Self-Calibration and Error Analysis for 2D Measurements

Two-dimensional measurement machines, such as microlithography and computed tomography systems, are subject to distortions in the measurement field due to imperfections in their hardware and software. Certified methods to characterize and quantify such distortions are urgently needed. An innovative self- calibrating scheme is tendered which eliminates the disadvantages of previous self-calibration approaches. To employ the method, a test object containing a grid of reference features is measured at several orientations and positions in the field of view. The proposed approach compensates for systematic errors due to the imprecise knowledge of construction and position of the test object during measurement. The approach converges to an exact correction in the absence of noise, and outputs a functional representation which can be used to evaluate the distortion at any point in the field of view. If successful, Phase 1 will: (1) demonstrate a robust, computationally efficient algorithm for determining the geometrical distortion inherent in any 2D measuring machine; (2) demonstrate a robust, computationally efficient algorithm for producing a function representation of the distortion; and (3) characterize the amplification of random errors in the calibration procedure for various levels of input noise.