# A Real-Time Automated System for Dual-Aperture Common-Path Interferometer Phase-Shifting
## 4 Results and Discussion  
Once the mechatronic system was implemented, computational tests were performed. The algorithm was proved using three simulated phase-shifted interference patterns labeled as (a), (b), and (c) in the LabView front panel, shown in Figure 5. The original function from the simulated phase steps of the interferograms was shown as reference in the plotting labeled as (e). Then, the proposed retrieving phase algorithm calculated the values of \(p,q,r\) from the simulated interferograms to obtain the phase step values of \(\alpha\). Table 1 shows the comparison between the proposed and calculated phase step values \(\alpha_{1}\) and \(\alpha_{2}\) and the absolute value of the error. Next, the algorithm calculated the wrapped phase function \(\phi_{w}\), observed in the plot (d). Finally, the unwrapped phase \(\phi_{u}\) is obtained, as it is shown in the plot labeled as (f) in the front panel image, as it is displayed to the user. The plot (f) corresponds to the retrieved 2D unwrapped phase function obtained from the algorithm, which can be compared with the 2D original function of the plot (e). This comparison is shown in plot (g) as the subtraction (error) between them (red curve). Additionally, the plot labeled as (h) shows the calculated 3D phase function. As can be observed in Table 1, the non-zero error is attributed to the limitation of the used SPGSI algorithm, which required a high number of interference fringes to reduce the error [26]. In the proposed system, the error is considered acceptable due to its advantages compared with the reported systems. In our approach, the proposed SPGSI algorithm exhibited noise immunity which allowed the calculation of the phase from the experimental interferograms, avoiding undergoing filtering processes [33]. In addition, equal spacing displacement is not required from the obtained interferograms and the needles special calibration procedures. Afterwards, experimental results were obtained. In order to generate the interference fringes, transparent acetate was used as the phase object placed in the probe window B of the object plane. It is worth noting that for experimental results, the angular displacements generated in each motor step are not equal. However, for the implemented algorithm, the equal steps condition is not mandatory since the SGPSI is capable of achieving phase shifts, even if these steps are unequal. Figure 6 shows a set of four CCD consecutive interference pattern captures. The images were arranged in two groups of three patterns. The first group, corresponding to the initial phase steps, includes the first three images  
Figure 4: Block diagram of the implemented SGPSI algorithm for the phase obtaining. whose intensities are \(I_{0}\), \(I_{1}\), and \(I_{2}\). The second group stands for the new phase for each step calculation and includes the second, third and, fourth images with intensities \(I_{1}\), \(I_{2}\), and \(I_{3}\). Then, the phase function \(\phi_{w}\) is obtained by calculating the values of \(\alpha_{1}\) and \(\alpha_{2}\) with the corresponding phase difference between each pair of interferograms. As a result of evaluating the set of experimental patterns, the wrapped and unwrapped phase is calculated from the obtained phase steps for each motor step. Figure 7 shows the front panel of LabView for the implemented algorithm. The plots labeled as (a), (b), and (c) correspond to the calculated phase shift for each step. The plot (d) corresponds to the calculated wrapped phase. The 2D and 3D plots for the retrieved phase are labeled as (e) and (f), respectively. As it can be observed, by using three consecutive experimental patterns it is possible to automatically obtain the phase function, without reprocessing the data.