An inverse projected-fringe technique based on simulating the system of a projector-part-camera is proposed for an on-machine inspection of axisymmetric parts. The parts considered for this study are relatively large, have high specular surfaces and have sharp slopes. A computer simulation-based method and the CAD model of the part was used to produce the inverse fringes as well as to find an appropriate trace passing through the symmetrical axis of the part that offers the best signal to noise ratio (SNR). This technique measures the deviation from a master-part and provides an accuracy of better than 10 microns for the part with a radial dimension of about 10 cm. It is shown that the proposed technique improves the SNR and the repeatability of the system compared to the standard fringe projection technique, in particular for the areas with a steep slope.

A signal with discrete frequency components has a zero bispectrum if no addition or subtraction of any of the frequencies equals one of the frequency components. The authors introduce the fractional bispectrum (FBS) transform in which for signals with zero bispectrum the FBS could be non-zero. It is shown that FBS has the same property as the bispectrum for signals with a Gaussian probability density function (PDF). The FBS of a zero mean signal with a Gaussian PDF is zero. Therefore, it can be used to significantly reduce the Gaussian noise.

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