Development of a GridPix X-ray polarimeter

In gaseous detectors it is possible to determine the polarization of an X-ray beam by tracking photoelectrons which are created in photoelectric interactions of the photons with the gas molecules. Based on the differential cross section of this interaction the emission angle of the photoelectrons is correlated with the polarization plane of the beam. Depending on the photon energy and on scattering of the photoelectrons on gas molecules the length of the relevant part of the track is only in the order of a few hundred microns. Thus, a high tracking resolution is needed. This is achieved with the GridPix [1] - a combination of the highly granular Timepix pixel ASIC [2] and a photolithographically postprocessed MicroMegas called InGrid which holes are aligned with the pixels of the ASIC. Such a detector was operated in a testbeam at the P09 beamline [3] of PETRA III with a 99% linear polarized beam and a modulation factor of 77% was measured. Furthermore, tests of different gas pressures and different beam energies were performed.


Introduction
Polarization of light is an often neglected feature of electromagnetic waves, which can be used for material science and astronomy. Usually, polarization filters are used to determine the direction and degree of polarization, as they only transmit a certain polarization direction. The intensity of the waves behind these filters is measured while the polarization filter is successively rotated. The intensities dependency on the angle can then be used to draw conclusions on the initial polarization. As this requires moving parts and several individual measurements it would be beneficial to measure the polarization state directly. This is possible with a gaseous detector for soft X-rays as the angular distribution of electrons created by the photoelectric effect is correlated with the polarization direction.

Measurement principle
Soft X-ray photons mainly interact with a gas volume via the photoelectric process. In this process the photon ionizes an atom and transfers its energy except for the binding energy to a shell electron which is then called photoelectron. This photoelectron further ionizes the gas along its flight path until its energy is below the minimum ionization energy of the gas. The differential cross section for the photoelectric effect with a linear polarized beam [4] is The angle θ denotes the the angle between the beam axis and the photoelectron direction while φ denotes the angle between the polarization direction of the photon and the direction of the photoelectron on a perpendicular plane to the beam axis. Thus a cos 2 angular distribution of photoelectrons perpendicular to the beam axis is expected. The probability for an emission of the photoelectron in the direction of the polarization is the highest while an emission perpendicular to the polarization direction has the lowest probability. Thus a measurement of the angular distribution of photoelectrons is sufficient to determine direction of polarization. It is also possible to determine the degree of polarization P = (I max − I min ) / (I max + I min ) with the maximum and minimum intensity because unpolarized parts of the beam contribute to the maximum and the minimum while the polarized parts contribute only to the maximum.
To perform this measurement a precise tracking of the photoelectrons is needed and the detector needs to be optimized for long tracks and high tracking resolution. Additionally the multiple scattering of photoelectrons on gas molecules needs to be minimized as the information about the initial direction is lost after scattering.

GridPix detector
The tracking of photoelectrons can be archived with the GridPix [2] detector which is a gaseous ionization detector consisting of a conversion region and an amplification region (cf. fig. 1). The 2 cm high conversion region is enclosed by a cathode with a 300 nm thick silicon nitride X-ray window and an anode with a cutout for the GridPix. Between the cathode and the anode a small electric drift field in the order of 500 V cm is applied. The GridPix acts as amplification stage and readout chip. It is a combination of the Timepix ASIC [1] developed by the Medipix collaboration and a photolithographically postprocessed gas amplification stage called InGrid (cf. fig. 2). The Timepix is a CMOS pixel chip with 256 × 256 pixels in a pitch of 55 µm. The height of the InGrid on top of the Timepix is 50 µm and its holes are aligned with the Timepix pixels. Here an electric field in the order of 60 kV cm is applied. Within the detector the electron and ion pairs created along the flight path of the photoelectron drift apart because of the electric flied between the cathode and anode. During the drift of the electrons towards the anode and the GridPix respectively they further interact with the gas which leads to diffusion. The electrons go through the holes of the grid and are amplified in the high electric field. The so created avalanches of electrons are collected by the Timepix pixels. It is read out in a frame-based mode with adjustable shutter times. It is set in a way that the readout dead time is as small as possible while also the probability for multiple events in the same frame is small.

Photoelectron track reconstruction
For the reconstruction of the photoelectron tracks two main steps are necessary: in a first step clusters in the individual Timepix frames are reconstructed and in the second step the initial angle of the photoelectrons is reconstructed. For the first step the TimepixAnalysis (https://github.com/Vindaar/TimepixAnalysis) framework is used.
It performs a pixel clustering with a search radius of 50 pixels. For each cluster the framework calculates the center of charge and the total charge. Furthermore, based on a fit of an ellipse the longitudinal and the transversal rms as well as the the eccentricity are determined. These parameters can be used for applying cuts on the data. As an example a cut on the energy is possible based on the total collected charge in a cluster. It is correlated with the energy of the photon as each electron created in the photoelectric effect and the following ionization is amplified in the same electric field. Thus the total collected charge for a specific photon energy is on average the same. With this cut photons of higher harmonics can be excluded from the analysis as they have an unknown degree of polarization.
The clusters are then used for the track reconstruction (based on [5]). For this a linear fit which goes through the center of charge is used. This fit minimizes the charge weighted quadratic distance of the pixels to the fit. As this is a fit to the full track the direction is biased by multiple  scattering of the photoelectrons. As this bias is largest towards the track end, it is beneficial to fit only the start of the track. Beginning and end of the track can be identified by exploiting the fact, that most of the charge is deposited towards the tracks end (bragg peak). After identifying the beginning of the track, it is divided into two parts by a perpendicular through the center of charge to the original fit. All pixels in the part of the end of the track are excluded form further reconstruction. For the remaining pixels the new center of charge is determined and again a linear fit based on the charge and position of these pixels is performed. The angle of this fit does then in general represent a better estimate of the initial photon direction. A visualization of this approach is shown in figure 3.
The distribution of angles is then fitted by a cos 2 -distribution based on the differential cross section (see equation 1). The so called modulation factor m is determined via the maximum f max and the minimum f min of the fitted distribution: In an ideal case the modulation factor would equal the degree of polarization P of the incoming beam. In reality it is smaller than that as the resolution of the detector and the tracking efficiency lead additional contributions in the intensity minimum.

Measurements and first results
As an example an angular distribution measured with a 99 % linear polarized beam at 7 keV and a He:CO 2 90:10 gas mixture at atmospheric pressure is shown in figure 4. For the tests the P09 beamline [3] of PETRA III was used. Cuts on the energy and the eccentricity of the events were applied. The information about the position of the very narrow beam spot was used as additional veto for event selection. A modulation factor of 77 % was archived. Further measurements to test different detector and beam parameters were done at the beamline. These measurements were performed with He:DME 80:20 at atmospheric pressure as  Figure 2. SEM picture of a GridPix with partially removed grid [6]. The distance between grid and the Timepix ASIC is 50 µm. well as at 1.5 bar. Beam energies between 6 keV and 11 keV were used. For all measurements again the modulation factor was determined via the angular distribution based on the two-step fit of individual events. In this case only a 3σ cut on the energy was applied. The results are shown in figure 5. For atmospheric pressure the modulation factor is constant between 7.6 keV and 11 keV. An explanation for the lower modulation factor at 6 keV is that at lower energies the length of the photoelectron tracks until the first scattering becomes shorter and also lower energetic photons convert earlier in the detection volume and thus the diffusion is higher. This decreases the tracking resolution and thus the modulation factor. The same explanation holds for 7.6 keV photons at 1.5 bar as the photoelectron tracks at higher pressure are generally shorter. So at higher pressures the same effect is visible at higher energies. At even higher energies an improvement with higher pressures is expected as visible at 11 keV for 1.5 bar as the diffusion drops with increasing pressure. So if the track is sufficiently long the negative influence of the pressure on the track length is outweighed by the positive influence on the diffusion. The overall worse modulation factor compared to figure 4 is explained by a missing cut on the eccentricity. Therefore events with early scattering are not excluded which increases the intensity minimum. Also no veto based on the beam spot was used. This analysis will be further improved in the future with additional cuts for the event selection and also expanded to measurements with He:CO 2 80:20.

Conclusion and outlook
A GridPix based X-ray polarimeter was developed and operated in testbeams at the P09 beamline [3] at PETRA III. For a 99 % polarized beam a modulation factor of 77 % was archived. The use of He:DME 80:20 was tested with different pressures and over a range of photon energies. While at low energies lower pressures are preferable a higher pressure can be beneficial for the modulation factor at higher energies.
The next steps are an optimization of the analysis to improve the event selection and the photoelectron track reconstruction. Furthermore, the detector will be upgraded to a Timepix3 [7] based GridPix which offers simultaneous time and charge measurements with a dead time free data driven readout. With this the rate capability of the detector can be improved.