# Alternative Design of Binary Phase Diffractive Optical Element with Non-\(\pi\) Phase Difference
## 1 Introduction  
In the past two decades, diffractive optical element (DOE) has received more and more attention due to its superior wavefront manipulation capability and unique advantages of high design flexibility, small size, and mass productivity. It expands the capabilities of conventional optics based on refraction or reflection and is now widely used in a broad range of applications, such as beam shaping [1; 2; 3], beam splitting [4; 5; 6], structured light projectors [7; 8; 9; 10], pattern generation [11; 12; 13; 14], optical security [15; 16; 17], and so on.  
In general, the most commonly used method for fabrication of DOE is the lithographic technique adapted from the microelectronics industry. This approach can generate microstructures with up to \(2^{n}\) phase levels by using \(n\) binary masks. For DOE, the more the quantized phase levels, the higher the diffraction efficiency. However, multiple lithographic processing steps increase manufacturing cost and time and may introduce mask alignment errors that decrease element performance. In addition, minimum feature size and aspect ratio of the microstructures may also constrain the fabrication of a multilevel structure. Therefore, continuous phase profile of a DOE is usually quantized into binary phase levels (\(0,\pi\)) [18; 19; 20], which needs only one photolithography and no mask alignment.  
In order to improve the efficiency of the binary phase DOE, [PERSON] et al. [21] considered the phase difference as a free parameter and then used the simulated annealing (SA) algorithm to optimize it together with the phase distribution. Diffraction efficiency of 74% can be obtained for the 3 \(\times\) 3 array generator with phase step of 0.815\(\pi\). In contrast, the efficiency of the conventional 0-\(\pi\) element is only 68%. However, it is not easy to find the optimal solution by optimizing the phase delay and distribution simultaneously. Subsequently, an improved approach was proposed by [PERSON] et al. [22]. The phase differencewas fixed and then the SA algorithm was employed to find the best phase distribution. All possible values of the phase difference between 0 and \(\pi\) were explored. Although this method can find the optimal solution, the calculation process is very time-consuming because for each phase shift, one round of the SA algorithm is performed.  
SA is a stochastic optimization algorithm [23]. To reach the global optimal solution, it needs to search enough time at each temperature. Therefore, the entire annealing process takes a lot of time. Compared with the SA algorithm, iterative Fourier transform algorithm (IFTA) [24], originally devised by [PERSON] and [PERSON] [25], is more efficient for the design of DOE, which has achieved considerable success in terms of less convergence time and clearer reconstruction. In this paper, a very simple and effective method based on the IFTA is presented to design the binary phase DOE with non-\(\pi\) phase difference. This method takes advantage of the special properties of the binary phase element and only needs to use the IFTA once. Compared with the existing methods based on the SA algorithm, design time can be greatly reduced while obtaining the same diffraction efficiency.