Journal of the Korean Physical Society, Vol. 50, No. 5, May 2007, pp. 1243∼1251 Optical Zoom System Design for Compact Digital Camera Using Lens Modules Sung-Chan Park,∗ Yong-Joo Jo, Byoung-Taek You and Sang-Hun Lee Department of Physics, Dankook University, Cheonan 330-714 (Received 5 February 2007) By use of lens modules and third-order aberration theory, a new design approach can be applied to the three-group inner-focus zoom system. The optimum initial design satisfying the specific requirements and its real lens design from the lens modules are presented. An initial design with a focal length range of 4.3 to 12.9 mm is derived by assigning appropriate first-order quantities and third-order aberrations to each module along with the constraints required for the optimum solutions. By using an automatic design method rather than analytic approaches, we separately designed a real lens for each group at given conjugates and then combined them to establish an actual zoom system. The combination of the separately designed groups results in a system that satisfies the basic properties of the zoom system consisting of the original lens modules. When the aberrations are balanced, the finally designed three-group zoom lens is expected to fulfill all the requirements of a compact digital zoom camera. PACS numbers: 42.15.Eq, 42.15.Fr Keywords: Lens module, Aberrations, Digital zoom camera I. INTRODUCTION without detailed prescriptions. Zoom lens design using lens modules has the following advantages: modules can be used for each of the moving groups, and the param- The zoom lens design is usually divided into two tasks. eters defining the specifications, the third-order aberra- One is paraxial studies based on thin-lens theory, which tion characteristics, and the positions of the groups for give the first-order parameters, such as the focal length zooming can be varied to obtain the optimum design sat- of each group, the zoom ratio, the focal length range, the isfying the requirements. zooming locus, etc. The other is to set up the zoom lens In this paper, lens modules and aberration theory are system from the paraxial studies and balance aberrations used to discuss the optimum initial design of three-group [1–5]. These approaches, however, have several disadvan- inner-focus zoom lenses. This initial zoom system is de- tages. It is difficult to determine if the solutions obtained signed to satisfy specific requirements, and the real lens from paraxial studies satisfy all the requirements for the designs are obtained from the lens modules by using an zoom lens, such as packaging constraints, specifications, automatic design method. In this process, the real lens overall length, and so on. Since the aberrations of this for each group is quickly designed to match the first- starting zoom lens are not corrected, aberration balanc- and third-order aberrations of the module. Compared to ing at all zoom positions requires much more effort in an analytic design, this approach can dramatically save the design of multi-group zoom systems. time and effort. Thus, the separately designed groups The difficulties due to paraxial analyses can be over- are then combined to form an actual zoom lens. Finally, come by using the lens module design reported by residual aberration balancing results in a zoom lens that Stavroudis and Mercado [6], Kuper and Rimmer [7], and has enough performance over a range of f-number from Park and Lee [8]. Lens modules are the mathemati- 3.2 at the wide-field extreme to 4.5 at the narrow-field cal constructs that can model a complex optical sys- extreme positions. This zoom lens is expected to fulfill tem without actually doing the detailed design. The lens all requirements of a compact digital zoom camera. modules discussed by Kuper and Rimmer are based on mock ray tracing, which consists of tracing rays through a lens specified by one of its eikonal function rather than II. LENS MODULE DESIGN FOR THE its curvature, thickness, and indices. Lens modules can THREE-GROUP INNER-FOCUS ZOOM be used as a starting point for the design of a real lens and SYSTEM to model an arbitrary lens from measurable quantities The layout of the three-group inner-focus zoom system ∗E-mail: [email protected]; Fax: +82-41-550-3429 is shown in Figure 1. From the object to the image side, -1243- -1244- Journal of the Korean Physical Society, Vol. 50, No. 5, May 2007 Fig. 1. Layout of the three-group inner-focus zoom system: (a) wide-field position, (b) zooming position, and (c) narrow-field position. Fig. 2. First-order parameters for specifying a lens system: (a) thick-lens elements and (b) the lens module. the zoom system is composed of a fixed front lens group, a second lens group for compensation, and a third lens group for zooming. Their powers are denoted by k1, k2, and k3, respectively. The first group is always fixed. While the third group moves to the object side to have a longer focal length, the second group should move to keep the image position stationary. When the displacement of the groups for zooming is zero, i.e., at position 1, the distances between the preced- ing group and the succeeding group are specified by d11, d21, d31, as shown in Figure 1. When the displacement of the third lens group is maximum, i.e., at position 3, the zoom system has its longest focal length, and posi- tion 2 is located halfway between position 1 and position 3. The displacement is positive if a group moves from Fig. 3. Optimized zoom system consisting of three lens left to right. The object is set at infinity [9]. modules. In a zoom system, each group is generally composed of several thick lens elements, as shown in Figure 2(a). In that figure, when the higher-order aberrations are ne- each group of the zoom system could be replaced by the glected, the thick lens system could be specified by its thick-lens module by specifying its focal length (FLM ), first-order quantities and the third-order Seidel image front focal length (FFM ), back focal length (BFM ), mag- aberrations at given conjugate points. In other words, if nification (MGM ), entrance pupil position (EPM ), en- we assign the first-order quantities and the third-order trance pupil diameter (EDM ), field angle (β), and the aberrations of lens modules to the thick-lens system, then third-order aberrations, as shown in Figure 2. both lenses are equivalent to each other within the limits We have set up the zoom camera system shown in of the first- and the third-order properties [7,9]. Hence, Figure 1 with three thick-lens modules, for which initial Optical Zoom System Design for Compact Digital··· – Sung-Chan Park et al. -1245- Fig. 4. Aberrations of an optimized zoom system consisting of three lens modules: (a) position 1 and (b) position 3. first-order inputs are appropriately given to work as a all zoom positions. Collisions between modules must be zoom system. It is based on the first and second modules avoided during zooming, and enough mounting space is having negative power, but the third module having pos- required. We next selected the overall length to be as itive power. The aperture stop of the zoom system is lo- short as possible for a compact zoom system. In this cated in front of the third module so that the system has case, we required the overall length to be less than 18 symmetrical configuration with respect to the stop. This mm. layout is good for aberration balancing. The air space In order to get an optimum zoom system, we opti- between each module should be ensured for the mount- mized the lens module prescriptions so that the specific ing space. Since lens modules do not reflect higher-order constraints were satisfied. The design variables are the aberrations, it is desirable to reduce the aperture and focal length, the front and back focal lengths, the conju- field size of the system so that the third-order aberra- gate points, the spacings, and the aberration coefficients tions are dominant. We have taken the zoom system of each module. Figure 3 shows the initial design of the with a half image size of 1 mm and an f-number of F/5 zoom system obtained from this process. Focal lengths at position 1 to F/7 at position 3. The distances between range from 4.3 to 12.9 mm, and aberrations are corrected modules are constrained to be longer than 0.5 mm over quite well, as shown in Figure 4. Table 1 shows the data -1246- Journal of the Korean Physical Society, Vol. 50, No. 5, May 2007 Table 1. Design data (in mm) for the lens modules in the optimized lens module zoom system. Module I Module II Module III FLM −36.8400 −7.9621 3.9705 FFMM (b) 38.2414 7.8676 −5.6551 BFM −36.0248 −8.4947 −1.6746 MGM 0.0 0.0 0.0 EDM 1.0 1.0 1.0 Fig. 5. Schematic diagram of the thick-lens system with Field (β) 1.0◦ 1.0◦ 1.0◦ five elements. Thickness 0.8472 0.6972 7.4074 W040 0.0890 0.0100 −0.0506 W131 −0.0034 −0.0147 0.0175 (SIII ), Petzval curves(SIV ), distortion(SV ), longitudi- W 0.0750 0.0018 0.0028 222 nal chromatic aberration (SL), and transverse chromatic W220 −0.0043 0.0010 0.0024 aberration (ST ) of this system are expressed in terms of W311 −0.0015 −0.0005 −0.0011 Gaussian brackets, as [11–14] F ocal length : f = 1/[k1, −d1/n1, k2, Table 2.