1.

INTRODUCTION

The Lunar Environment heliospheric X-ray Imager (LEXI¹) is a small self-contained X-ray telescope intended to operate on the lunar surface to observe solar wind charge exchange (SWCX) emission originating in the Earth’s magnetosheath due to the interaction of high-state ions in the compressed solar wind with the outer reaches of the Earth’s exosphere. The SWCX emission in the magnetosheath is of great interest to heliosphericists, as it allows, for the first time, direct imaging of the structure of the magnetic field within the magnetosphere, and will allow one to directly track the effects of reconnection by measuring the extent to which the magnetopause moves when signatures of reconnection are seen elsewhere. The SWCX emission in the magnetosheath is of interest to astrophysicists because it is a highly time variable foreground in the same emission lines generally used for plasma diagnostics; unless the SWCX can be characterized, minimized, or removed, it poses a significant problem in understanding X-ray emission from the Galaxy and beyond.

In order to image a substantial portion of the nose of the Earth’s magnetosheath, LEXI is a wide field (~9° by ~9°) soft (~0.1 to ~2.0 keV) X-ray telescope utilizing “lobster-eye” optics, also known as slumped micropore optics (SMPO). SMPO use square-pore glass microchannel plates to focus X-rays at grazing incidence in two dimensions. The optics are very lightweight while still robust, surviving harsh sounding rocket launches. The optics have short focal lengths and provide a rather unusual cruciform point spread function (PSF) with a strong central core of 10′ to 15′, an example of which is shown in Figure 1. Note that because the focussing planes are perpendicular to one another, the optic has inherent Cartesian axes. Although each individual microchannel plate or facet is small, they can be mosaicked to produce very large fields of view with an angular resolution that is small compared to the size of the FOV.

Figure 1.

Left: The LEXI optic in its holder. Right: The PSF for the central facet of LEXI taken with the PIXI camera at PANTER. The image is ~4.1° across and has been stretched to show the details of the arms of the PSF. The periodic dark lines roughly every 13′ are due to sub-bundles of pores in the SMPO.

The LEXI optic (Figure 1) is a three by three mosaic of 40 mm by 40 mm facets manufactured by Photonis. Each facet was specified to have a radius of curvature (R_C) of 750 mm and is set into an aluminum frame machined to hold the facets on the surface of a sphere with R_C=750 mm. Each facet directly supports an optical blocking filter (OBF) that is formed of a 200 nm film of LUXFilm® Polyimide and 30 nm of Al, which were applied by the Luxel Corporation. Most SMPO used in astrophysics are coated with iridium to increase their reflectivity. However, the LEXI SMPOs are bare glass, due to time and other constraints, which poses some unique calibration challenges.

The baseline calibration program for LEXI, so that its data can be used in a fully quantitative way, requires both knowledge of the effective area (or throughput) of the optic and knowledge of the size of the PSF, both as a function of the angle of incidence and as a function of energy. Unlike many types of optics, only a small portion of the optic contributes to focussing X-rays from a given direction. Thus, calibration of the LEXI optic, in essence, requires the characterization of each facet, individually. The SWCX emission that is the object of the LEXI study, as well as the bulk of the X-ray background to that emission, is primarily below 1-2 keV, while the OBF effectively cuts off the emission below 0.1 keV. Thus, the effective area and the PSF needed to be characterized over the 0.1-2.0 keV energy range.

2.

METHOD AND RESULTS

The LEXI optic calibration was done at the PANTER facility^{2, 3} in Neuried in the southwest of Munich over 21-25 February and 20-29 April 2022. PANTER is a facility of the Max-Planck-Institut für extraterrestrische Physik in Garching. The PANTER vacuum beamline is 120 m long, with a further 12 m long chamber, so that beam divergence is minimized. Two different CCD detectors can be used to characterize the optic (see Table 1) while an Amptek silicon drift detector (SDD) can be used to monitor the beam stability. The beam itself is provided by a very well characterized electron impact source with one of a number of targets.

Table 1.

PANTER Instruments.

*

Only the central 250×250 pixels are used.

2.2

Effective Area

It has been traditional, particularly with detectors with very limited energy resolution, to use strong X-ray lines to characterize the effective area at a limited number of discrete energies. Although this procedure allows one to then reconstruct the effective area for a particular input spectral shape, it is liable to errors near instrumental edges, where the reflectivity changes rapidly over a small energy range. However, given detectors with good energy resolution, one can characterize the effective area over the entire energy range of interest using an X-ray continuum source; the resolution around edges becomes a matter of the line spread function of the detector and the accumulated number of counts at that energy.

To characterize the LEXI optic over the 0.1-2.0 keV range we used an aluminum target to produce a “very low energy” continuum in the 0.2-2.0 keV range that also includes the O-K line at 0.525 keV. In addition, we used a Ti target behind a 1 µm thick Ti filter to produce a “low energy” continuum in the 0.6-4.0 keV range. We also made traditional line-based measurements in a variety of lines (see Table 3) to confirm the continuum measurements and to provide higher signal to noise images for PSF characterization.

Table 3.

FWHM of the PSF of each facet.

Line	Energy	Time/Position	Positions
B-K	0.183 keV	600 s	25
C-K	0.277 keV	300 s	13
Ti-L*	0.452 keV	600 s	13
O-K*	0.525 keV	600 s	76
Cu-L	0.929 keV	180 s	25
Al-K	1.49 keV	180 s	26
Ag-L	2.98 keV	180 s	13

*

Lines embedded in the continuum exposures.

We used the TRoPIC detector to measure the effective area with the very low energy continuum in 73 positions, spaced roughly 0.76° (or a quarter of a facet) apart (see Figure 2 and Figure 3) with a higher density of measurements in the center of the FOV. Further measurements were made with the low energy continuum and lines, primarily in the central column of facets, where the nose of the magnetopause will be placed. For each series of measurements, “flat field” images were taken when the optic was not between the source and the detector, the optic was then moved into position for the series of measurements, and then flat fields were taken after the series. The flat field images were used to determine the effective area, while the SDD measurements taken during the series were used to correct for small timescale variations in the beam, under the assumption that the beam behaves synchronously for all energies.

Figure 2.

Pattern of the directions at which the effective areas were measured. The dotted lines indicate facet boundaries. The closest spacing of locations is 0.79°, which is a quarter of a facet.

Figure 3.

Images of the PSF at O-K (0.525 keV) obtained from the very low energy continuum measurements. Comparison with the Figure 2 will show which images were taken with the source in the direction of the frame.

Figure 4 shows the effective area curve for the center of the center facet. (This is essentially the spectrum taken through the optic divided by the flat field spectrum, multiplied by the area of the detector and a geometric correction factor.) The results of the line measurements have been over-plotted. Uncertainties in the continuum measurements are ~1.5(~6)% at 0.5(1.0) keV and ~5(~7)% at 2.0(3.0) keV. It is clear that the effective area as a function of energy is very well characterized, even if the model seems to be significantly awry.

Figure 4.

The effective area as a function of energy for the center of the center facet. The thick black line is the data from the very low energy continuum; the thin black lines show the uncertainty. The purple line is the data from the low energy continuum; the uncertainty is also shown. The red line is a theoretical model of this optic. The blue line is the model reduced by a factor of 1.6. The green boxes with error bars show effective areas derived from the individual line measurements. The notation below the data indicates the various absorption edges in the absence of smoothing.

3.

COMPARISON TO THEORY

Our model for the effective area of the optic was derived from a Pore-By-Pore (PBP) ray-tracing routine^∗ using reflectivities for SiO₂ from henke.lbl.gov. This effective area was then multiplied by the transmission of the OBF, and convolved with an approximate spectral line spread function (LSF) of the TRoPIC detector. The effective area function of the optic is expected to show absorption edges at 0.099, 0.149, and 1.839 keV from the Si, and 0.543 from the O. The OBF introduces edges at ~0.072 and 1.559 keV (Al), 0.284 keV (C), 0.408 keV (N), and increases the depth of the O edge at 0.543 keV. The binning of the data and the smearing by the LSF cause the absorption edges to be not quite so sharp as one would expect, and obscures the relatively shallow edges due to N and Al.

Scaling the model by a constant factor does not produce the observed function; when the region between the O edge and the Si edge is well fit, the higher energy region is not, suggesting that the scaling is a function of energy. We also note that the area around the O edge is not well fit. There is some uncertainty in the amount of O in the OBF due to the oxidation of the Al, however that uncertainty is much smaller than the discrepancy here. The area below E~0.2 keV is not well fit either, however the beam emission here is rather weak and there are significant systematic uncertainties.

The discrepancy between measurement and model is not, to first order, surprising. There are a number of uncertainties concerning the reflectivities. First, the composition of the glass is proprietary, so it is not known to the experimenters. We have assumed that the reflectivity will be similar to that of SiO₂, and that trace ingredients will produce small edges. Second, we do not yet have measurements of the surface roughness within the SMPO pores. Previous work with Ir coated optics⁴ showed that the optics had 85% to 95% the expected throughput, so our initial model assumed no surface roughness.

We can explore this problem more fully if we co-add the appropriate data. Figure 5 shows the vignetting function for each of the scans passing through the center of the center facet. Although different facets do show different effective areas, the centers of each facet are comparable because the bulk of the throughput for a given direction is due to a region on the optic that is roughly the size of a facet. We can thus average the data from analogous positions, in this case the center of each facet, to produce a higher signal to noise effective area curve, though its absolute value will need to be adjusted for any particular facet. This curve is shown in Figure 6. We do not see any further edges.

Figure 5.

The effective area as a function of off-axis angle at 0.525 keV. Purple boxes: in the yaw direction, blue “x”s: in the pitch direction, green crosses: one diagonal, red diamonds: the other diagonal. The solid black line is a model vignetting function at the same energy, scaled to match the measurements.

Figure 6.

The effective area as a function of energy for the center of the facets. The very low energy continuum data are the average of eight measurements, while the low energy continuum data are the average of three measurements. The red line is the model of the effective area assuming no surface roughness. The blue lines are models with RMS surface roughnesses of 9 nm and 10 nm.

We again see that the model does not fit the data but, with the exception of higher than expected effective areas at E<0.2 keV, the shape seems reasonable; the problem is mostly the amplitude of the curve. We can again extract reflectivities from henke.lbl.gov, but this time applying a surface roughness correction using the Nevot-Croce approximation. We extracted reflectivities for RMS surface roughnesses of 5, 6, 7, 8, 9, and 10 nm. As surface roughness increases, reflectivity decreases more rapidly at higher energies than lower energies, and reflectivity decreases more rapidly at more normal incidence angles than more grazing angles. Since the total throughput of an SMPO is a complex convolution of reflectivity and distance from the optical axis, it is not always clear what will happen.

What we see is a relatively modest decrease at the highest energies due to very few of the high energy photons being reflected and most of the throughput being due to collimation. We see strong decreases in the middle energies (0.5-2.0 keV), and not so strong decreases at the lowest energies. No single surface roughness provides a satisfactory fit, particularly around the O edge. Indeed, the shape of the effective area curve after correction for surface roughness is arguably worse than the scaled model for a perfectly smooth optic, particularly between the C and O edges. A 10 nm RMS roughness is an order of magnitude greater than expected, and yet that curve just barely fits the two sides of the Si edge, which suggests that surface roughness does not explain the bulk of the mismatch between the model and measurements.

There are a number of possible sources for the discrepancy; an inadequate formulation for the surface roughness correction, an inadequate formulation of the glass composition, or an inadequate spectral line spread function. We are actively pursuing alternate formulations for the application of surface roughness. A brief survey of different types of glass suggests that the largest differences in reflectivity occur above 1 keV, perhaps causing the discrepancy across the Si edge, but not at lower energies. While an inadequate LSF might explain part of the discrepancy at the O edge, given that the modeled location of the C and Si edges is good suggests that it is not the problem.

4.

SUMMARY

Calibration of the LEXI optic at PANTER has exposed weaknesses in our capability to model SMPO with ray tracing while also indicating which improvements remain to be made in that modeling. Our PANTER results demonstrate that the LEXI optics will achieve a PSF smaller than 15′ over most of its FOV, and we have characterized the PSF shape over the bulk of the FOV. The effective area curve is well characterized, even if the shape is not entirely understood.