The application of non merit function based methods to the correction of optical systems

Abstract

A new non merit function based lens design algorithm has been developed which combines a quadratic approximation to the individual aberration variations with adaptive aberration control techniques. This has resulted in an increase in the magnitude of the applied parameter changes and a reduction in computing load relative to the linear adaptive method. Several examples are given which demonstrate that the new quadratic adaptive correction algorithm can find solutions not readily available to conventional gradient descent methods. To demonstrate the capabilities of the new algorithm two quite different stages of the design process have been investigated: the generation of starting designs with reduced higher order aberrations and the fine correction of optical systems. The generation of starting designs with reduced higher order aberrations has entailed the development of a new method for computing higher order aberrations which is explained in detail. The higher order aberrations were reduced using the quadratic adaptive correction algorithm for five initial lens designs which were then optimized using the damped least squares method. Different design forms were found using this technique but these were not consistently superior to the designs resulting from the exclusive use of damped least squares optimization. The fine correction of optical systems has been attempted by initially determining target values for the third order aberrations which optimize the Strehl ratio and then using the adaptive quadratic correction method to target these aberrations. This technique is described in detail and four examples are used to demonstrate the strengths and limitations of the method.