Improvement and Radiation-Resistance Study of an Optical Displacement Sensing System Based on a Position Sensitive Detector

Abstract

We report a method of improving the precision and resolution of sensing systems based on position sensitive detectors (PSDs). In the method, we improved the precision and resolution by reducing the gain of the condition circuit and conducting spatial filtering on the measured spot position. To demonstrate the method, we experimentally built a PSD-based displacement sensing system. With the system, a precision of 0.3 μm and a resolution of 0.5 μm were obtained. The precision is two orders of magnitude better than that obtained with the use of a commercial condition circuit (SPC02, SiTek, Partille, Sweden) and without using any filter. Moreover, we tested the radiation-resistance performance of the system using a ⁶⁰Co radiation source. The system kept the precision and resolution after exposure to radiation with a dose set to 100 krad. Our study is very useful to realize high-precision PSD-based sensing in space.

1. Introduction

Active vibration isolation systems play a critical role in space experiments and exploration, precise machining and metrology, and scientific research such as particle physics [1,2,3,4,5,6]. An indispensable part of an active vibration system is displacement measurement systems, which provide spatial vibration information used for vibration isolation [7,8,9]. A displacement measurement system should have high precision, resolution, and accuracy to meet the requirements of the above applications. For space applications, a displacement measurement system should additionally meet the requirements of small volume, light weight, and high radiation resistance so that it can be used as a payload. A displacement measurement system based on a position sensitive detector (PSD) is very attractive since it features a compact size, rapid response, and simplicity in principle [10]. Besides the popularity in space experiments, PSDs have wide applications, such as sensing humidity [11] and seawater refraction index [12], detecting underwater propeller wake [13] and the main shaft of wind turbines [14], distinguishing parenteral artificial nutrition injected to patients [15], and calibrating field for robots [16] and localizing robots [17]. As the resolution of a position sensing system based on a PSD is inversely proportional to the photocurrents of the PSD and proportional to the noise of the sensing system [18], studies on increasing the photocurrent of a PSD and decreasing the noise of such a measuring system have been widely reported. A promising way to increase photcurrents is using two-dimensional (2D) materials, such as graphene, and transition-metal chalcogenides instead of silicon [19,20]. In 2020, Wenhui Wang et al. demonstrated that the position sensitivity of a PSD using 2D materials and incident laser power just at the nano-watt level is an order of magnitude higher than that with using silicon materials and incident laser power at the milli-watt level [20]. In 2021, Hao jiang et al. demonstrated a 10-fold increase in the generated photocurrent by introducing gate manipulation in a graphene–silicon-on-insulator structure, compared with the counterpart without the gate modulation [21]. The noise of a PSD-based sensing system primarily originates from ambient light on the PSD, the PSD board, its condition circuit, and movements that cause the sensing system to shake. To get rid of ambient stray light, methods such as introducing a light cut-off filter, optimizing the configuration of the sensing system, and modulation detection and sample-hold detection are generally used [22]. In 2014, Mehdi Rahimi et al. proved that noise could be effectively removed by averaging a set of replicate measurements in the time domain [23]. What is more, Siwei Sun et al. reported a method to improve the position resolution of most types of PSDs, in which barrel distortion was introduced deliberately to enhance the positional resolution of a PSD through changing the sheet resistance ratio of the photosensitive area and border resistor [24]. The noise from the condition circuit is mainly caused by the amplifier [25]; hence, a possible way to decrease the noise of a PSD-based sensing system is by reducing the gain of the amplifier. However, currently, commercially available condition circuits generally have large gain, leading to a high noise level. To decrease the output noise voltage, self-designed circuits have been studied, e.g., condition circuits based on low-noise OPA111 op-amp [26] and TL074 op-amp [27] have been reported. Although the noise of these self-designed circuits is already lower than that of commercially available circuits, further decreasing the noise and optimizing other specifications are very important for many practical applications.

In this paper, we report a method for improving the precision and resolution of sensing systems based on PSDs and the radiation-resistance properties of a PSD-based displacement sensing system. In the method, we improved the precision and resolution by reducing the gain of the amplifier of the condition circuit and conducting spatial filtering on the measured spot position. We designed a condition circuit with a gain of the amplifier of ten thousand, which is an order of magnitude lower than that of a commercial condition circuit (SPC02, SiTek, Partille, Sweden), and compensated the gain by increasing the light power impinging on the PSD sensor. We experimentally demonstrated the method in a PSD-based displacement sensing system. We obtained a precision of 3.9 μm in the x direction and 3.3 μm in the y direction with the use of our condition circuit, which is an order of magnitude better than that obtained with the use of the commercial condition circuit. We further improved the precision to 0.3 μm by implementing spatial filtering employing a Butterworth low-pass filter with a cut-off frequency of 1 Hz. With the use of our method, a displacement resolution of 0.5 μm was acquired. In addition, the system kept the precision and resolution after being exposed to ⁶⁰Co radiation with a dose of 100 krad. Our study is very useful to realize high-precision PSD-based sensing in space.

2. Methods

Figure 1a depicts the schematic of a 2D PSD (2L10_SU7, SiTek, Partille, Sweden) and our designed condition circuit. This PSD was selected because its typical position non-linearity of 0.3% in the whole 10 mm × 10 mm active area is superior. The material of the PSD was silicon. The PSD had a three-layer structure, the P-type resistive layer with two contacts at the opposite ends as the front side, the middle low-doped N-type layer, and the N-type resistive layer with two contacts at opposite ends placed orthogonally to the contacts on the front side as the back side. The center of the PSD was defined as the origin point, the direction parallel to the contacts on the back side was defined as the x direction, and the direction parallel to the contacts on the front side was defined as the y direction. The condition circuit was composed of an amplifier module, an analog-to-digital (AD) module, and a control module. The amplifier module consisted of four amplifiers, A1, A2, A3, and A4 (ADTL084ARZ, Analog Devices, Inc., Wilmington, MA, USA), which were used to convert the four-output current signal, Iy₁, Iy₂, Ix₁, and Ix₂, of the PSD sensor to voltage signals and amplified the voltage signals by ten-thousand times. The amplifier had a noise value of 16 nV/√Hz and a bandwidth of 5 MHz. The voltage signal in the y direction had the opposite sign to the voltage signal in the x direction, which was required according to the manual of the PSD sensor. The AD module was used to digitalize the analog voltage signals. It consisted of an AD converter (ADS1258, Texas instruments, Dallas, TX, USA) and a peripheral circuit to operate the AD. The converter had 16 channels and 24 bit. The clock (CLK) and chip-selecting (CS) signals of this module were provided by the control module with FPGA (XC7Z020-CLG484, Xilinx, Santa Clara, CA, USA) for logic programming. The digital signal generated in the AD module was transmitted to the control module through the data communication ports in the two modules (TX in the AD module and RX in the control module). The digital signal was then transmitted to a computer by the control module through a serial port (SP) with a baud rate set to 115,200. The commands used to operate the AD module were sent by the control module through the command communication ports (RX in the AD module and TX in the control module). In the computer, we performed spatial filtering and calculated the position of the light spot on the PSD sensor. Figure 1b is a photo of the designed condition circuit. Figure 1c shows the displacement sensing system that was built to verify the performance of the designed condition circuit. The light source was LED (L10596-02, Hamamatsu, Iwata, Japan) with an output power of 3 mW, which was high enough to enhance the output signal of the condition circuit with low amplification gain. The beam diameter was collimated to ~2 mm. The distance between the LED and PSD sensor was about 3 cm. This distance guaranteed that the beam had not diverged at the PSD sensor. During the experiment, we carefully aligned the PSD and LED so that the light beam impinged the active surface of the PSD orthogonally to avoid any deterioration in precision and resolution and to make sure that the measured displacement reflected real displacement. An enclosure was used to shield the experiment from environmental disturbance as much as possible. The experiment was conducted on a marble optical platform with a vibration-isolated system at room temperature so that effects, such as vibration and temperature variation, on the experiments were negligible.

3. Results

We characterized the precision of our system. We aligned the light spot to the center of the PSD and then acquired the output of the PSD for about 20 s with the use of our self-designed condition circuit. We also acquired the output of the PSD employing a commercial condition circuit with the same time period for comparison. We obtained the position of the light spot on the PSD according to Equations (1) and (2), where Vx₁, Vx₂, Vy₁, and Vy₂ are the voltage converted from the output current of the PSD and L is half of the width of the PSD. Figure 2a and 2b, respectively, show the measured light-spot position using the two-condition circuit in the x direction and y direction. It can be seen that the variation in the spot position measured by the commercial circuit is much larger than that measured by our self-designed circuit in both directions. The standard deviation was about 8.4 μm in the x direction and 14.2 μm in the y direction for the commercial circuit, while these values were 1.3 μm in the x direction and 1.1 μm in the y direction for the self-designed circuit. The corresponding 3-sigma precision was about 25.2 μm in the x direction and 42.6 μm in the y direction for the commercial circuit and 3.9 μm in the x direction and 3.3 μm in the y direction for the self-designed circuit. Our circuit improves the precision almost by an order of magnitude. We then employed a Butterworth low-pass filter with a cut-off frequency of 1 Hz to further improve precision. Figure 3a and 3b, respectively, show the light-spot position when using the filter together with those without using the filter in the x direction and y direction. The precision in both directions was about 0.3 μm when the filter was used. With the use of the Butterworth low-pass filter, the precision effectively improved. Thus, in the following measurement, the self-designed driven circuit and Butterworth low-pass filter were used.

$$\mathrm{x}={\displaystyle \frac{{\mathrm{Vx}}_1-{\mathrm{Vx}}_2}{{\mathrm{Vx}}_2+{\mathrm{Vx}}_1}}\mathrm{L}$$

(1)

$$\mathrm{y}={\displaystyle \frac{{\mathrm{Vy}}_1-{\mathrm{Vy}}_2}{{\mathrm{Vy}}_2+{\mathrm{Vy}}_1}}\mathrm{L}$$

(2)

We estimated the resolution of our displacement measurement system. The schematic of the setup for this estimation is shown in Figure 4. We put the light source on a piezo stage (L-731.4ASD, Physik Instrumente, Karlsruhe, Germany) with a unidirectional repeatability of 50 nm and the PSD on the optical bench. We aligned the light source so that the output beam was incident on the area near the center of the PSD, which was the actual start point. We set a displacement and velocity value for the piezo stage. We controlled the stage to move in steps in the negative x direction and used the PSD to acquire the signal simultaneously. The measurement continued for 20 s after the displacement was finished. The above process was repeated 11 times. Similarly, we conducted the measurement in the y direction by rotating the PSD by 90°. We conducted this measurement on the area near the center of the PSD, although the measurable displacement range of the system was 8 mm, which was calculated by subtracting the spot diameter from the size of the PSD sensor. This is because the non-linearity in the center area is generally smaller than that in the outer area; thus, an accurate position of the light spot was obtained without any calibration. By subtracting two adjacent positions of the light spot, the displacement of the LED was achieved.

The results obtained in the two directions are very similar. Figure 5a, 5b, 5c, and 5d, respectively, show typical displacements measured in the x direction when we set the step size of the piezo stage to 7 μm, 0.7 μm, 0.5 μm, and 0.3 μm. Here, to show the results intuitively, we offset the date points so that the end points were at the origin point. It is shown that the response of the PSD in the time domain is a step function. We explain this phenomenon by the ratio of the movement time of the stage to the static measurement time. The time for the stage to finish each displacement was about 1 s, while the static measurement time was set to 20 s. Because of the small time ratio, the stage-moving process is not visible in Figure 5; thus, a step phenomenon can be observed. The system clearly resolved the displacement set to the piezo stage when the step size was 0.5 μm and above, and cross-talk happened when the step size was 0.3 μm. Thus, we defined 0.5 μm as the resolution of our system.

We tested the performance of our displacement measurement system when exposed to ⁶⁰Co radiation. The experiment was performed at the Institute of Low-Energy Nuclear Physics at Beijing Normal University. The ⁶⁰Co source was a single-grid planar source placed in a water well, which had a radioactivity value of 3.7 × 10¹⁴ Bq. Its dose rate was calibrated using Fricke dosimeters, both from Beijing Normal University and the National Institute of Metrology [28]. The total uncertainty of nominal doses was estimated at ±2% (2 sigma). We set the radiation dose from 50 krad to 100 krad with a step size of 10 krad. This dose range was chosen because components at high orbits generally have to withstand a total irradiation dose of 100 krad, and components that can only withstand a total irradiation dose below 50 krad are hardly considered at high orbits. The step size was chosen to ensure sufficient data points while maintaining time efficiency. The distance between the ⁶⁰Co source and our system was about 15 cm. Initially, we measured the system’s precision in this experimental platform with the ⁶⁰Co radiation source turned off. The ⁶⁰Co radiation source was raised to the experiment platform when it was turned on. We measured precision at each dose step for 100 s to fully study the effect of ⁶⁰Co radiation on precision. Figure 6a depicts the variation in radiation dose and the corresponding spot position in the x direction with time. When the ⁶⁰Co radiation source was turned off, the standard deviation and precision were 0.22 μm and 0.66 μm. When the radiation dose was set from 50 krad to 100 krad, the precision was hardly affected. Figure 6b depicts the variation in radiation dose and the corresponding spot position in the y direction with time. The standard deviation and precision were 0.18 μm and 0.54 μm at the beginning and were not affected when the ⁶⁰Co radiation source was turned on. Here, the precision was a little higher than that measured above; this is probably because it is difficult to completely block environment light and isolate environment vibration. Our system has good resistance to ⁶⁰Co radiation.

We measured the precision and resolution of our system after 48 h of annealing to fully estimate the influence of ⁶⁰Co radiation. We conducted the measurement in the same way as that conducted before radiation. Figure 7a shows the light-spot position measured in a 20 s period after annealing, together with that measured before radiation in the x direction. The standard deviation and precision after annealing were 0.15 μm and 0.45 μm, which are comparable with the values obtained before being exposed to radiation. A similar trend was obtained in the y direction, as shown in Figure 7b. The standard deviation and precision after annealing were 0.12 μm and 0.36 μm. Figure 8 shows the displacement measured by our annealed system when step displacements of 7 μm, 0.7 μm, 0.5 μm, and 0.3 μm were set. The results are similar to those shown in Figure 5, which means that our system kept the resolution of 0.5 μm after 48 h of annealing after being exposed to ⁶⁰Co radiation. When combining the results measured before radiation, during the radiation process, and after annealing, it can be concluded that our system is highly resilient to ⁶⁰Co radiation.

4. Discussion

The resolution of a PSD ΔR is determined by Equation (3), where L is the length of the photosensitive area, I_n is the noise current, and I_o is the total photocurrent. I_n is calculated using Equation (4), where I_s is the shot noise current originating from the photocurrent and dark current, I_j is thermal noise current generated from the interelectrode resistance on the PSD sensor, and I_en is the noise current from the equivalent input voltage noise of the amplifier. I_s, I_j, and I_en are, respectively, expressed by Equations (5)–(7), where q is the electron charge, B is the bandwidth, k is Boltzmann’s constant, T is absolute temperature, R_ie is the interelectrode resistance, and en is the equivalent input voltage noise of the amplifier. According to Equation (3), increasing the photocurrent and decreasing noise play an equal role in improving the resolution of a PSD. Although the use of 2D materials can effectively increase the photocurrent, the PSD using 2D materials is yet to be produced. A practical way is to design a condition circuit with low noise to increase the resolution. Compared to the commercial SPC02 circuit from Sitek, the noise of our circuit is about 30-times lower [29]. Moreover, our circuit outperforms in terms of bandwidth and operating temperature [29], as shown in

Table 1. Comparison between commercial circuit and self-designed circuit.

	SPC02 Circuit	Self-Designed Circuit
Noise voltage	3 mV	0.1 mV
Bandwidth	400 kHz	5 MHz
Dimension (Amplification part)	21 mm × 21 mm	33 mm × 33 mm
Operating temperature	70 °C maximum	−40~125 °C

. The noise, bandwidth, and operating temperature of our circuit are also superior to those of the commercial circuits from Hamamatsu [30]. Compared to the self-designed circuits that use elements with a similar operating temperature range [26,27], our circuit has lower-voltage noise density.

$$∆\mathrm{R}=\mathrm{L}\times {\displaystyle \frac{{\mathrm{I}}_{\mathrm{n}}}{{\mathrm{I}}_{\mathrm{o}}}}$$

(3)

$${\mathrm{I}}_{\mathrm{n}}=\sqrt{{\mathrm{I}}_{\mathrm{s}}^2+{\mathrm{I}}_{\mathrm{j}}^2+{\mathrm{I}}_{\mathrm{e}\mathrm{n}}^2}$$

(4)

$${\mathrm{I}}_{\mathrm{s}}=\sqrt{2\mathrm{q}({\mathrm{I}}_{\mathrm{o}}+{\mathrm{I}}_{\mathrm{D}})\mathrm{B}}$$

(5)

$${\mathrm{I}}_{\mathrm{j}}=\sqrt{{\displaystyle \frac{4\mathrm{k}\mathrm{T}\mathrm{B}}{{\mathrm{R}}_{\mathrm{i}\mathrm{e}}}}}$$

(6)

$${\mathrm{I}}_{\mathrm{e}\mathrm{n}}={\displaystyle \frac{\mathrm{e}\mathrm{n}}{{\mathrm{R}}_{\mathrm{i}\mathrm{e}}\sqrt{\mathrm{B}}}}$$

(7)

5. Conclusions

In summary, we introduced a method for improving the precision and resolution of sensing systems based on PSDs and the radiation-resistance properties of a PSD-based displacement sensing system. We improved the precision and resolution by reducing the gain of the amplifier of the condition circuit and conducting spatial filtering to the measured spot position. We designed a condition circuit with a gain of the amplifier of ten thousand, which is an order of magnitude lower than that of a commercial condition circuit, and compensated the gain by increasing light power impinging on the PSD sensor. We then conducted spatial filtering on the measured spot position using a Butterworth low-pass filter with a cut-off frequency of 1 Hz. With the use of our method, a precision of 0.3 μm and a resolution of 0.5 μm were obtained. The precision is two orders of magnitude better than that obtained with the use of a commercial condition circuit and without using any filter. In addition, the system kept the precision and resolution after being exposed to ⁶⁰Co radiation with the dose set to 100 krad. Our study is very useful to realize high-precision PSD-based sensing in space.