# Image Motion Measurement and Image Restoration System Based on an Inertial Reference Laser
## 5 Accuracy Verification for Image Motion measurement  
To verify the accuracy of the image motion measurement based on an inertial reference laser, the measurement data were compared with those of the Hartmann wavefront sensor. The Hartmann wavefront sensor obtained an accuracy better than 0.1 pixel (RMS) threshold for accuracy verification. The experiment process is summarized as follows.  
(1) Under the condition of a constant frequency or random vibrations, a vibration exciter was used to excite the camera along the Y axis;  
(2) The corresponding measurement data were recorded using the laser gyroscope, PSD, and Hartmann wavefront sensor;  
(3) The measurement data from the laser gyroscope and PSD were fused to obtain the image motion measurement curve based on an inertial reference laser.  
(4) The data measured by the Hartmann sensor were processed to obtain another curve.  
Figures 6-10 compare the two curves, from which the following conclusions can be obtained:  
(1) The difference between the two curves was less than 0.12 pixels (RMS), see Table 2 for details. The image motion measurement method based on an inertial reference laser reported a high measurement accuracy. In our field, it is acceptable that the image motion measurement accuracy is better than 0.2 pixel. The accuracy of image motion measurement could reach 0.12 pixel, which met the application requirements. The experimental results in Chapter 6 also proved this. (2) The sampling rate of the laser gyroscope and PSD were both 10 kHz, which was higher than that of the Hartmann wavefront sensor (550 Hz). Therefore, the measurement data contained high-frequency information that could precisely describe the image motion process. In addition, because the application of the Hartmann sensor involved image processing, the delay effect was obvious, and it was difficult to feed back the image motion information to the image stabilizer in real time, so it is suitable to store the image motion data for later image restoration. The method based on inertial reference laser proposed in this paper could read the image motion information in real time and feed it back to the image stabilization mirror, which is helpful to obtain a clear image in real time.  
For a further explanation of the measurement accuracy, the measurement accuracy of Hartmann sensor was better than 0.1 pixel (RMS), which was the conclusion obtained after a comparison with higher accuracy measurement equipment, but the true value could not be obtained. Compared with the Hartmann sensor, the image motion measurement error of the proposed method was less than 0.12 pixel (RMS).  
Figure 6: Comparison of the image motion measurement curves under the condition of 12.5 Hz constant frequency sinusoidal excitation.  
Figure 7: Comparison of image motion measurement curves under the condition of 20 Hz constant frequency sinusoidal excitation.  
Figure 8: Comparison of image motion measurement curves under the condition of 50 Hz constant frequency sinusoidal excitation.  
Figure 9: Comparison of image motion measurement curves under the condition of 110 Hz constant frequency sinusoidal excitation.  
Figure 10: Comparison of image motion measurement curves under the condition of random vibration excitation.