# Alternative Design of Binary Phase Diffractive Optical Element with Non-\(\pi\) Phase Difference
## 4 Experiment  
To further validate the proposed method, non 0-\(\pi\) DOEs for generating various diffraction orders distributions were fabricated and optically characterized. The lithography and reactive ion etching technique were adopted to create binary relief structures on the fused silica substrate. More detailed process flow can be found in [29]. Figure 7a shows the 2.5-inch mask and the fabricated two DOEs with etching depth of 550 and 661 nm. To simplify processing, eight phase distributions for the generation of eight different diffraction patterns were drawn on the same mask, represented by the number from 1 to 8 in the figure. Each had the same sampling interval of 1 \(\times\) 1 \(\mu\)m, period of 129 \(\times\) 129 \(\mu\)m, and total area of 1 \(\times\) 1 cm. Figure 7b shows the optical configuration used to test the performance of the fabricated DOEs. A monochromatic laser with a wavelength of 650 nm irradiated the DOE vertically, thus forming a far-field diffraction pattern on the white screen, which was then captured by the Cannon camera. The attenuator was used to adjust the intensity of the laser.  
Figure 6: The obtained optimal phase differences for the target patterns with different number of diffraction orders N.  
Figure 8 shows the captured diffraction patterns of the 1\({}^{\#}\) DOE with etching depth of 550 nm. It can be seen that light intensity of the zero order in Figure 8a-c was similar to that of other orders and the patterns were well reconstructed. However, the zero order was significantly brighter than other orders in Figure 8d-h. This difference was due to the fact that for the eight target patterns, the optimal phase difference of the designed non 0-\(\pi\) DOEs were not equal, and are 0.755\(\pi\), 0.755\(\pi\), 0.815\(\pi\), 0.905\(\pi\), 0.889\(\pi\), 0.854\(\pi\), 0.87\(\pi\), and 0.92\(\pi\), respectively. For the binary phase DOE with phase difference \(\varphi\), the theoretical etching depth was determined by \(\mathrm{d}=\lambda\varphi/(2(\mathrm{n}-1))\). Here the refractive index of the fused silica was \(\mathrm{n}=1.4565\) at the wavelength of \(\lambda=650\) nm. Then, the corresponding theoretical etching depths of the eight patterns were 537 nm, 537 nm, 580 nm, 644 nm, 633 nm, 608 nm, 619 nm, and 655 nm, respectively. Since the depth 550 nm of the 1\({}^{\#}\) DOE was similar to the target values of the patterns in Figure 8a-c, the reconstructed light fields were uniform. While for the patterns in Figure 8d-h, the depth was smaller than the theoretical depth. Therefore, the zero-order was stronger than other orders. Figure 9 shows the captured diffraction patterns of the 2\({}^{\#}\) DOE with etching depth of 661 nm. We can see that in this case the patterns in the Figure 8d-h were well reconstructed. For the patterns in Figure 9a-c, since the depth was much greater than the theoretical depth, the zero-order light was significantly weaker than the other orders. The experimental results are in good agreement with the numerical simulation, which showed that the proposed method is effective for non 0-\(\pi\) DOE design.  
Figure 7: (a) mask and the fabricated DOEs; (b)Experimental test system.