Infrared optical imaging system for unmanned aerial vehicle

Abstract

The invention discloses an infrared optical imaging system for an unmanned aerial vehicle, and belongs to the field of unmanned aerial vehicles, the infrared optical imaging system comprises an infrared optical imaging system arranged on a carrier support of the unmanned aerial vehicle, the system comprises a fairing, a lens group and a detector, the fairing is mounted at the head of the unmanned aerial vehicle, and the front surface and the rear surface of the fairing are concentric spherical surfaces; the lens group comprises a first meniscus lens, a second meniscus lens and a third meniscus lens which are sequentially arranged on the same optical axis, the first lens and the third lens are positive lenses, the second lens is a negative lens, and the rear side surface of the first lens and the front side surfaces of the second lens and the third lens are aspheric surfaces; the detector is located behind the lens group and receives the optimized infrared radiation image. Through the material combination of monocrystalline silicon, monocrystalline germanium and chalcogenide glass IRG206, a passive thermal compensation structure and a miniaturized and lightweight design, the cost is reduced, and the target detection precision and the equipment reliability in a complex environment are improved at the same time.

Description

Technical Field

[0001] The invention relates to the field of unmanned aerial vehicles, and in particular to an infrared optical imaging system for unmanned aerial vehicles. Background Art

[0002] With the widespread application of unmanned aerial vehicles in military reconnaissance, disaster monitoring, border patrols and civilian logistics, the demand for high-precision target identification and real-time tracking capabilities is becoming increasingly urgent. As the core component of unmanned aerial vehicles to perceive the environment, infrared optical imaging systems need to maintain stable performance under complex electromagnetic interference, extreme temperature fluctuations and high-speed maneuvers. However, the existing infrared systems integrated into unmanned aerial vehicles have the following technical bottlenecks: 1. Structural complexity and space occupancy issues: Traditional infrared optical imaging systems mostly use a multi-lens group design (such as more than 5 lenses) and a secondary imaging architecture, resulting in a total system length of more than 100mm, which is difficult to adapt to the strict restrictions on payload volume and weight of unmanned aerial vehicles. For example, if the infrared module of a drone optoelectronic pod is too large, it will be forced to sacrifice space for other sensors, seriously restricting the multi-task coordination capability.

[0003] 2. Insufficient reliability in wide temperature environment: The operating environment of unmanned aerial vehicles covers an extreme temperature range of -40℃ to +60℃, and conventional infrared optical imaging systems rely on active focusing mechanisms to compensate for thermal defocus, which not only increases the complexity of the system, but also makes mechanical components such as motors and guide rails prone to jamming in low-temperature environments, significantly increasing the failure rate. In addition, since the refractive index of the lens changes with temperature, the lens group is prone to poor system imaging quality in high and low temperature alternating scenarios.

[0004] 3. Installation efficiency and cost restrict large-scale application: Existing infrared systems often use diffraction surfaces or high-precision cemented lenses to improve imaging quality, but their installation and adjustment require high-precision optical platforms and skilled workers, and the installation and adjustment of a single system takes a long time. The widespread use of expensive materials such as zinc selenide (ZnSe) has pushed up manufacturing costs, making it difficult to meet the needs of low-cost, mass production in the civilian field.

[0005] 4. Limited dynamic target tracking capabilities: The tracking of high-speed maneuvering targets by unmanned aerial vehicles requires the optical imaging system to have fast response and field scanning capabilities, while the traditional fixed optical structure relies on the overall attitude adjustment of the aircraft, which increases the target loss rate. When unmanned aerial vehicles are tracking moving targets, if the field of view of the optical system is too small, the flight trajectory needs to be adjusted frequently, which seriously consumes the flight time.

[0006] In response to the above problems, the industry has tried to simplify the optical structure or introduce new materials for optimization, but most solutions are still limited to improving pure optical performance (such as resolution and transmittance), and have failed to fundamentally solve the core needs of unmanned aerial vehicles for lightweight integration, environmental robustness, and rapid deployment. Therefore, there is an urgent need for an infrared optical imaging system designed specifically for unmanned aerial vehicles that combines high performance and high reliability to break through the existing technical bottleneck and promote the practical application of unmanned platforms in complex scenarios. Summary of the invention

[0007] The present invention provides an infrared optical imaging system for an unmanned aerial vehicle, which can reduce costs and significantly improve target detection accuracy and equipment reliability in complex environments through miniaturization, lightweight, material innovation, and passive athermal design.

[0008] To achieve the above object, the technical solution adopted by the present invention is: an infrared optical imaging system for an unmanned aerial vehicle, including an infrared optical imaging system arranged on a carrier support of the unmanned aerial vehicle, the infrared optical imaging system including: The fairing is installed on the head of the UAV, and its front and rear surfaces are concentric spherical surfaces; A lens group is arranged at the rear of the fairing, and the lens group includes a first lens, a second lens and a third lens in a meniscus shape which are arranged in sequence from front to back on the same optical axis, wherein the first lens and the third lens are positive lenses, the second lens is a negative lens, and the rear side surface of the first lens and the front side surfaces of the second lens and the third lens are all aspherical surfaces; A detector is arranged behind the lens group, and the infrared radiation transmitted by the lens group is imaged on the imaging surface of the detector; The material of the fairing is hot-pressed magnesium fluoride, the material of the first lens is single crystal silicon, the material of the second lens is single crystal germanium, and the material of the third lens is chalcogenide glass IRG206.

[0009] Furthermore, the concave surfaces of the fairing, the first lens, the second lens and the third lens are all arranged toward the rear.

[0010] Preferably, the first lens, the second lens and the third lens respectively satisfy the following conditions: 0.8≤ f1 / f≤1.0, -0.7≤ f2 / f ≤-0.5, 0.6≤ f3 / f ≤0.8, wherein f is the focal length of the infrared optical imaging system, f1 is the focal length of the first lens, f2 is the focal length of the second lens, and f3 is the focal length of the third lens.

[0011] Preferably, the distance between the first lens and the second lens in the optical axis direction is T 23 , the distance between the second lens and the third lens in the optical axis direction is T34 , the thickness of the second lens in the optical axis direction is CT 3, and satisfy the following relationship: .

[0012] Furthermore, the fairing is a partially spherical structure as a whole, and its thickness is the difference between the curvature radii of the front and rear surfaces.

[0013] Furthermore, all lenses in the lens group are not provided with diffraction surfaces.

[0014] Furthermore, the fairing is fixedly arranged, and the lens group can rotate ±15° in the azimuth direction and the pitch direction relative to the fairing.

[0015] Furthermore, the distance from the front end of the fairing to the imaging surface is 58 mm. Furthermore, the distance between the rear surface of the third lens and the imaging plane in the optical axis direction is 6 mm.

[0016] Furthermore, the focal length of the infrared optical imaging system is 45 mm, the field of view is 12.2°×9.8°, the imaging surface diameter is 12.4 mm, and the working band is 3 μm to 5 μm; F#: 2.0, wherein the F# calculation formula is f / D, f is the focal length of the infrared optical imaging system, and D is the incident pupil diameter.

[0017] The beneficial effects of the present invention are: (1) The infrared optical imaging system of the present invention achieves a miniaturized mid-wave infrared athermal optical imaging system with a focal length of 45 mm, an image diameter of 12.4 mm, and a distortion of less than 0.25% by optimizing the intervals between lenses, reasonably allocating the optical power, and matching the optical materials of the lenses with only three lenses. The system has a total length of 58 mm and a back intercept of 6 mm, which is conducive to the design of the rear detector installation structure.

[0018] (2) All lenses of the present invention do not use diffraction surfaces, thereby avoiding energy loss caused by the diffraction efficiency of the diffraction surface and improving the overall transmittance and imaging quality of the lens. At the same time, the accuracy requirements for the installation and adjustment of the infrared optical imaging system are reduced, the installation and adjustment efficiency is improved, and it is conducive to mass production.

[0019] (3) The present invention realizes an optical passive athermal optical imaging system that can achieve good imaging in a wide temperature range of -40°C to +60°C through the synergistic cooperation between three different optical materials: single crystal silicon, single crystal germanium, and chalcogenide glass IRG206. There is no need to set up a focusing mechanism to compensate for the impact of temperature changes on imaging quality, which simplifies the system structure and improves product reliability. In addition, the lens with a larger aperture uses relatively low-priced single crystal silicon and chalcogenide glass IRG206 materials instead of expensive zinc selenide materials, which effectively reduces the system cost. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 A schematic diagram of the present invention applied to an unmanned aerial vehicle; Figure 2 is a light path diagram of the infrared optical imaging system of the present invention; Figure 3 The optical path diagram of the infrared optical imaging system of the present invention rotated by +15°; Figure 4 The optical path diagram of the infrared optical imaging system of the present invention rotated -15°; Figure 5 It is a transfer function diagram of the infrared optical imaging system of the present invention at room temperature of 20°C; Figure 6 It is a transfer function diagram of the infrared optical imaging system of the present invention at a low temperature of -40°C; Figure 7 It is a transfer function diagram of the infrared optical imaging system of the present invention at a high temperature of +60°C; Figure 8 It is a point diagram of the infrared optical imaging system of the present invention at room temperature 20°C; Fig. 9 It is a point diagram of the infrared optical imaging system of the present invention at a low temperature of -40°C; Fig.10 It is a point diagram of the infrared optical imaging system of the present invention at a high temperature of +60°C; Fig.11 It is a field curvature and distortion curve diagram of the infrared optical imaging system of the present invention; Fig.12 It is a relative illumination curve diagram of the infrared optical imaging system of the present invention.

[0021] Among them, 100. Unmanned aerial vehicle; 200. Infrared optical imaging system; 1. Fairing; 2. First lens; 3. Second lens; 4. Third lens; 5. Detector window protective glass; 6. Imaging surface. DETAILED DESCRIPTION

[0022] In order to make the above features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below in conjunction with the accompanying drawings. In the description of the present invention, it should be understood that if there are terms such as "upper", "lower", "front", "back", "left", "right" and the like indicating directions or positional relationships, they are only corresponding to Figure 2 of the present application to facilitate the description of the present invention, and do not indicate or imply that the device or element referred to must have a specific direction. The terms "first", "second", and "third" are only used for descriptive purposes and refer to the order in which the type of lenses appear, and cannot be understood as indicating or implying relative importance.

[0023] Throughout the specification, the same reference numerals refer to the same elements.In the drawings, the figures are by way of example only and are not drawn strictly to scale.

[0024] As common sense, the direction close to the object space is the object side, and the direction close to the image space is the image side. From the object side to the image side, the two sides of the lens are the incident side and the exit side. The object side refers to the side where the light enters, and the image side refers to the side where the light exits. "From front to back" is like Figure 2 The direction from left to right in the image is from the object side to the image side. The surface facing the object side of each lens is called the object side surface, and the surface facing the image side is called the image side surface.

[0025] Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.

[0026] like Figures 1 to 4 The infrared optical imaging system for an unmanned aerial vehicle shown in the figure comprises an infrared optical imaging system 200 arranged on a carrier support of the unmanned aerial vehicle 100. The carrier support is arranged at a position close to the head of the fuselage of the unmanned aerial vehicle 100, and is used to carry the infrared optical imaging system 200. The infrared optical imaging system 200 comprises a fairing 1, a lens group and a detector.

[0027] The front and rear surfaces of the fairing 1 are concentric spherical surfaces, and the fairing 1 is fixed to the head of the unmanned aerial vehicle 100. It adopts a partial spherical structure, and its thickness is the difference between the front and rear surface curvature radii, the front surface curvature radius is 105mm, the rear surface curvature radius is 100mm, and the thickness is 5mm.

[0028] The lens group is arranged behind the fairing 1, and the lens group includes a first lens 2, a second lens 3 and a third lens 4 which are arranged on the same optical axis and are spaced from front to back. The three lenses are all meniscus-shaped, the first lens 2 and the third lens 4 are positive lenses, and the second lens 3 is a negative lens. The rear surface (image surface) of the first lens 2 and the front surfaces (object surface) of the second lens 3 and the third lens 4 are aspherical surfaces. In addition, the concave surfaces of the fairing 1, the first lens 2, the second lens 3 and the third lens 4 are all arranged toward the rear (image side), the curvature radius of each lens surface is positive, and no diffraction surface is arranged on any lens in the lens group.

[0029] Preferably, the fairing 1 is made of hot-pressed magnesium fluoride (MgF2), the first lens 2 is made of single crystal silicon (SILICON), the second lens 3 is made of single crystal germanium (Ge), and the third lens 4 is made of chalcogenide glass IRG206.

[0030] The first lens 2 meets the following conditions: 0.8≤ f 1 / f≤1.0, where f is the focal length of the infrared optical imaging system, f 1 is the focal length of the first lens 2; the second lens 3 satisfies the following conditions: -0.7≤ f 2 / f ≤-0.5, where f is the focal length of the infrared optical imaging system, f 2 is the focal length of the second lens 3; the third lens 4 satisfies the following conditions: 0.6≤ f 3 / f ≤0.8, where f is the focal length of the infrared optical imaging system, f 3 is the focal length of the third lens 4.

[0031] The distance between the first lens 2 and the second lens 3 in the optical axis direction is T 23 , the distance between the second lens 3 and the third lens 4 in the optical axis direction is T 34 , the thickness of the second lens in the optical axis direction is CT 3, and satisfy the following relationship: .

[0032] The detector is located behind the lens group, and the infrared radiation transmitted by the lens group is imaged on the imaging surface 6 of the detector.

[0033] The distance from the front end of the fairing to the imaging surface is 58 mm, the distance between the rear surface of the third lens and the imaging surface in the optical axis direction is 6 mm, and the diameter of the imaging surface is 12.4 mm.

[0034] The infrared optical imaging system also includes a swing mechanism. The fairing 1 remains fixed and the swing mechanism is installed between the lens group and the fairing 1. One end of the swing mechanism is firmly connected to the lens group, and the other end is reliably connected to the fairing through a rotating joint or a similar structure to ensure structural stability and sealing. The swing mechanism is equipped with a special drive device, which drives the lens group composed of the first lens 2, the second lens 3, and the third lens 4 and the detector to rotate ±15° in the azimuth and pitch directions relative to the fairing 1 according to the system control instructions. It should be noted that the swing mechanism is a common design in this field, and the specific structure will not be repeated.

[0035] The light transmission path of the infrared optical imaging system of the present invention is that the light emitted by the infrared radiation of the external scene passes through the spherical fairing 1 and reaches the first lens 2, is converged by the first lens 2 and reaches the second lens 3, is diverged by the second lens 3 and reaches the third lens 4, is converged by the third lens 4 and passes through the detector window protective glass 5 to form an image on the image plane 6.

[0036] Table 1 shows the technical indicators achieved by the present invention, among which: F # (Infrared optical imaging system F The calculation formula is f / D , f is the focal length of the infrared optical imaging system, D is the entrance pupil diameter.

[0037] Table 1 Technical indicators of the infrared optical imaging system of the present invention Table 2 lists the detailed data of the infrared optical imaging system in this embodiment, which includes the surface type, radius of curvature, thickness, and material of each lens. The units of the radius of curvature and thickness of the lens are both mm, and the radius of curvature of the spherical and aspherical surfaces refers to the radius of curvature at the intersection of the lens surface and the optical axis. The "serial number" in Table 2 is counted along the direction of light propagation, such as the light beam incident surface of the fairing 1 is serial number S1, the light beam exit surface is serial number S2, and the serial numbers of other mirror surfaces are similar. The curved surfaces of the fairing 1, the first lens 2, the second lens 3, and the third lens 4 along the object side to the image side are marked as S1, S2, S3, S4, S5, S6, S7, and S8 respectively; "radius" represents the radius of curvature of the surface, and the principle for determining its positive and negative is: taking the intersection of the surface and the main optical axis as the starting point, the curved surface of the surface The center is taken as the end point. If the direction of the connecting line is the same as the direction of light propagation, it is positive, otherwise it is negative; if the surface is a plane, the radius of curvature of the surface is infinite; "Thickness" gives the distance between two adjacent surfaces on the optical axis. The principle of positive and negative judgment is: take the current surface vertex as the starting point and the next surface vertex as the end point. If the direction of the connecting line is the same as the direction of light propagation, it is positive, otherwise it is negative; if the material between the two surfaces is infrared material, the thickness represents the lens thickness, if there is no material between the two surfaces, it represents the air gap between the two lenses.

[0038] Table 2 Detailed data of the infrared optical imaging system in the embodiment of the present invention The surface of the first lens 2 facing the image side, namely the exit surface S4, the surface of the second lens 3 facing the object side, namely the incident surface S5, and the surface of the third lens 4 facing the object side, namely the incident surface S7, are all aspherical surfaces. The surface equations of the above-mentioned aspherical surfaces are: in, z (r) represents the distance vector height from the vertex of the aspheric surface when the aspheric surface is at a height of r along the optical axis. c is the curvature, c =1 / R , Rrepresents the radius of curvature of the lens surface, r is the radial coordinate perpendicular to the optical axis, k is the quadratic constant, A is the fourth-order aspheric coefficient, B Sixth-order aspheric coefficients, C is the eighth-order aspheric coefficient, D is the tenth-order aspheric coefficient.

[0039] Table 3 lists the aspheric coefficients of the surface of the first lens 2 facing the image side, i.e., the exit surface S4, the surface of the second lens 3 facing the object side, i.e., the incident surface S5, and the surface of the third lens 4 facing the object side, i.e., the incident surface S7 according to the present invention. The table uses scientific notation. For example, 8.1230e-006 represents 8.1230×10 -6 .

[0040] Table 3 Aspheric coefficients of infrared optical imaging system in the embodiment of the present invention After simulation with optical design software, a medium-wave cooled detector with a pixel size of 15 μm and a pixel number of 640×512 was selected, and the corresponding spatial frequency was 33 lp / mm, from Figure 5 , Figure 6 , Figure 7 It can be seen that under the conditions of room temperature 20°C, low temperature -40°C and high temperature +60°C, the transfer function of the infrared optical imaging system of the present invention is greater than 0.45. Figure 8 , Fig. 9 , Fig.10 From the point diagrams of the system at room temperature 20°C, low temperature -40°C and high temperature +60°C, it can be seen that the diffuse spot diameter is smaller than the Airy disk diameter under different focal lengths. Fig.11 The field curvature and distortion curves of the infrared optical imaging system shown show that the edge field distortion of the system is less than 0.25%. Fig.12 From the relative illumination curve, we can see that the relative illumination of the edge field of view of the system is greater than 85%.

[0041] In summary, the present invention significantly improves the performance and application potential of infrared optical imaging systems in the field of unmanned aerial vehicles through a series of technical innovations, and has the following outstanding advantages: (1) Lightweight and miniaturized design The present invention adopts a compact structure with only three lenses, and the total length of the infrared optical imaging system is only 58 mm. By optimizing the aspheric surface shape and the spacing between lenses, the overall volume and weight are effectively reduced. This design enables the infrared optical imaging system to be easily integrated into small UAVs (such as multi-rotor or fixed-wing) to avoid occupying the installation space of other sensors, providing strong support for the multi-functional integration of UAVs.

[0042] (2) Passive athermal material combination The present invention cleverly combines single crystal silicon, single crystal germanium and chalcogenide glass IRG206, making full use of the differences in the thermal properties of these three materials, and successfully offsetting the impact of temperature changes on the infrared optical imaging system. Within a wide temperature range of -40°C to +60°C, the focal length change rate of the system is greatly reduced, and there is no need to set up a complex focusing mechanism. This not only avoids the risk of mechanical focusing components getting stuck in harsh environments, but also enables the system to operate stably in extremely harsh environments such as high altitudes and polar regions, improving the environmental adaptability and reliability of the system.

[0043] (3) Low-cost manufacturing and efficient assembly In terms of material selection, the present invention uses relatively low-cost single crystal silicon and chalcogenide glass IRG206 to replace the expensive zinc selenide (ZnSe) in the traditional optical athermal system. At the same time, the process of directly machining aspheric surfaces with CNC machine tools avoids the complex diffraction surface process. These measures not only reduce material costs, but also greatly shorten the installation and adjustment time, improve production efficiency, and effectively promote the popularization and application of infrared optical imaging technology.

[0044] (4) High imaging quality and dynamic tracking capability The present invention optimizes the optical path with the help of a unique aspheric design, which can accurately correct aberration problems such as spherical aberration, field curvature and distortion, effectively improving the imaging quality. At the same time, with the ±15° field of view swing scanning function, the attitude adjustment frequency of the drone when tracking the target is reduced, enabling it to quickly and accurately lock and track high-speed moving targets, enhancing the system's dynamic tracking capability.

[0045] In short, the present invention has achieved a comprehensive breakthrough in the performance, cost and reliability of infrared optical imaging systems through material innovation, structural optimization and process innovation. It has successfully solved the core problems of large volume, severe temperature drift and complex assembly and adjustment in the prior art, expanded its large-scale application potential in the civilian field, and provided key technical support for the efficient operation of unmanned aerial vehicles in scenarios such as smart cities, agricultural ecology, and emergency rescue. It has important practical significance and broad application prospects.

[0046] Finally, it should be noted that the parts of the present invention that are not described in detail are all prior art. Those of ordinary skill in the art can understand that the above are only preferred examples of the invention and are not intended to limit the invention. Although the invention is described in detail with reference to the aforementioned examples, those of ordinary skill in the art can still modify the technical solutions recorded in the aforementioned examples, or replace some of the technical features therein with equivalents. Any modifications, equivalent replacements, etc. made within the spirit and principles of the invention should be included in the scope of protection of the invention.

Claims

1. An infrared optical imaging system for an unmanned aerial vehicle, characterized in that: The infrared optical imaging system includes an infrared optical imaging system arranged on a carrier support of an unmanned aerial vehicle, and the infrared optical imaging system includes: The fairing is installed on the head of the UAV, and its front and rear surfaces are concentric spherical surfaces; A lens group is arranged at the rear of the fairing, and the lens group includes a first lens, a second lens and a third lens in a meniscus shape which are arranged in sequence from front to back on the same optical axis, wherein the first lens and the third lens are positive lenses, the second lens is a negative lens, and the rear side surface of the first lens and the front side surfaces of the second lens and the third lens are all aspherical surfaces; A detector is arranged behind the lens group, and the infrared radiation transmitted by the lens group is imaged on the imaging surface of the detector; The material of the fairing is hot-pressed magnesium fluoride, the material of the first lens is single crystal silicon, the material of the second lens is single crystal germanium, and the material of the third lens is chalcogenide glass IRG206.

2. The infrared optical imaging system for unmanned aerial vehicles according to claim 1, characterized in that: The concave surfaces of the fairing, the first lens, the second lens and the third lens are all arranged toward the rear.

3. The infrared optical imaging system for unmanned aerial vehicles according to claim 2, characterized in that: The first lens, the second lens and the third lens respectively satisfy the following conditions: 0.8≤ f1 / f ≤1.0, -0.7≤ f2 / f ≤-0.5, 0.6≤ f3 / f ≤0.8, wherein f is the focal length of the infrared optical imaging system, f1 is the focal length of the first lens, f2 is the focal length of the second lens, and f3 is the focal length of the third lens.

4. An infrared optical imaging system for an unmanned aerial vehicle according to claim 1 or 3, characterized in that: The distance between the first lens and the second lens in the optical axis direction is T 23 , the distance between the second lens and the third lens in the optical axis direction is T 34 , the thickness of the second lens in the optical axis direction is CT 3, and satisfy the following relationship: 。 5. The infrared optical imaging system for unmanned aerial vehicle according to claim 1, characterized in that: The fairing is a partially spherical structure as a whole, and its thickness is the difference between the curvature radii of the front and rear surfaces.

6. The infrared optical imaging system for unmanned aerial vehicles according to claim 1, characterized in that: All lenses in the lens group are not provided with diffraction surfaces.

7. The infrared optical imaging system for unmanned aerial vehicles according to claim 1, characterized in that: The fairing is fixedly arranged, and the lens group can rotate ±15° in the azimuth direction and the pitch direction relative to the fairing.

8. The infrared optical imaging system for unmanned aerial vehicles according to claim 1, characterized in that: The distance from the front end of the fairing to the imaging surface is 58 mm.

9. The infrared optical imaging system for unmanned aerial vehicles according to claim 8, characterized in that: The distance between the rear surface of the third lens and the imaging surface in the optical axis direction is 6 mm.

10. The infrared optical imaging system for unmanned aerial vehicle according to claim 9, characterized in that: The infrared optical imaging system has a focal length of 45 mm, a field of view of 12.2°×9.8°, an imaging surface diameter of 12.4 mm, and an operating band of 3 μm to 5 μm; F#: 2.0, wherein the F# calculation formula is f / D, f is the focal length of the infrared optical imaging system, and D is the incident pupil diameter.

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