The successful exploitation of X-ray beams generated by modern synchrotron light sources, depends on a significant development of X-ray optics. X-ray mirrors are widely used at synchrotron light facilities for micro- and nano-focusing because of their achromaticity and large acceptance aperture. Moreover, X-ray active mirrors, such as bimorph and mechanically bendable mirrors, are widely used to generate either focused or defocused beams at Diamond Light Source. Although ex-situ metrology plays valuable role for measurement of X-ray mirrors [1-4], it is equally important to perform in-situ ccharacterization and optimisation of X-ray mirrors to achieve best performance under beamline conditions [5, 6]. In addition, accurate in-situ metrology is also essential to achieve diffraction-limited and coherence preserved beams . Over the last two decades, several in-situ metrology techniques have been developed to evaluate the performance of various X-ray optics [8-12]. Among them, the speckle based technique shows great potential for wide application since it can provide ultra-high angular sensitivity with simple experimental setup [13, 14]. To apply this technique to a range of beamlines for in-situ characterization of X-ray mirrors, a portable in-situ metrology device [15-17] needs to be developed. Here, we present the development and implementation of a portable metrology device based on the X-ray speckle-based approach. We demonstrate the performance of this device by optimising the performance of a bimorph X-ray mirrors and testing alignment of an X-ray mirror.
DEVELOPMENT OF THE IN-SITU METROLOGY DEVICE
A schematic of the mechanical layout of the device is shown in Figure 1. The entire setup has been purposefully designed on a modular base frame for coarse alignment and ease of portability. Such a frame can readily be fitted onto virtually any beamline. The diffuser is mounted on a piezo stage for precision scanning, which in turn is mounted on an assembly of three linear stages for alignment of the diffuser with the direct or reference X-ray beam. In addition, crossed gold wires of 200µm diameter are attached to the piezo stage to permit measurement of the X-ray beam size. Coarse alignment is performed manually, and the distance between the mirror focus and the diffuser can be freely chosen so as to optimize the angular sensitivity.
Further downstream, a CCD detector with a pixel size of 6.5µm is used to record the speckle pattern. A photodiode detector is also mounted on the detector stage to perform knife edge scan and measure the X-ray beam size. Both detectors are mounted on horizontal and vertical motorized translation stages for ease of alignment with the X-ray beam. All motorized stages are remotely controlled with an accuracy of 1µm via the Experimental Physics and Industrial Control System (EPICS) based on a Geo Brick LV system . This feature is especially useful if there is a need to characterize composite optics, such as Kirkpatrick-Baez (K-B) mirrors. Experiments were conducted at the Test beamline B16 at Diamond to test the functionality of the device. The photograph of the experimental assembly as installed on the beamline is shown in the bottom part of Figure 1. The portable system, consisting of the diffuser and detector, was mounted downstream of the test mirror on an optical table. The diffuser can be scanned either vertically or horizontally to retrieve the tangential slope error of the test mirrors. A standalone MATLAB GUI was used to calculate the wavefront radius of curvature by tracking the speckle displacement with cross-correlation algorithm .
APPLICATION FOR AT-WAVELENGTH METROLOGY
Characterization of an elliptical mirror
To investigate the functionality of the device, an elliptical mirror was characterized with three methods: in-situ with the diffuser placed upstream and downstream respectively (portable device), and ex-situ using the Diamond-NOM slope profilometer . Optical slope errors measured using the different techniques are shown in Figure 2. The design parameters of the mirror tested are: source to mirror distance p = 41.5 m, mirror to focus distance q = 0.1 m, and grazing incidence angle θ = 3 mrad. The polished region (70mm) of the mirror was fully illuminated with monochromatic 15keV X-rays from a double crystal monochromator (DCM). 80 images with a step size of 0.25 micron were collected to measure the tangential wavefront slope error for both in-situ measurements. As seen in Figure 2, the in-situ metrology measurements with the upstream diffuser agree well with the ex-situ Diamond-NOM data. It should be noted that the Diamond-NOM and the upstream diffuser measurements are directly related to errors on the mirror’s surface , whereas the downstream configuration measures the wavefront slope errors . One possible reason for the low frequency discrepancy between the downstream data and the other methods is that an ellipse was removed from slope data from the Diamond-NOM and the upstream scans, whereas only a simple linear fit was used to derive the wavefront slope error. Nevertheless, it is reassuring to see the same optical polishing errors appearing in all three sets of measurements.
Optimization of a bimorph mirror
To assess the feasibility of using the portable device for optimizing an active X-ray mirror, a deformable piezo bimorph mirror with 8 electrodes was investigated. The active length of the mirror is 120 mm, and it has an elliptical shape with: p = 41.5 m, q = 0.4 m, and θ = 3 mrad. The mirror was mounted on a motorized tower in the experimental hutch of B16 at 47m from the X-ray source. Since the mirror substrate is uncoated silica, X-rays with energy of 9.2 keV were selected by a DCM for good X-ray reflectivity. A standalone MATLAB GUI was used to calculate how each of the bimorph’s piezos respond to an applied voltage, the so-called piezo-response functions (PRF), by subtracting the values of wavefront slope (or inverse of radius of curvature) extracted from the jth to (j − 1)th measurement. PRF was obtained by incrementally applying 400V to each piezo electrode. Here, the PRF was determined in terms of inverse of radius of curvature for fast optimization and convergence. After deriving the PRF, the first set of optimized voltages gets automatically calculated and displayed on the GUI for user convenience. Values are also archived for further processing. To reduce the mirror’s slope error, voltages generated in the first iteration were applied to relevant electrodes, and another stack of speckle images was collected to evaluate the new error of the wavefront radius of curvature for a second iteration. This process is repeated until convergence occurs. A few iterations are typically sufficient to minimize the slope error and obtain the optimal set of voltages that gives the best X-ray focus. Figure 3 shows the measured wavefront slope error after application of voltages obtained for successive iterations. Slope error was reduced from 2.3 µrad (r.m.s) to 0.2 µrad (r.m.s) in three iterations only.
Alignment of an X-ray mirror
In addition to the characterization and optimization of X-ray mirrors, the portable device can also be used for in-situ alignment of X-ray mirrors. To demonstrate this, we used the same bimorph mirror as described in section 3.2. The portable device was placed outside the focal plane of the mirror, and the distance between the mirror and detector was set to L=1400 mm so as to increase, both the angular sensitivity and the spatial resolution of wavefront error measurement. For an elliptical focusing mirror, the wavefront error includes contributions from the upstream wavefront error, the mirror slope error and the aspherical error due to misalignment of mirror pitch angle. Therefore, the measured wavefront error will be higher if the mirror angle deviates from the designed value. This fact can be used to estimate and thus correct the misalignment of the mirror pitch angle. For this, a stack of speckle images is recorded by scanning the piezo position, and the same scan is repeated by varying the mirror angle pitch angle from 0.167° to 0.187°. The measured wavefront error (Aδ) and the corresponding wavefront radius of curvature (R) are shown in Figure 4. The wavefront radius of curvature decreases with an increase in the pitch angle, and it indicates that the mirror focal length f=L-R moves further downstream with the increase in the mirror pitch angle. As shown in Figure 4, the minimum of the wavefront error is at the pitch angle of 0.177° (blue dotted line) rather than the design value of 0.172°. It indicates that there is an angular offset in the mirror pitch angle settings. It should be noted that the more commonly used conventional knife edge scan technique is quite time consuming as several measurements are required to find the minimum beam size along the beam path. In contrast, the measurement process with the portable device is relative fast (1-2 minutes) for each pitch angle, where both the wavefront error and the wavefront radius of curvature can be derived simultaneously. It demonstrates that the speckle-based portable device can be routinely used for fast mirror alignment.
A speckle-based portable device has been developed for in-situ and at-wavelength metrology of X-ray mirrors at Diamond Light Source. We demonstrate that the best focus can be achieved within a few iterations for a bimorph mirror using this device. In addition, we show that the portable device can be used for in-situ characterization, optimization and alignment of X-ray mirrors. This compact device can be easily implemented on a variety of operational beamlines. This fast, compact and accurate speckle-based device is expected to find wide applications for in-situ characterization and optimization of X-ray mirrors for synchrotron radiation community.
This work was carried out with the support of the Diamond Light Source Ltd UK. We would like to acknowledge Andrew Malandain and Ian Pape for their technical assistance.
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