# Digital Shearography for NDT: Phase Measurement Technique and Recent Developments
## 3 Phase Measurement Technique
### Phase Measurement Technique: Spatial Phase-Shift Shearography
#### 3.2.2 Carrier-Frequency Spatial Phase-Shift Shearography
Spatial phase-shift systems that introduce carrier frequencies with other carriers, such as a double-aperture mask and a Michelson interferometer, have been developed to solve these problems. In 2006, [PERSON] et al. proposed a digital shearography system using a double-aperture mask as a carrier to introduce the carrier frequency [31; 32]. Compared to the system based on the Mach-Zehnder interferometer, the double-aperture-based system provides better phase map quality, comparable to that of the TPS-DS system. However, similar to the Mach-Zehnder system, the measurement size of the double-aperture-based system is also small due to the use of a collimated light source and dual apertures. The stability of the entire measurement system is also reduced due to its complex optical path, which also limits its application in the laboratory and industry. Both the Mach-Zehnder-based SPS-DS system and double-aperture SPS-DS system have the disadvantage of limited measurement area. A Michelson-based SPS-DS system also exists, which can be used to obtain a larger measurement area by embedding the 4f system [33; 34]. The SPS-DS system with a 4f system is shown in Figure 8a. The imaging range for this system is no longer affected by the beam splitting prism but only depends on the lens and the camera. Figure 8b,c show the field of view of the conventional shearography device and the 4f system. At the same measuring distance, the measuring area of the conventional device only covers the framed portion of the 4f system measurement result. Figure 7: Schematic of the Fourier spectrum of the image. The Michelson-based system has a simpler setup than the Mach-Zehnder and double-aperture systems, so it is relatively insensitive to external disturbances. Additionally, it is easy to change the shearing amount and shearing direction, making it the most widely used shearing device. However, the Michelson-based system typically requires a large shearing amount to enable the two side spectra to be separated from the center spectrum, while the Mach-Zehnder-based setup can easily be performed with a small or large shearing amount. In order to solve this problem, a special slit aperture can be used instead of the usual circular aperture [35]. Under the same shearing amount and aperture size, the slit aperture provides a larger spectral region containing the phase information. Experiments have shown that under the same experimental conditions, using the slit aperture requires a lower shearing amount, and the side spectral area after Fourier transform is much larger than that obtained using the circular aperture. This reduces the shearing amount required for the Michelson-based system and improves the quality of the phase map. Figure 9 shows the results of an application of the Michelson-based SPS-DS system for NDT of delaminations/disbonds of a composite plate. All images were captured during dynamic loading. The settings of the camera parameters, such as exposure time, shutter mode, and resolution, should be noted. For dynamic measurements, a short exposure time and global shutter should be chosen for a clear image. Figure 8: (**a**) The modified Michelson-based SPS-DS system with a 4f system; (**b**) measurement result by traditional shearography system; (**c**) measurement result by modified 4f system. In recent years, some new phase extraction algorithms and optimizations have been proposed [36; 37; 38; 39]. In 2014, [PERSON] et al. proposed an alternative approach for retrieving phase information from a sequence of images with unknown phase shifts [40]. The approach combines data from several good modulation points on the image to form an N-dimensional Lissajous ellipsis. An overall phase-shift value is determined from the fitted ellipsis for each interferogram, then the phase-shifted values are used to determine the phase value for each image pixel. In 2015, [PERSON] et al.