Three-dimensional Shape Measurement Of Membrane Mirror Based On Orthogonal Fringe Reflection

With the development of space technology，the space optical system is required towith the characteristics of high resolution, wide field of view and etc. Compared withtraditional mirrors, the membrane mirror made of flexible film material has the advantagesof folded or unfolded, lightweight, low cost and etc, and it is prospected to be used as largeaperture space optical element. At present, most researches are focused on the figurationprinciple and technology of membrane mirror. Its effective and high-precision shapedetection method is still at an exploratory stage. In this paper, based on the fringe reflectiontechnology, the deformed orthogonal fringes reflected by the mirror under testing arecaptured by a CCD camera, and then the shape of the membrane mirror can bereconstructed by calculating the phase changes of the fringes.The principle of the membrane mirror shape detection by applying the fringereflection technology is presented in detail firstly. A simple measurement system is set up.The relations between the phase changes of reflected fringes and shape function of themembrane mirror have been established. With orthogonal composite fringe used to beprojected as structured-light, the phase distributions of the fringe patterns would beextracted by using Fourier transform algorithm. As a result, it requires just two fringeimages to complete the shape reconstruction of a membrane mirror. Compared with1Dfringe Fourier transform algorithm and four-frame phase-shifting algorithm, it can greatlyimprove the simplicity of the shape measurement system.Then, the characteristics of a variety of phase unwrapping algorithms are analyzedand discussed. Phase unwrappings for noisy phase-map are simulated by using thesealgorithms. The imaging model of the CCD camera and the calibration method based on the2D plane target is researched. With the calibration experiment, parameters of themeasurement system are obtained and the reflected fringe images can be corrected.An experimental system is built up and the shape measurement result of a concavemirror with100-mm diameter and on a glass substrate obtained with this method iscompared with the result by using interferometer for testing the feasibility of the system.After that, the shape of a membrane mirror with100-mm diameter is detected. Thetheoretical accuracy of the ideal test system is obtained and analyzed. A various factorsaffecting the measurement accuracy are analyzed. The research of this paper would providetheoretical basis and technology support for the further research on the shape measurementof membrane mirror.