High-efficiency coherence-preserving harmonic rejection with crystal optics

A coherence-preserving harmonic-rejection scheme based on parallel crystal optics that achieves a total flux ratio of harmonic radiation to fundamental radiation on the order of 10−10 or lower is reported.

This Supporting Information documents the method we used to measure the flux ratio of the harmonic radiation (n = 3) to the fundamental radiation prior to their entrance to the harmonic-rejection crystal pair.
For this analysis, we used Al and Ti X-ray filters. Each set has 4 filters permitting thickness increments in 0.25 mm steps, i.e., either an Al or Ti total thickness of 0.25 mm, 0.50 mm, 0.75 mm, or 1.00 mm. We used a photodiode detector (First Sensor AG * , Berlin, Germany) to detect the transmitted X-ray intensity.
This photodiode detector is known to deliver a linear detection response in electrical current to X-ray intensity over a range exceeding 10 orders of magnitude. We placed the monochromator crystals in the beam (after the undulator) to analyze the photon flux of both the fundamental and harmonic radiations after the monochromator. The beamline does not have the capability to handle the white-beam X-rays, hence we cannot quantify the flux of the fundamental and harmonic radiation before the monochromator.
We set the X-ray energy of the fundamental radiation at 21 keV. Hence, the main harmonic contamination concern after the Si (111) where α1 and β1 are the X-ray transmission coefficients for 21 keV and 63 keV X-rays for the first filter combination, and α2 and β2 at another. C1 and C2 are the corresponding detector readouts. Using this pair of linear equations, with α and β calculated from the known filter thickness and X-ray energy, the X-ray intensities of the transmitted fundamental and harmonic radiations can be calculated.
The experimental results are listed in Table S1. We chose the sets of filters to ensure that, even after the monochromator and harmonic rejection crystals, the normalized photodiode readout (photodiode readout normalized by the amplifier gain) is two orders of magnitude above the background level of the photodiode detector (≈ 2.58 × 10 -9 ). At each filter setting, we used a 1 mm × 1 mm beam and counted the photodiode readouts for 5 s. With an incident photon flux at ≈ 10 13 mm -2 s -1 , this set of acquisition parameters ensures good sampling statistics. We also note that the photodiode has different responses to X-rays of different energies. Following the specification provided by the manufacturer, we estimated that * * Certain commercial equipment, instruments, or materials (or suppliers, or software, ...) are identified in this paper to foster understanding. Such identification does not imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the materials or equipment identified are necessarily the best available for the purpose.
at 21 keV and 63 keV, the X-ray absorption efficiencies for the detector are approximately 29 % and 4 %, respectively.

Table S1
Table S1: Photodiode readout and the calculated intensities of the fundamental radiation and harmonic radiation (n = 3) after the Si (111) monochromator.