## 3 Experimental Results  
To demonstrate the validity of the proposed method, we utilized the multi-angle stitching DHM system presented in Figure 1 to measure a large gradient convex microlens fabricated from fused silica with refractive index 1.458. The absolute height of the microlens measured by stylus profiler is 76.5 \(\upmu\)m and the largest oblique angle of profile is 24.52\({}^{\circ}\), as shown in Figure 7.  
Before the measurement, the angle parameters of four degrees of freedom stage for measuring the whole sample are unknown quantities, so we need to adjust arbitrarily the angle of rotary axes (R_X, R_Y) and observe the variation of the bright region of hologram. In this process, we can find several holograms whose bright areas overlap each other, and the combination of these areas can cover the whole topography of microlens, while rotation angles corresponding to these holograms as the actual angle parameters are recorded. As shown in Figure 8, nine holograms are captured by controlling the four degrees of freedom stage that offers nine different rotation angles to microlens. It is assumed that \(\theta\), \(\beta\) represent the rotation angles around R_X and R_Y axis, respectively. For the conventional DHM system, only Figure 8e, have a black ring region without fringes in which the corresponding topography information is lost due to the limitation of MO, can be collected. With our method, the remaining hologram (Figure 8a-d,f-i) which contain the information of black ring area are captured by our system, a larger gradient micro-structure can be characterized by adding bigger rotation angle to the sample. To show the effect of the diffraction calculation between tilted planes  
Figure 7: The outline of the sample measured by stylus profiler. proposed in Section 2.2.2, the difference between the unprocessed object wave (\(\theta=20^{\circ}\), \(\beta=0^{\circ}\)) and the processed object wave by the algorithm is illustrated as shown in Figure 9. The acquired image from CCD in Figure 8a have an elliptical outline because of the rotation of microlens around R_X axis. After using the algorithm, the outline of the image is restored to a circle as is shown in Figure 9c. The significant correction effect is also reflected in the phase images (Figure 9b,d). In addition to Figure 8e, the rest image is corrected by the diffraction calculation for correcting object waves and nine sub-surfaces is reconstructed by using the TLRA algorithm. After that, the sub-surface corresponding to Figure 8e is selected for reference sub-surface whose position is fixed, the coordinate of remaining eight sub-surface is adjusted according to the parameter of overlapping area between  
Figure 9: Between the direct-collected wave front (\(\theta=20^{\circ}\), \(\beta=0^{\circ}\)) and the wave front after employing the diffraction calculation (**a**) amplitude image of unprocessed wave front. (**b**) phase image of unprocessed wave front. (**c**) amplitude image of processed wave front by algorithm. (**d**) phase image of processed wave front by algorithm. other sub-surface and reference sub-surface. The complete surface shape which fuses all topography information of nine holograms in Figure 8 is shown in Figure 10b, Figure 10a denote the topography recorded from the conventional DHM system with restricted NA. For comparison, Figure 10c illustrates the horizontal profile along the red line in Figure 10a,b at the same time. In theory, the MO (NA = 0.3) in our experiment have the ability of a collection beam whose largest angle of inclination is 17.5\({}^{\circ}\) according to the formula: \(NA=n\sin\theta_{MAX}\). Nevertheless, we successfully gather the slope of the 24.48\({}^{\circ}\) in multi-angle stitching process, which is in good agreement with the stylus profiler result. The error is mainly due to the random noise of optical element, the irregularity of micro-structure itself and the residual alignment error.