An infrared optical system is a device that can detect and image infrared radiant energy emitted by an object. Infrared imaging systems are widely used in military applications such as short-range surveillance, fire control systems, target tracking systems, and thermal imaging equipment because of their excellent target detection capabilities despite limitations due to weather and atmospheric conditions.

Recent advances with highly sensitive infrared detectors have led to increased research on high-performance equipment, including infrared payloads on earth observation satellites and airborne-mounted cameras designed to acquire information from all directions and areas of interest [1–4]. There are various development challenges associated with airborne platform cameras because of the need for precise and clear imaging of target points in dynamic flight environments [5].

First, airborne cameras must be developed according to strict space and weight constraints. Second, these cameras are exposed to vibrations from aircraft and environmental factors such as temperature and pressure variations, which differ from ground conditions. Third, the camera’s operation, imaging technique, image acquisition method, and stabilization system all influence its driving mechanism and must therefore be carefully considered in its design [4, 6–9].

The Condor 2, DB-110 and dual-band EO/IR are representative examples of airborne camera systems [4, 6, 10–13]. These models are all installed at an angle perpendicular to the aircraft’s flight direction. A method of operation has been adopted to accommodate the various operating conditions of the aircraft.

The Condor 2 was developed by Elop. To resolve space and weight limitations, the Condor 2 uses a Ritch-Chretien optical system [10]. A beam splitter is installed behind the primary to separate the EO band and IR band, and whiskbroom scanning method was utilized using the pitch and roll gimbals for image taking [11].

The DB-110 is manufactured by Goodrich Corporation. The optical system uses a Cassegrain telescope type. The EO band passes through the beam splitter to form an image, while the IR band is reflected off the beam splitter at 45°, with incidence on the relay lens to form its image [12]. Using the pitch and roll gimbals, both the step-and-stare method and the continuously scanning method were adopted for image acquisition. Images are collected in the scan direction using the roll gimbal, while the forward movement of the aircraft is compensated by the pitch motion of the sensor [13].

The dual-band EO/IR system has been studied by the Agency for Defense Development (ADD) in Korea. This optical system uses a Cassegrain telescope type, as in the DB-110. A beam splitter is installed behind the primary mirror, allowing the EO band to pass through, and form an image on the charged-couple device (CCD) sensor. The IR band is reflected at 45° by the beam splitter, and directed into the relay lens [4]. The relay lens corrects aberrations and forms an image on the IR sensor. The relay lens was designed with a telecentric type to enable uniform magnification, allowing the reduction of perspective to be effective even when object moves forward, backward, left and right, or when images are taken from oblique angles. The step-and-stare imaging method was adopted using the pitch and roll gimbals [6].

This paper presents the design and analysis of a forward-looking airborne camera that is optimized for long-range observations considering space limitations using a mid-infrared detector. The initial optical system was designed considering three key conditions: Meeting space and weight requirements, ensuring weight balance for stabilization, and minimizing optical degradation caused by environmental changes as the harsh operating environment of an aircraft significantly affects performance. To satisfy these conditions, comprehensive analyses on the initial concept and detailed design process were conducted including the analysis of effects of temperature fluctuations and aircraft-induced vibrations, the proposal of a design method to minimize the impact of environmental changes on optical performance, and the development of an assembly method to obtain the target performance parameters, such as the modulation transfer function (MTF) and the field-of-view (FOV). The validity of the proposed design was confirmed by measuring these parameters with a manufactured camera.

The optical system presented in this paper differs from previously introduced systems, because it matches the aircraft’s direction with the line of sight (LOS) of the camera, resulting in a forward-looking structure [14]. To avoid aerodynamic forces and heating encountered during flight, an optical window is installed at an angle to the aircraft’s flight direction to protect the optical system. In addition, pitch and yaw gimbals are installed and operated to ensure the full range of LOS angles in various aircraft operating conditions. The total range of LOS angles is called the field of regard (FOR) [15].

The optical setup is mounted as shown in Fig. 1 and is controlled by a two-axises gimbal, for movement in the pitch and yaw directions [16, 17]. The optical system must ensure precise stabilization and compensate for environmental impacts to acquire high-quality images considering space and weight constraints.

Figure 1. Two-axis gimbal for the infrared optical system.

The optical system must be mounted on a two-axises gimbal assembly, which imposes constraints on the size, length, weight, and spatial geometry of the system. The configuration of the optical system greatly influences the gimbal’s size, weight, and driving characteristics, making spatial arrangement a critical factor in the design of optical assemblies [18]. The required specifications of the optical system are shown in Table 1. The detector used has a pixel size of 15 μm and an F-number of 4.0.

TABLE 1. Target and design specifications of the infrared optical system.

Parameters		Target	Designed Spec.
Wavelength (μm)		3.4–4.4	3.4–4.4
Focal Lengths (mm)		183	183
F-number		3.91–4.0	4.0
FOV (°)		12-0.03+0.03 × 12-0.03+0.03	1.2 × 1.2
Distortion (at All Field) (%)		Less than ±1	0.3
MTF (at Nyquist Frequency) (%)	Designed MTF	More than 35 at Center Field	36.3
	Athermalized (−30 ℃–+70 ℃) MTF	More than 35 at Center Field	35.8

3.1. Preliminary Design for Space Constraints

In the design process, the aberrations of an optical system should be minimized considering space constraints. The primary optical aberrations considered in the design process include spherical, astigmatism, coma, distortion, field curvature, and chromatic aberrations. In the design process, to minimize optical system aberrations, the radius of curvature, thickness, refractive index, and spacing between each optical component were used as variables.

First, the thicknesses of the optical surfaces were set to zero, and the initial design was obtained using a thin lens approach to arrange the optical surfaces and distribute the refractive power [19]. Second, the thicknesses of the optical surfaces were determined, and their curvatures were specified on the basis of the refractive power calculated by aberration theory. Third, the curvature, spacing, and thicknesses of the optical surfaces were fine-tuned with an optimization algorithm to meet the design specifications of the optical system. The basic design has an FOV of 1.2° × 1.2°, a focal length of 183 mm, and an F-number of 4.0. The geometry of the basic system is shown in Fig. 2.

Figure 2. Designing the base structure of an optical system.

Given that the optical system operates with a pitch range of −40° to +40° and a yaw range of −10° to +10°, the design must account for both the driving range and the mounting space. Designs were created for three cases, as shown in Table 2.

TABLE 2. Optical system configurations by case.

Case 1	Case 2	Case 3

Case 1 involves a structure in which the entire optical system is driven in the yaw and pitch directions by incorporating mirrors into the optical path. Case 2 features a structure in which the yaw and pitch are controlled by moving a mirror. In Case 3, a prism is used in the yaw-pitch drive configuration to optimize space. The design results for each case is explained in the Section 3. 2.

3.2. Design Results for Case 1

The optical system arrangement and drive geometry for Case 1 are shown in Fig. 3. The system is positioned within the mounting space using mirrors M1 and M2. The yaw and pitch are controlled by internal and external gimbals, with the rotation axis aligned with the aircraft axis. Gyros, encoders, and motors can be integrated into the gimbal to reduce the load on the internal and external components. However, a limitation is that the size of the optical window, which is used to enclose the system, increases with increasing drive range.

Figure 3. Optical system arrangement and drive geometry for Case 1.

3.3. Design Results for Case 2

The optical system arrangement and drive geometry for Case 2 are shown in Fig. 4. The system is configured within the internal space using mirrors M1 to M3. The scan drives of M1 and M2 function as stepping drives, with M1 being responsible for yaw movement within the inner gimbal. As shown in Fig. 5, M1 and M2 are both used to control the pitch drive of the outer gimbal. L1 to L6, M3, and the detector are fixed. The yaw drive rotation axis is aligned with the M1 and M2 beams, whereas the pitch drive rotation axis is centered on M2. The weight of the system can be decreased by reducing the number of driving components, which in turn reduces the loads on the inner and outer gimbals. As the window size increases, the risk of light interference owing to barrel separation increases, complicating the alignment along the optical axis. Since M1 and M2 are driven independently, synchronizing their rotation is challenging (e.g., when M2 rotates 5 degrees, M1 rotates 10 degrees) because of the difference in rotation angles when the motor pitch axis moves. This causes image rotation, which must be corrected, as shown in Fig. 6.

Figure 4. Optical system arrangement and drive geometry for Case 2.

Figure 5. Pitch direction drive of the optical system in Case 2: (a) Pitch value of −40° and (b) pitch value of +40°.

Figure 6. Image rotation caused by the optical system in Case 2.

3.4. Design Results for Case 3

The optical system arrangement and drive geometry for Case 3 are shown in Fig. 7. In this configuration, prisms are used to optimize the arrangement within the space. M1, M2, L1, and L2 are used to control the pitch axis, whereas M1–M2, L1–L6, and the prism are used to control the yaw drive. The detector is fixed in place. The pitch axis rotates about the L2 plane, and the yaw axis rotates about the L3 to L4 directions. However, limitations include difficulty in fitting the system within the available space, the increased window size, the additional load on the external gimbal, light interference due to barrel separation, optical axis alignment issues, gimbal axis offset, and the need for roll compensation due to image rotation. The layout of the optical system and pitch drive are shown in Fig. 8.

Figure 7. Optical system arrangement and drive geometry for Case 3.

Figure 8. Layout of the optical system in Case 3: (a) Layout of the optical system and (b) pitch drive layout of the optical system.

3.5. Summary of Design Results

Case 1 provides a simple and stable configuration, where the integration of gyros, encoders, and motors into the gimbal reduces the mechanical load on both internal and external components. However, the increase in optical window size with the expansion of the drive range poses a potential limitation. Case 2 minimizes system weight by reducing the number of driving components, which alleviates the load on the gimbals. Despite this advantage, the larger optical window introduces light interference issues, and the synchronization between M1 and M2 becomes challenging, leading to image rotation that necessitates correction. Case 3 offers a flexible design with the implementation of prisms, which enhance the spatial arrangement of components. Nevertheless, it presents significant challenges in fitting the system within the available space. Furthermore, the enlarged optical window induces greater mechanical stress and complicates optical alignment, while roll compensation is required to address image rotation.

Ultimately, Case 1 was selected as the optimal design for the optical system. Compared to the more complex synchronization and interference issues observed in Cases 2 and 3, its simplicity, ease of alignment, and reduced mechanical complexity make it a more stable and reliable solution. Although the enlarged window size in Case 1 is a limitation, the overall system stability and the integration advantages outweigh this drawback, making it the most suitable option for the optical system.

4.1. Optimized Design of the Optical System

The first consideration is the arrangement of the optical components within the available space, as outlined in the basic design (Case 1) in the previous section. The second consideration is minimizing performance variations by accounting for environmental impacts. One example is athermalization. Athermalization refers to the ability to maintain optical system performance despite changes in temperature. If athermalization is not achieved, the most significant degradation of the optical system owing to temperature changes is image blurring as the focal length changes.

When a system involving optical components with varying heat dispersion characteristics is designed, each aberration term can become imbalanced with temperature changes, leading to performance degradation. In this system, passive compensation methods are incorporated into the optical design. The passive compensation method is used to adjust the focal length of the optical system by exploiting the temperature characteristics of the lenses and the optical path without requiring additional devices, making it particularly useful for optical systems with space constraints [20].

The optimal optical system is illustrated in Fig. 9. Since the optical window in this system is mounted at an angle, the optical path was optimized by placing a mirror (M1) in front of the objective lens (L1). To efficiently position the detector assembly, including the sensor plane, within the optical system, an additional axial mirror (M2) was added. The ray bundle from a target at infinity passes through the optical window, is reflected by M1, and subsequently traverses the objective lenses (L1 and L2). The optical path was designed so that the light reflected by M2 passes through L3 to L6 and converges on the detector surface.

Figure 9. Layout of the optimized optical system.

In the design process, first- and third-order aberrations were analyzed to assess their impact on the performance of the optical system within each optical plane. The contributions of aspherical elements, as well as their compensation values, were analyzed. This analysis revealed that aspherical lenses are particularly effective in cases with high contributions from these elements. Consequently, aspheric surfaces were applied to the front surfaces of L1 and L2. The field stop was positioned on the middle upper surface located between L3 and L4 to minimize the influence of stray light on performance.

The physical air gaps between each mirror were also considered in the design constraints to optimize the optical lens design. For the design considering the effects of athermalization, the material used for the structure between L1 and L6 was titanium (Ti-6Al-4V, αL = 95.0 × 10⁻⁶/K), whereas the material used for the structure between L6 and the FPA was aluminum (Al7075, αL = 236.0 × 10⁻⁶/K). The lenses that most significantly affect athermalization performance are the objective lenses (L1 and L2).

In general, the use of a combination of magnesium and silicon materials leads to the best athermalization performance. For the other lenses, the materials were selected to achieve the best performance on the basis of variability in the material properties. The temperature-dependent properties of the lenses (such as dN/dT and dR/dT) and the thermal expansion coefficient (αL) were assumed to vary linearly with temperature. In the design process, a temperature ranges from −30 ℃ to 70 ℃ was considered. Given these two conditions, the materials used for the six lenses in the optimized optical system were as follows: Si (front surface : aspherical surface) for L1, Ge (front surface : aspherical surface) for L2, ZnSe for L3, Ge for L4, and Si for L5 and L6. In addition, mirrors M1 and M2 were made of B270 glass.

The layouts of the optimized optical systems at different pitch angles are shown in Table 3.

TABLE 3. Layouts of the optimized optical systems at different pitch driving angles.

Pitch (−40°)	Pitch (0°)	Pitch (+40°)

4.2. Optimized Design Results

The design specifications of the optical system are summarized in Table 1. The focal length was 183 mm, with an FOV of 1.2° × 1.2°. The designed optical system achieves an MTF of 36.3% in the 0-field case, as shown in Fig. 10, which satisfies and exceed the required MTF.

Figure 10. Modulation transfer function (MTF) of the designed infrared optical system.

The distortion aberration was designed to be 0.3% or less across all fields, and the result is shown in Fig. 11.

Figure 11. Optical distortion of the designed infrared optical system.

The athermalization design results are shown in Fig. 12. The results demonstrates that the MTF in the 0-field is effectively maintained between 36.3% and 35.8% across the temperature range of −30 ℃ to +70 ℃. The optical system consistently meets or exceeds the MTF requirement of 35.0% under all temperature conditions, as presented in the previous section II.

Figure 12. Results of the athermalization design of the designed infrared optical system.

5.1. Selection of Compensation Lenses for Assembly

The performance requirements for the fabricated system are shown in Table 4.

TABLE 4. System performance targets.

Parameters	Target
FOV (°)	12-0.03+0.03 × 12-0.03+0.03
System MTF (at the Nyquist Frequency) (%)	More than 10 at Center Field

The errors expected during the actual fabrication and assembly of the designed optical system are estimated, and fabrication tolerances are established to ensure that the produced system meets the performance specifications. This is achieved through sensitivity analyses.

When optical performance is treated as a dependent variable, its sensitivity is expressed by the magnitude of change in performance in response to specific variations in each independent variable affecting the system’s overall performance. The sensitivity of the Zernike coefficients of wavefront error is evaluated with respect to variations in optical lens parameters such as the radius of curvature, thickness, decenter, and tilt displacement [21].

An analysis of the sensitivity of the optical components to movements along the optical axis shows that the defocus component is the most significant factor in compensating for alignment errors caused by the lens assembly. As shown in Fig. 13, the Zernike sensitivity analysis for each component indicates that the Zernike coefficient C5 (defocus) is significantly larger than the others. In contrast, coefficients such as C4 (astigmatism), C6 (astigmatism at 45°), C8 (coma along the x-axis), C9 (coma along the y-axis), and C13 (spherical) are extremely small, with value around 10⁻³. The objective of this analysis is to calculate the change in defocus on the image surface when these lenses are displaced in 1.0 mm intervals (λ/mm). Consequently, the system’s FOV is 1.2° ± 0.03° × 1.2° ± 0.03°. Given the strict tolerance requirements for this system, it is crucial to select an appropriate compensator to obtain the specified FOV. Defocus sensitivity analysis of the optical components suggests that adjusting the distance between L1 and L2 is an effective method for fine-tuning the FOV.

Figure 13. Defocus sensitivity of each optical component in response to z-axis movements (The Zernike coefficients c5 (defocus) is significantly larger than the others, which are approximately on the order of 10⁻³).

Figure 14 shows the variation in the focal length and FOV with the distance between L1 and L2. Figure 15 presents the optomechanical design layout. The optical system is composed of five barrels. Barrel 1 contains mirror M1; Barrel 2 contains lens L1; Barrel 3 contains lens L2; Barrel 4 contains mirror M2; and Barrel 5 contains lenses L3, L4, L5, and L6. After the optical components are placed in their respective barrels, the barrels are assembled to form the complete optical system.

Figure 14. Changes in the focal length and field-of-view (FOV) with the distance between L1 and L2.

Figure 15. Optical system mechanical design layout.

5.2. Assembly Method

To measure the focal length of the lenses (L1–L6), the ImageMaster^® Universal model (Trioptics GmbH., Wedel, Germany) was used [22]. Owing to the folded structure of the optical system, the direction of the light entering the instrument is opposite to the direction from which the detector receives the light; That is, the optical system must be aligned inline to accurately measure the focal length. Barrel 4 contains M2. Since M2 is used only to redirect the light path, a straight optical system can be created by adjusting and replacing the light path segments corresponding to the distances between L2 and M2 and between M2 and L3. This approach is referred to as an in-line barrel. Figure 16 shows the structure of the in-line barrel.

Figure 16. Structure of the in-line barrel.

By adjusting the positions of L1 and L2, we measured the focal length in real time and determined the optimal distance between lenses, which was used to determine the thickness of the alignment shim. The system assembly process using this method is shown in Fig. 17, and the system depicted in Figs. 18(a) and 18(b) was assembled.

Figure 17. Flow chart of the assembly procedure.

Figure 18. Field-of-view (FOV) adjustment method: (a) Device configuration and (b) device setup.

This system was assembled as follows: First, the optimal distance was determined. The optimal distance between Barrels 2 and 3 was determined on the basis of real-time focal length measurements obtained using the assembly tool shown in Fig. 18(b). Then, the location shim was installed. The location shim corresponding to the optimal distance between Barrels 2 and 3 was mounted and bonded. The optical components were assembled. The in-line barrel was replaced with Barrel 4, and Barrels 1 through 5 were assembled. Next, the detector was mounted. Then, the imaging performance of the system was verified. An image performance measurement device was used to assess image quality. Finally, the shims were adjusted by adding or removing shims at the detector position as needed to achieve optimal image quality.

6.1. Overview of Performance Evaluation

In this section, the performance of the proposed optical system, which was designed and assembled as described in the previous sections, is evaluated to determine if the proposed system meets the target performance specifications outlined in Table 4. The MTF is a crucial criterion for evaluating the performance of imaging systems [23]. The FOV defines the extent of the observable area that can be imaged by the camera. Specifically, the FOV is a key performance parameter for this system, which affects the distant objects that can be detected with the proposed system [24].

As shown in Table 4, the system’s MTF is 0.1 or higher, and the FOV is $1.2{°}_{\text{-}0.03}^{+0.03}$ × $1.2{°}_{\text{-}0.03}^{+0.03}$. Figure 19 shows the setup used for measuring the MTF and FOV of the camera.

Figure 19. Experimental setup for the modulation transfer function (MTF) and field-of-view (FOV) measurements.

6.2. MTF Measurement

A half-moon target was used to measure the MTF. The collimator had a focal length (F_c) of 1,700 mm. The infrared beam from the half-moon target, which was emitted through the collimator, was focused onto the camera positioned on the left. The temperature difference between the target and background is set to 30 K. Fifty frames of the half-moon target was recorded with camera, then the average image file was generated. The acquired signal was Fourier-transformed, and the amplitude of the transformed results was derived to calculate the MTF value.

The MTF measurement results, as shown in Fig. 20, indicate that the MTF value was 12.7% at the Nyquist frequency, which meets the performance specifications for this system.

Figure 20. Modulation transfer function (MTF) results: (a) Half-moon target image (MTF search range: 50 pixels) and (b) MTF results (12.7% at 33.3 cycles/mm).

6.3. FOV Measurement

For the FOV measurement, a cross-target was used. The size (η) of the cross-target image corresponding to its image size (η′) can be calculated using the software. When the image (α′) is magnified onto the CCD surface, the relative size of the target (α) is determined as shown in Eq. (1):

The half field of view (θ) is derived from the collimator’s focal length (F_c) and the value of α. The full field-of-view is double the half field-of-view (θ). The method for measuring the FOV using the image size is shown in Fig. 21. Here, F_o is the focal length of the optical system.

Figure 21. Method for measuring field-of-view (FOV) using image size.

The FOV measurement results are shown in Fig. 22. The results indicate that the FOV was 1.200° × 1.200°, which meets the performance specifications for this system.

Figure 22. Field-of-view measurement results (1.200° × 1.200°).

In this study, we designed and analyzed an airborne camera for long-range forward imaging, considering the driving method and installation space. As a results, we created space using M1 and M2 and developed an optimal system configuration by using a yaw-pitch drive for the optical system. To meet the system’s design requirements of an MTF and FOV, a precise assembly method using an in-line barrel was proposed. This approach achieved an MTF of 12.7% and an FOV of 1.200° × 1.200°. These results indicate applicability in various fields that demand high-precision optical system.

However, since this study only measured performance in a laboratory environment, further research is necessary to verify performance in outdoor conditions, particularly for target imaging. This ongoing research could contribute to advancements in airborne camera technology.

Agency for Defense Development Grant funded by the Korean Government (924012318).

The authors declare no conflict of interest.

The data underlying the results presented in this paper are not publicly available at the time of publication but may be obtained from the authors upon reasonable request.