## 1 Introduction
Figure 1 shows that the change in the size of the resolution chart can be easily recognized when the object distance changes. However, the size of the resolution chart printed on a specific size cannot be changed according to the object distance. In addition, the space for measuring the resolution of the test lens increases as the inspection distance and resolution chart size increase. Therefore, another method must be employed to solve this technical problem. To reduce this inspection space for mobile phone camera optics, we also need to reduce the inspection distance. For this technical issue, the optical system must be placed between the test lens and resolution chart. This optical system should be constructed so that the resolution chart is enlarged to the desired inspection distance of the test lens. Hence, we need to use a converter or collimator. A converter is an optical system that converts the field angle of the optical system, such as the camera lens [12; 13]. Meanwhile, a collimator is an optical system that creates a collimated beam of light to diverge from an object at a finite distance [14; 15]. In the present study, a small resolution chart located at a finite distance must create a virtual image that is greatly enlarged over a long distance so that the features of the converter and collimator are well utilized. In this study, the optical system needed to measure the test lens is called a collimator. A collimator that reduces the inspection space of mobile phone camera optics has recently been studied [16; 17]. The collimator is an optical system that converts the beam emitted from the original point source into a collimated beam. As the distance from the collimator to the point source gets closer, the beam passing through the collimator becomes a diverged beam. At this time, the point where the extension line of the diverged beam meets the optical axis is the virtual image. Here, if the test lens is placed in front of the collimator (opposite the point source), the test lens can see the virtual image. Therefore, from the point of view of a test lens, it becomes a virtual object. Therefore, in the present work, we propose a new design method for a collimator that can measure resolution at various distances of the resolution chart. The virtual-image position of the resolution chart must be varied so that the test lens can be inspected at various distances. To implement this function, the virtual-image position must be varied by moving a specific lens inside the collimator. Therefore, a collimator with a focus-adjustable capability must be used. Section 2 describes the design process of our proposed focus-adjustable collimator system and illustrates the result of the paraxial power arrangement of the system. Section 3 presents the layout of an aberration-balanced collimator system at infinite and close positions to verify the capability of the proposed system. In addition, the modulation transfer-function curve of the designed collimator system is shown to verify the desirable optical system performance in inspecting the general phone cameras because the modulation transfer function (MTF) must be evaluated to commercialize the optical system in the industry. Section 4 presents the conclusion of this study.