# Zernike Coefficient Prediction Technique for Interference Based on Generation Adversarial Network
## 1 Introduction  
Aberration is the difference between an actual image and an ideal image in the optical system. Therefore, aberration is one of the essential reference indicators when designing an optical system. Usually, the aberration of a system is quantified when evaluating the system's performance, such as Seidel aberrations [1] and Zernike polynomials [2]. For example, the Zernike polynomials use a series of orthogonal polynomials for the unit circle [3].  
One method to measure aberration is an interferometer. The aberration information is recorded on the interference fringe image. Therefore, Zernike coefficients could be calculated using traditional optical equations, such as the interference phase shift method, the Fourier transform method, and the phase-shift method. The conventional conversion methods convert interference fringe images to Zernike coefficients and require two steps, which are complex mathematical calculations. First, the interference fringe image is converted into the wavefront difference or phase difference. Second, Zernike coefficients are calculated using the surface fitting method with Zernike polynomials [4].  
To simplify the calculation process, we use deep learning to obtain the Zernike coefficients from interference fringe images. A neural network learns from a lot of training datasets. After finishing the training, the model predicts the answer for the new image [5]. Therefore, this method does not need complex mathematical calculations and can expect the answers needed. In this paper, we use the Generative Adversarial Network (GAN) to predict Zernike coefficients quickly and simply.  
[PERSON] and others proposed the GAN model in 2014 to achieve unsupervised learning of adversarial networks [6]. The network architecture of the GAN model is composed of two networks as follows: the Generator network and the Discriminator network [7]. The goal of the Generator network is to generate images that are close to authentic images. The Discriminator network is an auxiliary role for training the Generator network to achieve unsupervised learning. The concept of Pix2 Pix is an image-to-image conversion method uses applications of the GAN model. Therefore, the GAN model generates training datasets, image recognition, image inpainting, and fake photography using human image synthesis technology (DeepFake) [8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19]. In previous research, many studies focused on fringe and aberration using deep learning [20; 21; 22; 23; 24], and we used GoogLeNet to predict Zernike coefficients [25]. The prediction accuracy is good but not good enough, so we study GAN to improve the prediction accuracy.  
According to the advantage of GAN image-to-image translation, we propose a novel usage for GAN in this paper. We design a mosaic image as the output image of the Generator, and each piece of the mosaic image links to the number of Zernike coefficients. That is a new concept of GAN for image-to-number translation. Therefore, we use GAN to predict Zernike coefficients (mosaic image) from interference fringe images directly. First, the training datasets are generated by Python with an optics formula since the interferometer cannot easily create many interference fringe images as the Generator's inputs. Then, we use optical software, VirtualLab (VL), to generate simulated images and to transfer learning to improve the accuracy with almost actual interference fringe images [26; 27]. According to the result, the prediction technique can predict the Zernike coefficients of an interference fringe from the interferometer in the future.