3.1. Semi-Physical Simulation Test for the Establishment of Inter-Satellite Laser Links
A three-stage acquisition strategy is adopted for the establishment of inter-satellite laser links in the Taiji program to suppress the pointing jitter of laser beams [
39]. When the semi-physical simulation test is conducted in the laboratory, the distance between the two spacecraft simulation platforms is limited to a few meters. As a result, the procedure used for aligning the two spacecrafts with the STR (star tracker) cannot be simulated; therefore, only the two-stage acquisition strategy based on the CCD (charge-coupled device) and QPD can be studied using the proposed semi-physical simulation experimental platform. The main technical parameters involved in the two-stage acquisition strategy are listed in
Table 1. The specification test for the pointing jitter value of 100 nrad/√Hz is needed within the uncertainty area range of ±23.9 μrad. Limited by the linearity range of DWS technology [
40,
41], the maximum detection FOV (field of view) of the QPD can only be set to 1.5 μrad; thus, the two-stage acquisition strategy based on the CCD and QPD is necessary to achieve both a large dynamic range and high measurement accuracy.
As depicted in
Figure 4, the receiving optical axis passes through not only the reference position of the CCD, but also the center of the QPD. The received laser beam (green line) emitted by the remote spacecraft is first acquired by the CCD. The specification for the residual error for the acquisition phase based on the CCD is 1 μrad. With an FOV of 1.5 μrad, the received laser beam can be detected by the QPD. Due to the Doppler shift originating from the relative motion between spacecrafts, heterodyne interferometry is adopted; thus, the received laser beam interferes with the local laser beam, which is projected onto the center of the QPD. Then, the beat signal phase is calculated using DWS technology [
41]. The two-dimensional angle of the pitch and yaw between the received laser beam and the local laser beam (also the receiving optical axis) is measured. Based on the measurement accuracy to the order of 1 nrad/√Hz, the pointing jitter can be suppressed to 100 nrad/√Hz; thus, precise pointing of laser is achieved. The DWS angle measurement is achieved using an SCI (science interferometer), which will be demonstrated in
Section 3.2. The local laser beam will also bedepicted, expressed as LASER1.
The acquisition process mentioned above should be simulated in the semi-physical simulation test to perform the specification test for a pointing jitter of 100 nrad/√Hz. The measurement accuracy of the test system must be 5~10 times higher than the targeted values; therefore, the semi-physical simulation system should have a test accuracy of at least 20 nrad/√Hz. This accuracy must be achieved in both the angle measurement and the simulation of the attitude adjustment.
The value of 1μrad is the designed residual error against the external FOV of the telescope. Since the magnification of telescope is 80X, the residual error at the CCD camera should be 80 μrad. A CCD camera (SH640, TEKWIN, Xi’an, China) is chosen to meet the requirements. The main technical parameters of the CCD camera are listed in
Table 2. The focal length of the imaging system is designed to be 150 mm. With the chosen CCD camera and spot centroid algorithm, the positioning accuracy can reach 0.1 pixels; thus, the two-dimensional angle measurement accuracy of the pitch and yaw between the real position of the received laser beam and the reference position (also the receiving optical axis) is calculated. With an accuracy of 10 μrad, the specification of the residual error can be met. Additionally, converting the FOV of the CCD to the external FOV of the telescope, a detection range of 800 μrad × 640 μrad can be obtained. The pointing uncertainty area range of ± 23.9 μrad can be completely covered.
With the CCD and spot centroid algorithm, the laser can be acquired in the FOV of the QPD. In the Taiji program, the diameter of the laser spot is designed to be 1 mm and the power is designed to be ca. 100 pW; thus, the QPD is required to have low NEP (noise equivalent power). To meet these requirements, a GD4542-20M QPD is chosen (China Electronic Technology Corporation, Chongqing, China), the technical parameters for which are listed in
Table 3.
As mentioned in the literature [
42], the two acquisition procedures based on CCD and QPD have strong coupling; therefore, by utilizing the DWS technology, not only can the effect of the acquisition phase based on the CCD be verified, but the specification test for the pointing jitter can also be performed. With testing accuracy in the region of 1 nrad/√Hz, the high-precision angle measurement requirements for the semi-physical simulation test system can also be met.
Another problem that needs to be solved is the simulation of high-resolution attitude adjustments. The attitude adjustment of the spacecraft is achieved through micro-thrusters. With minimum thrust in the order of μN magnitude, the resolution of the attitude adjustment can be achieved up to nrad magnitude. This is far beyond the limits of conventional mechanical motion. Piezoceramics technologies based on solid-state physics effects have infinite resolution potential in principle [
43]; thus, the simulation of high-resolution attitude adjustment can be achieved using a piezo-driven hexapod. Considering the weight of the optical interference platform (ca. 30 kg), a customized piezo-driven hexapod with the ability for both large load and high resolution is used.
According to the analysis above, the specification test for the pointing jitter can be performed using DWS technology. To achieve accurate measurements, the angle measured by the DWS should be calibrated before the test [
44]; therefore, only a motion capability of 100 nrad/√Hz needs to be satisfied for the customized piezo-driven hexapod, rather than 20 nrad/√Hz. To achieve a motion capability of 100 nrad/√Hz in the low millihertz frequency band, the corresponding specification requirement in the time domain cannot be met. It is well known that during conversion to the frequency domain, the signal in the time domain will be broken into components with different frequencies. If the resolution of 100 nrad can be achieved in the time domain, then the motion capability in the low millihertz frequency band will be less than 100 nrad/√Hz; thus, the specification requirements for the customized piezo-driven hexapod are as listed in
Table 4. The 3D model of the customized piezo-driven hexapod designed by PI (Physik Instrumente) [
45] is depicted in
Figure 5. By taking the parallel kinematics design using piezo actuators and parallel metrology capacitive sensors, motion in 6DoF (degrees of freedom) can be achieved.
The technical solution for the semi-physical simulation test for the establishment of inter-satellite laser links is shown in
Figure 6. The SCI is applied to achieve high-precision angle measurements using DWS technology. The piezo-driven hexapod is used to simulate high-resolution attitude adjustments for the spacecrafts. With the combination of DWS technology and piezo-driven hexapods, not only can the residual error of 1 μrad for the acquisition procedure based on the CCD be verified, but the pointing jitter of 100 nrad/√Hz for the establishment of the inter-satellite laser link can also be tested.
3.2. Semi-Physical Simulation Test for the Interferometry of Inter-Satellite Ranging
As mentioned earlier, distance fluctuations caused by gravitational waves between two freely suspended test masses, which are located in adjacent spacecrafts, are measured using laser interferometry. As shown in
Figure 7, the optical interference platform is mounted on the spacecraft. Although space is a microgravity environment, tiny vibrations still exist on the spacecraft. Inside the spacecraft, vibrations are treated as common mode noise, which can be suppressed [
29]. For the interferometry of inter-satellite ranging, vibrations are treated as differential mode noise, which cannot be eliminated; therefore, two freely suspended test masses are adopted as displacement reference benchmarks for the interferometry of space gravitational waves. The optical measurement process for distance fluctuations between two test masses is divided into three segments. One segment involves the interferometry of inter-satellite ranging between two optical interference platforms located in adjacent spacecrafts, while the other two segments involve the interferometry of TM (test mass) ranging between the optical interference platform and TM in each spacecraft.
The optical path design for the single-interference platform is depicted in
Figure 8a. LASER1 (red line) is split into three parts by BS1 (beam splitter 1) and BS2. Two parts involve local laser beam 1, the first part of which is directly projected onto the center of the QPDs after splitting by BS3 of SCI. The second part is first transmitted to the TM. Both LPs (linear polarizers) and ¼λ wave plates are used to alter the polarization state of the laser. After passing through a ¼λ wave plate twice, the transmission direction of the laser through PBSs (polarized beam splitters) is changed. The laser beam (blue line) is reflected by the TM, MR2 (mirror reflector), and PBS2 in turn. Then, it is projected onto the center of the QPDs after splitting by BS4 of the TMI (test mass interferometer). The third part, which is split by BS2, is emitted out. LASER2 (pink line) is local laser beam 2 on the same platform. It is only projected onto the center of the TMI’s QPDs.
After being emitted by the remote spacecraft, the third part of LASER1 is received by the local interference platform. Then, the received laser beam (green line) is captured by the CCD and QPDs of SCI one-by-one.
With the interference of the first part of LASER1 and the received laser beam, the interferometry of inter-satellite ranging is achieved using SCI. Meanwhile, with the interference of the second part of LASER1 reflected by the TM and LASER2, the interferometry of TM ranging is achieved using TMI. As described in
Section 3.1, the SCI is also used to carry out high-precision angle measurements using DWS technology at the same time. The 3D model of a single interference platform with only SCI is also shown in
Figure 8b.
In order to achieve ranging noise of 100 pm/√Hz, a series of technical specifications are proposed for the parameters of the optical interference platform, telescope, and lasers, as listed in
Table 5. To obtain the ideal interference effect, the two interfering beams need to be of equal height and parallel to each other; therefore, the degree of spot coincidence and included angle of the interfering beams are two parameters that need to be considered for the optical interference platform. Their corresponding technical specifications are guaranteed by the accuracy of the optical manufacturing and assembly processes. A joining technology named HCB (hydroxide-catalyzed bonding) is used in assembly of the optical interference platform. Optical components are bonded on a substrate made of zerodur. To ensure the scientific goals are achieved, high requirements are also placed on the telescope, including high wavefront quality, ultra-stable optical path stability, and extremely low stray light level. With a detailed design, high-precision optical manufacturing processes, and the use of an accurate alignment monitoring device, the corresponding technical specifications can be achieved. The frequency instability noise levels for LASER1 and LASER2 in
Figure 8a are the major noise sources in laser interferometry, so high requirements are proposed for the laser frequency stability. These are met using the PDH (Pound–Drever–Hall) stabilization technique.
In the semi-physical simulation test for interferometry of the inter-satellite ranging, the real working conditions in space should be simulated; however, when the simulation is conducted on the ground, gravity and ground vibration noise are two factors that cannot be ignored.
Due to the existence of gravity, it is difficult to simulate a freely suspended test mass on the ground. According to previous studies [
28,
29,
30,
31,
32,
33,
34], the specification test for interferometry ranging is conducted by measuring the system noise of the laser interference payload, in order to guarantee that the system noise is less than the specifications. The simulation of the freely suspended test mass is usually substituted by a fixed MR (mirror reflector) in a vacuum tank. As the common mode noise, the impact of the displacement fluctuation caused by various vibration noises on the interferometry ranging can be neglected. For the interferometry of inter-satellite ranging, two fixed MRs are needed. The noise caused by ground vibrations is differential mode noise. The relative displacement fluctuation between the two fixed MRs is much larger than the specifications, leading to test failure.
To perform a real semi-physical simulation test, two freely suspended test masses must be simulated while isolating disturbances from ground vibration noise to ensure that the relative motion between two test masses can be ignored. For this, multistage suspension technology is used [
46,
47,
48,
49], which was employed in LIGO. At the same time, an active control loop is imported. With the help of the millihertz-frequency and high-precision displacement sensor, the vibration noise in the low millihertz frequency band can be isolated through the active feedback control system. As a result, the freely suspended test mass can be simulated.
A schematic diagram and block diagram of the multi-stage suspension vibration isolation based on active control are shown in
Figure 9. A two-stage suspension is used. An active control system, which is achieved by utilizing technologies such as an inertial sensor, PID control, weak force driver, and precision machinery, is imported on TM 1. The control period for the active control is far less than the period for the ground vibration; thus, the ground vibration noise is isolated by the active control acting on TM 1 before it is transmitted to TM 2 and suspended at the second stage. As such, TM 2 can move freely in the horizontal direction. Through reasonable design of the suspension system and active control system, the displacement disturbance of TM2 in the low millihertz frequency band can be ensured to be in the order of the pm magnitude, so as to perform the semi-physical simulation of the freely suspended test mass. This challenging task is currently being tackled by another participating team from the Taiji program.
The spacecraft simulation platform is also affected by the ground vibration noise. According to [
50,
51], ground vibration noise is caused by natural phenomena and human activities. There are two main types of noise: one is noise with a frequency range above 0.5 Hz, caused by the shake of buildings, trees, and human activities; the other type is noise with a frequency range of 0.05~0.5 Hz caused by surface waves and body waves in the crust, which are originated from collisions on the coast by sea waves. For the simulation of the micro-vibration environment of a spacecraft, a commercial precision active vibration isolation platform is used for effective isolation of ground vibration noise. The precision active vibration isolation platform needs to be placed horizontally on the desktop. From the analysis above, it can be seen that the spacecraft simulation platform must have the ability for both micro-vibration and high-resolution attitude adjustment; therefore, the spacecraft simulation platform is made up of the precision active vibration isolation platform and the piezo-driven hexapod described in
Section 3.1, with the latter placed on the former. Based on these analyses, the TS150 [
52], whose isolation frequency can be as low as 0.7 Hz, is selected.
The technical solution to the semi-physical simulation test for the interferometry of inter-satellite ranging is shown in
Figure 10. Two test mass simulators, which are based on active suspension vibration isolation technology, are used to simulate the two freely suspended test masses in adjacent spacecrafts. The spacecraft simulation platforms, with the ability for both micro-vibration and high-resolution attitude adjustments, are used to simulate the spacecraft. The dual-spacecraft simulation platforms are placed between the two test mass simulators. Ranging noise of better than 100 pm/√Hz can be expected for the interferometry of inter-satellite ranging, which can be tested by measuring the system noise.
3.3. Semi-Physical Simulation of the Space Environment
When the semi-physical simulation is conducted on the ground, the temperature and pressure will influence the measurement results because of Rayleigh scattering, refractive index fluctuation, and optical element deformation [
53,
54]. To avoid these influences, a vacuum and cold-black space environment must be simulated in the semi-physical simulation test.
An oil-free vacuum tank with a heat sink, as shown in
Figure 11, is adopted to simulate the cosmic vacuum and cold-black environment. The inner wall of the vacuum tank is blackened, with the heat sink surrounding the outside. The heat sink is filled with liquid nitrogen to obtain a uniform low temperature, which is used to simulate the cold-black space environment. The main technical parameters of the vacuum tank are listed in
Table 6, which at a highly technical level can be achieved in the laboratory [
55,
56].
For the inter-satellite laser interference, simulation is required of the cosmic vacuum and cold-black environment where the two spacecrafts are located; therefore, the dual vacuum tank system shown in
Figure 12 is used for the simulation. The dual vacuum tank system is composed of two vacuum tanks with a heat sink and a vacuum pipeline, the length of which is 10 m and which connect the two tanks. The inner diameter of the pipeline is 1 m, so as to ensure enough room to complete the laser acquisition reciprocally when establishing the inter-satellite laser link. An optical table is designed for each vacuum tank to carry the spacecraft simulation platform and the laser interference payload. According to
Section 3.2, only ground vibration noise above 0.7 Hz can be isolated by the precision active vibration isolation platform. In order to minimize the impact of ground vibration noise on the laser interferometry, the optical table is also subjected to strict vibration isolation treatment. A two-stage vibration isolation method for the independent foundation plus active vibration isolation is adopted to ensure the vibration acceleration is attenuated to 10
−5 g within the frequency range of 0.1~100 Hz.