An automated approach to the alignment of compound refractive lenses

Abstract

Compound refractive lenses (CRLs) are established X-ray focusing optics, and are used to focus the beam or image the sample in many beamlines at X-ray facilities. While CRLs are quite established, the stack of single lens elements affords a very small numerical aperture because of the thick lens profile, making them far more difficult to align than classical optical lenses that obey the thin-lens approximation. This means that the alignment must be very precise and is highly sensitive to changes to the incident beam, often requiring regular readjustments. Some groups circumvent the full realignment procedure by using engineering controls (e.g. mounting optics) that sacrifice some of the beam's focusing precision, i.e. spot size, or resolution. While these choices minimize setup time, there are clear disadvantages. This work presents a new automated approach to align CRLs using a simple alignment apparatus that is easy to adapt and install at different types of X-ray experiments or facilities. This approach builds on recent CRL modeling efforts, using an approach based on the Stochastic Nelder-Mead (SNM) simplex method. This method is outlined and its efficacy is demonstrated with numerical simulation that is tested in real experiments conducted at the Advanced Photon Source to confirm its performance with a synchrotron beam. This work provides an opportunity to automate key instrumentation at X-ray facilities.

Keywords: alignment; beamline optics; compound refractive lens; optimization.

Figure 1

Schematic of the basic layout for the alignment detector, detailed in the blue box labeled Removable Alignment Camera, showing how it fits into a synchrotron experiment. We note that most of the detector optics can be customized based on the availability and beam parameters to set the magnification and field of view for the alignment system.

Figure 2

Three examples of positions in the search space with the corresponding conditions for alignment and noise issues. Image (a) shows the spot from a well aligned CRL, producing a tight and bright spot, while (b) shows a diffuse tail demonstrating its misalignment, and (c) shows only a diffuse streak from worse alignment still.

Figure 3

Here we directly compare (a) a high-resolution 2D raster scan of the FOM intensity F(p, M = 2) and (b) a Gaussian regressions of a lower-resolution 4D raster scan. Both scans depict a feature-scaled scan over (z, r _y ), fixing the remaining variables at

Figure 4

Panels (a), (b), and (c) depict I ₀, I ₆, and I ₆₂, respectively, which correspond to p ₀, p ₆, and p ₆₂, the initial, sixth, and final ‘best’ position recorded during one execution of Algorithm A.1. Evaluating each image with the FOM (3), we see that and correspond, respectively, to 14.03% and 48.29% of when M = 2.0.

Figure 5

We present the route taken by Algorithm A.1 ascending the FOM (6). We overlaid the 16 sequential ‘best’ positions upon a surface plot of the raster scans. Panel (a) depicts the z and r _y axes, and the y and r _z axes can be seen in panel (b). The opacity of the surface was decreased so the full paths remain visible.

Figure 6

Together, these scatter plots depict the best motor position recorded prior to manual termination of 30 executions of Algorithm A.1 (blue dots). The cross (red) represents the average of these recorded positions. We further illustrate the 68, 95, and 99.7% uncertainty regions as concentric ellipses centered at the mean. Panel (a) presents the z and r _y axes, while the y and r _z axes are in given in panel (b). Each execution was initialized from the same region in Ω, but the initial simplex was selected randomly (distributed uniformly) about p ₀.

Figure 7

Depicted are the spatial results of three Monte Carlo simulations, in two of the four total dimensions. We varied the additive noise parameter ς between each sampling. Panel (a) depicts the case where ς = 5.0 × 10⁻⁴, (b) shows the case where ς = 5.0 × 10⁻³, and (c) shows the ς = 5.0 × 10⁻² case. All results are depicted as blue scatter points above three blue confidence regions. The mean result is presented as a red cross.

Figure 8

Depicted are the spatial results of three Monte Carlo simulations, in two of the four total dimensions. We included the simulated beam jitter, and fix the additive noise parameter ς = 5.0 × 10⁻³, varying the reflection parameter within Algorithm A.1. Panel (a) shows our default choice, α = 1.0, panels (b) and (c) decrease the parameter to α = 0.75 and 0.5, respectively. The results are depicted as blue scatter points above three confidence regions, and a red cross depicting the mean result.