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Overview: In recent years, the measurement of freeform optical surfaces has attracted intensive attention in precision engineering. Off-line measurement using laboratory instruments causes remounting errors and low manufacturing efficiency, thus high precision in-situ measurement technologies are required. The phase measuring deflectometry is a powerful measuring technique for complex specular surfaces. Its measurement accuracy is comparable with conventional interferometry, but with higher flexibility, stability and dynamic range.
In this paper, an in-situ deflectometric measurement method is developed for the ultra-precision optical manufacturing with single point diamond turning. The measuring accuracy of deflectometry depends on the reliability of the geometrical positions between the camera, screen and workpiece, but it is difficult to conduct precise geometrical calibration using a third-party instrument in the situation of the in-situ measurement.
A self-calibration method is proposed to determine the positions of the camera and the screen. A world coordinate system is established by introducing a flat mirror without markers, rather than using high-precision metrological instruments. The rays are re-traced from the screen to the camera, and numerical optimization is performed on the global parameters, including the camera intrinsic parameters, the screen intrinsic parameters and the geometric transformations by minimizing sum of the squared tracing deviations. Only four images need to be captured, hereby reducing the operating complexity and improving the measuring efficiency.
The behaviors of the position error and form error of the measured surface can be discriminated according to the statistical properties of the tracing deviations, and the axial position of the workpiece can be determined accordingly. By fully utilizing the nominal model, the conventional one-way position-form mapping is converted into a two-way mapping problem. Extra detections can in turn be avoided, and the measuring efficiency and range of freeform surfaces can be greatly improved. The whole aperture cannot be measured simultaneously due to the limit of the imaging scope of the camera used. A positioning method is proposed to specify the pose/location of the measured sub-aperture surface. Reverse ray-tracing from the camera to the screen via the measured surface is conducted, and a rotary stage carrying the workpiece is rotated to provide external constraints. The particle swarm optimization method is adopted to solve this problem.
Several typical optical surfaces including an off-axis paraboloid mirror are measured using the proposed deflectometric measuring method. Experimental results demonstrate that the measurement error is within 150 nm. The superior performance prove that this method is of significance for the technical development of ultra-precision intelligent manufacturing.
Correspondences between screen and camera pixels.
In-situ deflectometric measuring system in SPDT
Coordinate systems in geometrical self-calibration
Flow-chart of geometrical self-calibration
Tracing deviations of multi-pixels.
Flowchart of iterative optimization of in-situ measurement
Height sub-problem
Form sub-problem
Initial particles of PSO.
Flowchart of positioning workpiece with PSO
Spherical reflective mirror
Interferometric measurement of spherical mirror
Measurement result of spherical mirror.
Hollow off-axis paraboloid mirror
Deformed fringes of hollow off-axis paraboloid mirror.
Measurement results of hollow off-axis paraboloid mirror.