Experimental verification of improvement of phase shifting moire´ interferometry using wavelet-based image processing

Abstract

Phase shifting interferometry is combined with wavelet-based image processing techniques to extract precise phase information for applications of moiré interferometry. Specifically, a diffraction grating identical to the specimen grating is used to introduce the additional phase shifts needed to implement phase shifting moiré interferometry. The phase map is calculated with the four-step phase shifting algorithm with 90-deg relative shifts between adjacent frames. Subsequently, continuous wavelet transform processing is applied to the derived phase map to remove the noise and extract precise phase information. This precise phase map is then used to calculate the in-plane strain of the specimen under loading. A curve-smoothing algorithm based on a discrete wavelet transform is applied to the resultant in-plane strain map to eliminate the noise generated through the derivative calculation. To demonstrate the usefulness of this technique, uniform vertical loading is applied to a three-layer ball grid array (BGA) package and the strain is experimentally obtained. The reconstructed phase and in-plane strains are compared to the simulation results obtained using Ansys ® .

3-D Reconstruction of Human Face Using the Derivative Moiré Topography

“…II. A detailed procedure from (11) to (16) is offered for verification of the proposed method as displayed in Table 1 where phases before unwrapping are obtained from (9), and from these data the final unwrapped phases are successfully calculated using (11)-(16). The negative phases illustrate relatively lowered phases with respect to the highest altitude of cheek in Fig.…”

“…To eliminate noise occurring in a wrapped phase map, cosine transform or wavelet transform has been tried [9][10][11][12]. The projection Moiré topography with phase shifting method provides simple and reliable wrapped phase images for objects with -π/2 to π/2 range, called 2π ambiguity, however it is very difficult to convert this wrapped phase to a noise free unwrapped phase map.…”

Automatic Full Strain Field Moiré Interferometry Measurement with Nano-scale Resolution

“…The relation between shifted phase and movement step of the beam splitting grating is given by [12] as:…”

Diffraction phase microscopy: retrieving phase contours on living cells with a wavelet-based space-scale analysis

“…[68][69][70][71][72][73][74][75] More than a simple signal filtering tool, the wavelet transform analysis can also offer the possibility of a direct computation of the phase of the interferometry image, thanks to a wavelet transform ridge detection algorithm. [59][60][61][62]64,66,67,75 The 2-D CWT of an interferogram IðxÞ withx ¼ ðx; yÞ is defined as…”

“…To our knowledge, the first attempt to use a wavelet transform as a processing tool with white-light interferometry dates back to 1997. 58 Since then many teams have used this tool with success, in one dimension [59][60][61][62][63][64][65][66][67] as well as in two dimensions. [68][69][70][71][72][73][74][75] More than a simple signal filtering tool, the wavelet transform analysis can also offer the possibility of a direct computation of the phase of the interferometry image, thanks to a wavelet transform ridge detection algorithm.…”