Research on the Technology of a Compact Double-Layer Multispectral Filter-Wheel Mechanism Driven by a Single Motor

Abstract

Spatial multispectral imaging technology can selectively image in specific spectral bands, and the filter wheel is a core component for multispectral selection. At present, there are relatively few types of spectral bands for the filter wheel under limited space/weight constraints. Addressing the challenges presented by this issue, this paper introduces an innovative design approach for the development of a double-layer or even multi-layer filter wheel that is operated by a solitary motor in conjunction with a differential gear mechanism, enabling a vast array of spectral segment combinations within a highly compact layout. A detailed design is implemented for the double-layer filter wheel, including comprehensive modal and dynamic analyses. The results of the modal analysis attested to the structural stability of the component, and the outcomes of the dynamic analysis validated the component’s timely and reliable switching capabilities. A prototype was meticulously crafted and subjected to rigorous testing. The switching functionality was validated during these tests, concurrently affirming the accuracy of the finite element analysis results. Additionally, spectral and application testing confirmed the number of spectral segments and the practical utility of the components. The research presented in this article introduces an innovative design concept for multispectral imaging filter-wheel mechanisms, providing a valuable reference and profound insights for the design and arrangement of a double-layer or even multi-layer filter wheel.

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]. Wang Yue and colleagues have designed a large-scale, high-precision, and rigid single-layer rotating filter-wheel mechanism for spatial multispectral imaging [9]. Bao He and others have developed a single-layer filter wheel with five filters for a stationary orbit space multispectral remote sensor [10]. Jia Huili 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]. Abhinanda Kapoor and associates have designed and developed a motorless single-layer filter-wheel drive mechanism, actuated by 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. Chen Bing 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.

2. Theory and Methods

The transmission, reflection, and absorption spectral properties of the coating surface make the filter achieve its filtering function [14]. By referring the product catalog of the optical giant Edmund, it is known that the types of filters usually include bandpass, longpass, shortpass, and notch filters, etc. An example is shown in Figure 1 [15].

This article elucidates the design principle behind a multi-layer filter-wheel mechanism, essential for achieving various spectral combinations. Using the double-layer filter wheel as a case study, the mechanism is revealed. Figure 2 illustrates the setup, detailed as follows: the upper gear houses m filters labeled P1, P2… Pm, while the lower gear contains n filters labeled Q1, Q2… Qn, with m and n being coprime. A motor drives the double-layered small gear, which in turn rotates the upper and lower gears. Through precise transmission ratio design, a single revolution of the small gear prompts the upper gear to rotate 1/m of a revolution and the lower gear to rotate 1/n of a revolution, synchronously advancing both gears to the next filter position. This principle is extendable to a multi-layer filter wheel, provided the number of filters in each layer remains coprime.

Each rotation of the small gear constitutes a single work step, beginning with the initial filter combination of Q1 and P1. As we proceed, after one work step, the combination shifts to Q2 and P2. Upon completing m work steps, the upper gear has made a full revolution, while the lower gear has turned m/n of a revolution. Notably, the upper gear resets to P1, but the lower gear does not return to Q1 due to the relative primality of m and n. After the m*n step, the upper gear rotates n revolution and the lower gear rotates m revolution, and the upper gear returns to P1 and the lower gear return to Q1; the P1 Q1 combination first overlapped after the first work step, and during this process there are a total of m*n steps, which proves the existence of m*n combinations. The operation of this mechanism is illustrated in Figure 3. For practical use, selecting m and n as consecutive numbers maximizes the number of possible combinations within a given volume, enhancing the versatility of the filter-wheel system.

In order to meet the above functions, the gear parameters need to satisfy Formula (1).

$$\begin{array}{c}\left(Z_{up1}+Z_{up2}\right)\cdot m_{gear}=\left(Z_{low1}+Z_{low2}\right)\cdot m_{gear}\\ Z_{up1}/Z_{up2}=1/m\\ Z_{low1}/Z_{low2}=1/n\end{array}$$

(1)

where Z_up1 is the upper-layer small-gear teeth number, Z_up2 is the number of upper-layer big-gear teeth, Z_low1 is the number of lower-layer small-gear teeth, Z_low2 is the number of lower-layer small-gear teeth, m_gear is the gear module, m is the number of upper layer filters, and n is the number of lower layer filters. According to Formula (1), the small-gear parameter should satisfy Formula (2).

$$Z_{up1}/Z_{low1}=\left(n+1\right)/\left(m+1\right)$$

(2)

Considering factors such as volume and the number of spectral segments, this article selects m as 5 and n as 4, resulting in a total of 20 spectral combinations. Based on Formula (2), Z_up1/Z_low1 = 5/6. However, to prevent root cutting [16], the number of teeth must be greater than 17. Additionally, to reduce manufacturing complexity and control the overall size, it is essential to minimize the number of gear teeth. After careful consideration, the number of teeth on all gears is as follows: Z_up1 = 20, Z_low1 = 24, Z_up2 = 100, Z_low2 = 96.

3. Component Design

3.1. Structural Design

The filter-wheel mechanism investigated in this article is applied to a space star sensor. This sensor consists of a reflective optical system and a filter-wheel component. The reflective optical system comprises five mirrors, as depicted in Figure 4a. The filter-wheel component mainly consists of a lens, a double-layer filter-wheel mechanism, detector components, as well as supporting structures and accessories, as shown in Figure 4a,b. Based on the theory and method in Section 2, this article mainly conducted a study on the filter-wheel mechanism.

Based on the above structure, the upper layer filters are numbered as 1, 2, 3, 4, and 5. Correspondingly, the lower-layer filters are numbered as A, B, C, and D, as shown in Figure 5.

When the upper-level assembly star sensor is in operation, the filter-wheel component plays a critical role in filtering out background light across various spectral bands. This process is essential for enhancing the signal-to-noise ratio of the target star’s detection signal. In order to meet specific working conditions and maximize spectral types, the spectral types have been designed and are detailed in

Table 1. Design of transmission wavelength for the upper and lower filter wheel.

Upper Gear		Lower Gear
Code	Transmission Wavelength	Code	Transmission Wavelength
1	≤700 nm	A	≥760 nm
2	≤800 nm	B	≥400 nm
3	≤900 nm	C	≥500 nm
4	≤1150 nm	D	≥560 nm
5	≤1200 nm

.

The total number of filter spectrum combinations achieved is 20, with the opaque A1 combination serving as the calibration for the initial position.

Table 2. Detailed types of spectral bands and combination numbers for double-layer filter wheel.

Work Step Number	Combination Code	Spectral Details		Work Step Number	Combination Code	Spectral Details
1	A1	760 nm	700 nm	12	D2	560 nm	800 nm
2	B2	400 nm	800 nm	13	A3	760 nm	900 nm
3	C3	500 nm	900 nm	14	B4	400 nm	1150 nm
4	D4	560 nm	1150 nm	15	C5	500 nm	1200 nm
5	A5	760 nm	1200 nm	16	D1	560 nm	700 nm
6	B1	400 nm	700 nm	17	A2	760 nm	800 nm
7	C2	500 nm	800 nm	18	B3	400 nm	900 nm
8	D3	560 nm	900 nm	19	C4	500 nm	1150 nm
9	A4	760 nm	1150 nm	20	D5	560 nm	1200 nm
10	B5	400 nm	1200 nm	21	A1	760 nm	700 nm
11	C1	500 nm	700 nm

displays all possible spectral combinations. To ensure timely operations, the switching time between adjacent combinations must not exceed 0.15 s, and the maximum allowable switching time for any combination is capped at 0.6 s.

3.2. Motor Selection

Based on the information provided from Table 1, the filter-wheel system is designed to switch between various spectral filters with a maximum of 10 work steps for any combination, with the motor capable of bidirectional rotation. For instance, A1 to C1 takes 10 steps, while A1 to B5 or D2 takes 9 steps. To meet these requirements, it is crucial to select a motor that can operate at the necessary speeds and has the torque to drive the filter-wheel mechanism effectively. The motor selection process is detailed in Figure 6.

The motor’s time–displacement curve typically forms a trapezoid, reflecting the process of acceleration, constant speed, and deceleration to reach the target. As seen in Figure 7a, if the target is nearby, the curve becomes triangular, indicating that the motor must begin decelerating before reaching full speed to prevent overshooting, as depicted in Figure 7b.

To optimize the switching time, the preliminary motor selection is guided by the reference curve in Figure 7b. To ensure a safety margin, the design calculates the maximum switching time for any filter combination as 0.5 s. For adjacent combinations, the switching time is computed to be 0.1 s; the calculation method satisfies Formula (3).

$$\begin{array}{l}{\displaystyle \frac{t_1{n}_1}{2}}=R_1\\ a_1={\displaystyle \frac{2n_1}{t_1}}\\ {\displaystyle \frac{t_{10}{n}_{10}}{2}}=R_{10}\\ a_{10}={\displaystyle \frac{2n_{10}}{t_{10}}}\end{array}$$

(3)

where t₁ is the adjacent switching time, which is 0.1 s; n₁ is the maximum speed of small gear during adjacent switching process, and the unit is r/s; R₁ is the number of revolutions of the small gear during the adjacent switching process, which is 1 r; a₁ is the acceleration of the small gear during the adjacent switching process, and the unit is r/s². t₁₀ is the maximum switching time, which is 0.5 s; n₁₀ is the maximum speed of the small gear during the maximum switching process, and the unit is r/s; R₁₀ is the number of revolutions of the small gear during the maximum switching process, which is 10 revolutions; a₁₀ is the acceleration of the small gear during the maximum switching process, and the unit is r/s².

After calculation, n₁ = 20 r/s, a₁ = 400 r/s², n₁₀ = 40 r/s, a₁ = 160 r/s². Based on these calculation results and in conjunction with the standardized specifications of the motor and gearbox product series, a certain brand of motor and gearbox combination has been preliminarily selected to drive the small gear. The DC motor is equipped with an encoder that provides displacement, velocity, and acceleration control functions. The parameters are detailed in

Table 3. Parameters of motor and gearbox.

	Reduction Ratio	Torque	Maximum Stalling Torque	Rated Speed	Maximum Speed	Maximum Acceleration
Motor	4:1	0.0025 N·m	0.005 N·m	166.67 r/s	233.33 r/s	1666.67 r/s2
Gearbox		0.01 N·m	0.02 N·m	41.67 r/s	58.33 r/s	416.67 r/s2

.

The switching time is verified based on the actual parameters of the selected motor. The adjacent switching time is 0.098 s, the shape of the motor displacement curve is similar to Figure 7b. The maximum switching time is 0.34 s, and the shape of the motor displacement curve is similar to Figure 7a; this is because the actual acceleration (416.67 r/s²) is greater than needed (160 r/s²), so the motor reaches its rated speed faster, while also resulting in a shorter time than expected.

Next, the torque of gear is verified. The purpose of torque verification method is to ensure that the motor can drive the filter wheel to achieve maximum acceleration. The verification process refers to Formula (4).

$$\begin{array}{c}{T}_D-T_1-T_2-T_3=J_z\cdot \alpha \\ J_Z=J_M+{\displaystyle \frac{J_1}{{i_1}^2}}+{\displaystyle \frac{J_2}{{i_2}^2}}+{\displaystyle \frac{J_3}{{i_3}^2}}\\ T_1=T_{up}{\displaystyle \frac{1}{i_i\eta }}\\ T_2=T_{low}{\displaystyle \frac{1}{i_2\eta }}\\ T_3=T_{small}{\displaystyle \frac{1}{i_3}}\\ T_{up}=T_{low}=T_{small}=n·f_s·N_{load}·{\displaystyle \frac{(D+d)}{4}}\end{array}$$

(4)

where T_D is the required output torque of the gearbox, α is the maximum acceleration of gearbox, which is 2616.67 rad/s; T_up, T_low, T_small are the static loads of the upper gear, lower gear, and small gear; n is the number of bearings that match each gear, which is 2; N_load is the load of bearings—to improve the reliability coefficient, N_load is set to the weight of all gears, which is 0.2 N; D is the outer diameter of bearings, which is 8 mm; d is the inner diameter of bearings, which is 5 mm; f_s is the coefficient of friction, which is 0.3; i₁, i₂, i₃ are the transmission ratio of the gearbox shaft relative to the upper gear, lower gear, and small gear, which are 5, 4, and 1, respectively; η is the transmission efficiency of the gear, which is 0.9; T₁, T₂, and T₃ are the static loads converted from the upper gear, lower gear, and small gear to the gearbox shaft, which are 8.7 × 10⁻⁵ N·m, 1.08 × 10⁻⁴ N·m, 3.9 × 10⁻⁴ Nm, respectively; J_M is the moment of inertia of the motor and gearbox, which is 2.4 × 10⁻⁷ kg·m²; J₁, J₂, and J₃ are the moment of inertia of the upper gear, lower gear, and small gear relative to their own rotation axis, which are 5.1 × 10⁻⁶ kg·m², 4.3 × 10⁻⁶ kg·m², 3 × 10⁻⁸ kg·m², respectively; J_Z is the total moment of inertia converted to the gearbox shaft, which is 7.4 × 10⁻⁷ kg·m². After the calculation, T_D is 0.0025 N·m, which is far less than the torque of the gearbox 0.01 N·m. Here, the motor selection is completed.

4. Finite Element Analysis

For the filter-wheel component, it is necessary to verify that the switching process can be completed without any damage. Therefore, a modal analysis is conducted to ensure that there is no risk of resonance during operation. Compared to traditional static analysis, the simulation results of dynamic analysis are more accurate and reliable [17]. Hence, a transient dynamic analysis is used to verify that the filter wheel can complete the switching process within the design time frame and that the maximum stress experienced by the mechanism during the switching process is less than the allowable value of the material. The material property parameter settings during analysis are detailed in

Table 4. Material property parameters.

Material	Density	Elastic Modulus	Poisson’s Ratio	Tensile Strength
Aluminum alloy 6061	2.85 kg/m3	69 GPa	0.33	205 MPa
PEK	1.30 kg/m3	4.0 GPa	0.38	105 MPa
Silica	2.20 kg/m3	72 GPa	0.2	110 MPa

. In the analysis, the gear material is set to PEK, the structural component material is set to aluminum alloy, and the filter material is set to silica.

4.1. Modal Analysis

The double-layer filter-wheel component designed has a high lightweighting rate. Further modal analysis is required to verify the sufficient local and overall stiffness of the structure.

Table 5. The results of the first three modal analyses.

Order	Vibration Mode	Frequency (Hz)	Vibration Form
1		470.81	PCB board rotates around the X-axis
2		479	Reinforcing vibrates along the Y-axis
3		479.23	Reinforcing vibrates along the X-axis

shows the first three modes of the component.

The analysis reveals that the first-order modal of the double-layer filter-wheel assembly is at 470 Hz, with a vibration direction distinct from the motor’s rotation. The motor’s rated speed of 10,000 rpm corresponds to an angular frequency of 167 Hz, which is significantly lower than the first modal, thus reducing the risk of resonance during operation.

4.2. Dynamic Analysis of Switching Between Adjacent Combinations

Figure 8 shows the dynamic analysis model, with parameters set according to the details provided in Section 3.2. The static loads on all gear are 3.9 × 10⁻⁴ N·m. Each gear is configured to rotate specifically around its individual axis.

According to the content in Section 3.2, the input conditions applied to the small gear set are shown in Figure 9a below. The rotation angle is 360°, and the maximum angular velocity is 128.217 rad/s, with an acceleration of 2616.67 rad/s². The speed unit is converted from r/s to rad/s. The dynamics analysis results are shown in Figure 9b,c. It can be seen that the angular displacement and velocity of the upper and lower gears are inversely proportional to the transmission ratio with respect to the small gear. While the small gear rotates 360°, the upper gear rotates 72° and the lower gear rotates 90°. The angular acceleration exhibits certain fluctuation characteristics, which is due to the nonlinear interaction between gear meshing and elastic deformation [18]. The average angular acceleration is also proportional to the transmission ratio with the small gear. Figure 9d shows the torque of the small gear. The average torque during acceleration is about 0.0015 Nm, while it is slightly smaller during deceleration. This is because the frictional resistance acts opposite to the driving force during acceleration and in the same direction during deceleration. The torque during both acceleration and deceleration is much smaller than the rated torque of the gearbox (0.01 Nm), and the torque margin coefficient is larger than 6. The dynamic analysis results demonstrate that the component has the ability to complete the switching of adjacent combinations within the set time.

The maximum stress of mechanism during switching process is calculated by dynamic analysis, as shown in Figure 10. Figure 11 shows the stress cloud maps at three different times. The maximum stress is about 0.88 Mpa, occurring at the contact position between two gears, much less than the strength of the PEK material 105 MPa [19], and the strength margin coefficient is larger than 117.

4.3. Dynamic Analysis of Switching Between Adjacent Combinations

According to the content in Section 3.2, the input conditions applied to the small gear set are shown in Figure 12a below. The rotation angle is 3600°, while the maximum angular velocity is 261.67 rad/s, the two inflection points of the speed trapezoidal curve are at 0.1 s and 0.24 s, and the acceleration is 2616.67 rad/s². The dynamics analysis results are shown in Figure 12b,c. Similar to the analysis in Section 4.2, the average of angular acceleration, the angular displacement, and velocity of the upper and lower gears is inversely proportional to the transmission ratio with the small gear. While the small gear rotates 3600°, the upper gear rotates 720°, and the lower gear rotates 900°. Figure 12d shows the torque of the small gear; the average value during acceleration is also about 0.0015 Nm, with a torque margin coefficient larger than 6. The dynamic analysis results demonstrate that the component has the ability to complete the switch of 10 combinations within the set time.

The maximum stress of the mechanism during the switching process is calculated by dynamic analysis, as shown in Figure 13. Figure 14 shows the stress cloud maps at three different times. The maximum stress is about 0.89 Mpa, occurring at the contact position between two gears, much less than the strength of the PEK material 105 MPa, and the strength margin coefficient is also larger than 117.

4.4. Dynamic Analysis of Switching Between Adjacent Combinations

The dynamic characteristics of the mechanism is analyzed when a torque of 0.01 Nm is applied to the small gear. The result of the dynamic analysis is shown in Figure 15. The results indicate that as the angular velocity increases, the fluctuation of angular acceleration becomes greater, but the average value of acceleration remains basically unchanged, and the average value of acceleration of the small gear is about 20,000 rad/s², which is 3185 r/s. This is larger than the maximum acceleration of the gearbox (416.67 r/s), which once again indicates that the torque margin coefficient is sufficient.

The maximum stress of the mechanism during constant torque acceleration is calculated by dynamic analysis, as shown in Figure 16. Figure 17 shows the stress cloud maps at three different times during the acceleration process. The maximum stress is about 3 Mpa, occurring at the contact position between two gears, much less than 105 MPa, and the strength margin coefficient is larger than 35.

5. Performance Test

Above, the final design and simulation analysis verification of the filter-wheel component have been completed. Here, we have processed and assembled the final component without a casing, as shown in Figure 18, which weighs less than 212 g.

To assess the filter wheel’s performance, its switching function and responsiveness are gauged through a switching time trial. A spectral analysis is conducted to gather data on all spectral segment combinations, while application tests confirm the component’s utility in engineering contexts. Figure 19 illustrates the switching time test, where a high-speed camera records the transition, capturing multiple frames to measure the switching duration.

5.1. Switching Between Adjacent Combinations

The following image shows the process of switching between adjacent combinations captured at a frame rate of 480 Hz; the upper gear faces the recording equipment. The last still image before startup is recorded as the 0th frame; the 0th, 8th, 16th, 24th, 32nd, 40th, and 47th frames are shown in Figure 20a–g, corresponding to 0 s, 0.0167 s, 0.0333 s, 0.05 s, 0.0667 s, 0.0833 s, 0.098 s, respectively. Compare the velocity curve in Figure 9b as a theoretical reference, corresponding to seven states: stationary, accelerating, about to reach maximum angular velocity, decelerating after reaching maximum angular velocity, decelerating, about to stop, and already stopped. During this period, the upper gear rotated 1/5 of a revolution. The results of different frame images indicate that the switching process conforms to the theoretical speed time curve, verifying that the switching time of adjacent combinations is less than 0.1 s, which is consistent with the results of the dynamic analysis.

5.2. Switching Between 10 Combinations

By using the same testing method as in Section 5.1, the 0th, 24th, 48th, 52nd, 64th, 115th, 139th, and 162nd frames of switching between 10 combinations are obtained, as shown in Figure 21a–h, corresponding to 0 s, 0.05 s, 0.1 s, 0.108 s, 0.133 s, 0.246 s, 0.29 s, 0.338 s, respectively. Compare the velocity curve in Figure 12b as a theoretical reference, corresponding to eight states: stationary, accelerating, reaching maximum angular velocity, uniform angular velocity state 1, uniform angular velocity state 2, preparing to decelerate, decelerating, and already stopped. In the reference theoretical velocity curve, the time between 52nd and 64th is 0.05 s; during this period, the upper gears rotate 75°. The time between 64th and 115th is 0.106 s; during this period, the upper gears rotate 319°. The upper gear has rotated two revolutions during the entire process. The results of different frame images indicate that the switching process conforms to the theoretical speed time curve, verifying that the switching time of adjacent combinations is less than 0.34 s, which is consistent with the results of the dynamic analysis.

5.3. Test Margin with Counterweight

To assess the system’s performance under severe conditions, a margin test was carried out. As indicated by the analysis in Section 4.2, Section 4.3 and Section 4.4, the torque margin coefficient exceeds 6, and the strength margin coefficient is greater than 35. Consequently, the test was performed with a 6-fold margin. Two counterweights were precision-machined to mimic five times the rotational inertia of the double-layer filter wheel. To prevent redundancy with the previous discussion, only the switching of 10 combinations with the counterweight test is presented here. Figure 22 illustrates the process of switching between 10 combinations with the counterweight, demonstrating that the component’s margin coefficient is indeed greater than 6, thus confirming the accuracy of the analysis results.

5.4. Spectral Testing of 20 Combinations

After testing the switching time, the spectral filtering capability of the filter wheel must be evaluated to confirm its ability to select and switch between multiple spectra. The testing location is depicted in Figure 23.

The spectral filtering function of the filter wheel was tested by sequentially switching all spectral combinations, yielding 20 spectral bandwidth test results. The test outcomes for the spectral segment information are depicted in Figure 24. It is evident that the spectral segment switching corresponds with the design outlined in Table 2, and the filter wheel is capable of selecting and switching between multiple spectral bands.

5.5. Application Testing

Finally, the component is applied to a star sensor for testing, with a 450 nm narrowband spectrum as the background, and a 800 nm narrowband starlight as the target. The detection signal-to-noise ratio of the star sensor across different spectral bands is tested, and the results are presented in

Table 6. Detection signal-to-noise ratio under different spectral combinations.

Combination Number	Spectral Details	Detection Signal-to-Noise Ratio
A1	760 nm~700 nm	No target
B2	400 nm~800 nm	Background saturation
C3	500 nm~900 nm	2.5
D4	560 nm~1150 nm	12.8
A5	760 nm~1200 nm	15.9
B1	400 nm~700 nm	Background saturation
C2	500 nm~800 nm	No target
D3	560 nm~900 nm	12.0
A4	760 nm~1150 nm	22.9
B5	400 nm~1200 nm	Background saturation
C1	500 nm~700 nm	No target
D2	560 nm~800 nm	No target
A3	760 nm~900 nm	19.7
B4	400 nm~1150 nm	Background saturation
C5	500 nm~1200 nm	3.7
D1	560 nm~700 nm	No target
A2	760 nm~800 nm	No target
B3	400 nm~900 nm	Background saturation
C4	500 nm~1150 nm	2.6
D5	560 nm~1200 nm	11.5

.

The test results indicate that the detection signal-to-noise ratio can be significantly enhanced by selecting appropriate spectral bands, thereby validating the engineering application value of the mechanism discussed in this paper.

6. Conclusions

This article first puts forward a design approach for a double-layer or even multi-layer filter wheel driven by a single motor and differential gear, which can achieve more spectral bands under the same envelope. The detailed design of the double-layer filter wheel applied to a certain star sensor is carried out based on this approach. To verify that there is no resonance risk during operation, the modal is analyzed, and the results indicate that the first-order mode is 470 Hz and there is no risk of resonance during operation. Then, a transient dynamic analysis is used to verify that it can complete the switching process within the designated time and that the maximum stress of the mechanism is less than the allowable value of the material during the switching process. The final component is processed and manufactured based on the final design. It has been proven that the filter wheel can complete spectral switching within the specified time under normal and weighted conditions by the switch test. This proves the correctness of the analysis results. In addition, spectral testing and application testing are conducted; spectral testing has yielded information on all possible combinations of spectral segments. The application tests have demonstrated that the selection of appropriate spectral segments can significantly enhance the signal-to-noise ratio in detection. This validates the engineering application value of the dual-layer filter-wheel mechanism discussed in this paper. The work in this paper can provide guidance for the design and selection, analysis, testing, and validation of the double-layer filter wheel.

7. Patents

Ma, L.; Tan, S.; Zhang, X.; Wu, H.; Ma, S. A Multi-Layer Filter Wheel Structure and Multispectral Imaging Device. 202310745305, 16 October 2024.