Freeform optical elements have wide applications in optics, manufacturing, and precision industries. Due to the diversity of the nonrotationally symmetrical nature of a surface profile, few noncontact measurement techniques have been proposed or reported. This paper proposes and develops a new reference-free beam-sampling (RFBS) methodology and system for this particular application. The RFBS system uses the beam itself as an optical probe to sample the surface. Through introducing lateral disturbance to the modulated beam, the curvature matrix of the sample is measured. Simulation and experiments have been conducted to investigate the method's capability and study the configuration, so as to optimize the system. It is shown that a tens of nanometers measurement accuracy is achieved, even for surfaces with a peak valley value of more than 1 mm. The feasibility and effectiveness of the RFBS methodology is proven.
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