# Digital Shearography for NDT: Phase Measurement Technique and Recent Developments
## 3 Phase Measurement Technique
### Phase Measurement Technique: Spatial Phase-Shift Shearography
#### 3.2.1 Multichannel Spatial Phase-Shift Shearography  
Multichannel spatial phase-shift shearography can be divided into the multidetector method and the single-detector method. Among them, the multidetector method generally uses three or more CCD cameras to simultaneously acquire a speckle interferogram with a known fixed phase difference [28]. Although this method can perform dynamic measurements, the system is complicated, has a large error, and the setting of the phase shift between multiple cameras is difficult to implement, making the method unsuitable for practical applications. A method of obtaining spatial phase shift using only a single CCD camera was later proposed [29]. One method of doing this is to divide a single CCD into at least three imaging regions, then introduce a fixed phase difference between each region. This method requires the use of a large number of wave plates, gratings, and polarizers, which is costly and difficult to adjust. Another method uses a single pixel as a channel to introduce a phase difference between pixels covered by the same speckle, resulting in a spatial phase shift [30]. Figure 5 is a schematic of the method. The interpixel intensity is calculated to determine the phase value, which in turn obtains the phase value of the entire image.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
\begin{tabular}{c} Acceptable phase map quality, only for static measurements, and more accurate calculation. \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table}
Table 1: The common temporal phase-shift algorithms.  
By setting the reference beam at an appropriate angle \(\alpha\), the optical path difference (OPD) between two adjacent pixels can be created as follows:  
\[OPD=S\times\sin\alpha \tag{9}\]  
where \(S\) is the pixel size. If the laser wavelength is \(\lambda\), the phase shift can be calculated by the following formula:  
\[\delta=2\pi\cdot\frac{OPD}{\lambda}=2\pi\cdot(S\cdot\frac{\sin\alpha}{\lambda}) \tag{10}\]  
Thus, for a given wavelength and pixel size, the phase difference can be determined by setting the appropriate reference beam angle. Assuming that the optical path difference by adjusting the angle \(\alpha\) is \(\lambda/4\) and the phase difference between pixels is \(\pi/2\), then the phase difference can be calculated using Equations (8) and (9). After loading, the same process can be used to calculate the phase distribution under loading conditions.  
The adjacent pixel phase-shift method can obtain the phase distribution from a single speckle pattern and is suitable for dynamic measurement. However, in practical applications, this method has reduced spatial resolution due to its need for at least three pixel points to determine the phase distribution of one point. Another problem with this method is that these three or more pixels should have the same values for A and B as shown in Equations (3) and (4). Although it can be partly realized by adjusting the aperture of the camera, it is not highly accurate, resulting in a noisy phase map. Moreover, only one dimension can be measured in one speckle pattern. Therefore, a carrier frequency method was proposed to enhance the quality of the phase map and the ability to extract information from multiple dimensions in a single image.