Absolute optical flatness testing by surface shape reconstruction using Zernike polynomials

Absolute measurement is an effective way to obtain high-precision optical surface measurements. This paper describes a convenient absolute testing approach that allows reconstruction of surfaces using Zernike polynomials. This method requires a classical three-flat measurement and a one-rotation measurement before reconstructing the surface. Utilizing a well-established procedure, the absolute surface profile of the testing surface can be reconstructed with more Zernike orders than are provided by Fritz's method. In particular, simulation of the testing error through recalculation of the test surface profile at a different angle could provide the optimized angle with a minimum testing error. This implies that an additional rotation measurement for the optimized angle can improve testing accuracy. The experimental results of a 100-mm flat surface provided a reflected root mean square (RMS) of 2.6 nm and a residual RMS of 0.1 nm.