## 3 Results  
Figure 2a-d show a set of four raw interferograms acquired during one complete period of the phase modulation, corresponding to \(E_{1}\), \(E_{2}\), \(E_{3}\), and \(E_{4}\) of Equation (1), respectively. Each image has a pixel resolution of \(512\times 512\). The optical path length of the RM was adjusted to the bottom of the coin surface. Owing to the short coherence length of the source, we can see the interference fringes only at the bottom of the coin surface, or out of the letter regions. However, as was previously mentioned, owing to the finite coherence length, the phase of the fringe varies across the bottom surface. A closer look verifies that the phases of the four interferograms are slightly different to each other. It should be noted again that the four interferograms were captured at four different phases of the PZT modulation. It was confirmed that the surfaces of the letters were located at a height of 20-25 \(\upmu\)m above the bottom surface. Figure 1: The schematic of the full-field optical coherence tomography (FF-OCT) system. BS, beam splitter; L, lens; CCD, charge coupled device; NDF, neutral density filter; RM, reference mirror; PZT, piezoelectric transducer; WG, window glass; AM, angled mirror; MO, microscope objective lens. From the four raw images of Figure 2, the squares of two intermediate images of Equations (8) and (9) were calculated, the results of which are shown in Figure 3. In these figures, we can see that there are numerous interference fringes at the bottom surface. One important aspect is that the image in Figure 3a is much brighter than that in Figure 3b. This indicates that the two constants, \(F\) and \(G\), are not the same. From these observations, we can see that the phase modulation parameters, \(B\) and \(\theta\), were not properly applied in the hardware-based adjustments. The letter regions of the coin are dark in both images, which means that the surfaces of the letter are located out of the coherence length of the light source. To estimate the ratio between \(F\) and \(G\) in Equation (12), an area average of each intermediate image was conducted according to Equation (13) with a varying window size. The size of the average window was changed from a size of \(1\times 1\) to \(512\times 512\). In other words, we calculated a series of 512  
Figure 3: The intermediate images, (**a**,**b**), calculated by taking squares of Equations (8) and (9). There are interference fringes at the bottom surface and the letter regions are dark. Furthermore, the difference in brightness between the two images is severe. White scale bars: 200 \(\upmu\)m.  
Figure 2: A set of four interferograms of a Philippine one peso coin, acquired at a depth during one complete period of phase modulation. The images (**a**–**d**) correspond to \(E_{1}\), \(E_{2}\), \(E_{3}\), and \(E_{4}\) of Equation (1), respectively. Two letters, A and L, are identified with the red arrow in (**f**), an enlarged image of the photograph (**e**). The imaging plane is the bottom of the coin surface. White scale bars: 200 \(\upmu\)m.  
different \(\Gamma\)s to test their convergence with the size of the area-average window. The result is shown in Figure 4. Interestingly, the \(\Gamma\) varied severely with the window size at the beginning, but it then converged to a value of 1.51 from a pixel resolution of \(320\times 320\). From this result, the constant \(G\) was corrected. With the corrected \(G\) and the original \(F\) values, the intermediate images of Figure 3 were re-calculated and re-depicted in Figure 5. We can see that, with the \(\Gamma\) factor correction, the brightness levels in Figure 5a,b become similar to each other. At least in principle, the two intermediate images given by Equations (8) and (9) are \(90^{\circ}\) out of phase. Thus, after equalizing the constants \(F\) and \(G\), by taking the sum of the two images of Figure 5, we can finally reconstruct the corrected en face image using Equation (14).