The optical materials used in infrared optics exhibit significant changes in the refractive index owing to temperature variations compared to those used in visible optics. Mechanical components such as mounts and housings for optical parts also undergo expansion and contraction in response to temperature changes. This induces a change in the focal length and results in blurred images, which degrades the image quality of the infrared optical system [1–3].

Approaches to athermalization are categorized into mechanical and optical methods, and mechanical methods can be subcategorized into passive and active ones [4–6]. The passive mechanical method uses the difference in thermal expansion coefficients with the mechanical support of the lenses. This approach is useful in cases where the focal length is short, such as imaging lenses [7]. The active mechanical method uses electronic motors and circuits to move the lenses or lens groups. This method is effective when the values to be corrected according to the magnification are different, such as in a zoom system [8, 9]. The optical method compensates for thermal defocus by using the difference in the characteristics of the optical materials with respect to temperature. The key point of this method is to properly select and combine optical materials to compensate for focus errors due to temperature variations in the optical system [10, 11].

The optimum athermalization method should be selected based on factors such as the equipment used, the temperature ranges, and the configuration of the optical system. The long-wavelength infrared (LWIR) camera is an optical system with zoom capability. Its structure consists of a magnification lens for zooming and a compensation lens for focus adjustment. These two lens groups are designed to enable precise movement along the optical axis, driven by individual motors. Therefore, an active mechanical athermalization method is appropriate.

To implement active mechanical athermalization, we analyze the defocus sensitivity of the designed optical system and then select accurate focus control parameters. Using optical design software such as Zemax or Code-V, we can easily calculate the amount of focus shift resulting from temperature and magnification variation. Using optimum focus control parameters, this focus shift can be effectively compensated for, resulting minimized image degradation.

In this study, we implemented an athermal compensation driver program that automatically adjusts the positioning of each lens in response to temperature changes by inputting specific adjustment parameters. When the lens is driven according to temperature changes, it is necessary to verify this athermal method in order to check how well the image quality is maintained. To test the proposed approach in the context of temperature variations, both the camera and the collimator are placed inside a temperature chamber. An image of the target on the collimator is observed on a monitor outside the temperature chamber.

We validate the accuracy of our athermal analysis by comparing the focusing lens displacement measured in the actual test, with the displacement derived from the simulated athermal analysis. Here, the focusing lens denotes the compensation lens in this LWIR zoom system. Using the amount of movement of the focusing lens displaced from the reference position at each temperature, we determine the position of the focusing lens and then upload this information to the encoder to implement an automatic focusing mechanism. Finally, we verify the athermal performance of this approach using an automatic focusing mechanism with laboratory and outdoor tests. The details are described in the following sections.

Table 1 shows the targeted specifications and results of the designed zoom lens system with a zoom ratio of 3×. Accounting for weight and volume, the targeted specifications are defined based on a lens diameter of 70 mm or less and a total track length of 100 mm or less. When the lens is in the tele and wide positions, the modulation transfer function (MTF) values at the image center are set to 20% or higher, and the distortion is set to within ±5%. As shown in Fig. 1, this optical zoom system consists of three groups and four elements. During the zooming process, the first group G1 (L1) remains fixed status, and the second group G2 (L2 and L3) moves along the optical axis to change the lens magnification. The third group G3 (L4) is a compensator that compensates for the image displacement caused by the movement of G2.

Figure 1. Layouts of the designed 3× long-wavelength infrared (LWIR) zoom system.

TABLE 1. Target and designed specifications of the 3× LWIR zoom lens system.

Parameters		Target	Designed Spec.
Wavelength (μm)		8–12	8–12
Focal Lengths (mm)		25–75.1	24.5–75.1
F-number	Tele Position	1.6	1.6
	Wide Position	1.45	1.45
FOV (°)	Tele Position	9.3 × 7.0 (±0.3)	9.4 × 7.0
	Wide Position	28.0 × 21.0 (±0.3)	28.2 × 21.3
MTF (at Nyquist Frequency) (%)	Tele Position	More than 20 (at Center Field)	20.9
	Wide Position		25.8
Distortion (%)	Tele Position	Less than ±5	1.5
	Wide Position	Less than ±10	−10.2
Max Diameter (mm)		Less than 70	70
Overall Length (mm)		Less than 100	95.3
Relative Illumination (%)		More than 95	96
Weight (g)		Less than 170	162

G1, G2, and G3 are arranged in a P-N-P configuration [12]. Here, P refers to the positively powered group, and N refers to the negatively powered group. If G1 has a positive power, this system has the advantages of a high zoom ratio and compact size. All lenses, L1 through L4, are made of germanium. Additionally, to achieve good performance in the tele position, the front surface of L1 is designed in an aspherical shape, and a diffractive optical element (DOE) is introduced into the rear surface. The DOE surface is a kinoform type with rotational symmetry. The diffraction order of the DOE is the first one, the design wavelength is 10 μm, and the phase coefficient (C1) is −2.9355 × 10⁻⁵ mm. Considering manufacturability and scattering due to the diffraction pattern, the DOE is set to have three diffraction zones (the number of rings is three). Figure 2 shows the MTF of the finally designed 3× LWIR optical zoom system at three zoom positions.

Figure 2. Modulation transfer function of the designed 3× long-wavelength infrared (LWIR) zoom system: (a) at tele, (b) middle, and (c) wide positions.

The simplest method of athermalizing an optical system is to move the focal plane array (FPA) or the primary objective lens, which influences the main refractive power of the system. The method of moving the FPA requires an additional drive motor, and has the disadvantage that all electronic circuit boards related to the FPA must also be moved. Meanwhile, the method of moving the objective lens is mechanically challenging, and also not desirable to ensure the system sealing.

As a result, the best approach is to move another lens that has the appropriate movement range required to have zoom magnification [13, 14]. To determine the best lens for athermal compensation, we analyzed the defocus sensitivity of the image according to movements in the magnification lens and the compensator lens. This analysis aims to calculate the changes in defocus on the image surface when these lenses are moved into 1.0 mm intervals. The defocus sensitivities calculated for all lenses are shown in Fig. 3. In that figure, the units are λ/mm.

Figure 3. Defocus sensitivity analysis results.

When the magnification lens L3 is moved by 1.0 mm at the middle position, the amount of defocus changes in the image plane is only 0.0911 λ/mm. This means that regardless of how much the magnification lens (L3) is moved to correct the defocus caused by temperature changes, the defocus error does not diminish.

This analysis result in Fig. 3 shows that compensation can be achieved using L2 or L4. Considering the operational convenience of the system as shown in Fig. 1, it is reasonable to keep the magnification lens (L2) fixed and move the compensation lens (L4) to solve image defocus errors. The operating temperature range in the zoom camera system is from −30 ℃ to 50 ℃. The thermal compensation of the optical zoom system must be precisely achieved within this temperature range. In this study, the housing connecting the lenses is made of aluminum. The properties of materials used for the simulation are listed in Table 2 [15, 16].

TABLE 2. Properties of the lens and housing materials.

Parameters	Ge	Al
Refractive Index n (at 10 μm)	4.003	-
Thermal Coefficient dn/dT (×10−6/K)	400	-
Thermal Expansion Coefficient αL (×10−6/K)	5.8	23.4

The simulation for athermal analysis was conducted at intervals of 10 ℃. For each temperature, the position of the compensation lens was determined when the wavelength-weighted RMS spot size on the axis was minimized. At the tele position, the amount of defocus changes of the optical system was 0.297 mm at +50 ℃, and −0.496 mm at −30 ℃. At the wide position, the amount of defocus changes was 0.097 mm at +50 ℃ and −0.162 mm at −30 ℃. As the magnification decreases, the focal length becomes shorter, which leads to a reduced magnitude of defocus due to temperature change.

When the one-quarter wave Rayleigh criteria is applied to evaluate the image performance, the allowable depth of focus at the central wavelength of 10 μm is 0.102 mm. When comparing the maximum defocus (−0.496 mm) caused by temperature changes to the depth of focus (0.012 mm), it is too large to limit the image quality of the LWIR camera at various temperatures.

The optimal positions of the magnification lens and the correction lens are determined to compensate for the defocused image owing to temperature changes at each zoom magnification for various temperatures. From a standard temperature of 20 ℃, the variance of temperature changes, ∆T, was applied in both the positive and negative directions to perform athermalization. The results of the MTF changes before and after temperature compensations are shown in Fig. 4.

Figure 4. Modulation transfer function (MTF) simulation results before and after temperature compensations for each zoom position: (a) at tele, (b) middle, and (c) wide positions.

Table 3 lists the movement amounts of the compensation lens (L4) obtained from the simulated athermal analysis for athermalization. They are calculated in 5 ℃ increments at three zoom positions, from the reference position at 20 ℃.

TABLE 3. Amounts of movement of the compensation lens obtained from the simulated athermal analysis for athermalization.

Temperature (℃)	L4 (mm)
	Tele Position	Middle Position	Wide Position
−30	−0.816	−0.460	−0.301
−25	−0.737	−0.414	−0.271
−20	−0.657	−0.368	−0.241
−15	−0.577	−0.322	−0.211
−10	−0.497	−0.275	−0.180
−5	−0.416	−0.229	−0.150
0	−0.335	−0.182	−0.119
5	−0.254	−0.136	−0.089
10	−0.173	−0.089	−0.059
15	−0.087	−0.045	−0.030
20	0	0	0
25	0.078	0.048	0.030
30	0.156	0.097	0.061
35	0.239	0.144	0.091
40	0.323	0.191	0.121
45	0.406	0.238	0.151
50	0.49	0.285	0.181

To intuitively analyze the simulated athermal results, the movement amounts of the compensation lens for athermalization are graphically displayed for various temperatures at three zoom positions in Fig. 5. The magnification lens is fixed for all zoom positions, and athermalization is conducted by moving the compensation lens only. At the tele position, the compensation lens moves linearly within the range of −0.816 mm to 0.490 mm. At the middle and wide positions, the compensation lens also moves linearly within the range of −0.460 mm to 0.285 mm and within the range of −0.301 mm to 0.181 mm, respectively. In Table 3 and Fig. 5, note that there is no movement of the compensation lens at the reference temperature of 20 ℃ at all zoom positions.

Figure 5. The movement behavior of the compensation lens for athermalization at three zoom positions obtained from the simulated athermal analysis.

The primary function related to thermal compensation in the optical drive system involves changing the movement path of the optical elements according to the temperature. First, the internal temperature of the optical system is measured, and then the lens is moved along a path suitable for that temperature. Considering the results of the simulated athermal analysis of Table 3 and Fig. 5 for the 3× LWIR zoom system, a motor control board is designed to ensure that the system’s image performance does not degrade even though the temperature changes.

The optical system drive device uses two Arm-A9 cores in a field programmable gate array (FPGA) to send signals to the DC motor driver and step motor driver circuits, which execute the control functions. Using these motors, the variator and compensator are established with hardware configurations and software implementations to enable continuous zooming from wide (1×) to tele (3×) positions, as shown in Fig. 6.

Figure 6. Hardware configuration of the 3× long-wavelength infrared (LWIR) zoom system for autofocusing.

The driving program for the optical system consists of lens movement and thermal compensation functions. The first process executed in the main program is the initialization of the optical system. It takes place when the power is turned on or a computer initialization signal is generated. During the initialization process, the two lenses (magnification and compensation lenses) located at arbitrary positions move from the wide to the tele positions. Then, while counting the encoder positions, they return to the initial tele position. Second, focus adjustment is performed. The focus adjustment lens starts at the left end and moves all the way to the right end, then moves to the initial position where the left direction is the start. Third, the internal temperature of the optical system is measured. The digital temperature sensor can measure temperatures ranging from −55 ℃ to 150 ℃, within a measurement error of ±0.3 ℃. The temperature sensor sends the measured data to the control board in a serial format with a 16-bit length. Fourth, zooming path selection is performed. Using the measured temperature information, the appropriate zooming path for the corresponding temperature is selected. The zooming paths for thermal compensation are based on measurement data in 10 ℃ increments across a range from −30 ℃ to 50 ℃. The derived polynomial formulas are input into the DC motor and step motor encoders. The fifth step involves moving the zooming lens and adjusting the focus for thermal compensation. After measuring the temperature inside the optical system, the zooming lens is moved to either a lower or higher magnification. The moving path of this lens is the trajectory already determined by considering the current internal temperature of the optical system. The final step is to decide whether to move the compensation lens.

If this lens moves to the position determined from the simulated athermal analysis, the focus, including athermalization, is completely performed.

It is necessary to determine whether simulated athermal analysis can be applied to real manufactured systems. To reduce the testing time in the temperature range from −30 ℃ to 50 ℃, the tests are conducted at 10 ℃ intervals centered at about +20 ℃, i.e., the reference temperature for optical system design. The time interval required to move from the current temperature to the next temperature section is set to 2 hours. Of this 2-hour period, one and a half hours are spent adjusting the equipment to the temperature, and the remaining 30 minutes are allocated for measuring the image quality.

5.1. Test Equipment

The experimental equipment used for the athermal test includes a collimator and a temperature chamber. The optical system is installed inside the temperature chamber, which serves to regulate the temperature so that the optical system is exposed to the desired temperature environment. The chamber is equipped with an infrared window made of germanium glass that connects the inside and the outside of the chamber.

In this study, due to the spatial limitations of the available temperature chamber, the LWIR optical zoom system is placed inside the chamber, while the collimator is set up outside the chamber. The image signal from the high-resolution target on the collimator is acquired by the camera through the chamber’s infrared optical window, and it is observed on a monitor connected outside the chamber.

The collimator is a device that replicates long distance images. Essentially, it produces parallel light. The infrared beam emitted from the collimator passes through the infrared window of the temperature chamber and is incident on the camera, focusing on the detector. The collimator used in the experiment is a CDT 660 (Inframet Co., Stare Babice, Poland). The specifications are listed in Table 4. The experimental equipment is set up as shown in Fig. 7, and the athermal test is performed.

Figure 7. Experimental setup for the athermal test.

TABLE 4. Specifications of the collimator.

Parameters	Values
Focal Length (mm)	600
Aperture (mm)	60
Weight (kg)	10
Target	Half-moon, Four-bar
Four-bar Target Resolution (cy/mrad)	3

5.2. Test Methods

The camera is installed inside the temperature chamber as shown in Fig. 7, and it is mounted to be level with the collimator. Here, we should check whether the camera is operating correctly. After adjusting the temperature of the chamber and stabilizing the camera at that temperature, we check the sharpness of the image of the target at each zoom position. Typically, the resolution of a target, such as a four-bar, is visually checked during an athermal test to determine the camera’s optimal focus position. However, this method has the disadvantage that the degree of resolution for the image varies from observer to observer.

To solve this difficulty, we propose in-house software that can numerically represent the image contrast. We call that parameter the live contrast ratio (LCR). The position of the compensator at which the LCR value is highest can be defined as the best focus position, and this position is recorded. Using the LCR values, an additional test should be conducted to evaluate the validity of the zooming path for athermalization at each temperature. This test is conducted to verify how well the target is resolved at different magnifications and temperatures. For the athermal test, the chamber’s temperature range is set from −30 ℃ to 50 ℃. This temperature section is set up by dividing it into 10 °C intervals.

After setting the chamber temperature to 50 ℃ and stabilizing it for about two hours, we should check the image of the half-moon target emitted from the collimator. This sequence of experimental steps is shown in Fig. 8. The test results show good agreement with the simulated athermal analysis data across all temperature ranges.

Figure 8. Athermal test procedures.

5.3. Athermal Test Results

The athermal test is conducted with two main objectives. The first goal is to verify the applicability of the simulated athermal analysis results to the actual operational software of the LWIR camera. The second purpose is to make sure that this automatic focusing function works normally by inputting data obtained from the athermal test into the equipment software.

Figure 9 illustrates the images with the highest LCR for the half-moon target by the LWIR zoom lens. The compensation lens position yielding the highest LCR is used to define the optimal focus position. Figures 10, 11, and 12 show the compensation lens displacements measured from the reference position of 20 ℃ with temperature at each zoom position, and they are compared to those of the simulated athermal analysis results. From Figs. 10, 11, and 12, it can be confirmed that both results are almost the same. The actual compensation lens moves linearly at all zoom positions, which is also similar to the simulated athermal analysis.

Figure 9. Live contrast ratios measured at each zoom position with various temperatures.

Figure 10. Comparison of the simulated athermal analysis results and actually measured results at the tele position.

Figure 11. Comparison of the simulated athermal analysis results and actually measured results at the middle position.

Figure 12. Comparison of the simulated athermal analysis results and actually measured results at the wide position.

There is no noticeable variation between the simulated athermal analysis and real test results at all zoom positions and temperature ranges. When measured at extreme temperatures of −30 °C and 50 °C, a small deviation is observed at the middle position, with a value of 0.0735 mm at −30 °C. When the compensation lens (L4) moves by 0.0735 mm, that yields an image plane shift of approximately 0.0437 mm. Since this value is less than the allowable depth of focus of 0.102 mm, it has a negligible effect on the optical system’s performance. Therefore, it can be confirmed that there are no significant issues even if the system is operated only by the results of the simulated athermal analysis.

However, to achieve more accurate athermalization performance, we implement an autofocus adjustment function by inserting the data obtained from real athermal testing into the equipment. It is necessary to verify whether the imaging performance meets the relevant requirements by using a target corresponding to 3 cy/mrad. Since this experiment is a test to check whether the autofocus function works normally, it is carried out in 10 °C intervals from 10 °C to 40 °C. Upon activation of the autofocus function, one can observe that the four-bar targets are clearly resolved for each zoom position, as shown in Table 5.

TABLE 5. Resolved images of the four-bar targets after autofocusing at each temperature and zoom position.

Position	Temperature (℃)
	10	20	30	40
Tele Position
Middle Position
Wide Position

We have obtained the temperature-dependent polynomial coefficients that were extracted from the compensation lens displacement measured at various temperatures, and they have been applied to the encoder. Through the athermal test outlined above the athermal test outlined above, it is confirmed that the proposed autofocus function in this study works well.

In order to verify the autofocus function derived from the laboratory, outdoor tests were conducted on the developed camera in two different environments.

The first test is to obtain the images for buildings 1 km away at tele and wide positions while keeping the camera on the ground. This experiment is to check whether the autofocus function performs well at each zoom position. The weather conditions during the test are as follows: Visibility of 15 km, temperature of 10.5 °C, and humidity of 55%. The exposure time of this system is automatically set. The LWIR image is displayed by receiving a 14-bit image from the sensor of the camera. This means that the pixel values are in the range of 0 to 16,384 (2¹⁴).

The automatic exposure time is defined in such a way that the range of pixel values in the image is between 30% and 40%. In this outdoor test, the automatic exposure time is 8 ms, and the average image pixel value is 5,542 (33%). Figure 13 shows the test results for outdoor images at tele and wide positions. Thus, the image is notably resolved for each zoom position. In the case of the tele position, details such as the window frames in buildings are distinguishable.

Figure 13. Outdoor images taken at 1 km (at 10.5 ℃): (a) image at the tele position and (b) image at the wide position.

The second test is to obtain the images of a vehicle located 600 m away at the tele position by mounting the camera on an actual operational drone at an altitude of 500 m above ground level. This is to ensure that the autofocus function performs well even in the following operating environments: Visibility of 15 km, temperature of 30 °C, and humidity of 60%. The exposure time is 8 ms, and the average image (pixel) level is 5,897 (36%). As shown in Fig. 14, the target vehicle is clearly observed, confirming the success of imaging.

Figure 14. Outdoor test image taken at a slant range of 0.6 km (at 30 ℃).

As a result, these two outdoor tests confirm that the proposed autofocus system in this study performs well at all zoom positions.

Through the defocus sensitivity analyses owing to temperature change, we have simulated athermal analysis for the 3× LWIR zoom camera lens. In addition, to verify that our athermal approach is effective, we have performed real athermal tests over a wide temperature range of −30 °C to 50 °C. During the athermal tests, we gradually lowered the temperature from 50 °C to −30 °C and observed images at various temperatures.

From the simulated athermal analysis, we first set the position of the compensation lens at the corresponding temperature and zoom position. Then the compensation lens was elaboratively moved to serve the highest LCR for the target, which yielded the accurate measurement of LCR, regardless of the observer. From this experiment, it was confirmed that the compensation lens locations in the actual test results were closely matched to those in the simulated athermal analysis.

The compensation lens positions obtained from the previous athermal test results were entered into the encoder to activate the autofocus function. Subsequently, images of a four-bar target were acquired at various temperatures and zoom positions to verify the image resolution. Notably, the target was effectively resolved within the operational temperature range.

To verify the autofocus function derived in this study, outdoor tests were conducted on the developed camera in two different environments. The first test was to obtain images for buildings 1 km away at tele and wide positions while keeping the camera on the ground.

The second one was to obtain images of a vehicle located 600 m away at the tele position by mounting the camera on a drone at an altitude of 500 m above ground level. Clearly resolved images were obtained for both outdoor tests at each zoom position. Thus, these two outdoor tests confirm that the autofocus system suggested in this study performs well at all zoom positions.

In conclusion, the proposed athermal analysis and test approaches are expected to provide a useful means of realizing an athermal system.

We would like to express our thanks to Siyoun Choi of LIG Nex1 for support in manufacturing and measurement.

Agency for Defense Development Grant Funded by the Korean Government (912984301).

The authors declare no conflicts of interest.

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.