## 3 Results and Discussion  
The viability of the proposed reconstruction technique for wavelength-tuning common-path DHM was assessed experimentally. A micro-lens array was used as a functional micro-optics sample to establish a consistent experimental procedure. The details of this process follow. A glass basal plate was placed on the specimen stage in the imaging plane of the micro-objective. Phase-shifting holograms were then recorded by a CMOS camera as the laser wavelength was tuned according to Formula (2). Figure 4a shows an example of a recorded hologram, in which the holographic interferometry fringe is evident in the magnified portion of the image. Basal phase differences, and the corresponding wrapped and unwrapped phases, were then calculated using Equation (6), as shown in Figure 4b,c. Figure 4: Reconstructed phase data for the basal plate, including (**a**) the hologram, (**b**) the wrapped phase map, and (**c**) the unwrapped phase map. A micro-lens array with a lens diameter of 150 \(\upmu\)m, a designed sag height of 2.6 \(\upmu\)m, and a refractive index of 1.515 was placed on the basal plate. Its position was adjusted to match the imaging plane of the micro-objective. The holograms were collected after laser tuning, with phase differences modulated by the micro-lens array (see Figure 5a). The wrapped and unwrapped phases could then be determined, as shown in Figure 5b,c. According the Equation (9), the phase difference modulated by the micro-lens array was determined using a subtraction algorithm. Figure 6 shows the results of subtracting Figure 4c from Figure 5c. In the proposed technique, phase-shifting holograms can be acquired without any mechanical movement. In addition, the magnified portion of the hologram shown in Figure 4a clearly exhibits an interferometry fringe. As such, a phase-shifting algorithm (as opposed to a fast Fourier transform as shown in Figure 6c,d) was adopted to reconstruct the phase, to prevent the elimination of high-frequency information. It is evident that the reconstructed phase results include more frequency components and a detailed structure. The resulting phase measurements were verified using the 3D profile of a micro-lens in a cross-test experiment. Phase results were translated to the physical objective profile by considering the central wavelength of the tuning laser, the refractive index of the specimen, and the lateral device magnification. The systematic magnification was determined to be 9.5x based on calibration with a USAF 1951 resolution target. The 3D profile of the micro-lens array was acquired using a central wavelength of 632.85 nm and a refractive index of 1.515, as shown in Figure 7a. The section profile for the array was calculated along the dashed line of Figure 7a, as represented by the blue line in Figure 7b. Figure 5: Reconstructed phase data for the micro-lens array, including (**a**) the hologram, (**b**) the wrapped phase map, and (**c**) the unwrapped phase map. Figure 6: The results of phase measurements for the micro-lens array, including **(a)** the 2D map and **(b)** the 3D distribution reconstructed by phase shifting, **(c)** the 2D map, and **(d)** the 3D distribution reconstructed by fast Fourier transform. Figure 7: Measurement results for the micro-lens array, including **(a)** the 2D map, **(b)** a profile map along the dashed line shown in **(a)**, and **(c)** the residual error. A cross test was implemented to verify the correctness of the proposed DHM technique, using a ZYGO NEWVIEW 8200 3D optical surface profiler with a 10\(\times\) Mirau interferometry objective. The raw data were recorded as DAT format files and uploaded to MATLAB. Section lines were then extracted as indicated by the red line in Figure 7b. It is evident from the figure that these two measurements of the micro-lens array profile are in excellent agreement. Some residual error was observed (a PV value of 0.7 \(\upmu\)m, RMS value of 0.16 \(\upmu\)m), as shown in Figure 7c.