# High-Precision Light Spot Position Detection in Low SNR Condition Based on Quadrant Detector
## 5 Experiment Results  
The experiment platform is shown in Figure 4. The laser source we use in the experiment is a modulated laser source with a wavelength of 1550 nm, whose output laser is intensity modulated by a cosine signal of 125 kHz. The data width of the ADC output is 16 bits, and the sampling frequency of the ADC is 100 MHz. The QD, whose active radius of 0.5 mm with a gap width of 0.1 mm, is mounted on a 3-dimensional micro-displacement motion stage in order to get the accurate position of the spot light. We recorded that the spot radius was 0.42 mm, and the QD output SNR is \(-10\) dB. Here we define that \(x_{0}\) is the calculated x coordinate, and \(X\) is the real x coordinate; then we can get the deviation of the spot position (here we regard the coordinate y having the same distribution as x, so we only use the x coordinate for calculation):  
\[\delta_{x}=x_{0}-X \tag{16}\]  
There are 800 data points in one period after ADC. Here, we take one period of photocurrent data output from QD using the direct method. For the proposed method, the four electric signals are separately processed in Kalman filters. Before Kalman filtering, we calculate the DC offsets and give an inverse gain to eliminate them. The input modulated signals of one quadrant are shown in Figure 5.  
In Figure 5a, the input signal is so dense that in order to see the details, we need to zoom in, as seen in Figure 5b. However, it is also not obvious for us to find out the distribution of the input signals in Figure 5b. Here, we use the peak values of the signals in every period after ADC as the measurement values. Then we take the peak values of every period, which are directly proportional to the amplitude illustrated on QD, into the iterative formula to estimate the position. The measurement signals contain the real position signals and the noise, where the real position signals should be the same in theory. Therefore, we presume that the variance of the measurement noise is the same as the variance of the measurement signals. In addition, we assume the initial value of the state X(0) is the mean value of the measurement matrix, and then we can calculate the initial covariance P(0). Finally, we use Kalman filtering to estimate the amplitude of the beacon light. We first take 10 points of peak values into calculation, After the calculation, we can compare the performance of the two processing methods. The experiment results are shown in Figure 6.  
Figure 4: Experiment platform. Figure 5: (**a**) The input modulated signals; (**b**) the input modulated signals which are zoomed in on to see the details. In Figure 6a, the black dotted line represents the ideal situations, where the calculated coordinate is the same as the real coordinate. However, there are gaps between the diodes, causing the non-linearity of the QDs between measurement values and real values. The blue solid line represents the direct detection method, and the red solid line represents the proposed improved detection method. The two lines show that the proposed method improves the linearity of QD over the direct method. In Figure 6b, the absolute errors of the proposed method are also smaller than the direct method. We then add the measurement values up to 40 points, with the experiment results shown in Figure 7.  
In Figure 7, we can see that the linearity is almost the same, but the absolute errors decrease compared with Figure 6.  
We continue adding the measurement values up to 80 points until the absolute errors do not change, which means the filtering algorithm is already convergent. The experiment results are shown in Figure 8. The decreases in absolute errors are not obvious, so we apply quantified calculation later. Here, we use root-mean-square (RMS) errors to express the result:  
\[\delta_{R}=\sqrt{\sum_{i=1}^{N}\delta_{i}^{2}/N} \tag{17}\]  
\[\delta_{x}=x_{0}-X \tag{16}\]0 **(a)** The calculated x coordinate curves using the two methods (10 points Kalman filtering); **(b)** the absolute errors using the two methods (10 points Kalman filtering).