Development of a geometric model for an all-reflective camera system

Currently in photogrammetry conventional camera optics, which are based on a combination of lenses, are solely used. These systems are also called refractive systems. The usage of refractive systems implies a general drawback for some applications. Due to the chromatic aberration of lenses, i.e. slightly different imaging functions for different spectral bands, a significant loss of image quality and geometric accuracy has to be accepted. This fact is important especially for applications that require imaging a wide spectral range. Conventional cameras are not able to satisfactorily capture the ultraviolet or near infrared spectral range in addition to the visible.These chromatic aberration problems can be completely be avoided in all-reflective optical systems, i.e. camera objectives which are completely based on mirrors. The paper will briefly describe the developed all-reflective optical systems designed for optical metrology purposes.A general disadvantage of the design of normal or wide angle all-reflective systems is the asymmetry of the mirror arrangement, which leads to large asymmetric geometric image distortions. These distortions cannot be modeled with standard methods of photogrammetry. Furthermore, the complete system is also more sensitive to local deviations from the ideal mirror surface. Therefore we developed a suitable geometric model, which is adapted to the special case. The model is based on the collinearity condition, extended by a specific additional parameter set optimized with regard to the characteristics of an all-reflective unobscured system. We will show various model variants based on the additional parameter sets of Brown, Ebner and Grün as well as Legendre polynomials, Chebyshev polynomials and Fourier series. The paper discusses the potential of these models to correct the distortion of an all-reflective unobscured optical system prototype based on four aspherical mirrors on the basis of test field self-calibration and describes different approaches to consider local deviations from the nominal aspherical mirror surface with the help of the finite elements method.