Nonlinear Error Analysis And Compensation Technology For Low Frequency Homodyne Laser Interference Vibration Measurement

Homodyne laser interference vibration measurement is a key technology in low frequency vibration calibration. But the nonlinear error during the measurement process is one of the most important factor restricting the further improves of its measurement accuracy and performance. The polarization mixing and polarization loss existed in the traditional homodyne laser interferometer optical path cause significantly nonlinear error. Also, there are many adjustable devices in the traditional optical path which increase the difficulty of adjustment, and the deviation of the rotation angle can cause significant non-orthogonal error. In the signal processing progress, only DC offset error and unequal amplitudes error compensation method has simple mathematical relationship and may easily achieve real-time compensation. The non-orthogonal error correction is more difficult. Therefore, the nonlinear error compensation technology of homodyne laser interference vibration measurement has become one of the key technologies in low frequency vibration calibration.This dissertation” Nonlinear error analysis and compensation technology for low frequency homodyne laser interference vibration measurement” mainly aimed to the issue that there is significantly nonlinear error in the traditional homodyne laser vibrometer and the non-orthogonal error is difficult to achieve real-time compensation. Based on deeply analyzing the characteristics of the non-ideal optical components and the nonlinear error mathematical model of traditional homodyne laser interference optical path based on PBS, a homodyne laser interference optical path based on NPBS is proposed. Its nonlinear error mathematical model and cooperative compensation method is established and tested by experiments. The main research contents of this dissertation are as follows:The characteristics of the optical components are deeply analyzed, especially for the NPBS and corner cube prism which are used to be simplified as ideal state during mathematical model building. The Jones matrix of those components is given under the ideal state and the actual state.A detailed mathematical model of nonlinear error is given by the traditional homodyne laser interference optical path based on PBS. Then the relationship between non-ideal characteristics of optical components with nonlinear error, the rotation angle of adjustable devices with non-orthogonal error is analyzed. The defect of the adjustable devices and non-orthogonal error that significant and difficult to compensate is pointed out by theoretical analysis.A homodyne laser interference optical path based on NPBS and a cooperative compensation method is proposed. Then establish the nonlinear error mathematical model with the impact of all error sources. Finally analyze the relationship between the rotation angles of adjustable devices with non-orthogonal error. Prove that this optical path has the advantages of simple structure, easy adjustment, non-orthogonal error easy compensating, which improve the defect of the traditional homodyne optical path. Based on the performance of this optical path, a cooperative compensation method is proposed. Firstly rotate the adjustment device to minimize non-orthogonal error, and then use peak value method to compensate DC offset error and unequal amplitude error. This method solves the problem that the traditional non-orthogonal error correction algorithm is very complicated and difficult to realize real-time compensation.On the basis of the above research, some experiments are established to measure the performance of this vibration measurement system. The experimental results show that the relationship between the rotation angles of adjustable devices with non-orthogonal error is as same as the theory simulation, and the cooperative compensation method can effectively reduce the nonlinear error in the optical path. The displacement resolution is 0.2nm, short-term stability peak-to-peak value is 1nm, long-term stability peak-to-peak value is 20 nm, the nonlinear error after compensation is 0.4nm, the standard deviation of vibration measurement repeatability is 0.7nm, and the relative measurement error of vibration amplitude can below 0.75%. The whole system has good performance and technical advantages.