## 3 Results and Discussion
### Optical Experimental Results  
A Mach-Zehnder interference system is set up as shown in Figure 4. The laser light goes through a spatial filter and a collimator to form planar wavefronts. Then, the plane wave is divided into two beams by beam splitter 2. One of the beams illuminates test sample 6 to produce object wavefront. Another one is taken as the reference wavefront through optical flat glass plate 4. The two wavefronts interfere with each other on the recording plane to form an in-line hologram (in-phase-hologram), which can be recorded by CCD camera 8. The wavelength of He-Ne Laser is 632.8 nm, and the size of the captured holograms is 960 \(\times\) 1280 pixels with each pixel size of 4.65 \(\upmu\)m, giving \(l\approx\) 4.6 mm for 1000 pixels. Optical flat glass plate 4 is a phase-shifting element. The change of the phase of the reference can be achieved by rotating the optical flat glass plate to obtain the quadrature hologram. The method to carry out \(\pi/2\) phase-shifting and calibration is detailed in the literature [17] (see pp. 1565-1566 of the literature). The recording distance is \(d=75.6\) mm. Figure 3: Reconstructed phase using our proposed method. (**a**) 3D reconstructed phase distribution; (**b**) Phase line trace along Y at X-pixel = 50 on Figure 3a (blue curve) and the same section of the original phase (red curve). Figure 2: Reconstructed phase using [PERSON]’s method. (**a**) 3D reconstructed phase distribution; (**b**) Phase line trace along Y at X-pixel = 50 on Figure 2a and the same section of the original phase. We have performed optical experiments to explain the influence of the zeroth-order term in the complex hologram for phase retrieval and to verify the effectiveness of our proposed method in recovering the reference-wave intensity. The test sample is a capital letter \"C\" engraved on a round piece of glass plate, shown in Figure 5. The diameter of the round glass plate is 25 mm, and the size of the letter \"C\" is about 1.4 mm \(\times\) 0.8 mm, i.e., \(\omega_{0}\approx 0.7\) mm, with a line width of \(r\approx 0.047\) mm. All parameters used in the experiment satisfy the criteria established in Equations (9) and (10). In Figure 6a-c, we present the captured in-phase hologram, \(I_{I}\), the quadrature hologram, \(I_{Q}\), and the intensity of the complex hologram \(I_{+\text{i}}\) as constructed by Equation (6). Figure 4: System setup of two-step quadrature phase-shifting holography (QPSH). (**a**) Experimental optical system; (**b**) Schematic illustration of Figure 3a: 1 = He-Ne laser and collimator, 2, 7 = Beam splitter, 3, 5 = Reflective mirror, 4 = Optical flat glass plate, 6 = Test sample, 8 = charge-coupled device (CCD), 9 = Computer. Figure 5: A letter “C” engraved on the glass plate as test sample. (**a**) Dimension figure for glass plate; (**b**) Test sample on system setup; (**c**) Partial enlarged view of Figure 5b. The letter ‘C” is seen on the second quadrant of the figure. After Reference [18]. Figure 6: Two phase-shifting holograms and constructed hologram in recording plane. (**a**) In-phase hologram \(I_{I}\); (**b**) Quadrature hologram \(I_{Q}\); (**c**) Magnitude of Complex hologram \(I_{+\text{i}}\). After Reference [18]. We have reconstructed the part of the complex hologram enclosed by the white dotted rectangular area in Figure 6c. Results are shown in Figure 7. Figure 7a presents the two-dimensional phase map in grayscale, and Figure 7b,c show the three-dimensional phase distribution corresponding to the different views. It is obvious that the retrieved phase is contaminated by the existence of the zeroth-order beam due to the bias term or the zeroth-order term, \(A\cdot(1+\mathrm{i})\), in Equation (7). To recover the reference-wave intensity from the complex hologram, we have estimated \(A\) by selecting certain area (we used a \(3\times 3\) matrix to find \(A\)) far away from the diffraction pattern of the letter \"C\" in the complex hologram where negligible diffraction of the letter \"C\" has occurred.