Dimensional and optical metrology of ultra-stable exactly-constrained KB mirror sets

Abstract

At 4th-generation synchrotron nanoprobes with optimized photon density, focusing optics systems often require mirrors arrangements with high demagnification factors to achieve diffraction-limited beam sizes (∠ 100 nm) and still high photon flux. All the components’ contributions to the surface error must be at the same level (a few nanometers) and angular stability (lower than 10 nrad RMS) becomes a bottleneck issue. Therefore, the design of ultra-stable mirror mechanics has to follow a systems perspective, where precision engineering, metrology and alignment strategies are considered simultaneously. For the latest design at Sirius/LNLS, an exactly-constrained KB set with minimum number of adjustment degrees for increased stiffness and stability was also bounded by an alignment error budget in the order of tens of microns by construction, pushing metrology limits during alignment and validation phases. This work presents a two-phase strategy for metrology-assisted assembly and figure validation of elliptical mirror sets, starting at a Fizeau Interferometer system (FZI) and finishing at a Coordinate Measuring Machine (CMM). The first phase validates surface quality by scanning mirror position and automatically realigning interferometry fringe patterns, while pixel-level stitching techniques are employed to characterize the surface error over the mirror’s length. The stitching algorithm includes self-calibration of lens errors and uses multiple CPU cores for expedite processing. The second phase consists of fiducializing the elliptical figures of each mirror into their own substrates and assembling both mirrors with regard to each other by using a least-squares fit of the center and rotation angle of each fixed ellipse, obtained from the manufacturer’s documentation, and confirmed at the first phase. This workflow was applied and demonstrated at an ultra-stable exactly-constrained KB system, reaching sufficient alignment accuracy.

Diagnostics of KB mirrors misalignments using Zernike rectangular polynomials and neural networks

“…The alignment tolerances for the TARUMÃ KB mirrors have been previously studied with geometric optics 15 and are presented in table 1, together with the accuracy of alignment during the installation procedure of the KB mirrors. 16 The alignment tolerances are defined as the amount of misalignment needed to increase the beam size by more than 10% at best focus.…”