Abstract
The deflectometry provides a powerful metrological technique enabling the high-precision testing of reflective surfaces with high dynamic range, such as aspheric and freeform surfaces. In the fringe-illumination deflectometry based on reverse-Hartmann-test configuration, the calibration of system geometry is required to achieve "null" testing. However, the system miscalibration can introduce a significant systematic error in the testing results. A general double-step calibration method, which is based on the low-order Zernike aberration optimization and high-order aberration separation, is proposed to separate and eliminate the geometrical error due to system miscalibration. Both the numerical simulation and experiments have been performed to validate the feasibility of the proposed calibration method. The proposed method provides a general way for the accurate calibration of system geometrical error, avoids the over-correction and is feasible for the testing of various complex freeform surfaces.
Highlights
With the development of optical design and fabrication, especially the increasing demand of system performance improvement, various types of optical surfaces including aspheric and freeform surfaces have been widely applied in illuminating [1], display [2,3] and imaging systems [4,5,6], etc
In the reflective surface testing based on reverse Hartmann test, the surface error can be measured according to the virtual “null” testing, in which ray tracing of the test system model obtained from the measured system geometry is performed
The system geometry parameter including the positions of camera aperture, test surface and illumination screen, was measured by a coordinate measurement machine (CMM) (Hexagon Metrology Global Classic, accuracy 5.0 μm and resolution 0.078 μm)
Summary
With the development of optical design and fabrication, especially the increasing demand of system performance improvement, various types of optical surfaces including aspheric and freeform surfaces have been widely applied in illuminating [1], display [2,3] and imaging systems [4,5,6], etc. To lower the requirement on the calibration of system geometry, a computer-aided reverse optimization with iterative ray tracing, in which the surface error is taken as the global minimum of the departure from its ideal state, has been proposed to eliminate the additive geometrical errors [14] This optimization method could lead to over-correction and it is more suitable for the precise surface with small error. In the reflective surface testing based on reverse Hartmann test, the surface error can be measured according to the virtual “null” testing, in which ray tracing of the test system model obtained from the measured system geometry is performed. According to the surface integration method [18], the surface error map under test can be reconstructed from the slope differences (Δwx , Δwy )
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