The Effect Of Optical Freedform Surface Machining Errors On The Optical Properties

Optical freeform surface is without any rotational symmetry. Compared with the existing rotational symmetric non-spherical surface, freeform optical components have many advantages, such as improving the quality of the optical system's image, reducing the optical system components'number and size, and increasing the flexibility of optical design. Due to these advantages, the optical freeform components have a very wide range of applications in optoelectronics products and optical communication products. However, due to complexity of geometric features of the optical free surface, and the higher requirement of the surface' accuracy and surface' quality, the machining and testing process are extremely difficult. No matter what kind of processing methods, it will inevitably produce the surface error and surface roughness on the machined surface during the process of freeform surface machining. Because of the presence of the surface error and roughness, the performances of the optical system are reduced. Therefore, studying the effect of the surface error and surface roughness on optical properties becomes increasingly important.In this paper, the method of Gaussian filter is employed to isolate the surface error and the surface roughness. In that way, the effects of the surface error and the surface roughness on the optical properties are studied, respectively. For the optical freeform surface with the surface error, use wave aberration to evaluate the machined surface. For the optical freeform surface with the surface roughness, use the scattering surface transfer function to evaluate the machined surface.The methods of solving the wavefront aberration includes:ray tracing, calculation of the optical path difference of the actual wavefront and the ideal wavefront and so on. For the existing ray tracing methods of the non-spherical surface, iterative algorithm is mainly used to calculate the intersecting point of the incident ray with the traditional non-spherical surface, then the vector refraction law is applied to calculate the optical path. However, as for the selection of the iterative point, there will be "pseudo-intersection" and "light spill" during the whole process, then lead to failure. To avoid this problem, I proposed a method that discrete the optical surface, make the ray light incident on the discrete points directly, and then use the vector refraction law for ray tracing. By verifying the spherical ray tracing, it proved the proposed method is feasible. The problems mentioned above can be avoided by using this algorithm which is relatively simple. After ray tracing, the Zernike polynomial fitting method is used to fit the idea wavefront and actual wavefront. Then the error is solved between the idea wavefront and actual wavefront, which can be used to evaluate the optical properties.Surface roughness has a direct impact on the optical surface. In the existing surface scattering theories, Harvey-Shack scattering theory is studied on the linear system theory, suitable for studying the scattering of any incident angle. However, the transfer function which derived on the basis of the Harvey-Shack scattering theory is suitable for the plane. For the optical freeform surface, the base level is no longer flat, but the freeform surface. In this paper, the roughness optical freeform surface will be regarded as a random field, then use the statistical methods to make a mathematical derivation on the roughness surface. The conclusion is that:the surface scatter transfer function derived from the Harvey-Shack theory does not depend on the base level. So, in this paper, we isolate the surface roughness from the optical freeform surface, and use this transfer function to evaluate it. Through Fourier transform, we can establish the relationship between the point spread function and scattering angle. And then make an evaluation on the roughness.