Toroidal surfaces have wide applications in optics and manufacturing industry. Due to the strong aspherical surface profile of a toroidal surface, there are few optical measurement techniques proposed or reported for its measurement. This paper proposed digital Shack Hartmann wavefront sensor (SHWS) with extendable dynamic range. Instead of the traditional spherical lenslet array, which cannot sample the wavefront in two directions simultaneously, an elliptical lenslet array realized by a spatial light modulator (SLM), which provides different optical powers in two directions, is used in the system. With the incorporation of the extended version of the traditional SHWS, the reference-free wavefront sensor (RFWS), curvature matrix is measured, which can be further reconstructed into the surface profile. Both numerical simulation and experimental study has been conducted and the feasibility of measuring toroidal surfaces in the RFWS system with an elliptical lenslet array is proven.
In a wavefront sensing system, the raw data for surface reconstruction, either the slope matrix or curvature matrix, is obtained through centroiding on the focal spot images. Centroiding is to calculate the first moment within a certain area of interest, which encloses the focal spot. As the distribution of focal spots is correlated to the surface sampling condition, while a uniform rectangular grid is good enough to register all the focal spots of a uniformly sampled near flat surface, the focal spots of aspherical or freeform surfaces have varying shapes and sizes depending on the surface geometry. In this case, the normal registration method is not applicable. This paper proposed a dynamic focal spots registration algorithm to automatically analyze the image, identify and register every focal spot for centroiding at one go. Through experiment on a freeform surface with polynomial coefficients up to 10th order, the feasibility and effectiveness of the proposed algorithm is proved.
A Shack-Hartmann wavefront sensor (SHWS) uses a lenslet array to sample incoming wavefront on an image sensor,
which is usually a Charge Coupled Device (CCD). By measuring the shift of centroids on CCD compared to reference
spots, wavefront profile is reconstructed and therefore test surface shape is revealed. There are various factors that affect
the performance of SHWS. In order to study how and to which extend does each factor affect reconstruction result, we
established a simulation platform for SHWS in MATLAB. Through this platform, detailed properties and affecting
factors were analyzed. Based on the system-oriented platform, we obtained some interesting findings, which are very
important in the design of S-H wavefront sensors. In this paper, the performance-affecting significance of the key
properties of the light beam, the diverging angle, the intensity distribution, and the intensity of the light beam, is
simulated, analyzed and concluded. The simulation results are useful guide for the selection, design and preparation of
the sensing light beam.