Principle of polarization measurement

In the soft-gamma-ray domain, Compton scattering is the dominant process in photon–matter interaction. Compton scattering preserves the polarization information of the linearly polarized photons to a certain degree. When linearly polarized photons and matter undergo Compton scattering, the azimuthal angle distribution of the scattered photons is related to the degree of polarization and the direction of polarization of the incident photons. The soft-gamma-ray polarimeter used in this study was based on this principle to detect gamma-ray polarization signals in the universe.

If the initial gamma ray is linearly polarized, Compton scattering can be graphically demonstrated, as shown in Fig. 1. Additionally, the Compton scattering differential cross section of a linearly polarized photon can be expressed by the Klein–Nishina formula [18] $\begin{array}{l}\frac{\text{d}\sigma }{\text{d}\text{Ω}}=\frac{r_0^2}{2}{\left(\frac{E^{\text{'}}}{E}\right)}^2\left(\frac{E}{E^{\text{'}}}+\frac{E^{\text{'}}}{E}-2{{\displaystyle \sin }}^2\theta {{\displaystyle \cos }}^2\eta \right)\\ =\frac{r_0^2}{2}{\left(\frac{E^{\text{'}}}{E}\right)}^2\\ \left\{\frac{E}{E^{\text{'}}}+\frac{E^{\text{'}}}{E}-{{\displaystyle \sin }}^2\theta +{{\displaystyle \sin }}^2\theta \cos \left[2\left(\eta +\frac{\pi }{2}\right)\right]\right\},\end{array}$ (1) where r₀ is the classical electron radius, E is the incident or initial photon energy, E’ is the scattered photon energy, θ is the Compton scattering angle, and η is the angle between the direction of the scattered photon and the polarization direction of the incident photon (i.e., the azimuthal angle), as shown in Fig. 1. E’/E in Eq. (1) is represented by the Compton equation [1] $\frac{E^{\text{'}}}{E}={\left[1+\frac{E}{m_{\text{e}}{c}^2}\left(1-\cos \theta \right)\right]}^{-1}\mathrm{,}$ (2) where $m_e{c}^2$ denotes the rest mass energy of an electron. Equation (1) indicates that linearly polarized photons tend to scatter perpendicularly to the incident polarization vector (minimizing the term $2{{\displaystyle \sin }}^2\theta {{\displaystyle \cos }}^2\eta$). Additionally, when both E’/E and θ are constants, the differential scattering cross section of the polarized photons follows the $\cos \left[2\left(\eta +\pi /2\right)\right]$ distribution, that is, the variation in the number of scattered photons with the azimuthal angle η follows the cosine distribution. In practice, the incident photon energy E and scattering angle θ often take a range of values; our measurement is an average, but the averaged azimuth still follows a cosine distribution.

Fig. 1Full-screen View

Schematic of Compton scattering of a linearly polarized photon.

In most cases, because η cannot be measured directly, the polarization information of the incident linearly polarized photons cannot be obtained by measuring η. Given the above practical situation, the angle φ is introduced as the Compton scattering azimuth, which is the angle between the polarized scattered photon plane and the x-axis, as shown in Fig. 1. The polarization signatures of the source of incident linearly polarized photons are reflected in the distribution of the azimuthal angle φ: $f\left(\phi \right)=A\left\{1+\mu \cos \left[2\left(\phi -{\phi }_0\right)+\pi \right]\right\}\mathrm{,}$ (3) which can easily be deduced from Eq. (1). Here, φ₀ represents the polarization angle of the incident photon or the direction of the original polarization vector (see Fig. 1), A is the offset of the distribution of the azimuthal scatter angle (see Fig. 2), and μ is a significant parameter called the modulation factor, which describes the polarization response of a polarimeter. The modulation curve derived by Eq. (3) is shown in Figs. 2. The modulation factor μ is expressed as: $\mu =\frac{F_{\max }-F_{\min }}{F_{\max }+F_{\min }}=\frac{B}{A}=\frac{{{\displaystyle \sin }}^2\theta }{\frac{E^{\text{'}}}{E}+\frac{E}{E^{\text{'}}}-{{\displaystyle \sin }}^2\theta }\mathrm{,}$ (4) which can be derived from Eqs. (1), (2), and (3), where F_max, F_min, A, and B are presented in Fig. 2. For a fully (100%) linearly polarized photon beam, the modulation factor is μ₁₀₀, whereas for a photon beam of an unknown degree of polarization, the modulation factor is μ. The degree of polarization of the incident photons can be obtained as: $P=\frac{\mu }{{\mu }_{100}}\mathrm{,}$ (5) where P is a positive value between 0 and 1.

Fig. 2Full-screen View

(Color online) Distribution of the azimuthal scatter angle φ.

Figure 3 illustrates the relationship (the functional relationship expressed by Eq. (4)) among the modulation factor μ₁₀₀, which is a key performance parameter of the polarimeter, the Compton scatter angle θ, and the incident photon energy E. As seen in Fig. 3, the modulation of the azimuthal distribution is most significant at lower energies and medium scattering angles. Photons with extremely large (θ≈180°) or small (θ≈0°) scattering angles carry little polarization information. Additionally, the modulation factor μ₁₀₀ decreases significantly with an increase in the photon energy.

Fig. 3Full-screen View

(Color online) Modulation factor μ₁₀₀ as a function of the Compton scattering angle θ and the incident photon energy E.

In addition to the modulation factor, the minimum detectable polarization (MDP; also known as polarization sensitivity, i.e., the detection limit of the degree of polarization [30]) describes the performance of a polarimeter. MDP is used to determine the polarization detection capability of a polarimeter and can be calculated as [1]: $MDP=\frac{n_{\sigma }}{{\mu }_{100}S}\sqrt{\frac{S+B}{T}}\mathrm{,}$ (6) where $n_{\sigma }$ is related to the expected confidence level of the detection (e.g., $n_{\sigma }=3$), and S and B are the count rates of the source and background (after all event selection cuts are applied) in observation time T, respectively. As can be seen from Eq. (6), MDP is related to five parameters. In general, $n_{\sigma }$, μ₁₀₀, and T are constants when the confidence level, polarimeter, and observation time are fixed. Thus, the MDP is only affected by S and B, and the MDP improves with increasing S and worsens with increasing B. Given that the angular resolution is used as the key event selection condition when calculating S and B, S and B are related to the angular resolution of the detector. In fact, the excellence of the angular resolution has almost no effect on S, whereas it has a significant effect on B. When the angular resolution is excellent, B decreases, which results in better MDP for the polarimeter. In contrast, when the angular resolution is poor, B increases, which leads to worse MDP for the polarimeter. Therefore, the angular resolution significantly affects the polarization sensitivity of a polarimeter, which provides a valuable guide for the design of polarimeters.

Polarimeter design

In this study, a polarimeter was designed to detect the polarization of linearly polarized gamma rays in the energy range of 0.1–10 MeV based on the Compton scattering principle. The structural design of the proposed polarimeter is illustrated in Fig. 4, where the entire model contains only active materials. The polarimeter is mainly composed of three detection subsystems: a silicon converter (blue) located in the upper center of the polarimeter, a CsI absorber (red) surrounding the converter on five sides (except for the top side), and an organic plastic scintillator anticoincidence shield (ACS; green), which envelops the two subdetectors mentioned above. The entire detector containing only the sensitive material has a size of 26 cm × 26 cm × 20 cm and a mass of ∼15 kg. The design details and descriptions of each subdetector of the polarimeter are given below.

Fig. 4Full-screen View

(Color online) Wireframe model (left) and mass model (right) of the polarimeter, which consists of the outer organic plastic scintillator anticoincidence shield (green), a silicon converter (blue) located in the upper middle, and a CsI absorber (red) surrounding the five sides of the converter.

Converter The converter plays a vital role in the polarimeter and performs two main tasks: 1) the first Compton interaction occurs in the converter, and 2) the converter records the deposited energy and interaction positions of all generated particles. To accomplish these tasks, the converter is required to be able to increase the Compton scattering probability of photons, stop recoil electrons, and have excellent energy and position resolution. A multilayer double-sided silicon strip detector was found to be the best converter design choice. Silicon, a low-Z material, has a higher Compton cross-section than medium-Z and high-Z materials such as Ge and CdZnTe in the 0.1–10 MeV energy range. The double-sided silicon strip detector has a low threshold and guarantees excellent energy and two-dimensional (i.e., in the X- and Y-directions) position resolution. Furthermore, multiple thin-layer configurations can enlarge the Compton scattering cross-section, provide longitudinal position information, and track and absorb recoil electron energy. The geometric model of the converter and its physical location in the system are shown in blue in Fig. 4. The detailed design parameters are listed in Table 1.

Absorber The absorber (also known as the calorimeter) is required to stop the scattered Compton photons and measure their energy and position. Additionally, because Compton scattering polarization is significant at larger scattering angles and lower energies, the absorber must be able to measure large-angle-scattered photons. Finally, the absorber acts as a barrier to reduce the radiation from the space-orbit environment to the converter and improve the background rejection of the entire detector. Therefore, the absorber that meets these requirements needs to use high-Z materials as the detection medium, have good energy and position resolution, have a large acceptance of scattered photons, and surround the converter as much as possible. The CsI scintillator is a better choice as a sensitive material for the absorber because of its high density, large atomic number, high light yield, good mechanical properties, not easily deliquescent, high detection efficiency, ease of processing into small pixels of various shapes, availability in large quantities, and reasonable price [31]. A pixel-type absorber comprising CsI crystals was used as the final solution. Two types of crystal cells were used: cubic and bar shaped. The geometric configuration of the absorber and its physical position in the system are shown in red in Fig. 4. The design parameters are listed in Table 1.

Considering the power consumption and space constraints of a compact microsatellite, we adopted silicon photomultipliers (SiPMs) as the photoelectric converters for CsI crystals instead of traditional photomultiplier tubes (PMTs). SiPMs have low power consumption, low weight, small size, fast time response, large self-gain (10⁵–10⁶), high signal-to-noise ratio, and insensitivity to magnetic fields [29, 32]. Each small cubic crystal coupled the photoelectric converter only on the side facing away from the silicon converter to minimize the passive material between the converter and the absorber. A dual-ended readout scheme was used for the bar crystals. To verify the feasibility of this scheme, we conducted a detailed test study on a CsI detection cell in the laboratory (see Refs. [31, 33]). The experimental results showed that the CsI detection cell exhibited good performance; the energy resolution was close to 5% (full width at half maximum; FWHM), and the longitudinal position resolution was approximately 5 mm (FWHM) for the 662 keV gamma-ray emitted by the ¹³⁷Cs source. The dual-ended readout method not only ensures better energy resolution but also provides position information along the crystal bar direction (Z-direction).

ACS The ACS of the polarimeter is primarily used to prevent background events induced primarily by charged particles (e.g., protons, alphas, electrons, and positrons) in the orbital environment in space (described in Sect. 2.4). A shell-shaped hollow plastic scintillator with a thickness of 1 cm was used as an anti-coincidence shield to completely cover the converter and absorber. The green part in Fig. 4 shows the geometric configuration of the ACS and its physical location in the entire system. Some of the design parameters are listed in Table 1.

Simulation and analysis tools

The Medium Energy Gamma-ray Astronomy library (MEGAlib) [34] is an open-source Monte Carlo simulation and data analysis package that is entirely written in C++ and based on ROOT [35] and Geant4 [36]. It was explicitly designed for gamma-ray detectors in the low-to-medium-energy region. It can be used for the design of detector geometry and simulation of the interaction process of gamma rays and other particles with matter, as well as for data analysis. The reliability of the MEGAlib package for the simulation and data analysis of low- and medium-energy gamma-ray detectors has been recognized by researchers in this field. MEGAlib has been successfully applied to various hard X-ray/gamma-ray telescope projects and studies in space and on the ground, such as MEGA [37], COSI [26], AMEGO [38], COMPTEL [39], ACT [40], TIGRE [41], e-ASTROGAM [7], and a combined Compton and coded-aperture telescope for medium-energy gamma-ray astrophysics [42].

The simulation of a detector based on MEGAlib first requires the creation of a realistic geometry using the Geomega package contained in MEGAlib [34, 37, 41], as shown in Fig. 4. The geometry includes the shape, size, location, material, and properties of the surrounding environment for each volume that constitutes the detector. The cosmic simulator Cosima, integrated with the MEGAlib package, was used to perform Monte Carlo simulations [34, 37, 41]. Cosima can combine Geant4 and a specified source to simulate particle transport and interaction with geometric materials and then generate an output file that stores the simulated interaction information. Simulation data analysis was performed using Revan and Mimrec contained in MEGAlib [34, 37, 41, 43]. We then obtained the simulation results. Additionally, MEGAlib uses background data generated by the LEOBackground software package [44], which is written entirely in Python, to simulate the low-earth orbit (LEO) environment. The above is only a brief overview of the functions of the main subpackages of MEGAlib (for a detailed description and usage see Refs. [34, 37, 41, 43, 44]).

Simulation method

Currently, simulation experiments are the primary methods used to investigate the performance of our polarimeter. In this section, we detail the polarimeter simulation method, including an overview of the simulation experiment flow, a detailed configuration of the performance parameters of each subdetector, a configuration of the particle sources (gamma-ray sources and background sources), and a brief data analysis process.

Figure 5 shows a brief flowchart of our simulation experiments using the MEGAlib package. First, a realistic geometric model of the detector was constructed, and reasonable performance parameters were set for the detector to adapt the simulation to reality. Additionally, the gamma rays and background sources were configured. Note that along with the particle sources configuration, items such as the physics lists, data output formats, data storage files, and simulation stop conditions were also set. Next, Geant4 was called by MEGAlib to complete the Monte Carlo simulation. The simulated data were then reconstructed (i.e., Compton event reconstruction) using the proven event reconstruction algorithm in MEGAlib. Finally, the simulation results were obtained after a high-level analysis of the reconstructed events using MEGAlib.

Fig. 5Full-screen View

Brief flow of simulation experiments using MEGAlib.

A realistic geometric model of the polarimeter, constructed using the MEGAlib package, is shown in Fig. 4 and described in detail in Sect. 2.2. To ensure that the simulation results accurately reflect the condition of the detector, the setting of the simulation parameters is crucial. Reasonable parameters can provide more realistic and reliable results regarding the performance of the detector obtained by the simulation experiment. The double-sided silicon strip detectors comprising the converter were assumed to have a uniform energy resolution of 10 keV FWHM, a noise threshold of 15 keV, and a trigger threshold of 30 keV [37]. The position resolution of the converter was determined by the number of strips and the thickness of each silicon wafer (as described in Sect. 2.2). For the CsI absorber, energy resolutions of 15% FWHM at 100 keV, 9% FWHM at 350 keV, 6.5% FWHM at 511 keV, 5% FWHM at 662 keV, 3.5% FWHM at 1000 keV, and 2.7% FWHM at 5000 keV were set. Furthermore, a noise threshold of 30 keV and a trigger threshold of 50 keV were selected [31, 33, 37]. The depth resolution (Z-direction) of the 6 cm CsI crystal was assumed to be 0.5 cm FWHM [31, 33], but no depth resolution was provided for the 2 cm cubic crystal. Additionally, the geometry of the crystals determined their spatial resolution; the specific parameters are described in Sect. 2.2. The organic plastic scintillator ACS used an energy resolution of 10 keV (1σ Gaussian), a trigger threshold of 100 keV, and a detection efficiency of 99.9% for the charged particles.

Because the MEGAlib package provides the function of user-defined particle sources, we can flexibly set the particle sources for the simulation according to our requirements. For our purposes, we used a monochromatic, negative power law, and file format (generated by the LEOBackground software package) for the energy spectrum, as well as beam parameters for the far-field point source (i.e., homogeneous beam) and far-field area source. When setting up the particle sources, we considered the fact that far-field sources are so far away that they arrive at the detector in the form of plane waves. Three types of sources were used in our simulation experiments. First, a monochromatic homogeneous beam with a flux of 1.0 ph/cm²/s was simulated and used to irradiate a polarimeter mass model. The polarization response of the polarimeter was studied by varying the energy, angle, and polarization direction of the incident photons. Next, the homogeneous beam was repeated using a power-law energy spectrum to simulate a discrete celestial source of linearly polarized gamma rays (i.e., a Crab-like source). For the Crab-like source, events were generated by linearly polarized and unpolarized photon beams with an energy spectrum of 4×10^-3E^-2 ph/cm²/s/MeV between 0.1 and 10 MeV [45]. A simulation experiment was performed using this type of source to investigate the polarization response of the polarimeter to realistically polarized photons and its polarization performance. Third, an isotropic beam source (i.e., a far-field area source) with the spectrum in file form was constructed and used to simulate the space–orbit environment. Because the polarimeter is expected to complete a satellite mission, the impact of the complex space-orbit environment on the detector should be considered. The background environment depends largely on the orbit in which the satellite operates. In this case, a typical LEO with an altitude of 550 km and an inclination of 0° was selected. The detection of the corresponding orbital background environments by the Beppo-SAX [46] and AGILE [47] missions has made orbital background environments such as this one well-known. Figure 6 shows the background environment used in the polarimeter simulation experiments, which was calculated and provided by the LEOBackground software package. The background components in Fig. 6 consist of cosmic and albedo photons, hadrons (e.g., neutrons, protons, and alphas), and leptons (e.g., electrons and positrons). The energy spectra in the file form used for the simulation experiments were the background energy spectra.

Fig. 6Full-screen View

(Color online) Background environment of the polarimeter on an orbit with an altitude of 550 km and a 0° inclination.

For the data analysis, a coincident event filter was first adopted to select events that satisfied at least one hit in the converter and at least one hit in the absorber. Next, the Compton sequence reconstruction (CSR) algorithm with trajectory tracking [37] was applied to the selected events for Compton event reconstruction, which requires the first hit of the event to occur in the converter. Information related to the incident photon, such as its initial energy, incident direction, and scattering angle, can then be obtained. The above were performed by Revan in MEGAlib. The event selection method ensures the integrity of Compton events and plays a vital role in reducing background events. Finally, the reconstructed events were further processed and analyzed using the Mimrec tool in MEGAlib, including event cuts, plotting of the reconstructed energy spectrum, evaluation of the angular resolution measurement (ARM), specified as the angular distance between a known source position and the closest reconstructed position on the Compton cone, calculation and correction of modulation curves, and image reconstruction. When we analyzed the reconstructed events, we adopted the same fixed event cuts for events generated by monoenergetic photons, including a $\pm 3\sigma$ photopeak energy window and $\pm 3\sigma$ ARM cut. Moreover, there was a variable event cut, namely, the scattering angle cut, which was adjusted according to the different photon energies, and the scattering angle window was roughly chosen between 40° and 110°. For events generated by Crab-like sources, both a $\pm 3\sigma$ ARM window and a [60°, 110°] Compton scattering angle window were applied as event cuts and no energy cut was used. The same event analysis method was used for events generated by background sources in the polarimeter. After data processing, the distribution of azimuthal scattering angles was obtained. The polarization information of the incident photons was obtained from the parameters fitted to the azimuthal distribution.

Polarization response to monoenergetic photons

Fully linearly polarized (100%) and non-polarized (0%) homogeneous on-axis photon beams with an energy of 200 keV were used in the simulation experiments; the other configuration parameters of both beams were identical (hereafter, photon beams are considered to be on-axis incidences unless otherwise specified). For a 100%-linearly polarized photon beam, the polarization vectors were (1, 0, 0). Raw azimuthal scatter angle distributions were obtained after analyzing the simulated data, as shown in Fig. 8. As shown in Fig. 8, the polarimeter responds to polarized photons (blue curve) more than unpolarized photons (black curve). However, although the blue curve approximately follows a cosine distribution, it is affected and distorted by systematic modulation owing to the nonuniformity of the detector; thus the data might be difficult to fit using Eq. (3). Additionally, for the azimuthal angle distribution generated by the unpolarized photons in the detector (see the black curve in Fig. 8), an apparent spurious modulation (the black curve is not uniformly distributed) was observed owing to the nonuniformity of the detector response along the azimuthal angle (i.e., the effect of nonuniform response). Therefore, the raw azimuthal angle distribution must be corrected to eliminate the effect of systematic modulation on the modulation curve. To obtain the corrected azimuthal angle distribution, we use the following formula [2, 37] $f_{\text{cor}}\left(\phi \right)=\frac{f\left(\phi \right)}{f_{\text{non}}\left(\phi \right)}$ (7) to correct the raw distribution. Here, f(φ) is the raw azimuthal angle distribution generated by polarized photons (blue curve in Fig. 8), f_non(φ) is the azimuthal angle distribution produced by unpolarized photons with the same energy and incident direction as polarized photons (black curve in Fig. 8), and f_cor(φ) is the corrected azimuthal angle distribution. Figure 9 presents the corrected modulation curve (hereafter, all the modulation curves shown and analyzed are corrected). Compared with the raw modulation curve (blue curve in Fig. 8), the corrected modulation curve follows the cosine distribution perfectly and can be fitted well by Eq. (3) (see Fig. 9). A modulation factor μ₁₀₀ of 0.80±0.01 was calculated using the fitting parameters. Furthermore, a polarization direction of the incident photons of 0.2°±0.2° was obtained, which was in good agreement with the actual direction (0°). The simulation results demonstrate that the polarization response and performance of the polarimeter were excellent.

Fig. 8Full-screen View

(Color online) Raw azimuthal scatter angle distributions obtained from simulations for on-axis incidence of 100% (blue) and 0% (black) linearly polarized photon beams with energies of 200 keV.

Fig. 9Full-screen View

(Color online) Azimuthal scatter angle distribution was obtained after the correction of the raw distribution (blue) in Fig. 8. The red curve was generated by fitting the corrected distribution using Eq. (3).

Figure 10 shows the corrected modulation curves fitted using Eq. (3) for four different polarization directions of a photon beam with an energy of 200 keV. The polarization parameters, such as the polarization angle and modulation factor of incident photons, for four different polarization directions were obtained and are listed in Table 2. The simulation results indicate that the polarimeter can precisely determine the polarization angle with an error of 0.2°, regardless of the change in the polarization direction of the incident photons.

Fig. 10Full-screen View

(Color online) Corrected modulation curves and their best-fit curves (red). The polarization directions of the photon beams are 0° (black), -60° (green), -90° (blue), and -180° (magenta), respectively.

During the data analysis, the Compton scattering events produced by polarized photons with an energy of 200 keV were selected with the Compton scattering angle as the filtering condition. The dependence of the modulation factor on the Compton scattering angle was also obtained. As shown in Fig. 11(a), the modulation factor is smaller for large and small scattering angles but increases significantly for medium scattering angles. Figure 11(b) shows the relationship between the energy of the incident polarized photons (100, 200, 300, 500, 800, 1000, 2000, 3000, 5000, and 10000 keV) and the modulation factor, which is found to decrease with increasing incident photon energy. The simulation results are shown in Fig. 11. We conclude that the modulation of the azimuthal angle distribution is most significant at lower energies and medium Compton scattering angles, which is consistent with the theoretical results shown in Fig. 3.

Fig. 11Full-screen View

(Color online) Dependence of the modulation factor on the Compton scattering angle (left panel, (a)) and the photon energy (right panel, (b)) for the monoenergetic photons.

Polarized photons with energies of 200, 500, and 1000 keV were simulated to be incident on the polarimeter at five polar angles (0°, 20°, 40°, 60°, and 80°). Subsequently, three curves for the modulation factor versus the incident polar angle were obtained, as shown in Fig. 12. The three relationship curves show that the modulation factor is almost unaffected by off-axis incidence (independent of the incident polar angle of the photon), indicating that the polarimeter can maintain a stable and remarkable polarization response to photons with different incidence angles. Additionally, the results verified that this polarimeter design had a large FoV.

Fig. 12Full-screen View

(Color online) Dependence of the modulation factor on the incident polar angle for photons with energies of 200, 500, and 1000 keV.

Polarization response to a Crab-like source

Two Crab-like sources with a fully linearly polarized (100%) gamma-ray beam and an unpolarized (0%) gamma-ray beam (see Sect. 2.4 for detailed parameters) were used in the simulation experiments of on-axis incidence on the polarimeter, provided that all other configurations were the same. A modulation factor of 0.76±0.01 was obtained by fitting the corrected modulation curve generated by 100% linearly polarized photons using Eq. (3). The polarimeter responds well to continuous polarization photon spectra and is sensitive to monoenergetic polarization photon spectra.

Because the polarization degree of the polarized photons emitted by cosmic gamma-ray sources may sometimes be partially polarized, it is necessary to study the polarization response of the polarimeter to photons with different polarization degrees. The simulated modulation factor μ (see Eq. (4)) and simulated polarization degree P (see Eq. (5)) were obtained by illuminating the polarimeter with photon beams emitted by Crab-like sources with different degrees of polarization (1.0, 0.8, 0.6, 0.4, 0.2, and 0.1). The simulation results for the two polarization parameters are listed in Table 3. From the data in the first and third columns of Table 3, we find that the modulation factor decreases as the polarization degree of the photon decreases, which indicates that the sensitivity of the detector to photons with a small polarization degree decreases; this phenomenon is consistent with the theory. Further, the data in the first and second columns of Table 3 show that the simulated polarization degrees are in good agreement with the actual set polarization degrees within the error tolerance. Therefore, the polarimeter can preserve or accurately recover the polarization degree of the incident photons.

MDP can be defined using Eq. (6) and characterizes the minimum polarization that a polarimeter can detect. When the Crab-like source and background components were used for the simulation experiments of the polarimeter, the relationship curve between MDP@3σ and the observation time was obtained. As shown in Fig. 13, the polarization detection capability of the polarimeter increased with the observation time. During the 24-hour observation period, the MDP@3σ of the polarimeter was 8.2%. When the observation time reached 10⁶ s (∼277.8 h), the polarimeter detected a 2.4% polarized Crab-like source. In conclusion, the polarimeter with an excellent polarization detection capability can be used to detect the polarization information of soft gamma rays in space to study various astronomical sources.

Fig. 13Full-screen View

MDP of the polarimeter for a Crab-like source as a function of the observation time.