Nano-precision metrology of X-ray mirrors with laser speckle angular measurement

Sub-nanometre quality X-ray mirrors created using ion beam figuring

Ion beam figuring (IBF) is a powerful technique for figure correction of X-ray mirrors to a high accuracy. Here, recent technical advancements in the IBF instrument developed at Diamond Light Source are presented and experimental results for figuring of X-ray mirrors are given. The IBF system is equipped with a stable DC gridded ion source (120 mm diameter), a four-axis motion stage to manipulate the optic, a Faraday cup to monitor the ion-beam current, and a camera for alignment. A novel laser speckle angular measurement instrument also provides on-board metrology. To demonstrate the IBF system's capabilities, two silicon X-ray mirrors were processed. For 1D correction, a height error of 0.08 nm r.m.s. and a slope error of 44 nrad r.m.s. were achieved. For 2D correction over a 67 mm × 17 mm clear aperture, a height error of 0.8 nm r.m.s. and a slope error of 230 nrad r.m.s. were obtained. For the 1D case, this optical quality is comparable with the highest-grade, commercially available, X-ray optics.

Ion beam figuring for X-ray mirrors: history, state-of-the-art and future prospects

Synchrotron light sources require X-ray optics with extremely demanding accuracy for the surface profile, with less than 100 nrad slope errors and sub-nanometre height errors. Such errors are challenging to achieve for aspheres using traditional polishing methods. However, post-polishing error correction can be performed using techniques such as ion beam figuring (IBF) to improve optics to the desired quality. This work presents a brief overview of the history of IBF, introduces some of the challenges for obtaining such demanding figure errors, and highlights the work done at several in-house IBF facilities at synchrotron light sources worldwide to obtain state-of-the-art optical quality.

A nano-radian precision absolute local slope measurement method for X-ray reflectors

Ultra-precise reflectors in the advanced light source facilities urgently call for local slope error measurements with nano-radian precision. However, the existing methods currently utilized in the long trace profiler systems struggle to meet the requirements. In this paper, we present a weak-value amplification enhanced absolute local slope measurement scheme, in which the surface height difference between two adjacent points can be measured directly with precision on the pico-meter level. As a result, the absolute local slope measurement reaches a record precision level of 9.7 nrad (RMS) with a small lateral separation of 0.5 mm. Comparing to the existing methods, our scheme is more disturbance-resistant, more compact and cost-effective. The local curvature measuring capability is also validated with two synchronously parallel local slope measurement paths, between which the separation is set as 2mm. A local curvature measurement is obtained with precision of 3.4 × 10^-6m^-1 (RMS) and its corresponding slope variation is 6.8 nrad. Our method exhibits important application prospects in the field of ultra-precise surface fabrication inspection.

Distributed focusing reduces mirror error sensitivity on x-ray beamlines

The appearance of very low emittance, high-power synchrotron sources has resulted in ever longer beamlines, often requiring a very weak curvature on the mirrors that transport the beam to the experiment, where the radius of curvature is on the order of kilometers. Manufacturing weakly curved, low figure error grazing incidence mirrors is difficult as the mirrors must be manufactured to an accuracy comparable to the wavelength of the transmitted light. Often the delivered mirrors have figure errors at various length scales (general shape, slope errors, roughness), which compromise image quality. An error in general shape, like the radii of a toroidal mirror, results in long-sighted or short-sighted imaging that is not so simply corrected by changing the distances and incidence angles as the mirror controls the beam focus in both vertical and horizontal directions; for a toroidal mirror, the tangential and sagittal radii need to match correctly for the desired focusing effect. Adaptive downstream optics can compensate for this. In this paper, an alternative method to reduce the sensitivity to a large radius error outside the specified tolerance range in the first mirror of a plane grating monochromator beamline at MAX IV is presented. It is found that distributed focusing by two passive, fixed radius mirrors reduces greatly the sensitivity to the radius errors in both mirrors. The radius tolerance of a mirror initially found to be unacceptable for single stage focusing is easily accommodated on both mirrors in distributed focusing, without compromising the imaging capability.

Mixed stitching interferometry with correction from one-dimensional profile measurements for high-precision X-ray mirrors

This work presents a mixed stitching interferometry method with correction from one-dimensional profile measurements. This method can correct the error of stitching angles among different subapertures using the relatively accurate one-dimensional profiles of the mirror, e.g., provided by the contact profilometer. The measurement accuracy is simulated and analyzed. The repeatability error is decreased by averaging multiple measurements of the one-dimensional profile and using multiple profiles at different measurement positions. Finally, the measurement result of an elliptical mirror is presented and compared with the global algorithm-based stitching, and the error of the original profiles is reduced to one-third. This result shows that this method can effectively suppress the accumulation of stitching angle errors in classic global algorithm-based stitching. The accuracy of this method can be further improved by using high-precision one-dimensional profile measurements such as the nanometer optical component measuring machine (NOM).

Fast wavefront sensing for X-ray optics with an alternating speckle tracking technique

Advances in accelerator technologies have enabled the continuous development of synchrotron radiation and X-ray free electron laser (XFEL) sources. At the same time, it has been critical to perform in-situ wavefront sensing to aid delivery of high-quality X-ray beams to the end users of these facilities. The speckle-based scanning technique has obtained popularity due to its high spatial resolution and superior sensitivity compared to other wavefront sensing methods. However, these advantages often come at the expense of longer data acquisition times since multiple images have to be collected to derive the necessary wavefront information. Whereas initial speckle tracking techniques could obtain wavefront information relatively quickly, the installation of additional hardware was routinely required to do so. Here, we propose a novel speckle-based approach, termed Alternating Speckle Tracking (AST), to perform fast wavefront sensing within a conventional beamline setup. The wavefront information derived from the new technique has proven to be valuable for many applications that require temporal resolution. Importantly, both horizontal and vertical wavefront information can be simultaneously derived by moving the speckle generator along the diagonal direction. We expect this method will be widely used by the synchrotron radiation and XFEL community in the future.