The removal of misalignment aberrations is a key problem in the null test of cylindrical surfaces. Although the quadratic polynomial with two variables and the orthogonal Chebyshev polynomials have been used to separate the misalignment aberrations from the extracted phase data, there is no physical meaning corresponding to the polynomials coefficients. Additionally, the Runge phenomenon may occur when the high-order polynomials are employed. In this paper, all the possible aberrations caused by the adjustment errors were analyzed. Based on the first-order approximate principle, the mathematical models, which describe the relationship between the misalignment aberrations and the possible adjustment errors, were deduced. With these mathematical expressions, all the possible adjustment errors can be estimated by using the least-squares fitting algorithm, and then the genuine surface deviations can be obtained by subtracting the misalignment aberrations from the extracted phase data. Computer simulations and experiments have been conducted to demonstrate the validity and feasibility, which show more than 96% misalignment aberrations can be removed. Compared with the existing methods, the proposed model provides a feasible way to estimate adjustment errors with better accuracy.
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