Scientists from the Shanghai Institute of Optics and Fine Mechanics (SIOM) of the Chinese Academy of Sciences, have for the first time proposed an iterative adaptive optimization algorithm using space-variant spherical models, which eliminates the high-slope ambiguity in deflectometry, thus achieving high-precision freeform surface measurement without nominal surface models.
This study greatly improves the flexibility and stability of monocular deflectometry, expands the measurement ability of monocular deflectometry to complex optical components without nominal surface models, and lays a foundation for the development of intelligent optical manufacturing in the future. Results were published in Optics Express on April 11.
Compared with spherical/aspherical surface, freeform surface has the advantages of flexible design, improved image quality, expanded field of view and simplified system structure, which will contribute to revolutionary development to optical system and become a promising and hot research direction of precision optics. However, it is a great challenge to accurately and flexibly measure the surface because of its asymmetry.
Deflectometry has the advantages of high precision, large dynamic measurement range and strong anti-interference ability, and has the potential to achieve high-precision in-situ measurement of complex optical surfaces. However, there is a high-slope ambiguity issue, because the indefinite ray directions of the screen cause many possible combinations between the measured height and the normal vector. The monocular deflectometry has sharp difficulty to measure the unknown surface shape or surface shape error scenarios (such as error of grinding surface shape and rough cast phase realize the level of microns and even millimeters).
To solve this problem, the researchers proposed the iterative adaptive optimization algorithm, which provided initial solution of the measured freeform surface, and realized high-precision deflectometry of the complex free-form surfaces without prior model conditions.
According to the specular reflection theorem, the four-dimensional spherical parameter (X, Y, Z, R) problem was simplified to the one-dimensional spherical radius parameter (R) optimization problem. And according to the self-constraint conditions of deflectometry, the radius parameters of space sphere were calculated iteratively and the adaptive optimization of space sphere model was realized.
In addition, in order to satisfy the accurate model estimation of the complex freeform surface, the freeform surface was approximated by the space-variant sphere model. The iterative reconstruction error was used to achieve adaptive segmentation of freeform surfaces, thereby completing the high-precision reconstruction of complex freeform surfaces.
This method plays an important role in the measurement of complex freeform surfaces with unknown models, and can greatly release the positioning accuracy requirements of the workpiece, and improve the ability and application range of monocular deflectometry.
Measurement results of complex freeform surface. (Image by SIOM)
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