The setup of the optical imaging system is shown in Fig. 6. The amplitude and phase masks mounted on the mechanical assembly as shown in Fig. 6. By rotating this mechanical body, the amplitude and phase mask will be rotated by the same angle. So. The point spread function will rotate by the same angle. Figure 7 shows the point spread function with the responding angles. As shown in Fig. 7, when the mechanical body rotates, the point spread function will rotate the same angle at *ψ* = 0.

In this article, we use the blind post processing to achieve the high-resolution image. As shown in Ref. [16], the blind post processing can correct the effect of the optical aberrations. In this article, we use the Richardson-Lucy deconvolution to achieve the blind post processing, and the iterative formula for an image can be presented by

**o** **t+1** **=o** **t** **×{[g/(o** **t** ⊗**h)]** ⊗**h****r****};**

**o** **t+1** **=max(o** **t+1** ,**0)**

**h** **t+1** **= h** **t** **×{[g/(o****t+1**⊗**h)]** ⊗**o****r****t+1****}**

**h** **t+1** **=norm(max(h** **t+1** ,**0))**

where o is the object; g is the input image; h is the system point spread function; hr is the flipped point spread function; t is the number of iterations; ⊗ is the convolution operator.

Since there are four raw images, the iterative process can be presented by,

**o** **1** **t + 1** **= o** **1** **t** **×{[g****1****/(o**⊗**h****1****t****)]** ⊗**h****r1****t****}**

**o** **1** **t + 1** **=norm(max(o** **1** **t + 1** ,**0))**

**h** **1** **t + 1** **= h** **1** **t** **×{[g****1****/( o****1****t + 1**⊗**h****1****t****)]** ⊗**o****r1****t+1****}**

**h** **1** **t + 1** **=norm(max(h** **1** **t + 1** ,**0))**

**o** **2** **t + 1** **= o** **1** **t + 1** **×{[g** **2** **/(o** **1** **t + 1** ⊗**h****2****t****)** ⊗**]h****r2****t****}**

**o** **2** **t + 1** **= norm(max(o** **2** **t + 1** ,**0))**

**h** **2** **t + 1** **= h** **2** **t** **×{[g****1****/( o****2****t + 1**⊗**h****2****t****)]** ⊗**o****r2****t+1****}**

**h** **2** **t + 1** **=norm(max(h** **2** **t + 1** ,**0))**

**o** **3** **t + 1** **= o** **2** **t + 1** ***{[g** **3** **/(o** **2** **t + 1** ***h** **3** **t** **)]*h** **r3** **t** **}**

**o** **3** **t + 1** **= norm(max(o** **3** **t + 1** ,**0))**

**h** **3** **t + 1** **= h** **3** **t** **×{[g****1****/(o****3****t + 1**⊗**h****3****t****)]** ⊗**o****r3****t+1****}**

**h** **3** **t + 1** **=norm(max(h** **3** **t + 1** ,**0))**

**o** **4** **t + 1** **= o** **3** **t + 1** **×{[g** **4** **/(o** **3** **t + 1** ⊗**h****4****t****)]** ⊗**h****r4****t****}**

**o** **4** **t + 1** **= norm(max(o** **4** **t + 1** ,**0))**

**h** **4** **t + 1** **= h** **4** **t** **×{[g****1****/( o****4****t + 1**⊗**h****4****t****)]** ⊗ **o****r4****t+1****}**

**h** **4** **t + 1** **=norm(max(h** **4** **t + 1** ,**0))**

**o** **1** **t + 1** **= o** **4** **t + 1**

**end**

where g1, g2, g3 and g4 are the images obtained by the point spread functions with the rotating angles of 0° (h1), 90° (h2), 135° (h3) and 45° (h4), respectively. h1, h2, h3 and h4 are the system point spread function with the rotating angles of 0°, 90°, 135° and 45°, respectively. h1r, h2r, h3r and h4r are the flipped h1, h2, h3 and h4, respectively. o1r, o2r, o3r and o4r are the flipped o1, o2, o3 and o4, respectively. Norm(.) represents normalized calculation; t is the number of iterations; ⊗ is the convolution operator.

In order to show the imaging effectiveness, we perform the comparison of the proposed method with the imaging system with the quartic phase mask. For the digital processing, the starting parameters are: *o*1 = norm(g1 + g2 + g3+g4); h1, h2, h3 and h4 are the point spread functions at *ψ =* 0 for four different angels. Based on the starting conditions, the simulation results are shown in Fig. 8 for difference defocus of ψ = 0, ψ = 5 and ψ = 10. Figure 8 shows the images of the quartic phase mask and the proposed method. The proposed method is shown in top of the Fig. 8. The image of the quartic phase mask is shown in bottom of the Fig. 8. From Fig. 8, the edge of the spokes images of the proposed method are sharper than that of the quartic phase mask at all defocus values. This means that the proposed method can be used to improve the image quality.