Stigmatic grazing-incidence flat-field grating spectrograph

Spatiotemporal response of concave VLS grating to ultra-short X-ray pulses

In soft X-ray free-electron laser (FEL) beamlines, variable-line-spacing (VLS) gratings are often used as dispersive components of monochromators and spectrometers due to their combined dispersion and focusing properties. X-ray FEL pulses passing through the VLS grating can result in not only transverse focusing but also spatiotemporal coupling effects, such as pulse front tilt, pulse front rotation, and pulse stretching. In this paper, we present a theoretical study of the spatiotemporal response of concave VLS gratings to ultra-short X-ray pulses. The theoretical analysis indicates that the tilt angle of the non-zero diffraction orders varies with the propagation distance, and disappears at the focus, where the focal lengths and pulse stretching differ for different diffraction orders. The model demonstrates the pulse duration after the concave VLS grating is the convolution of the initial pulse duration and the stretching term induced by dispersion, while the beam size at the focus in x dimension is the convolution of the geometric scaling beam size and the dispersion term. This work provides a mathematical explanation for the spatiotemporal response of concave VLS grating to ultra-short X-ray pulses and offers valuable insights into the design of FEL grating monochromators, spectrometers, pulse compressors, and pulse stretchers.

Towards an extremely high resolution broad-band flat-field spectrometer in the `water window'

The optical design of a novel spectrometer is presented, combining a cylindrically convex pre-mirror with a cylindrically concave varied-line-spacing grating (both in the meridional) to deliver a resolving power of 100000-200000 in the `water window' (2-5 nm). Most remarkably, the extremely high spectral resolution is achieved for an effective meridional source size of 50 µm (r.m.s.); this property could potentially be applied to diagnose SASE-FEL and well resolve individual single spikes in its radiation spectrum. The overall optical aberrations of the system are well analysed and compensated, providing an excellent flat-field at the detector domain throughout the whole spectral range. Also, a machine-learning scheme - SVM - is introduced to explore and reconstruct the optimal system with high efficiency.

High-resolution stigmatic spectrograph for a wavelength range of 12.5-30 nm

We describe a broadband (12.5-30 nm) extreme ultraviolet (XUV) spectrograph, which is stigmatic throughout its operating range. The instrument employs a near-normal-incidence aperiodic Mo/Si multilayer mirror and a grazing-incidence plane varied line-space (VLS) grating. Strict stigmatism is fulfilled simultaneously at two wavelengths and the condition of practical stigmatism is fulfilled over two octaves in wavelength. The vertically space-resolved line spectra of multiple charge ions from laser plasma were recorded to demonstrate a spectral resolving power of 10³ and a spatial resolution of ~26 μm, both figures corresponding to two detector pixels. The electron density was evaluated from the Stark broadening of the Balmer line Hβ (135 Å) of C VI in the plasma excited by 0.5 J, 8 ns, 1.06 μm pulses.

A sagittally confined high-resolution spectrometer in the `water window'

The authors report a novel scheme for a grazing-incidence spectrometer forming an excellent meridional flat field in its detector domain to deliver the desired spectral resolution throughout the full designated spectral range, while reducing the sagittal astigmatism substantially to enhance the spectral intensity. The optical properties of the system are thoroughly investigated and optimized, and the detector plane is fitted well to the meridional or sagittal focal curves. The authors demonstrated that a resolving power of 6000-18000 could be achieved within the `water window' (2-5 nm) for an effective meridional source size of 200 µm (r.m.s.), and it would be further improved to 20000-40000 if the source size was confined to 50 µm (r.m.s.).

Laser differential confocal radius measurement method for the cylindrical surfaces

This paper proposes a laser differential confocal cylindrical radius of curvature measurement (DCCRM) method for high accuracy measurement of the radius of curvature of the cylindrical lens. Based on the property that the null point of an axial intensity curve precisely corresponds to the focus of the objective in a differential confocal system (DCS), the DCCRM uses the null point of the DCS axial intensity curve to precisely identify the cat's eye position and confocal position of the test cylindrical lens. The distance between the two positions is measured accurately using a laser distance instrument, thus achieving high precision radius measurement. In comparison with existing measurement methods, the proposed DCCRM has high measurement precision and strong environmental anti-interference capability. Theoretical analyses and preliminary experimental results indicate that the DCCRM has a relative measurement uncertainty of better than 0.03% and provides a new approach for a high precision radius measurement of the cylindrical lens.

Grazing-incidence spectrometer for soft X-ray solar imaging spectroscopy

The design and realization of a stigmatic grazing-incidence instrument for space applications to solar imaging spectroscopy is presented. We propose an optical layout in which imaging and spectral capabilities are decoupled by the use of crossed cylindrical mirrors. The design consists of a double telescope and a spectrograph: telescope I consists of a single cylindrical mirror with parabolic section, focusing the radiation on the entrance slit of the spectrograph in the spectral dispersion plane; telescope II consists of two cylindrical mirrors with aspherical section in Wolter configuration focusing the radiation on the spectrograph focal plane in the direction perpendicular to the spectral dispersion plane; the spectrograph consists of a grazing-incidence spherical variable-line-spaced grating with flat-field properties. Telescope II is crossed with respect to the grating and telescope I, i.e., is mounted with its tangential planes coincident with the grating equatorial plane, to decouple spectral and spatial focusing properties. The spectral resolution is preserved also for off-axis angles. The instrument that has been realized operates in the 4-26 nm spectral range and has a field of view of 0.5 deg to image the full Sun disk.

Optical design of a stigmatic extreme-ultraviolet spectroscopic system for emission and absorption studies of laser-produced plasmas

The design of a stigmatic spectroscopic system for diagnostics of laser-produced plasmas in the 2.5-40-nm region is presented. The system consists of a grazing-incidence toroidal mirror that focuses the radiation emitted by a laser-produced plasma onto the entrance slit of a spectrograph. The latter has a grazing-incidence spherical variable-line-spaced grating with flat-field properties coupled to a spherical focusing mirror that compensates for the astigmatism. The mirror is crossed with respect to the grating; i.e., it is mounted with its tangential plane coincident with the equatorial plane of the grating. The spectrum is acquired by an extreme-UV- (EUV-) enhanced CCD detector with high quantum efficiency. This stigmatic design also has spectral and spatial resolution capability for extended sources: The spectral resolution is also preserved for off-plane points, whereas the spatial resolution decreases for points far from the optical axis. The expected performance is presented and compared with that of a stigmatic design with a plane variable-line-spaced grating illuminated in converging light.

Grazing-incidence telescope-spectrograph for space solar-imaging spectroscopy

The design of a stigmatic grazing-incidence instrument for space applications to solar-imaging spectroscopy is presented. It consists of a double telescope and a spectrograph: Telescope I consists of a single cylindrical mirror with parabolic section, focusing the radiation on the entrance slit of the spectrograph in the spectral dispersion plane; telescope II consists of two cylindrical mirrors with aspherical section in a Wolter configuration, focusing the radiation on the spectrograph focal plane in the direction perpendicular to the spectral dispersion plane. The spectrograph consists of a grazing-incidence spherical variable-line-spaced grating with flat-field properties. Telescope II is crossed with respect to the grating and telescope I; i.e., it is mounted with its tangential planes coincident with the grating equatorial plane. The spectrum is acquired by a detector mounted at near-normal incidence with respect to the direction of the exit beam. The spectral resolution is also preserved for off-axis angles. The effective collecting area of the instrument can be preserved by adoption of a nested configuration for telescope II without degradation of the spectral resolution.

Design of a high-throughput grazing-incidence flat-field spectrometer

The optical design of a high-throughput grazing-incidence flat-field spectrometer is presented. The spectral focal curve is almost a straight line because of the flat-field focusing properties of spherical variable-line-spaced gratings. The angular acceptance in the direction perpendicular to the plane of dispersion is maximized by means of a focusing spherical mirror mounted with its tangential plane coincident with the sagittal plane of the grating. Analytical calculations for the determination of the optimum mirror parameters are presented. A spectrometer for high-throughput experiments in the 800-60-eV region is designed with an extreme-ultraviolet-enhanced CCD detector: when the available flux is compared with that of a spectrometer with the same kinds of grating and detector but without a focusing mirror, the increase is as much as a factor 3.

Space-resolving flat-field extreme ultraviolet spectrograph system and its aberration analysis with wave-front aberration

The Nam aberration of a flat-field extreme ultraviolet spectrograph system, composed of a varied line-spacing concave grating and a toroidal mirror, was analyzed by calculating the wave-front aberration with respect to an astigmatic reference surface. The toroidal mirror was used to compensate for the astigmatism that was due to the grazing incidence of light at the concave grating. The spectrograph system could form a space-resolved spectrum along the sagittal direction. The spectral and spatial resolutions of the spectrograph system were estimated from the root-mean-square spot size. The actual spectral resolution of the spectrograph system was measured from extreme ultraviolet spectra obtained from plasmas produced by an iodine laser having an energy of 0.5 J in a 4-ns duration, and it was compared with the calculated value.

High-gain x-ray lasing at 11.1 nm in sodiumlike copper driven by a 20-J, 2-ps Nd:glass laser

Evidence of high gain pumped by recombination has been observed in the 5g-4f transition at 11.1 nm in sodiumlike copper ions with use of a 20-J 2-ps Nd:glass laser system. The time- and space-integrated gain coefficient was 8.8 +/- 1.4 cm(-1), indicating a single-transit amplification of ~60 times. This experiment has shown that 2 ps is the optimum pulse duration to drive the sodiumlike copper recombination x-ray lasing at 11.1 nm.