Effect of the nonlinearity of the CCD in Fourier transform profilometry on spectrum overlapping and measurement accuracy

In Fourier transform profilometry （FTP）, we must restrain spectrum overlapping caused by the nonlinearity of the charge coupled device （CCD） and increase the measurement accuracy of the object shape. Firstly, the causes of producing higher-order spectrum components and inducing spectrum overlapping are analysed theoretically, and a simple physical ex- planation and analytical deduction are given. Secondly, aiming to suppress spectrum overlapping and improve measurement accuracy, the influence of spatial carrier frequency of projection grating on them is analysed. A method of increasing the spatial carrier frequency of projection grating to restrain or reduce the spectrum overlapping significantly is proposed. We then analyze the mechanism of how the spectrum overlapping is reduced. Finally, the simulation results and experimental measurements verify the correction of the proposed theory and method.

2- DFourier Transform Method for Optical Measurement of 3 - DSurface

A method of 2-D Fourier transform used in 3-D surface profilometry is proposed,analyzed and compared with 1-D Fourier transform method in theory and practical measuring result.It was proved that the 2-D Fourier transform method has more advantages over 1-D Fourier transform method in biggest crook-rate limits,accuracy and sensitivity of measuring.Study on measuring object surface details with large crook-rate changing accurately used new higher-power index low-pass filter of spatial frequency domain.A new method of automatic produced reference grating image and error-correcting is proposed.One undeform row of deform grating image is used to extend a complete reference grating image,and some error-correcting method is used to process the result to get accurate surface shape and the deflection of reference surface normal line deviated from the axle of camera.By this new method,one deform rectangle grating image is only used to get the 3-D shape accurately.

Measurement of a discontinuous object based on a dual-frequency grating

The dual-frequency grating measurement theory is proposed in order to carry out the measurement of a discontinuous object. Firstly, the reason why frequency spectra are produced by low frequency gratings and high frequency gratings in the field of frequency is analysed, and the relationship between the wrapped-phase and the unwrapping-phase is discussed. Secondly, a method to combine the advantages of the two kinds of gratings is proposed： one stripe is produced in the mutation part of the object measured by a suitable low frequency grating designed by MATLAB, then the phase produced by the low frequency grating need not be unfolded. The integer series of stripes is produced by a high frequency grating designed by MATLAB based on the frequency ratio of the two kinds of gratings and the high frequency wrapped-phase, and the high frequency unwrapping-phase is then obtained. In order to verify the correctness of the theoretical analysis, a steep discontinuous object of 600×600 pixels and 10.00 mm in height is simulated and a discontinuous object of ladder shape which is 32.00 mm in height is used in experiment. Both the simulation and the experiment can restore the discontinuous object height accurately by using the dual-frequency grating measurement theory.