| Freeform optical element is more and more widely used in many optoelectronic systems such as illumination system,display system and biomedical system, because it can correct several image aberrations effectively as well as simplify optical system structure. However, it is extremely difficult to manufacture and measure freeform surface with sufficient accuracy because of its more "freedom", which impedes the application of it in image optics. Therefore the accurate metrology of freeform surface has become a focus in filed of optics.So far, there are no mature and reliable methods for testing freeform surface with high precision. Attentions have been paid to Tilted-Wave-Interferometry(TWI) because of its great dynamic measurement range, nano precision, short time topography test mode and universal test advantage. Since TWI was presented for testing aspherical surface, a number of key technologies must be solved when TWI is used in the measurement of freeform surface.According to the feature of the freeform surface and the principle of TWI, this dissertation studies the key technologies on the design method of TWI system, the accurate assessment of the test surface error, the flexible calibration method for TWI system and the positioning technology for tested surface. The specific analyses are shown as below:To solve the problem that the math model of most null test interferometer is not proper for TWI system, a design scheme is presented to combine both reverse ray tracing and black box principle. And tilted wave non-null interferometric math model including a step iterative algorithm is proposed in order to obtain the design parameters and optimization goals for the key optical elements in TWI. By the suggested method, the TWI for testing freeform surface was realized.Because the common ray tracing method is not suitable for non-rotational asymmetrical optical system, a tilted wave non-null interferometric ray tracing model composed by the algorithms for calculating the direction and length of vector rays is presented, based on vector optics theory. By the proposed ray tracing model, a computer generated wave (CGW) simulation program was made according to the configuration of TWI. It is proved that the simulation program is accurate enough for characterizing TWI by a lot of experiments.The non-null test mode will lead the relation between the fringe and surface error to be indirectly and introduce great retrace error in the process of measurement. Hence, an accurate assessment of the test surface error from the fringe plays a central role in the measurement with TWI. Based on the principles of Hamiltion’s characteristic functions and perturbation theory, we have proposed a novel method for assessing surface error in the test of freeform element with TWI system, combining both CGW simulation technology and retrace errors elimination algorithm. The method in this work can calculate the surface error from the fringe directly like a common interferometer. The results of the simulation reveal that the accuracy of the algorithm presented by us is better than X/20(PV-Peak to Valley value).In order to calibrate the great system error produced by manufacture and misalignment which can’t be eliminated in non-common path configuration, a flexible calibration method for TWI system, which placed a standard calibration sphere at different locations in test space to the case of a source array, is suggested based on the principles of Hamiltion’s characteristic functions and perturbation theory. We characterized the complete behaviour of the interferometer by this calibration method and acquired all the system error wavefronts,which were introduced into the CGW simulation program for improving the calculation accuracy.Compared with spherical and aspherical element, the space position of the freeform surface has six degrees of freedom because of the non-rotational and asymmetry, which makes the misalignment error introduced by the position of the tested surface in TWI greater than common interferometer. In order to solve this problem, a novel alignment method in virtual moire fringe way is presented, which can make the match errors between the real measurement position and ideal position smaller than5um in x, y, z directions and0.4°in rotational direction. By means of advanced alignment method, the wavefront error introduced by space position of freeform surface is better than λ/20(PV).An eyeglass with freeform surface was measured by our TWI system and the results were compared with the data measured by profilometer in the end of this dissertation. The results of the experiment prove that the method in this work is highly flexible and can measure freeform surfaces that deviate from their best-fit sphere up to7°with the accuracy better than λ/10(PV). |
PDF Full Text Request