The system performance of many industrial products is dominated by the surface profile accuracy of their primary component, thus it is of great essence to achieve high precision profile characterization. The chromatic confocal technology provides an effective means for precise measurement of surface profile, yet there exists non-negligible errors when measuring transparent curved component. The aim of this paper is to investigate the effects of the curvature of component on the confocal rays and obtain its bilateral surface profile by chromatic confocal technology simultaneously.The assumption of tilted plate approximation for curved specimen was made. By adopting the optical ray tracing analysis, a modified model was then proposed to correct the measurement error existed in the traditional one. The validity of the proposed model is conducted by 2D bilateral profile measurements of the hemispherical shells after the calibration with tilted fused silica plates. Experimental results show that the proposed model significantly improves the measurement accuracy of bilateral profile of curved transparent components at large equivalent tilt angle. This method overcomes the drawbacks of other spatial coordinate based profile measurement methods, and achieves high accuracy simultaneous measurement of bilateral profile of transparent components.

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D-optimal experiment design is accomplished [3][4][5][6]. Analytical solutions are deduced.(1) Error Model Equation ofthe Single AccelerometerThe model equation of accelerometer is defined as a series that mathematically relates the accelerometer output to the components of applied acceleration, angular velocity, and angular acceleration along the accelerometer reference axes. In respect that the excitation of high order of accelerometer model is so small in the test of gravitational field, the static error model equation of quartz accelerometers becomes [2]where E is accelerometer output in accelerometer output units (such as volts), ai' a p ' a o are applied acceleration components along the Input Axis(IA) , Pendulum axis(PA) and Output Axis(OA)is scale factor(output units per g), k} is corrected value of scale factor,KiP' K io are cross-coupling coefficients (glg2), e is measurement and process noise and unmodeled error(g).Assume that the accelerometer tumbles about OA in the gravitational field, then the component ofgravity isWhere G is the local acceleration of gravity, be is the error of angle-setting of table, 8 0 is the misalignment angle ofIA about OA. Then the error model equation of accelerometer tumbling about OA isAbstract-Model identification of accelerometer is one of the most pervasive problems in calibration test of accelerometer. A method of calibrating dual orthogonal accelerometers on two-axis table is presented to eliminate the effect ofthe angle-setting error on calibration, thus enhancing identification precision of the accelerometer. The correlation ofthe model coefficients ofdual orthogonal accelerometers is analyzed and the D-optimal experiment design is accomplished. Furthermore analytical solutions are deduced. The simulation experiment and measured data suggests that the standard deviation of identification of dual orthogonal accelerometers is one order of magnitude less than that of single accelerometer. Therefore, the precision of identifying the error model of accelerometer is improved.

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