating wavefront, and use the advantages of the two methods to obtain the groove error compensation value. Comparative ruling experiments prove that grating wavefront quality is significantly improved after compensation of the groove errors caused by the refractive index of air.

Complex spatiotemporal coupling distortion pre-compensation with double-compressors for an ultra-intense femtosecond laser.

In an ultra-intense femtosecond chirped-pulse amplification laser, the imperfect diffraction wave-fronts of the second and the third gratings of the compressor, where spatio-spectral coupling exists, could introduce a complex spatiotemporal coupling distortion (STCD) and degrade the pulsed beam in both near- and far-fields. Here, we propose a method of double-compressors for pre-compensation. By inserting a scaled down compressor (small compressor) with a deformable retro-reflection mirror into the beam-line, the frequency-dependent wave-front distortion, i.e., the complex STCD, could be removed. We simulate the results in two different ultra-intense femtosecond lasers with 80 and 400 nm bandwidths for comparison, and near ideal focused peak intensities could be obtained in both cases. Meanwhile, the influences of several miss-matching effects, which might appear in engineering, are also analyzed and discussed for applications.

Effect of thickness non-uniformity of large-area grating metal film on grating diffraction wavefront

As the grating area increases, the non-uniformity of the metal film thickness becomes one of the main factors affecting both the grating surface error and the wavefront of the grating diffraction order. We study the theoretical model of the relationship between the metal film thickness non-uniformity and the grating diffraction wavefront error, analyze the effects of the relevant factors on the thickness of the metal films, and determine the values of these factors using theoretical and experimental methods. We also perform a ruling experiment to verify that the wavefront quality of the grating increases with improvement in the film thickness uniformity.

A model for the trajectory of the transverse detonation resulting from re-initiation of a diffracted detonation

A semi-analytical model is presented for predicting the trajectory of the transverse detonation during the re-initiation process of a diffracted cellular detonation wave from a channel. Numerical simulations based on the two-dimensional reactive Euler equations with a detailed hydrogen/oxygen chemistry model were first performed to observe key characteristics of cellular detonation wave diffraction and to obtain required input parameters for the model construction. The present numerical observations indicate that the transverse detonation stems from a location on the expansion wave front, and the horizontal distance from this initial location to the channel exit can be scaled by a constant multiplied by the detonation cell width for large deviation angles of the channel. The velocity of the transverse detonation basically equals the Chapman–Jouguet detonation wave velocity consisting of two orthogonal components: the expansion velocity of the diffracted wave front and the relative velocity to the diffracted wave front. The shape of the decoupled wave front is not affected by local explosion and thus can be predicted by the Chester–Chisnell–Whitham theory. Based on these numerical observations and the Chester–Chisnell–Whitham theory, a semi-analytical model is constructed to predict the wave trajectories as well as the distances of the wall reflection point for various deviation angles and initial pressures. The model prediction agrees with the corresponding numerical results. The model result shows that the distance of the wall reflection point varies from 15 to 20 multiples of the cell width with a minimal dependence on deviation angle, independent of the initial pressure. The trajectory calculated by the model is self-similar and determined by the horizontal distance of the initial location. The dimensionless trajectories divided by the horizontal distance are coincident for different initial pressures.

Real time monitoring technology for full aperture grating diffraction wavefront with high frequency error

To improve the grating ruling efficiency and success rate, this report documents a method to indirectly measure the error trajectory of space coordinates produced by ruling and indexing systems. The errors were corrected based on the proposed active control system. According to the residual errors after correction, a mathematical model of the full aperture grating diffraction wavefront with high frequency error information was reconstructed in real time. Based on this mathematical model, two gratings were ruled with or without the aid of an error correction system, respectively, and the reconstructed grating diffraction wavefront values were obtained to verify the effectiveness of this method. For larger gratings, the grating diffraction wavefront can also be reconstructed in real time with long time ruling. The experimental result demonstrated that the grating quality can be judged by monitoring the grating diffraction wavefront in real time.

Precision optical path alignment system for point diffraction interferometer based on image information.

In a point diffraction interferometer, the existence of alignment error between an objective convergent spot and a diffraction pinhole can lead to wavefront error and diffraction intensity reduction. Meanwhile, the contrast of the point diffraction interferograms probably decreases in this procedure. These changes will have significant influence on its inspection precision. A precise alignment system of an optical path for a point diffraction interferometer is proposed in this paper. First, diffraction theory is used to analyze the mathematical relationships of alignment error to diffraction wavefront error and numerical aperture and wavefront error to pinhole size. Then, according to the requirement, the scheme of an optical path alignment system is designed. In this stage, alignment images as well as intensities of a reflected and diffracted beam from the point diffraction plate will be acquired. In addition, an image processing algorithm for measuring alignment error is designed, and a mathematical model between quantities of measurement and control is constructed. Finally, implementation and experiment of this method are also introduced. Misalignment situations, including lateral translation, longitudinal defocus, and tilt error, are well eliminated, and the quality of interferograms is also improved. From the results, it can be concluded that the system is of desirable precision and efficiency.

Fast method to detect and calculate displacement errors in a Littrow grating-based interferometer.

Grating-based interferometers play important roles in precision displacement measurements. Gratings are the core components of grating-based interferometers, and grating surface errors and line errors seriously affect measurement accuracy, especially in systems with Littrow configurations. A fast, accurate method to calculate displacement errors caused by grating surface errors and line errors in a grating-based interferometer with a Littrow configuration is proposed. Displacement errors are calculated using the diffracted wavefronts at the ±1st orders of the grating. Experimental comparison of the displacements of a grating-based interferometer and a laser interferometer verifies the correctness of the proposed method. The differences between the calculated and measured displacement error results are within 40nm. The method is accurate, fast, and low cost and is highly significant for system error compensation and improvement of the measurement accuracy of grating-based interferometers.