Objective Unmanned Aerial Vehicle (UAV) photogrammetry serves as a high-efficiency, flexible, and cost-effective complement to traditional aerial surveying. Payload limitations necessitate UAVs to employ non-metric cameras, whose interior orientation elements cannot be measured in real-time and rely on pre-calibration. Temperature variations induce focal length drift in lenses, causing deviations in interior orientation elements. This introduces scale errors into photogrammetric models, propagating directly to 3D ground coordinate errors and degrading overall measurement accuracy and reliability. Consequently, enhancing focal length thermal stability is critical for UAV mapping precision. Athermalization design is essential to mitigate focal length variation. Current research (passive optical, passive mechanical, active electro-mechanical) primarily focuses on maintaining imaging quality over specific temperature ranges, with significantly less attention directed toward focal length stability under thermal load. Existing focal length thermal stability methods—such as lens power/material distribution, mechanical compensation, and wavefront coding—often exhibit low material matching efficiency or complex structural designs. These limitations hinder their suitability for UAV mapping lenses demanding high precision, lightweight construction, and low cost. Image-space telecentric lenses, vital for enhancing geospatial accuracy and resolution in mapping, present additional challenges due to their complex multi-element designs restricting traditional athermalization approaches. A novel focal length thermal stabilization method based on combinatorial spacer material selection is proposed.
Methods The proposed method accounts for the influence of assembly methods on variations in air thickness (
Fig.1) and quantitatively analyzes the effects of temperature on lens refractive index, optical surface curvature, and thickness. The Gaussian matrix enables rapid calculation of the optical system’s focal length without introducing image-space parameters. A coupled mathematical model integrating temperature, spacer thermal expansion coefficients (CTE), and system focal length is established based on matrix optics theory. Multiple individual mechanical spacers within the lens barrel are treated as an integrated combinatorial design unit. Using this mathematical model, the globally optimal material combination is solved under the constraints of available spacer materials with the objective of minimizing focal length variation. This approach transforms the traditional method of manual spacer material matching into a quantifiable optimization process, significantly improving material selection efficiency(
Fig.4).
Results and DiscussionsTaking an airborne image-space telecentric lens (focal length: 23.9719 mm) as an example, thermal stability design of the focal length was performed. Mechanical structure design (
Fig.7) and tolerance analysis (
Fig.8) ensured structural design rationality. The range of optional materials for the four spacer rings was analyzed (
Tab.1), and combinatorial material selection was performed using the proposed mathematical model (
Tab.5). After thermal stability design, within the temperature range of (20±40) ℃, the focal length variation was reduced from [-12.2 μm, +12.4 μm] (
Tab.3) to [-4.9 μm, +5.1 μm] (
Tab.6), representing a 59.35% reduction in total variation (
Fig.9), demonstrating the feasibility and effectiveness of the proposed method. Furthermore, the total focal length variation accounts for 68% of the system's depth of focus, leaving sufficient margin for factors such as adjustment errors and mechanical vibrations, thereby enhancing imaging quality stability under complex working conditions.
Conclusions A novel thermal stability design method for the focal length of airborne mapping lenses is presented. By constructing a coupled model of temperature, material CTE, and system focal length, and treating the spacer assembly as an optimization unit, global matching of spacer materials is achieved, effectively reducing the impact of temperature on the focal length of the system. Application to an airborne image-space telecentric lens demonstrated a 59.35% reduction in focal length variation over (20±40) ℃, with the total variation being less than the system's depth of focus, meeting the comprehensive requirements of UAV-borne high-precision mapping for focal length stability and imaging quality. Compared to traditional passive optical athermalization designs, which face high complexity challenges in multi-lens systems, and complex mechanical athermalization structures that increase volume, weight, and reduce stability, the proposed method transforms traditional empirical spacer material selection into a quantifiable optimization process through parametric modeling. Focal length thermal stability is enhanced solely by replacing spacer materials, avoiding alterations to the initial structural parameters of the optical system, offering advantages of low design complexity and high engineering operability.