# Reliability-Enhanced Camera Lens Module Classification Using Semi-Supervised Regression Method
## 1 Introduction  
The recent development of bezel-less smartphones necessitates a large-scale production of the camera lens module before it is ready for use in the assembly stage. A camera lens module, which is normally placed at the front and back of a smartphone, consists of several spherical and aspheric lens stacked vertically inside a customized barrel [1]. Figure 1 illustrates the exploded view of an ordinary camera lens module. The determination of a well-made camera lens module relies upon the combination of the upright lens configuration as well as several external factors including barrel thickness and lens diameter [1]. With the number of factors that influence the performance of a module reaching a few hundred, it is important to understand which ones are more significant in its overall performance. Just as importantly, one must figure out the future modification of the factors to achieve a higher yield rate on the production of camera modules. One of the key factors, lens arrangement, directly determines the amount and the focus of light hitting the sensor. The main purpose of stacking multiple lenses in the right arrangement is to reduce the light from a large screen to fit the small size of the sensor. Modulation Transfer Function (MTF), a continuous variable that indicates the definition of the image created by the focused light, is a commonly used measure to compare the performance of optical systems. In definition, MTF is the magnitude response of an optical system to sinusoids of various spatial frequencies. In this study, MTF is used as the target variable to represent the quality of a lens module. Despite the huge impact on the quality, the traditional method to find the right arrangement is to simply turn each lens one at a time by a certain amount of degrees manually until the requirement is met. The procedure includes multiple inspections of every 10 products sampled when an issue is discovered from already manufactured products. By plotting the MTF curve of each product, either lens re-arrangement or thickness modification of a spacer and the lenses is made. Modifying the thickness of a spacer and lenses is done if the vertices are concentrated at a wrong spot. On the other hand, the lens re-arrangement is conducted when the vertex of MTF curve is lower than a threshold value, which is usually the most common case. It is a more preferred option since it is easier to do than the other. The lenses are normally rotated 45 degrees clockwise from their original positions. This kind of task is not only time-consuming but it also does not guarantee a better result after it has been conducted. In addition, no reliable way to screen the effect of slight modification in real-time exists, implying that one sample can be tested only after it is completely capped inside a barrel. Such repetitive and tedious operation necessitated an automated system to foresee the outcome of products without the assembly. Over the past few years, deep learning has emerged as a powerful tool in many engineering fields such as image processing, voice recognition and natural language processing, triggered by the advent of a fast computing hardware, e.g., GPU [2]. Its wide range of applicability has brought a new trend in both research and industrial sectors of our society, leading to the development of the popular deep neural network (DNN), convolutional neural network (CNN), recurrent neural network (RNN), and autoencoder [2]. DNN is simply an extension of the ordinary neural network with a single hidden layer, and a simplified model representation of the complex human brain. It is often referred to as a multi-layered perceptron network that is capable of understanding the non-linear nature of high-dimensional feature space. This is due to the non-linear activation function applied after the nodes of the hidden networks. Despite its huge potential as a non-linear function approximator, one of the limitations of DNN is that it normally requires a sufficient amount of data to provide reliable output.