With the development of optical pumping technology [1, 2], spin-polarized atoms have been used in many practical applications, such as bio-magnetism atomic sensors [3], atomic magnetometers [4], atomic gyroscopes [5], and so on. The gyroscope is one of the necessary sensors for the Inertial Navigation System (INS), which plays an important role in many facilities which need accurate position, velocity, and orientation information. The inertial measurement device based on spin-polarized atoms has become a hot spot. Spinpolarized atoms will precess at an atomic-species-dependent frequency when subjected to an external magnetic field [6]. The physical rotation of the device containing such atoms will modify the frequency in proportion to the rotation rate. The novel device makes use of detecting the precession frequency to measure the rotation rate [7]. According to the theoretical analysis and experimental results, the ASIMD has many advantages [8-11]. Moreover, the nature of the device’s structure is inherently immune to external vibration. Because the ASIMD replaces the mechanical rotor with spin-polarized atoms, it does not have any mechanical collisions and friction, and it offers promise for applications with high precision [5]. The angle-random walk (ARW) of 0.002 Hz and the bias instability of 0.04 °/h based on the atomic spin gyroscope have been achieved and it has the potential advantage to achieve the best performance gyroscope in the future [12].
The output signal of the IMU has a definite proportional relationship with the attitude angular velocity of the moving carrier. The degree of the IMU’s accuracy affects the precision of the INS directly. Due to the influence of many factors such as machining processes, the external environment and so on, the characteristics of the relationship between the gyroscope’s input and output signals is nonlinear. It leads to errors in the scale factor. At present, many scholars have made contributions in the calibration of the scale factor. Some researchers established the relevant mathematic model of scale factor on full range and put forward the corresponding compensated methods [13, 14]. Others carried out their research aiming at the characteristics of scale factor error such as asymmetric positions, nonlinear problems and so on [15, 16]. Some research works have been proved valid by the experimentally verified results, and the errors have been reduced in different degrees [13-16]. The method of using the high precision IMU as a standard has been generally adopted in these traditional methods to determine the scale factor, and most of the research aimed at the common gyroscopes and focused on the mathematical process without the considerations of the work principle of the device.
The ASIMD is a new kind of gyroscope, and it is still in the stage of development without official methods for scale factor calibration. In this paper, we have calibrated the scale factor for the device based on the mature product (IMU) at first. However, the experimental results have been influenced by many factors such as the precision control of the frequency for the optical platform, the precision adjustment of the amplitude for the platform, the decrease of system errors and so on. In the view of these problems, we have changed the test method. According to the characteristics of the device, we calibrated the scale factor based on the gyromagnetic ratio of the noble gas, and it has been tested accurately by the related theoretical analysis and experimental verification.
The basic theory of the ASIMD is based on the effect of nuclear magnetic resonance [10, 12]. The principle can be described as follows:
Here is the polarization of nuclear spins belonging to the noble gas, and it contains three orthogonal components,, , and is the spin-polarization of the outer most electrons belonging to alkali-atoms, and it contains three orthogonal components, , and is the spin-polarization of the outermost electrons belonging to alkali-atoms along the x direction, which can be used to describe the output signal of the equipment;
Eq. (4) shows that the ASIMD is based on the pattern of the angular rate model. Because the device is a new type of inertial measurement device, there are no mature standards for the scale factor calibration. According to the features of the ASIMD, a test scheme is designed to calibrate the scale factor for the device. The scale factor is always used in the inertial technology, as shown in the following equation.
Here V is the output voltage signal of the ASIMD, and its unit is V; Ω is the angular rate signal of the carrier detected by the ASIMD, and it is the input signal with the unit °/s; K is the scale factor, and its unit is °/s/V.
The original output signal of the device is a voltage signal, which needs to be converted to an angular rate signal to match with the input signal. The inertial measurement unit (IMU) based on interference fiber optic gyros (IFOGs) can be used to assist the atomic spin inertial measurement device to implement this function. The atomic spin inertial measurement device and the IMU are fixed on the same optical platform. The IMU consists of three IFOGs based on angular rate model and three accelerometers, which can be used to measure the carrier motion information including translational motion and rotary motion in three perpendicular directions.
The ASIMD (the size of the ASIMD is 1800 mm (Length) × 1500 mm (Width)) was installed on the optical platform. The optical platform can be supported through the six airbearing legs, which makes the device rotate around the support legs slightly. Because spaces available for motion of the gasbags of the legs are limited, the maximum rotation angle is about ±2°. In order to provide a measurement criterion of angular velocity for the atomic spin inertial measurement device, high precision fiber optic IMU was fixed on the optical platform together with the atomic spin inertial measurement unit. High precision fiber optic gyroscopes can measure the angular velocity of the device, playing an important part in calibrating the output signal of the atomic spin inertial measurement device. The test hardware structure diagram and the physical graph are shown as follows.
The optical platform was driven around the y-axis with small amplitude. The results of angular rate along the y-axis detected by the high precision optical fiber gyroscopes (the sampling frequency of the gyroscope is 200 Hz and the bias instability of the gyroscope is 0.03 °/h) and the ASIMD were shown as follows. The output results of the two kinds of devices were subjected to least-squares model fitting, as shown in Fig. 3.
Making use of scale factor calibration coefficient, the output signal of ASIMD can be transformed into the angular velocity from the voltage signal, which is in contrast to IMU in Fig. 4. There are many factors causing the errors and they can be mainly divided into two categories.
Firstly, because the experimental platform is supported by the air-bearing legs, the driven amplitude of the optical platform is very small. The maximum driven amplitude of the optical platform was about 0.2°, as seen in Fig. 4. Under this condition, the random errors have a great influence on the results of the experiment, and it led to the inaccuracy of the scale factor.
Secondly, the driven frequency of the platform cannot be controlled accurately. According to the amplitude-frequency curve, most vibration frequencies of the optical platform were less than 5 Hz, and the driven frequency was mainly focused on 1.133 Hz, as shown in Fig. 5. The bandwidth of the ASIMD needs to be confirmed, which may influence the experimental results. According to the Fig. 6, the adjustment time of the system is about 0.4s. The bandwidth (0 dB) of the ASIMD is less than 2.5 Hz. The signal amplitude whose frequency was higher than 2.5 Hz has been attenuated because of the bandwidth limit of the ASIMD. Under this condition, the scale factor calibration of the ASIMD may be inaccurate.
According to the Eq. (1) to (3), the right hand side of the Eq. (3) can be simplified and merged. Thus, the output signal of the ASIMD can be simplified into the following expression.
According to the Eq. (5), the scale factor can be described with the letter
According to the output signal of the ASIMD which is shown in Eq. (4), we took its partial respect to the magnetic field
Based on the above theories, we carried out related experimental research work. The core sensitive header of the device was a square glass cell with a side of length 2 cm. The cell, containing a droplet of cesium, 5 torr xenon 129 and 1 atm nitrogen, was heated to 100 ℃ with average relative error of 0.5 ℃. The power of the pumping light was 100 mW. The power of the probe light was 4 mW. After about one hour, the system had reached steady working condition. In order to get the signal , we modulate the magnetic field
According to the Eq. (7) to (8), the experimental test points can be used to fit a curved line. The scale factor can be determined by the fitting coefficients
The fitting results of the experiments are shown in Table 1. Choosing coefficient of determination (R-square) as the judging standard, the best results of the two important fitting coefficients were -5159, -94.07 for
[TABLE 1.] The experimental results for parameters fitting
The experimental results for parameters fitting
In this paper, we calibrated the scale factor for the ASIMD device by using a new method, which utilized its self-signal rather than other calibration equipment to determine the scale factor with small errors. At first, the IMU was used to calibrate the scale factor for the ASIMD. However, the output signal of the ASIMD always fell behind the output signal of the IMU because of the limits of the ASIMD’s bandwidth. Then, the method to determine the scale factor in a self-consistent way by using the gyromagnetic ratio of the noble gas was presented, and it has been verified by multi-group experiments.
In the future, we intend to implement an inertial measurement with different spin-polarized noble gases and to find the most suitable noble gas for our application.