Zernike Polynomial Fitting of a Deformed Surface
Application ID: 100611
This tutorial shows how the displacement field of a deformed surface can be fit to a Zernike polynomial basis. The method of linear least-squares fitting is made significantly easier when fitting to an orthonormal basis, such as the Zernike polynomials on a circle.
The displacement field is compared to the superposition of the piston, defocus, and spherical aberration terms with coefficients obtained via linear least-squares fitting. The remaining terms are negligible due to the symmetry of the displacement field.
This model example illustrates applications of this type that would nominally be built using the following products:
however, additional products may be required to completely define and model it. Furthermore, this example may also be defined and modeled using components from the following product combinations:
- COMSOL Multiphysics® and
- either the MEMS Module, Metal Processing Module, or Structural Mechanics Module
The combination of COMSOL® products required to model your application depends on several factors and may include boundary conditions, material properties, physics interfaces, and part libraries. Particular functionality may be common to several products. To determine the right combination of products for your modeling needs, review the Specification Chart and make use of a free evaluation license. The COMSOL Sales and Support teams are available for answering any questions you may have regarding this.