Stray light test facility

The SLTF beamline consists of a 1.2-m-diameter beam tube feeding a 3-m diameter (14 m long with taper) test chamber. In addition to three large roughing pumps able to pump down the beamline to $5\times {10}^{-3}\mathrm{Torr}$ in 2 h, there are three large cryopumps that allow the facility to reach a few ×${10}^{-6}\mathrm{Torr}$ after an additional 2 to 3 h. The MMA under calibration is mounted in the test chamber atop a hexapod that enables precise linear control in all axes and precise angular control in tip and pan. At a distance of 4.17 m along the optical axis (the effective focal length of the MMA at 100-m source distance) are the facility detectors used to measure the MMA response. These detectors consisted of a fast silicon drift detector (SDD) with known effective area and a charge coupled device (CCD) camera with fine ($13.5\mu \mathrm{m}$) pixels to measure the MMA point spread function. Both detectors are mounted on a high-precision moveable stage to allow positioning perpendicular to the beam direction. The precision is about $2\mu \mathrm{m}$ and the stages can carry $\sim 36\mathrm{kg}$ over a range of $\sim 600\mathrm{mm}$ in both $X$ and $Y$. With this system, one can precisely position the various focal plane detectors in the center of the focused beam from the optic; switch between the various detectors mounted on the detector plate; and move the detectors off to the side to enable direct measurements of the incident x-ray flux unobstructed by the optic under test. After initial MMA calibrations, the flight spare DU was also mounted on the detector stage.

The hexapod to which an MMA was mounted is vacuum compatible and has a precision better than $0.5\mu \mathrm{m}$ in $X$, $Y$, and $Z$, and better than 1 arcsecond in the three rotation angles. The hexapod has a linear range of $\pm 50\mathrm{mm}$ in $X$ and $Y$ and $\pm 25\mathrm{mm}$ in $Z$, and a load capacity of 40 kg. There is also software to allow the hexapod to be “dithered” (moved in a continuous Lissajous-type pattern in $X$ and $Y$) to simulate spacecraft dithering during flight.

The primary x-ray sources used for x-ray calibration at SLTF are Trufocus models 6050 and 6051 L. The model 6050 is air cooled and has a maximum beam current of 1 mA, whereas the 6051 is water cooled with a maximum beam current of 2 mA (otherwise, except for the anode material, the sources are identical). IXPE calibration used model 6050 tubes with Mo and Fe anodes and a model 6051 with a Ti anode. These tubes are vacuum sealed with a 0.005-in.-thick Be window and have a focal spot size smaller than 1 mm. The facility also has a small Manson source with an Al 6061 anode, capable of operating up to a potential of 10 kV, with a beam current up to about 0.75 mA. This source was used for one IXPE measurement (spurious modulation from an unpolarized source) with an Al filter with optical depth of two.

IXPE also purchased custom x-ray tubes from Trufocus for use with matched crystals as polarized x-ray sources. The characteristics of these polarized sources are shown in Table 3. These sources can operate with potentials up to 30 kV and beam currents nominally up to 30 mA for an x-ray power of $\sim 900\mathrm{W}$. IXPE used three of these water-cooled windowless sources with Rh, Ti, and Fe anodes coupled with Ge (111), Si (220), and a Si (400) crystals to produce $>99\%$ polarized x-rays. The degree of polarization is set by the Bragg angle.

Table 3

Characteristics of the SLTF polarized sources.

There is also an x-ray filter system to reduce the continuum emission and emphasize the characteristic x-ray line to produce a more monochromatic source. Filters include Al (for use with Al-K), Nb (for use with Mo-L), Pd (for use with Rh), and Ti, Fe, and Ni (for use with Cu). The filter thicknesses all have an optical depth of 2. There is also an optical blocking filter for use with the windowless x-ray sources. This filter is aluminized polyimide with a circular aperture of 1 cm and mounted in a CF 2.75 gate valve. In addition to serving as a filter to block optical light emitted from the x-ray source, the valve also served as a vacuum separation gate to keep the pressure in the source system at $<{10}^{-6}\mathrm{Torr}$ to protect the windowless sources from possible pressure variations in the rest of the beamline.

MMA effective area

The appropriate ratio of the SDD measurements, multiplied by the $50{\mathrm{mm}}^2$ SDD area, gives the effective area of the MMA at a finite-source-distance of 97.950 m (the distance from the x-ray source to the MMA node). A correction, verified by a ray-trace analysis, is applied to the finite-source-distance area to give the on-orbit infinite-source-distance effective area. The on-axis MMA line-source effective areas measured during calibration are given in Table 4. The uncertainty in these is $\pm 3\%$, ($1\text{-}\sigma$). The results of the continuum effective area measurements for each of the three flight MMAs are shown in Fig. 8. These continuum measurements are made without x-ray source filtering and use the bremsstrahlung continuum and the fine energy resolution of the SDD.

Table 4

IXPE MMA effective areas as measured at 2.3 and 4.5 keV during calibration at the MSFC SLTF. The areas have been corrected to infinite source distance as discussed in the text.

Fig. 8

Effective area (measured and best-fit model) for a point source at infinity as a function of energy for the three flight MMAs.

Half power diameter

The half-power diameter (HPD) of each MMA was measured using a CCD camera at the focus of the optic, with filtered x-ray sources producing lines at nominally 2.3 keV (Mo-L) and 4.5 keV (Ti-K) along with some (filtered) continuum emission. The detector region used for this measurement was chosen to be the same as that used for the effective area, i.e., a circle of diameter 8 mm, which is $\sim 16$ times the MMA HPD. We estimate, based on CCD measurements, that greater than 98% of the flux is within this region at 2.3 keV, and greater than 95% at 6.4 keV. Flat fields, taken immediately before and after the measurements, were used to subtract offsets and noise contributions in individual pixels. The diameter containing half the flux within the measurement region was then determined and converted to an angle using the measured image distance ($\sim 4.17\mathrm{m}$) for the 100-m object distance at the SLTF. Results are tabulated in Table 5. MMA1 was significantly better than MMA2 and MMA3, despite predictions made during the shell installation process where metrology indicated they would all have similar angular resolution. It is suspected that spider distortions occurred in MMA2 and MMA3 during the later exterior housing installations, but this is still under investigation and will be the subject of a future publication. Note that the mirror HPD is by far the dominant contributor to the overall angular resolution.

Table 5

Measured HPD at 2.3 and 4.5 keV for MMA1, 2, and 3.

Ghost rays

Ghost rays were measured for a series of off-axis angles for each MMA. Measurements were made out to 1 deg as simulations showed that it was not possible for a singly reflected ray to reach the detector above this angle. The measurements showed that the flux from an off-axis source was reduced by a factor of more than 230 over what the source would be on axis. This easily met a requirement of $\ge 100$ reduction, set by planned observations of weak extended emission near the galactic center.

Instrument calibration equipment and assembly integration and verification test calibration equipment

There are two instrument calibration stations, the instrument calibration equipment (ICE) and assembly integration and verification test calibration equipment (ACE). The two stations are shown in Fig. 12 and are discussed in detail in the paper by Muleri et al.¹³ X-ray sources can be mounted on both test stations. However, the ICE offers a full-fledged set of manual and motorized stages to align and move the source beam in a controlled way, even during a measurement, whereas the ACE was equipped only with a subset of available sources. Nevertheless, these sources provided the capability to perform tests with ACE and, contemporaneously, with ICE. The most time-consuming calibrations are the calibration of the response to unpolarized radiation because of statistical considerations.

Fig. 12

The ICE and ACE calibration stations in Italy during calibration of DU2 flight model on the ICE and the instrument testing with DSU-EM (engineering model) and DU1, 3 (flight models) and the spare unit on the ACE.

A set of manual and motorized stages allow adjustment of the beam direction with respect to the unit in calibration. These stages allow: movement of the DU in the plane orthogonal to the incident beam with an accuracy of $2\mu \mathrm{m}$ (over a range of 100 mm); rotation of the DU on the azimuthal plane orthogonal to the incident beam with an accuracy of 7 arcsec to measure the response at different polarization angles; tip/tilting of the DU to align it to the incident beam; and averaging residual polarization of unpolarized sources. The x-ray source is mounted on a mechanical support that permits adjustment of its position and inclination with respect to the DU. Finally, a manual translation stage allows one to slide the source assembly to three separate positions to perform the calibration with the DU or to illuminate commercial detectors.

Unpolarized sources

Unpolarized sources in the ICE cover the entire 2 to 8 keV energy range of IXPE (Table 7). Only in a few cases, it is possible to use a “genuine” unpolarized source where any intrinsic source polarization is much lower than the statistical significance achieved in the calibration. To ensure that the unpolarized sources are truly unpolarized, we adopted a simple procedure to decouple any intrinsic source polarization and the response of the instrument to completely unpolarized radiation. The procedure, described in Ref. 14, is based on the repetition of the measurement with the source set at two different azimuthal angles differing by 90 deg.

Table 7

Intrinsic polarization of the ICE x-ray sources measured with DU1.

Both radioactive sources and x-ray tubes were used. Radioactive nuclei emit unpolarized radiation and ${}^{55}\mathrm{Fe}$ sources were used. This nuclide has half-life of 2.737 years and it decays into ${}^{55}\mathrm{Mn}$ for K-capture with emission of Mn fluorescence lines $\mathrm{K}\alpha$ (5.90 keV, 90%) and $\mathrm{K}\beta$ (6.49 keV, 10%). Both lines are expected to be unpolarized from first principles and no hint of polarization was found (see Table 7, which also lists the intrinsic polarization measured from the other x-ray sources).

Measurements were carried out with x-ray tubes in two different configurations: one direct and one for the extraction of fluorescence emission from a target. In the direct configuration, the DU is illuminated with the direct emission of the x-ray tube (or ${}^{55}\mathrm{Fe}$), which is comprised of unpolarized fluorescence lines plus continuum emission. The latter may be partially polarized depending on the details of the x-ray tube emission geometry.

Polarized sources

The polarized sources exploit the use of Bragg reflection as close to 45 deg as possible to produce an almost 100%-polarized beam. The characteristics of these sources, with their calculated degree of polarization, are listed in Table 8.

Table 8

Polarized sources used during DU calibrations.

Quantum efficiency

The quantum efficiency of the DU is the product of the quantum efficiency of the GPD and the x-ray transmission of the UV/ion filter placed at the bottom of the collimator. It was measured during calibration at INAF-IAPS for each DU.¹⁵ The x-ray transmission of the ion-UV filter was independently measured for all the flight units and is compatible with the nominal transmission expected for the filter composition ($1.06\mu \mathrm{m}$ of LUXFilm^® polyimide + 50 nm Al).¹⁶

The quantum efficiency of the GPD depends substantially on the absorption gap thickness, the gas pressure, and the transmission of the Beryllium window. The absorption gap thickness is known with high precision by metrology measurements, whereas the gas pressure decreases with time due to the capture of gas molecules by the materials inside the GPD gas cell. The pressure variation has been closely monitored since a few days after initial gas filling and shows a well-established progression to an asymptotic value, which will be substantially reached by launch (see Sec. Long-term pressure variation). The quantum efficiency expected at launch is shown in Table 9, extrapolated from measurements made during calibration.

Table 9

DU quantum efficiency assuming a launch date of December 9, 2021.

Each DU contains a gray (attenuating) filter on the filter and calibration wheel for handling high intensity sources. The x-ray transmission of the gray filter was measured at different energies.¹⁰ The measured transmission is consistent with the nominal thickness of the filter—a 3 mil ($76.2\mu \mathrm{m}$) Kapton foil allowing for tolerances. Results are shown in Table 10.

Table 10

Gray filter x-ray transmission.

Energy resolution

We made use of flat field data obtained with the polarized sources to measure the energy resolution. Because of the use of Bragg crystals, these sources are highly monochromatic. Spectral data were taken in 100 spots of $500\text{-}\mu \mathrm{m}$ radius from the flat field data. The energy resolution was then calculated by fitting with a Gaussian the gain-corrected energy spectrum and dividing the measured FWHM by its peak. The energy resolution as a function of energy for the three flight DUs is shown in Fig. 13.

Fig. 13

Energy resolution as a function of energy for the flight DUs.

Timing

The GPD provides, for each processed event, a trigger output that is used to time tag each event with $1\mu \mathrm{s}$ resolution and 1 to $2\mu \mathrm{s}$ accuracy due to the use of a global positioning system that provides a pulse per second, and temperature-controlled 1-MHz oscillators. The time for ASIC readout and subsequent processing by the back-end electronics is such that the dead time is 1.1 to 1.2 ms (depending on energy) per event. This gives about 12% deadtime for the bright Crab Nebula. Note that the polarization response of the ASIC does not depend on the dead time fraction (e.g., on the source rate).

Spatial resolution

During ground calibrations, the intrinsic spatial resolution was estimated by measuring the HPD using an on-axis beam with a diameter less than $39\mu \mathrm{m}$ (measured by a CCD test detector). Measurements were performed for both polarized and unpolarized sources and in different locations across the sensitive area of the detectors. Details of these measurements are given in a dedicated paper.¹⁷ Table 11 shows the average of results obtained for the three flight DUs.

Table 11

Mean spatial resolution of IXPE flight DUs as a function of energy.

Modulation factor

The modulation amplitude is the fractional variation in the number of detected events versus position angle. The “modulation factor” is the modulation amplitude for 100% linearly polarized radiation. The calibration of the modulation factor is described in detail in the paper by Di Marco et al.¹⁸ The modulation factor was measured at different energies and angles to estimate the accuracy of the polarization angle and to check that spurious modulation (see Sec. Spurious modulation) is properly subtracted. An important outcome of these measurements is that the modulation factor of the flight detectors is uniform over the detector-sensitive surface and is not dependent on the position angle.

Calibration data have been analyzed subtracting spurious modulation Stokes parameters using the methods described in Ref. 14 and using the weighting approach described in Ref. 19. From these data, and accounting for the secular change in pressure (see Sec. Long-term pressure variation), it is possible to estimate the modulation factor as a function of energy as shown in Fig. 14 for the time of launch set to December 9, 2021.

Fig. 14

Modulation factor as function of energy for the IXPE DUs estimated at time of IXPE launch. Values are derived from ground calibration data after correcting for spurious modulation and applying weighting.

Spurious modulation

The response of an ideal polarimeter to unpolarized radiation would show no variation of the position angle as the device is rotated about the line of sight. However, the IXPE focal plane detectors show, especially at low energy, a low amplitude, nearly-cos² variation of the position angle for unpolarized x-rays in detector coordinates. Although the root causes of such spurious modulation have been thoroughly investigated,¹² the effect is hard to model and therefore was fully calibrated. The response of each DU, including the flight spare, was measured at six energies over the entire FOV, and with higher statistics in its center where the brightest sources will be observed.

The Stokes parameters of the spurious modulation¹⁴ are shown as a function of energy in Fig. 15. In the plot, the contribution from the three IXPE DUs is appropriately summed accounting for the fact that they are clocked at 120 deg with respect to each other. Spurious modulation has also been shown to be constant with temperature and counting rate by tests conducted with a number of prototype GPDs.¹² The spurious modulation will be removed, event-by-event, during data processing.¹²

Fig. 15

Stokes parameters as a function of energy of the detector-averaged spurious modulation accounting for the 120-deg clocking of the detectors. The effect is removed during the on-ground data processing.

Rate-dependent gain variations

The fine pitch of the IXPE GEMs makes them susceptible to rate-dependent gain variations due to temporary charge build-up. When the detector is irradiated, part of the charge from the avalanche can be temporarily deposited onto the dielectric substrate in the GEM holes, affecting the configuration of the electric field, and causing local (and reversible) changes in the gas gain. Since the charge trapping is not permanent, a competing discharging process is continuously at play, causing the gain to drift toward the initial value when the input energy flux is low enough.

Although the charging effect was largely mitigated by a dedicated fine tuning of the production process in the development stage of the mission, it is still present at a level that needs to be corrected for to achieve an accurate estimate of the energy and, since the modulation factor is energy-dependent, to correctly infer the source polarization from the measured modulation. For a typical x-ray celestial source, the charging effect will be of the order of a few %, on timescales of several hours to a day. For very bright sources, we anticipate gain variations up to 10% on much shorter timescales.

To this end, we have developed a complete phenomenological model that allows us to measure and correct such gain variations, based on the energy flux measured by the GPD as a function of time and position across the active surface. (We emphasize that all the necessary information is included in the science data that are collected during normal observations and that the onboard calibration sources can be used to ensure that there are no systematic drifts over long observations.) The reader is referred to Sec. 7.2 and Appendix A of Ref. 12.

Long-term pressure variation

During the development of the IXPE instrument, we realized that the internal gas pressure underwent a long-term decrease, over timescales of months, reaching an asymptotic value $\sim 150\mathrm{mbar}$ below the initial pressure of nominally 800 mbar.¹² This observation, initially hinted at by a slow increase of the gas gain, has since been confirmed by several indirect measurements including the evolution of the quantum efficiency and the average track length at a given energy, as well as direct measurements of the vertical displacement of the Be window.

The effect has been systematically monitored using a dozen (nominally identical) detectors, with test data amounting to more than 30 GPD-years equivalent of operation. We note that the energy resolution shows no sign of degradation with time, clearly indicating that the root cause is not a real leak between the gas cell and the external world. The “virtual leak” is most likely connected to an adsorption phenomenon within the GPD itself. The pressure decrease is unambiguously saturating with time, and in fact, all three IXPE detectors are all already within a few % of the expected asymptotic value (Table 12). Given the concavity of the time evolution, the current time derivative of the pressure, typically of the order of a 1 to 10 mbar per year, can be taken as a generous upper limit to the additional variations that we might expect on orbit. Also, the onboard calibration sources will allow us to monitor the detector evolution continuously during the mission, through the measurement of the counting rate and the average track length.

Table 12

Detector launch and asymptotic pressures.

Calibration data and simulations indicate that the impact of this pressure variation on the polarimetric sensitivity is mild. While the detector quantum efficiency scales linearly with the pressure, causing a net loss of telescope effective area, the modulation factor increases as the pressure decreases, owing to fact that the tracks become more elongated. The net effect of these two competing processes is that the relative loss of sensitivity, expressed as the broadband minimum detectable polarization for a typical source spectrum, is $<2\%$. Once the calibrated corrections are made, there is no net effect.

Background

The IXPE background is expected to be negligible for any planned observations of point-like sources. Polarimetry is in fact photon starved and typically possible only with the brighter sources for each class, and this reduces the background requirement on the detectors. However, for some observations of extended and low-surface-brightness sources (such as molecular clouds in the Galactic center and SN1006), background may be an issue and some background suppression techniques need to be applied to the data. We evaluated the background expected for IXPE²⁰ by modeling the spacecraft, detailing the detector geometry, and considering the major components of background such as cosmic x-ray background, albedo gamma-ray and albedo neutrons, primary electrons, positrons, protons and alphas, and secondary electrons, positrons, and neutrons. The expected counting rate without any background rejection, other than the energy threshold (2 to 8 keV) is $4.7\times {10}^{-2}\mathrm{c}/\mathrm{s}/{\mathrm{cm}}^2/\mathrm{DU}$ averaged over the focal plane. After background rejection techniques are applied, this becomes $1.16\times {10}^{-3}\mathrm{c}/\mathrm{s}/{\mathrm{cm}}^2/\mathrm{DU}$. Background rejection criteria include track size, track skewness, track elongation, charge density, cluster number, and border pixels. The major contribution of unrejected background is delta-rays from electron and positrons, which produce tracks indistinguishable from photoelectron tracks.

Flight system angular resolution

The system angular resolution is the resolution expected in flight and combines the effects discussed in Sec. 7.3.2 with uncertainties in aspect and also MMA to detector separations compared with measured focal lengths. These projected values are shown in Table 15, where the first data line shows the native measured MMA resolution (as reported in Sec. Half power diameter), the second line adds in the effects of the detector spatial resolution and defocusing due to the finite gas depth, and the final line adds in the aspect and the focal length effects.

Table 15

IXPE flight system angular resolution.