## 1 Introduction  
In recent years, multispectral imaging technology has become increasingly vital across various domains, including remote sensing, reconnaissance, medical diagnostics, and agricultural production [1; 2; 3; 4; 5]. This technology necessitates the selective filtering of light, allowing only specific spectral bands to pass through while blocking others, a task typically achieved using a filter wheel for spectral selection and switching. For instance, the James Webb Space Telescope employs a single-layer filter-wheel mechanism equipped with 18 distinct spectral range filters, which is centered and driven by a DC brushless torque motor [6; 7]. A similar rotating filter-wheel mechanism is applied in the Euclid satellite by the European Space Agency [8]. [PERSON] and colleagues have designed a large-scale, high-precision, and rigid single-layer rotating filter-wheel mechanism for spatial multispectral imaging [9]. [PERSON] and others have developed a single-layer filter wheel with five filters for a stationary orbit space multispectral remote sensor [10]. [PERSON] and team have created a single-layer filter wheel for a space camera, supported at the circumferential outer edge using large-sized thin-walled bearings [11]. [PERSON] and associates have designed and developed a motorless single-layer filter-wheel drive mechanism, actuatedby an eccentrically mounted pin and the sequential activation of three shape-memory alloy wires, which saves motor weight but is limited to three spectral bands and requires more space and complex pulley mechanisms [12]. The aforementioned technologies are based on a single-layer filter wheel, but there is also research on a double-layer filter wheel. [PERSON] and co-researchers have designed a double-layer filter-wheel mechanism driven by two ultra-thin stepper motors, effectively combining a two single-layer filter wheel with motors [13].  
Despite the numerous advancements in filter-wheel structures, most of the research has focused on single-layer designs. When the filter aperture is fixed, the number of spectral types that can be accommodated by a single-layer filter wheel is directly proportional to its volume and weight, and it is very difficult to achieve complex spectra (such as the spectral notch band) with a single filter. Moreover, the current double-layer filter-wheel technology, controlled by dual motors, increases the weight/volume and control complexity of the motors and their associated components. Addressing these challenges, this article innovatively proposes a design approach for a double-layer or even multi-layer filter wheel powered by a single motor and differential gear. This structure has the potential to multiply the number of spectral bands by the number of filters in each layer, significantly exceeding the capacity of the filter wheel within the same space and weight constraints. Additionally, this design saves space and weight by using only one motor, simplifying control in the process.  
The spectral types and structures of the filter-wheel mechanism based on the single motor and differential gear double-layer design have been designed. Finite element analysis is employed to examine the modal and dynamic characteristics of the filter-wheel component, thereby verifying the stability, feasibility, and timely implementation of the component. Following the final design, the component is integrated, and its performance is thoroughly tested. The analysis and testing results affirm that the components align with the design specifications and possess significant application value.