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A real-time and accurate characterization of the X-ray beam size is essential to enable a large variety of different experiments at free-electron laser facilities. Typically, ablative imprints are employed to determine shape and size of µm-focused X-ray beams. The high accuracy of this state-of-the-art method comes at the expense of the time required to perform an ex-situ image analysis. In contrast, diffraction at a curved grating with suitably varying period and orientation forms a magnified image of the X-ray beam, which can be recorded by a 2D pixelated detector providing beam size and pointing jitter in real time. In this manuscript, we compare results obtained with both techniques, address their advantages and limitations, and demonstrate their excellent agreement. We present an extensive characterization of the FEL beam focused to ≈1 µm by two Kirkpatrick-Baez (KB) mirrors, along with optical metrology slope profiles demonstrating their exceptionally high quality. This work provides a systematic and comprehensive study of the accuracy provided by curved gratings in real-time imaging of X-ray beams at a free-electron laser facility. It is applied here to soft X-rays and can be extended to the hard X-ray range. Furthermore, curved gratings, in combination with a suitable detector, can provide spatial properties of µm-focused X-ray beams at MHz repetition rate.

The European XFEL is a free-electron laser (FEL) with a superconducting linear accelerator and three beamlines (SASE1, SASE2, and SASE3) covering the energy range from 250 eV to 24 keV. The SASE3 beamline is dedicated to the soft x-ray range (0.25-3 keV) and is designed to operate in both monochromatic and non-monochromatic mode. A variable line spacing - plane grating (VLS-PG) monochromator is placed along the beam transport system for the monochromatic mode. The VLS parameters of the grating profile are challenging from a manufacturing and measuring perspective, especially at the desired length of 530 mm. A shorter grating of 150 mm has been procured to allow early operation of the facility. We describe the characterization method that was used to assess the VLS parameters of the grating using Fizeau interferometry. The method is intrinsically absolute and limited only by the quality of the test grating and the noise level. Further measurements using a white-light-interferometry profilometer are also reported. We discuss the possibility of extending the method to the future 530 mm long grating.

A precise spectral characterization of every single pulse is required in many x-ray free-electron laser (XFEL) experiments due to the fluctuating spectral content of self-amplified spontaneous emission (SASE) beams. Bent single-crystal spectrometers can provide sufficient spectral resolution to resolve the SASE spikes while also covering the full SASE bandwidth. To better withstand the high heat load induced by the 4.5 MHz repetition rate of pulses at the forthcoming European XFEL facility, a spectrometer based on single-crystal diamond has been developed. We report a direct comparison of the diamond spectrometer with its Si counterpart in experiments performed at the Linac Coherent Light Source.

We propose a method to control and to adjust in a closed-loop a bendable x-ray mirror using displacement-measuring devices. For this purpose, the usage of capacitive and interferometric sensors is investigated and compared. We installed the sensors in a bender setup and used them to continuously measure the position and shape of the mirror in the lab. The sensors are vacuum-compatible such that the same concept can also be applied in final conditions. The measurement is used to keep the calibration of the system and to create a closed-loop control compensating for external influences: in a demonstration measurement, using a 950 mm long bendable mirror, the mirror sagitta is kept stable inside a range of 10 nm Peak-To-Valley (P-V).

A method to provide absolute planarity measurements through an interferometric oblique incidence setup and an iterative algorithm is presented. With only three measurements, the calibration of absolute planarity is achieved in a fast and effective manner. Demonstration with synthetic data is provided, and the possible application to very long flat mirrors is pointed out.

A model for the optical path difference introduced by a soap bubble in transmission is described. The model is then used with interferometric data to solve for the fringe order, and to define a procedure to extract the global film thickness in presence of turbulence flows occurring during the drainage process due to gravity. Experimental results on soap bubbles examined in single-pass phase-shift interferometry are presented.

An accurate control of the optical properties of single crystal diamond during microfabrication processes such as ion implantation plays a crucial role in the engineering of integrated photonic devices. In this work we present a systematic study of the variation of both real and imaginary parts of the refractive index of single crystal diamond, when damaged with 2 and 3 MeV protons at low-medium fluences (range: 10(15) - 10(17) cm(-2)). After implanting in 125 × 125 μm(2) areas with a scanning ion microbeam, the variation of optical pathlength of the implanted regions was measured with laser interferometric microscopy, while their optical transmission was studied using a spectrometric set-up with micrometric spatial resolution. On the basis of a model taking into account the strongly non-uniform damage profile in the bulk sample, the variation of the complex refractive index as a function of damage density was evaluated.

Cases of long-term deformation of fused silica flats are reported. The phenomenon is detected at the scale of the nanometer, and exhibits a time constant of the order of 9 years. The observed deformation appears related to gravity and constraints, but a change of physical properties locally resulting in non-homothetic behavior is also hypothesized.

An iterative algorithm to analyze three-flat test data for absolute planarity measurements is presented. Using the properties of Zernike polynomial representations, results are achieved in a fast and effective manner. Details and demonstrative examples are provided.

Absolute planarity measurements by interferometry are classically made using three flats, compared two by two in the course of four or more tests. Data reduction is performed with various analytical methods. Here we present instead a data processing algorithm that converges to solution numerically by iteration. Examples are presented both on synthetic interferograms and on experimental data. High accuracy and versatility of the approach are demonstrated.