A spatial algorithm to reduce phase wraps from two dimensional signals in fringe projection profilometry

© 2015 Elsevier Ltd. All rights reserved. In this paper, we present a novel algorithm to reduce the number of phase wraps in two dimensional signals in fringe projection profilometry. The technique operates in the spatial domain, and achieves a significant computational saving with regard to existing methods based on frequency shifting. The method works by estimating the modes of the first differences distribution in each axial direction. These are used to generate a tilted plane, which is subtracted from the entire phase map. Finally, the result is re-wrapped to obtain a phase map with fewer wraps. The method may be able to completely eliminate the phase wraps in many cases, or can achieve a significant phase wrap reduction that helps the subsequent unwrapping of the signal. The algorithm has been exhaustively tested across a large number of real and simulated signals, showing similar results compared to approaches operating in the frequency domain, but at significantly lower running times

Fast fringe pattern phase demodulation using FIR Hilbert transformers

This paper suggests the use of FIR Hilbert transformers to extract the phase of fringe patterns. This method is computationally faster than any known spatial method that produces wrapped phase maps. Also, the algorithm does not require any parameters to be adjusted which are dependent upon the specific fringe pattern that is being processed, or upon the particular setup of the optical fringe projection system that is being used. It is therefore particularly suitable for full algorithmic automation. The accuracy and validity of the suggested method has been tested using both computer-generated and real fringe patterns. This novel algorithm has been proposed for its advantages in terms of computational processing speed as it is the fastest available method to extract the wrapped phase information from a fringe pattern

Simple and accurate empirical absolute volume calibration of a multi-sensor fringe projection system

This paper suggests a novel absolute empirical calibration method for a multi-sensor fringe projection system. The optical setup of the projector-camera sensor can be arbitrary. The term absolute calibration here means that the centre of the three dimensional coordinates in the resultant calibrated volume coincides with a preset centre to the three-dimensional real-world coordinate system. The use of a zero-phase fringe marking spot is proposed to increase depth calibration accuracy, where the spot centre is determined with sub-pixel accuracy. Also, a new method is proposed for transversal calibration. Depth and transversal calibration methods have been tested using both single sensor and three-sensor fringe projection systems. The standard deviation of the error produced by this system is 0.25 mm. The calibrated volume produced by this method is 400 mm×400 mm×140 m

Shifting of wrapped phase maps in the frequency domain using a rational number

The number of phase wraps in an image can be either reduced, or completely eliminated, by transforming the image into the frequency domain using a Fourier transform, and then shifting the spectrum towards the origin. After this, the spectrum is transformed back to the spatial domain using the inverse Fourier transform and finally the phase is extracted using the arctangent function. However, it is a common concern that the spectrum can be shifted only by an integer number, meaning that the phase wrap reduction is often not optimal. In this paper we propose an algorithm than enables the spectrum to be frequency shifted by a rational number. The principle of the proposed method is confirmed both by using an initial computer simulation and is subsequently validated experimentally on real fringe patterns. The technique may offer in some cases the prospects of removing the necessity for a phase unwrapping process altogether and/or speeding up the phase unwrapping process. This may be beneficial in terms of potential increases in signal recovery robustness and also for use in time-critical applications

Fringe pattern analysis using a one-dimensional modified Morlet continuous wavelet transform

This paper proposes the use of a modified Morlet wavelet in order to demodulate fringe patterns in conjunction with the one-dimensional continuous wavelet transform (1D-CWT). Our investigations demonstrate that the modified Morlet wavelet produces better results compared to the conventional Morlet wavelet when used in fringe pattern analysis. This novel technique offers superior performance in analysing fringe patterns from objects that exhibit large height variations. This new technique has been used in conjunction with the direct maximum ridge extraction algorithm and an improvement in performance is observed. The algorithm has been tested using both computer-generated and real fringe patterns; and was found to be suitable for fringe pattern demodulation and robust in operation