## 2 Methods  
In general, a zoom optical system refers to an optical system wherein the magnification changes continuously, the position of the image surface is fixed, and the focal length changes based on the object distance variance [27; 28]. As shown in Figure 1a, in an optical system wherein the size of the imaging element is fixed, the focal length is short and long at the wide-angle and telephoto ends, respectively, and varies depending on the angle of view. If the angle of view is fixed in a zoom optical system designed following the conventional method, the maximum height of the chief ray in the image plane changes, as shown in Figure 1b. The focal distance and image height exhibit a proportional relationship [29; 30; 31]. When the angle of view is fixed, the image height decreases at short focal distances and increases at long focal distances [32; 33]. Using this phenomenon, if the angle of view is fixed as per the size of the imaging element proposed in the THz optical system, the focal length of the optical system changes according to the size of the imaging element. Figure 2 illustrates the relationship between the focal length and angle of view, where, \(\theta\), \(y\), and \(H2\) are the half angle of view, image height, and location of the second major surface, respectively, and \(f\) is the effective focal length (EFL), which is the distance from the second principal plane to the focal point. The maximum angle of incidence of the chief ray is referred to as the half FOV (HOF), which indicates the range that can be achieved in the optical system. The half angle of the view was determined by the maximum size of the imaging device [34]. The half-angle size \(y\) of the imaging device is expressed as Equation (1). \[y=f\cdot\tan\theta, \tag{1}\]  
where \(\theta\) and \(f\) are the half angle of view and the focal length, respectively. In general, the size of an imaging device is fixed; therefore, the angle of view of the optical system is determined by the focal length of the optical system. As shown in Equation (1), the angle of view decreases, the focal length increases, and vice versa. Figure 3 shows the angle of view according to the focal length of the optical system. Figure 1: Relationship between focal length and angle of view in (**a**) general optical system and (**b**) optical system for THz applications. Figure 2: Relationship between focal length and field of view. In general optics, a lens with a focal length of 50 mm is referred to as a standard lens [35]. Compared with a standard lens, an optical system with a larger angle of view and a shorter focal length of 35 mm or less is referred to as a wide-angle lens, and an optical system with a smaller angle of view and a longer focal length of 70 mm or more is called a telephoto lens. However, the proposed optical system had a fixed angle of view and large image height; thus, the focal length is greater than 50 mm. Therefore, the mode with a relatively small focal length, owing to the relatively small size of the image, is referred to as the wide-angle end, and the mode with a relatively long focal length is referred to as the telephoto end. Our proposed optical system has a field of view in the telephoto range. Equivalent lenses refer to lenses with different axial thicknesses but the same total refractive power and paraxial optical properties regarding peripheral rays. The process of converting a specific lens into an equivalent lens of a different thickness is referred to as equivalent lens conversion, which is useful for the initial design or local changes in optical systems [36]. A lack of change in the paraxial optical properties indicates that the total refractive power and height at which the paraxial ray enters the principal plane are the same. The equivalent lens transformation conditions can be expressed as a quadratic equation. Therefore, no solution may exist. Having two real roots implies that another solution exists with the same thickness and characteristics, albeit with a different radius of curvature.