The use of polynomials offers several benefits in optomechanical analysis including improving data interpretation and providing efficient means of data transfer. Zernike polynomials are a popular form and are well suited for use with optical systems. Fitting Zernike polynomials to FEA-derived mechanical response quantities provides a compact representation of hundreds or thousands of data points whose individual terms may be readily interpreted for insight into the mechanical and optical behavior. Use of an orthogonal set of polynomials such as the Zernike set allows the ability to remove terms that may be correctable such as during optical alignment and for systems that have active focus control. Polynomials also serve as an effective vehicle to transfer data between mechanical and optical software tools facilitating integration of the mechanical and optical analysis models. The Zernike polynomials are the most commonly used polynomials; however, other useful polynomial forms include annular Zernikes, X-Y, Legendre-Fourier, and aspheric polynomials.
Zernike and Other Useful Polynomials