We propose a direct two-dimensional Fourier domain fitting-free method to determine the period of a Ronchi ruling. A precise method to measure a spatial frequency target’s quality and fidelity is highly desired as the pattern period directly affects every aspect of a spatial frequency target-based metrology, including the accuracy and precision of the measurement or evaluations. A standard Talbot experimental apparatus and the Talbot effect are used to obtain and model our data. To determine the period of the ruling directly, only a common digital camera, with a protective glass and an air gap in front of the sensor array, and a Ronchi ruling of chrome deposited on a glass substrate are required. The Talbot effect-based crossing point modeling technique requires no calibration or
Rectangular pupils are employed in many optical applications such as lasers and anamorphic optics, as well as for detection and metrology systems such as some Shack−Hartmann wavefront sensors and deflectometry systems. For optical fabrication, testing, and analysis in the rectangular domain, it is important to have a well-defined set of polynomials that are orthonormal over a rectangular pupil. Since we often measure the gradient of a wavefront or surface, it is necessary to have a polynomial set that is orthogonal over a rectangular pupil in the vector domain as well. We derive curl (called C) polynomials based on two-dimensional (2-D) versions of Chebyshev polynomials of the first kind. Previous work derived a set of polynomials (called G polynomials) that are obtained from the gradients of the 2-D Chebyshev polynomials. We show how the two sets together can be used as a complete representation of any vector data in the rectangular domain. The curl polynomials themselves or the complete set of G and C polynomials has many interesting applications. Two of those applications shown are systematic error analysis and correction in deflectometry systems and mapping imaging distortion.
This paper presents the detail fabrication process and metrology applied to the mirror from the grinding to finish, that include extremely stable hydraulic support, IR and Visible deflectometry, Interferometry and Computer Controlled fabrication process developed at the University of Arizona.
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