Zoom Locus Research Articles

A Novel Analytical Interpolation Approach for Determining the Locus of a Zoom Lens Optical System

In an optical system with multiple lens groups and increased zoom magnification levels, achieving a smooth zoom locus is increasingly difficult. Traditional methods for calculating zoom loci often involve complex and time-consuming formulas. Consequently, we utilized the Padé approximation in optical design software to compute the zoom locus analytically, irrespective of the number of zoom positions (nodes). The initial data were used to assign orders to rational function polynomials, facilitating Padé approximation. If the image surface extended beyond the depth of focus (DOF), a node was added, with adjustments made until it fell within the DOF range. Furthermore, Padé approximation was performed to prevent singularities. The loci of all lens groups in the optical system can be expressed in a rational function format. Specifically, the numerator and denominator polynomial degrees were 20° and 1°, respectively, with their sum being the total number of nodes. In addition, we calculated the zoom locus by increasing the numerator sequence to minimize the occurrence of the singularity and added the node automatically to enable zoom locus calculation in all optical systems. Accordingly, we could make fast calculations, unlike conventional methods, using complex and time-consuming simultaneous equations. Therefore, we could express the locus of the compensated group in the form of a smooth function, as presently shown.

Computation of Analytical Zoom Locus Using Padé Approximation

When the number of lens groups is large, the zoom locus becomes complicated and thus cannot be determined by analytical means. By the conventional calculation method, it is possible to calculate the zoom locus only when a specific lens group is fixed or the number of lens groups is small. To solve this problem, we employed the Padé approximation to find the locus of each group of zoom lenses as an analytic form of a rational function consisting of the ratio of polynomials, programmed in MATLAB. The Padé approximation is obtained from the initial data of the locus of each lens group. Subsequently, we verify that the obtained locus of lens groups satisfies the effective focal length (EFL) and the back focal length (BFL). Afterwards, the Padé approximation was applied again to confirm that the error of BFL is within the depth of focus for all zoom positions. In this way, the zoom locus for each lens group of the optical system with many moving lens groups was obtained as an analytical rational function. The practicality of this method was verified by application to a complicated zoom lens system with five or more lens groups using preset patents.

Design of an 8x Four-group Inner-focus Zoom System Using a Focus Tunable Lens

This study presents an 8x four-group inner-focus zoom lens with one-moving group for a compact camera by use of a focus tunable lens (FTL). In the initial design stage, we obtained the powers of lens groups by paraxial design based on thin lens theory, and then set up the zoom system composed of four lens modules. Instead of numerically analytic analysis for the zoom locus, we suggest simple analysis for that using lens modules optimized. After replacing four groups with equivalent thick lens modules, the power of the fourth group, which includes a focus tunable lens, is designed to be changed to fix the image plane at all positions. From this design process, we can realize an 8x four-group zoom system having one moving group by employing a focus tunable lens. The final designed zoom lens has focal lengths of 4 mm to 32 mm and apertures of F/3.5 to F/4.5 at wide and tele positions, respectively.

Paraxial design method based on an analytic calculation and its application to a three-group inner-focus zoom system

A paraxial design method based on an analytic calculation is presented to overcome the problems of the conventional approaches in initial zoom lens design. We analytically derive a set of available zoom equations for a three-group inner-focus zoom system by using the matrix representation for paraxial ray tracing. We also develop a program tool to obtain the powers of the lens groups and total track length from the zoom equations. These powers of the lens groups are used to calculate the zoom locus; then the powers of the lens groups and the zoom locus are evaluated to see if the constraints are satisfied. If not, the power of each lens group is changed to meet the constraints. The stability of this iterative paraxial design method has been confirmed and applied to the initial design for a three-group inner-focus zoom system having a focal length of 3.0 to 9.0 mm. The total track length of this zoom lens is 12.37 mm at all zoom positions, and the apertures are F/3.5 at the wide and F/4.5 at the tele positions. In conclusion, this design procedure results in a 3x compact zoom lens system useful for a mobile camera.

Unified Analytic Calculation Method for Zoom Loci of Zoom Lens Systems with a Finite Object Distance

The number of lens groups in modern zoom camera systems is increased above that of conventional systems in order to improve the speed of the auto focus with the high quality image. As a result, it is difficult to calculate zoom loci using the conventional analytic method, and even the recent one-step advanced numerical calculation method is not optimal because of the time-consuming problem generated by the iteration method. In this paper, in order to solve this problem, we suggest a new unified analytic method for zoom lens loci with finite object distance including infinite object distance. This method is induced by systematically analyzing various distances between the object and other groups including the first lens group, for various situations corresponding to zooming equations of the finite lens systems after using a spline interpolation for each lens group. And we confirm the justification of the new method by using various zoom lens examples. By using this method, we can easily and quickly obtain the zoom lens loci not only without any calculation process of iteration but also without any limit on the group number and the object distance in every zoom lens system.

Evaluation of a Corrected Cam for an Interchangeable Lens with a Distance Window

Recently, the number of camera companies that produce commercializing interchangeable lens systems such as digital single lens reflex (DSLR) and compact system camera (CSC) lenses has been gradually increasing. These interchangeable lenses have various kinds of lenses with distinct specifications. In particular, the distance window among these specifications is the function most preferred by customers. Mechanical manual zoom and manual focus in these high end camera lenses with a distance window are in particular desirable specifications and are required for product quality. However, the AF lens group is linked to the zoom cam and moves. Because the AF lens group moves along with the object distance, we can not realize the distance window with only zoom locus calculation. In this paper, in order to solve the problem, we suggest an optical calculation method for a corrected AF zoom cam for an interchangeable lens with a distance window to achieve product differentiation and analyze the error in the calculation.

무한물점용 줌 렌즈 광학계의 줌 궤적에 대한 해석적 계산법

무한물점으로 취급하는 카메라 광학계의 경우, 자동초점(auto-focus) 속도를 빠르게 하기 위해 기존 광학계와 다른 형태로 광학설계를 하게 된다. 이 때문에 군의 개수가 늘어나므로, 기존의 해석적인 방법으로는 궤적 계산이 어렵고, 또한 수치해석적인 방법은 시간이 많이 걸리는 단점이 있다. 본 논문에서는 각 군을 스플라인 보간을 한 뒤, 주어진 뒤정점초점거리와 유효초점거리를 만족하도록 1개 또는 2개 군의 이동량을 해석적으로 구해 줌 궤적을 계산하는 해석적인 방법을 제안하고 이를 유도한다. 이 방법은 무한물점용 줌 렌즈 광학계에서 군수의 제한 없이 모든 광학계에 대해 반복적인 계산없이 해석적인 궤적을 구할 수 있으며, 다양한 예제를 통하여 그 효용성을 보였다. In case of the optical camera system with an infinite object distance, optical designs different from previous systems are required to speed up the auto-focus. As the number of lens groups is increased due to this, the conventional analytic method found it difficult to calculate the locus, and even the one-step advanced calculation method also had the trouble of taking a lot of time. In this paper, we suggested an analytic method for calculating the zoom loci by analyzing movement of one or two groups for situations corresponding to the given back focal length and effective focal length after taking a spline interpolation for each lens group. With this method, we would not only calculate the analytic zoom loci without iterations in every optical system without placing a limit on the group number at the zoom lens systems with the infinite object distance, but we would also show the utilities of this method through many examples.

大面阵中波红外连续变焦光学系统设计

A mid-wavelength continuous zoom optical system was presented for a staring Focal Plane Array(FPA) infrared detector by cooling assembly.The optical system with an optical configuration of reflect mirror fold was composed of a zoom object lens system and a secondary imaging system including seven lenses and two reflectors.On the basis of zoom principles,the systemic structure and design parameters were given by using special optical design software,then the schematic diagram and imaging quality were investigated.Finally,the performance and indexes of the system were verified.The results indicate that the system can offer a 50-500 mm continuous zoom and 100% cold shield efficiency.Moreover,the Modulation Transfer Function(MTF) in whole fields at Nyquist frequency is over 0.35 and the whole field distortion is below 2%.These results show that the system is characterized by high resolution,thermal sensibility,excellent images and smooth zoom locus.

一种8倍可见光变焦光学系统设计

An example of 8× ratio visible zoom system with mechanic compensator was designed.The focal length and angle of vision of the system were 6.5~52 mm and 6.6°~52°,respectively.The modulation transfer function(MTF) is above 0.6 within the whole focal range at spatial frequency of 75 lp/mm,and approaches the diffraction limit.RMS value of spot diameter was investigated.The cam curves after optimization was given.The system has the advantages of simple structure,high image quality,short zoom path and smooth zoom locus etc.

가우스 괄호법을 이용한 유한 물점을 갖는 줌 렌즈에 대한 일반적인 수치해석적 근축광선 줌 궤적 추적

가우스 괄호법을 이용하여 무한 물점을 포함한 모든 유한 물점을 대상으로 하는 모든 복잡한 줌 렌즈에서 사용가능한 일반적인 근축광선 줌 궤적 추적식을 유도하였다. 이를 Visual Basic으로 프로그램화하여 수치해석적으로 줌 궤적을 구하였다. 이 결과 이 식의 해는 물체의 거리에 관계없이 모든 종류의 줌 렌즈에서 줌 궤적에 대한 초기설계에 유연하면서 통합적으로 적용할 수 있다. 이 식의 유용성을 증명하기 위하여 <TEX>$M_{4a}$</TEX>와 <TEX>$M_{4h}$</TEX> 형태의 4군 줌 렌즈들과 <TEX>$M_{5n}$</TEX> 형태의 5군 줌 렌즈의 줌 궤적을 유한 물점에 대해서 빠르게 산출할 수 있음을 보였다. We theoretically derive the set of general paraxial zoom locus equations for all zoom lens systems with finite object distance, including the infinite object distance case, by using the Gaussian bracket method and matrix representation of paraxial ray tracing. We make the zoom locus program by means of a numerical calculation method according to these equations in Visual Basic Language. Consequently, the solutions of this method can be consistently and flexibly used in all types of zoom lens in the step of initial design about zoom loci. Finally, in order to verify the justification and usefulness of this method, we show that two examples, such as <TEX>$M_{4a}$</TEX> and <TEX>$M_{4h}$</TEX> types of 4 groups, and one example, <TEX>$M_{5n}$</TEX> type of 5 groups, which are very complicated zoom lens systems, can be rapidly and diversely traced through various interpolations by using this program.

가우스 괄호법을 이용한 줌 렌즈의 조출량에 대한 수치해석 계산법

When the object distance of a zoom lens with finite object distances is varied, we can fix the image at a fixed image plane by moving only one zoom lens group (autofocus group) without moving all zoom lens groups for the autofocus. We theoretically formulated and numerically calculated the moving distances of the autofocus group by using Gaussian brackets and a paraxial ray tracing method. The solutions of this method can be consistently and flexibly used in the initial design for the moving distance of autofocus group within these zoom loci in all types of zoom lens. Finally, in order to verify the usefulness of this method, we show that the moving distance of an autofocus group can be rapidly and diversely obtained in one example of zoom lens type.

가우스 괄호법을 이용한 무한 물점을 갖는 복잡한 줌 렌즈의 수치해석적인 근축광선 줌 궤적 추적법

가우스 괄호법을 이용하여 카메라 렌즈와 같이 무한 물점을 대상으로 하는 모든 복잡한 줌 렌즈에서 사용가능한 근축광선 줌 궤적 추적식을 이론적으로 유도하였다. 그리고 이를 Visual Basic으로 프로그램화하여 수치해석적으로 줌 궤적을 구하였다. 이 방법은 근축광선 추적식을 가우스 괄호법에 적용시켰기 때문에 다양한 줌 형태에 따른 구속조건의 공식을 매우 간편하고 알기 쉽게 단순화시켜준다. 이 결과 이 식의 해는 모든 종류의 줌 렌즈에서 줌 궤적에 대한 초기설계에 유연하면서 통합적으로 적용할 수 있다. 이 식의 유용성을 증명하기 위하여 4군과 5군의 매우 복잡한 줌 렌즈계의 줌 궤적을 다양한 보간법으로 빠르게 산출해 낼 수 있음을 보였다. We theoretically derive the set of utilizable paraxial zoom locus equations for all complicated zoom lens systems with infinite object distance, such as a camera zoom lens, by using the Gaussian bracket method and the matrix representation of paraxial ray tracing. And we make the zoom locus program according to these equations in Visual Basic. Since we have applied the paraxial ray tracing equations into Gaussian bracket representation, the resultant program systematically simplifies various constraints of the zoom loci of various N group types. Consequently, the solutions of this method can be consistently used in all types of zoom lens in the step of initial design about zoom loci. Finally, in order to verify the usefulness of this method, we show that one example among 4 groups and that among 5 groups, which are very complex zoom lens systems, can be rapidly and with versatility traced through various interpolations by using this program.

First-order analysis of a three-lens afocal zoom system

A general analysis for the first-order design of a three-lens afocal zoom system with one lens fixed is presented. The reasonable solution areas in the focal length diagrams with positive or negative mag- nification are derived and shown graphically. The relation between the two separations of the three lenses in zooming is found to be a hyper- bola. According to the different locations of hyperbola centers, four cases are analyzed. From the four hyperbolic graphs, we get five different types of zoom systems. For each zoom type, we find the maximum range of magnification and the position where the maximum or minimum system length occurs during zooming. The zoom loci for the first or sec- ond lens fixed are also discussed. © 1997 Society of Photo-Optical Instrumenta- tion Engineers. (S0091-3286(97)02204-6)