Spatial 3-D Nonlinear Calibration Technique for Psd

Spatial 3-D nonlinear calibration technique for PSD

GUO Lifeng*, ZHANG Guoxiong, ZHENG Qi, GONG Qiang, LIU Wenyao

State Key Laboratory of Precision Measuring Technology and Instruments, Tianjin University, Tianjin, China 300072

ABSTRACT

A 3-D nonlinear calibration technique for Position sensitive detector (PSD) in long distance laser collimating measurement is proposed. An automatic calibration system was developed to measure the nonlinearity of a 2-D PSD in 3-D space. It is mainly composed of a high accurate 2-D motorized translational stage, a high precision distance measuring device, and a computer-based data acquisition and control system. With the aid of the calibration system, the nonlinear characteristic of 2-D PSD is checked in a long collimating distance up to 78 meters. The calibration experiment was carried out for a series of distance, e.g. every 15 meters. The results showed that the nonlinearity of 2-D PSD is different evidently when the PSD element is at different distance from the laser head. One calculating method is defined to evaluate the nonlinear errors. The spatial 3-D mapping relationship between the actual displacements of the incident light and the coordinates of 2-D PSD outputs is established using a multilayer feedforward neural network.

Keywords: position sensitive detector (PSD), calibration, nonlinearity, laser collimating measurement, neural network

1. INTRODUCTION

Position Sensitive Detector (PSD) is a type of position sensor utilizing the lateral photoelectric effect of a semiconductor junction. Unlike discrete element detectors such as CCD, PSD is composed of a monolithic detector with no discrete elements and provides continuous position data of the intensity center of the incident beam. Moreover, PSD features high position resolution, high-speed response, simple operating circuit, and high reliability. These characteristics make it especially suit for the laser beam alignment, displacement and vibration monitoring, position and angle sensing, automatic range finder systems, etc. Unfortunately, due to some nonideal factors, such as internal dark current, terminal capacitance, interelectrode resistance, etc., the relationship between the current or voltage outputs and position deviations is often nonlinear1-4. This defect has limited its application to some extent. So users must cut down the nonlinear error while using it in high precision fields.

Several solutions have been given for enhancing the linearity of PSD. Huang Meizhen and Lin Bin improved the linearity of a single side tetra-lateral 2-D PSD by optimizing its structure parameters2-4. Several other authors tested the nonlinearity of 2-PSD through experiments and compensate it using function approximation method5,6. In general applications with PSD, the distance between PSD and light source is usually not more than a few meters. The nonlinearity of PSD is basically consistent in the range of measurement. So the current studies about the nonlinearity of 2-D PSD are mostly carried out in the 2-D planar domain. But in long distance laser collimating measurement at the range up to several decades of meters, the intensity and shape of the incident light pot is different evidently at different distance. A reasonable presumption is that the nonlinearity of PSD will be different at different distance.

A calibration method to explore the 3-D nonlinearity of 2-D PSD in long distance laser collimating measurement is proposed in this paper. An automatic calibration device was developed to check the nonlinearity and a back-propagation neural network is used to fit the spatial 3-D mapping relationship between the actual displacements of the incident light and the coordinates of 2-D PSD outputs at different collimating distance.

2. THE PRINCIPLE OF PSD

A sectional view of common PSD with P-N-N+ structure is shown in Fig. 1. The P-type resistive layer is formed on an N-type high-resistive silicon substrate, and serves as the active area for photoelectric conversion. A pair of output

*guolifeng@vip.sina.com; phone 086 022 27404740-4; fax 086 022 27890428

electrodes are formed on both ends of the P-layer for extracting position signals. On the backside of the silicon substrate is an N+-type layer to which a common electrode is connected. The N-layer will be fully depleted if a proper reverse bias voltage is applied on the common electrode. When an incident beam strikes the PSD, electric charges proportional to the light intensity are generated at the incident position. These photoelectrons diffuse quickly in the heavily doped N+-layer. Then the N+-layer becomes a unipotential layer. In the P-type resistive layer, the hole current flows laterally toward the electrodes on the boundary because of the photopotential gradient in the lateral direction. This phenomenon is called the lateral photoeffect.

The position of the intensity center of the incident beam can be calculated by testing the output photocurrent. The position of the light spot on a two-dimensional pin-cushion type PSD, as shown in Fig. 2, is calculated from conversion Formulas (1) and (2).

(1)

(2)

where Ix1 , Ix2, Iy1, Iy2 are currents through pins X1, X2, Y1, Y2, respectively.

For enhancement of signal noise ratio and convenience for subsequent circuits, the current signal is often converted into voltage signal, and then processed according to Formulas (1) and (2). The diagram of the signal switching and processing module is shown in Fig. 3.

VR, which equals about 8V, is the reverse voltage of the PSD element. The value of the feedback resistor Rf depends on the input current, and others resistors have the same value. The operational amplifier adopted in the current-to-voltage converting circuits should be a kind of low drift amplifier, such as TL071, etc. The dividing circuits can be realized by using analog divider, AD538, etc.

3. 3-D CALIBRATION SYSTEM

From Formulas (1) and (2), it can be seen that the position coordinates of the incident beam are linearly related to the corresponding differences among the photocurrents of the PSD. But due to the intrinsic defects of the PSD (dark current, terminal