Modeling And Optimal Design Of Optical System For Offner Field Imaging Spectrometer

Imaging spectrometers are the optical instruments, which can simultaneously acquire the spectral and spatial characteristics of an object, and combine them into one image cube. It solves the problem of "no spectral imaging" and "non-spectral imaging" in the traditional fields of optical science.Compared to the flat or concave grating-based imaging spectrometer, the Offner imaging spectrometer which utilizes a convex grating as the diffractive element takes the advantages of large numerical aperture, no Smile, small spectral Keystone, compact volume, relatively easy processing and assembly, and so on. Currently, Offner imaging spectrometers have been widely applied to the areas such as satellite remote sensing, geological exploration, precision agriculture, manufacturing, and military reconnaissance. The main design methods include the numerical ray-tracing and the analytical design based on the aberration theory of the signal grating. In both theoretical and practical aspects, it is a significant topic to study the imaging properties and optimal design of the Offner imaging spectrometer.This thesis mainly focuses on modeling and optimization of the optical system in Offner imaging spectrometer. The goal of modeling is to build the analytical function among image point, object point and system parameters; and the goal of optimization is to provide the appropriate system parameters to meet application requirements. The main research works in this thesis are as follows:(1) For the Offner optical system, the numerical model is derived using numerical ray-tracing method according to Fermat's principle, and then a third order analytical model is obtained using series expansion method, which is also a third order aberration theory of the optical system. Analytical model provides aberration coefficients in analytical form, which are the analytical functions among structural parameters, grating parameters and element parameters. The accuracy of the analytical model is verified and the sources of model error are analyzed through numerical experiments. With the analytical aberration coefficients Coma, spherical aberration, and astigmatism and distortion are discussed in detail. This fills the gap in the aberration theory of multi-element optical system, makes a deeper understanding of the imaging properties of the system, and provides theoretical guidance for system optimization design. (2) Considering the ideal imaging condition, a single optimization model is constructed using the third order aberration theory. Genetic algorithm is applied to determine the system parameters. The results show that genetic algorithm is capable of solving the optimal design problem with high performance. The optimal design results are validated from the aspects of spectral resolution, Smile, spectral Keystone, the cut-off frequency of modulation transfer function, and so on.(3) Taking into account the computational complexity of the objective function, application of Kriging model which is an approximate technique for complex model speeds up the optimal design process of Offner optimal system. First, discusses the effect of different sampling methods on the accuracy of Kriging model, and then discusses the performance of Kriging model in non-linear modeling area. The Kriging models of aberration coefficients and merit functions at multiple design wavelengths are established through training data sampled from design space. Experimental results show that in the optimization process, the combination of Kriging model and the exact analytical model, taking into account the system performance at multiple wavelengths, can enhance the time efficiency of optimal design, but also ensure the optimality of design results in the whole spectral range.(4) Considering the multi-objective properties of the design problem, multi-objective optimization algorithms suitable for engineering application are developed and applied to the Offner optical system design problem. To enhance the efficiency of the algorithms and the practicality of optimal results, decision maker'preference based on multiple weighted sums is incorporated into multi-objective evolutionary algorithms and robust algorithms. These two novel methods can effectively reduce the search space, make the optimal results located only in the region of decision-maker's interest, so that improve the resolution of the resulting solutions. Both numerical experiments and design examples demonstrate the algorithm performance.These studies are conducted for optimal design of Offner optical system, but they are also of great significance when applying evolutionary algorithm to solve other complex engineering optimization problems.