1. Introduction
Optical images are one of the most direct forms of external information accessible to humans. Compared to fixed-focus optical systems with a fixed field of view, zoom systems, with the core component zoom lens, can continuously change focal length by adjusting the relative positions of internal lenses. This characteristic brings zoom systems continuous variation in field of view and magnification to acquire high-resolution images, which makes zoom systems significantly advantageous in dynamic and complex environments, leading to widespread applications in photography, scientific research, security, and defense. However, zoom systems exhibit a significant issue of zoom delay, which refers to the transition time between short and long focal lengths during high-ratio continuous zoom. Excessive zoom delay can lead to the loss of critical targets during focal length switching, thereby impacting the efficiency and accuracy of information acquisition and event processing. This problem primarily affects applications requiring rapid response and high-precision tracking. For example, in security applications, zoom delay may hinder cameras from capturing critical footage in time. Therefore, addressing zoom delay while keeping high image quality is crucial for improving the performance and effectiveness of zoom optical systems.
Generally, methods for decreasing zoom time can be approximately classified into two categories: shortening zoom travel and increasing the velocity. For the former, people have made great efforts to utilize novel zoom methods such as the multiple-moving-groups method, liquid lenses and Alvarez lenses, to reduce movements of constituent optical elements. Y. Liu et al. [
1] presented a 50× five-group zoom lens design with three moving elements, making the displacement of all components smaller and the total length shorter. Z. Jiang et al. [
2] proposed a continuous optical zoom microscopy imaging system based on liquid lenses, in which continuous zooming is achieved by modulating the focal length of liquid lenses when changing the applied driving voltage. The magnification can change from ∼9.6× to ∼22.2× with a response time of ∼50 ms. Y. Zou et al. [
3] reported an ultra-compact 3× optical zoom endoscope containing two tunable Alvarez lenses. Due to moving in directions perpendicular to the optical axis, the required movements for its constituent optical elements are less than 110 μm, and the zoom time is about 15 ms. However, compared to traditional zoom lens design, the multiple-moving-groups method does not significantly reduce the zoom travel, and as the number of components increases, the inter-group errors and assembly difficulties also rapidly rise. Also, there are some drawbacks for liquid lenses, such as short lifespan, aberrations from gravitational effects and precise voltage modulation. For Alvarez lenses, it is challenging in optical design to achieve high-magnification zoom and high-quality image through the variation of a single continuous surface, and the difficulty in processing freeform surfaces makes it hard to manufacture large-diameter components. Therefore, the above methods in shortening zoom travel are not suitable for our design [
4,
5], in which the image quality of the large-component zoom lens is the most significant.
As for the latter, it appears that there is a trend of optimizing and reducing the transmission mechanism to reduce friction and wear in order to increase zoom speed in traditional mechanically compensated zoom lenses. In the early development of zoom lenses, cams were ingeniously employed to mechanically guide moving groups along designated trajectories by slots and guide pins. Nevertheless, the complicated structure of cam slots and pins causes high processing difficulty and cost, and the friction between them reduces the lifespan. Studies on optimization of cam curves are continuous, for example, H. Li et al. [
6] optimized the pressure angle of the cam curve in an 8× zoom system by using a particle swarm optimization algorithm, to improve the design efficiency and solve the cam motion jamming issue. Following control technology improvement, control algorithms began to replace cam slots with more precise positioning, and the transmission mechanism is only the threaded rod between the motor and moving group, eliminating one stage of transmission. For instance, P. Zhou et al. [
7] designed a 55× infrared continuous zoom imaging system by utilizing a stepper motor with an encoder and threaded rod. In contrast to rotary motors, which require transmission mechanisms to convert rotary motion into linear one, linear motors can directly drive moving groups for linear motion without a transmission mechanism, minimizing friction and making rapid zooming possible. In terms of zoom lenses, linear motors can be categorized into ultrasonic motor (USM) [
8] and voice coil motor (VCM). USM can achieve high-speed focusing; however, the movement is based on friction between the wear surfaces, making USM unsuitable for long zoom travel. In comparison, VCM is the most likely candidate for rapid zooming. C. Liu et al. [
9] introduced a miniature closed-loop VCM with small size, high positioning repeatability (<5 μm) and fast response (<10 ms) for autofocus in mobile phone cameras. C. Hsieh et al. [
10] proposed a compact VCM for optical zoom modules in smartphone cameras, featuring long displacement (±5.25 mm) and short response time (<50 ms).
Although it seems that VCM is the most suitable choice for high-magnification rapid zoom lenses, currently, VCMs are mainly applied in drive modules for focusing, low-magnification zooming, aperture and optical image stabilization, corresponding to relatively short travel. The demand for long zoom travel inevitably increases the size of VCM, posing challenges in designing a VCM that provides sufficient driving force within the constraints of limited dimensions. Therefore, it is significant to build models for VCM and analyze its electromagnetic characteristics, balancing driving force and size, which has attracted much interest. L. Li et al. [
11] analyzed a flat VCM with a Halbach array structure for a precision positioning system. The method of images is adopted to predict the distributions of global and local magnetic fields for obtaining flux density formulae. C. Luo et al. [
12] believed that due to intermittent duty and reciprocating linear motion, it is easy to neglect bad thrust characteristic conditions and limit VCM to obtain a higher thrust density when only increasing the air-gap flux density. Thus, they utilized equivalent magnetic circuit model and finite element method (FEM) to analyze the thrust characteristic. Z. Zhang et al. [
13] have provided a theoretical reference and experimental data of a two-degree-of-freedom VCM for multidimensional complex motion systems with a simple structure, small size, and great force. In their work, the proposed VCM has high average values and lower ripple ratios of linear-thrust and swing-torque. S. Kang et al. [
14] have proposed a miniaturized cylindrical VCM with a symmetric stator, with the advantages of enhancing uniformity of magnetic flux density in the air gap and reducing leakage flux. Z. Jiang et al. [
15] proposed a novel magnetic circuit design and corresponding force calculation method to reduce the size of horizontal linear vibration motors. However, there have been few studies reported on the systematic optimal structural design of VCM, which significantly hinders its widespread application.
In this work, to address challenges in rapid zoom for high-magnification zoom lenses, the structural design of VCM for rapid zoom optical systems is systematically analyzed through numerical computations of magnetic field distributions. From single permanent magnet, FEM results correspond to experimental results. Both FEM and equivalent magnetic charge (EMC) [
16] results confirm that increasing permanent magnet thickness while reducing its lateral dimensions will contribute to enhancement in magnetic flux density. Furthermore, the influence of structural parameters like magnet width and yoke thickness of VCM is analyzed, validating the yoke’s critical role in suppressing edge effects and optimizing magnetic circuit efficiency. Based on analytical computation, the yoke thickness equals magnet thickness (
k =
h) configuration achieves optimal volumetric efficiency, maintaining field intensity. For VCM with fixed parameters, the optimal magnet width range is determined considering both the magnetic flux confinement effect of the yokes and the edge flux leakage of the magnet. Moreover, a simple EMC calculation method is proposed for rapid and accurate determination of the magnetic field distribution in the VCM air gap. Based on systematic magnetic field analysis, optimal structural parameters for VCM are determined for 40× rapid zoom lens with cost and space limitations. Driving force
Fdrive = 5.58 N for the designed VCM is nearly 5 times the demand force
Fd = 1.06 N, and prototype fabrication of the rapid zoom lens is successfully accomplished. The actual trajectory shows that the moving group reaches 35.4 mm destination in 0.18 s, and photographs confirm that the rapid zoom system achieves a 100-ms-level smooth transition from short-focus to long-focus state. This rapid zoom optical system shows great potential in applications including security surveillance, industrial visual inspection, and intelligent logistics management.
3. Performance Evaluation for Rapid Zoom Lens with VCM
As described above, these results confirm that the systematic design process of optimal structural parameters for VCM is determined in ideal conditions. In this section, a VCM has been designed for a certain rapid zoom lens with cost and space limitations.
Figure 9a presents the schematic of a 40× rapid zoom lens with a focal length range of 7.5–300 mm. In this optical system, two zoom groups are driven by different VCMs, as shown in
Figure 9b. As an example, the VCM with a larger stroke is analyzed. The load (weight
ml = 40.8 g), including zoom group and copper coil, is driven by VCM in S-curve trajectory [
4] with a stroke of 35.4 mm. For the rapid zoom lens, zoom time should be controlled within 0.2 s, and the corresponding demand acceleration
al is larger than 16 m/s
2. Considering the actual using posture where the lens may be positioned vertically downward, the zoom group should be driven against the force of gravity. Thus, the demand driving force
Fd for VCM should be satisfied:
Fd ≥
ml (
al +
g), i.e.,
Fd ≥ 1.06 N.
The permanent magnet length am = 49 mm is based on the displacement requirements of stroke and coil size, while the thickness h = 3 mm is selected considering cost constraints. The yoke length ay = 51 mm is slightly longer than am. Following the inflection point condition (k ≈ h) for both magnetic flux density growth and flatness improvement, the yoke thickness k is set as k = 2.5 mm. Considering the gap between coil and yoke, air gap δ0 is determined as δ0 = 2.8 mm, which is slightly larger than the coil thickness (2 mm). Parametric sweep analysis of magnet width b under am = 50 mm revealed that the recommended optimal b ranges from 10 mm to 30 mm, and b = 20 mm yields relatively large magnetic flux density in the air-gap central region.
For the VCM with these structural parameters, FEM and simplified EMC model are used to calculate axial
Bz distribution in the working air gap region (white dashed line), as illustrated in
Figure 9c. Through EMC calculations (blue curve) and FEM simulation (red curve) results, average
Bz value is about 0.45 T within the effective stroke. Goodness-of-fit R
2 for the two results exceeds 0.98, confirming the accuracy of the proposed simplified EMC model with high computational efficiency. The copper coil is modelled as stranded with total turns
N = 400 and resistivity
. The VCM operates under
U = 12 V DC power supply with current
I = 1.55 A, and the axial driving force is calculated according to the Ampere force law:
Fdrive =
NBzIle =
NBzIb = 5.58 N, where
le =
b indicates effective length in the magnetic field. Driving force
Fdrive = 5.58 N for the designed VCM is nearly 5 times the demand force
Fd = 1.06 N. Similarly, the structural design of VCM for another zoom group can be finalized in the same method. So far, the systematic design of optimal structural parameters for VCMs has been achieved for a certain rapid zoom lens.
Building upon the optimized VCM driving architecture, prototype fabrication and optical alignment of the rapid zoom lens are successfully accomplished.
Figure 10a shows the actual trajectory including four turns of a moving group, which is driven by VCM and controlled in linear motion with a stroke of 35.4 mm. It costs about 0.18 s for the moving group to reach the destination during a trip, and rapid zoom is characterized by corresponding optical performance experiments in
Figure 10b. At
t = 0 s, the rapid zoom lens operates in short-focus state, providing wide-angle surveillance covering multiple targets across two buildings and parking areas. After transition to long-focus state at
t = 0.2 s, the system successfully captures a high-resolution image of the white vehicle, corresponding to the central marked red frame in short-focus state. Experimental results confirm that the rapid zoom system achieves a 100-ms-level smooth transition between global scene perception (short-focus state) and local feature identification (long-focus state). This rapid-response dual-modal cooperative operation characteristic effectively satisfies stringent requirements for dynamic imaging systems in applications including security surveillance (target detection-identity recognition), industrial visual inspection (defect localization-microscopic analysis), and intelligent logistics management (area scanning-barcode reading).
4. Conclusions
In conclusion, this study systematically analyzes the structural design of the voice coil motor for high-magnification rapid zoom optical systems through numerical computations of magnetic field distributions. From the single permanent magnet, FEM simulation results correspond to Gauss meter experimental results. Both FEM and EMC results confirm that increasing the permanent magnet thickness while reducing its lateral dimensions will contribute to a significant enhancement in magnetic flux density. Furthermore, the influence of structural parameters like magnet width and yoke thickness of a simplified moving-coil VCM is analyzed, validating the yoke’s critical role in suppressing edge effects and optimizing magnetic circuit efficiency. For fixed VCM parameters (a = 50 mm, b = 20 mm, h = 3 mm, δ0 = 3 mm), k = 3 mm corresponds to the inflection point for both flux density growth and flatness improvement, where k = h configuration achieves optimal volumetric efficiency, maintaining field intensity. For VCM (a = 50 mm, k = h = δ0 = 3 mm), the recommended optimal magnet width b ranges from 10 mm to 30 mm, considering both the magnetic flux confinement effect of yokes and edge flux leakage of wider magnet. Moreover, a simple EMC calculation method is proposed for rapid and accurate determination of the Bz distribution in the VCM air gap. Based on systematic magnetic field analysis in ideal conditions, optimal structural parameters for VCM are determined for a 40× rapid zoom lens with cost and space limitations. The VCM with a larger stroke is analyzed, and driving force Fdrive = 5.58 N for the designed VCM is nearly 5 times the demand force Fd = 1.06 N. Prototype fabrication and optical alignment of the rapid zoom lens are successfully accomplished, building upon the optimized VCM driving architecture. The actual trajectory shows that it costs about 0.18 s for the moving group to reach the destination during a 35.4 mm trip, and experimental photographs confirm that the rapid zoom system achieves 100-ms-level smooth transition between global scene perception (short-focus state) and local feature identification (long-focus state). This rapid zoom optical system shows great potential in applications including security surveillance, industrial visual inspection, and intelligent logistics management.