With the development of science and technology, laser semi-active guided weapons play an important role in modern warfare. In many actual battles, the laser semi-active guided weapon plays the key roles of clearing fixed points and attacking moving targets. Due to the particularity of the application, the requirements for shooting accuracy are getting higher [1, 2]. However, there are many factors that restrict the accuracy of guided-weapon firing, and the irradiation accuracy of the irradiation source is one of the key factors. The purpose of this paper is to analyze the irradiation accuracy of the laser-irradiation source by designing a laser-irradiation-accuracy test system. This test system has great potential in improving the guidance precision of guided weapons.

Generally, there are two methods of laser-irradiation-accuracy testing: the direct test method, and the indirect test method. The direct test method is to install multiple sets of detector arrays on the test target board, with the laser being directly irradiated upon the target-board detector for detection. Subsequent signal processing is used to obtain the laser spot’s energy-density distribution. The center of gravity of the light spot is compared to the known center of mass of the target plate, thereby obtaining the irradiation accuracy. The direct test method is characterized in that it can be directly measured without intermediate transmission changes, and at the same time the energy of the laser beam irradiated upon the target can be measured. The disadvantages are the limited testing range and the lack of measurement accuracy of the light spot’s image. The method only works for a light spot that has a detector on the target plate, and the number of detectors is generally in the hundreds. It is difficult to ensure the consistency of the detector; when the detector is used for a long time, its response rate will change, which greatly reduces measurement accuracy.

Therefore, in this paper we use the indirect test method, where a diffuse-reflection target board is used to receive the incident laser beam, and then a charge-coupled devices (CCD) is used to track and collect the laser spot on the target board to obtain the laser spot’s image. The spot size and the coordinates of its center of gravity are analyzed to calculate the laser-irradiation accuracy. The indirect test method possesses the advantages of convenient operation, high sensitivity, low output noise, large dynamic range, good stability, and no contact. It can directly obtain the light-intensity distribution of the laser spot [3].

In this indirect test method, the key issue is to design an optical system that meets the test requirements, so that the target plate at a certain distance along with the spot illuminated on it can be imaged, and a certain target resolution requirement can be met.

A reasonable design scheme is the key to the realization of such a test system. The laser-irradiation-accuracy test contains an irradiation-distribution test and an irradiation-capability test, according to the test requirements. It is necessary to provide both the distributions of the light spot at a certain distance and the actual position of the center of gravity of the light spot. According to the actual needs, the CCD imaging method is selected for detection. Because the wavelength of the laser beam is in the near infrared and the target is in visible light, in this article we select the proper detection device to suit this wavelength range. According to the index of the detecting device, the parameters of the optical system are calculated, the optical structure is designed, and the influence of stray light in the structure is analyzed [4].

2.1. System Indicators

The measured target is located at a distance of 1 km, the target size is 4.6 m × 2.3 m, and the spot diameter is 1.5 m. The camera’s field of view is required to be less than 3°, and the accuracy of the hit-ratio measurement is 100 mm (relative to the target plate).

2.2. Camera Selection

The test system consists of a telephoto optical system, CCD imaging system, image-processing system, and an industrial computer. Because visible light (target) and near-infrared light (spot) are imaged on the same CCD at the same time, a camera with good spectral response in both the visible and near-infrared bands must be selected.

According to the requirements for the CCD, the XSW-640-TE1 CCD (XenICs, Seoul, Korea) is selected. It has the advantages of a wide response range and good response characteristics at visible and near-infrared wavelengths. The specific parameters are shown in Table 1 and Fig. 1.

TABLE 1. Main parameters of the XSW-640-TE1 camera.

Index	Value
Spectral range	400 nm–1700 nm
Image format	640 × 512
Pixel pitch	20 μm
Image size	12.8 mm × 10.24 mm
Response	0.4 A/W (550 nm), 0.8 A/W (1064 nm)
Frequency	100 Hz
Camera size	45 m (W) × 45 mm (H) × 37 mm (L)

Figure 1. The spectral response curve of the XSW-640-TE1 CCD.

Through analysis, the responsivity of the camera is about 0.4 A/W at 550 nm and about 0.8 A/W at 1064 nm, which meets the detection requirements for target plates and near-infrared spots.

2.3. Determination of the Optical System’s Parameters

2.3.1. Focal length

The imaging optical system installed on a turntable is used for imaging with a moving target plate 1 km away. To image the target plate on the CCD at all times, the imaging surface of the target plate is designed to occupy only 1/6 of the CCD size. The focal length of the optical system can be obtained by

where D is the diagonal dimension of the target plate, L is the distance between the imaging optical system and the target plate, and d is the diagonal dimension of the CCD image. In this design, D = 5.2 m, L = 1 km, and d = 16.4 mm. According to Eq. (1), the focal length is calculated to be 540 mm.

2.3.2. Field of view

The full-field angle of the optical system can be obtained by

The full field angle 2 ω of this optical system is calculated to be 1.74°, which satisfies the requirement that the camera’s field of view be less than 3°.

2.3.3. F-number

The imaging optical system usually requires that the diameter of the Airy spot be smaller than one pixel. The diameter of the Airy spot is calculated by

where d_airy is the Airy spot’s diameter and l is the wavelength. The system is aimed at imaging a visible-light target plate and near-infrared spot. Therefore, the diameter of the Airy spot of the visible-light target-plate imaging and the near-infrared spot imaging should be less than one pixel. The pixel size of the CCD is 20 μm, the visible-light wavelength is 560 nm, and the near-infrared wavelength is 1064 nm. After calculation, F_visible is 14.6, F_infrared is 7.7, and F is finally set to 7.5.

2.4. Structural Design and Image-quality Evaluation of the Optical System

Since this system is aimed at imaging the visible-light target plate and the near-infrared light spot, the visible-light target plate involves the spectral range 486–656 nm, while the infrared spot’s spectral range is 1000–1100 nm, and the system’s focal length f ̍ = 540 mm and aperture is 72 mm.Taking into account that stray light needs to be eliminated, that the laser-irradiation-test system must be easy to install on the tracking turntable, and that the system needs to be miniaturized, this system adopts an improved Cassegrain format. The improved Cassegrain system is a fold-reflection optical system, which can greatly reduce the tube length and chromatic aberration [5, 6]. In a traditional Cassegrain system, the primary mirror is a paraboloid and the secondary mirror is a hyperboloid. Parabolic and hyperbolic machining is difficult, and shape detection is complex. Therefore, an improved Cassegrain system is needed in which the primary and secondary mirrors are spherical [7, 8]. However, for long-distance objects, spherical mirrors have undercorrected spherical aberration. Spherical aberration is calculated by

When the incident height h and refractive index n are constant, the smaller the value of f, the smaller the absolute value of the spherical aberration generated. Therefore, on the object side, a low-optical-power lens group is added to correct the system’s spherical aberration.

Symmetrical structure has a good correction effect on aberrations. A symmetrical structure can reduce system coma, astigmatism, field curvature, and distortion. The achromatic condition is

A combination of positive and negative lenses made of two glasses with different Abbe numbers can achromatize. To avoid the optical power being too large, the difference between the Abbe numbers of the two glasses should be as large as possible. Our system contains a symmetrical double-cemented lens group. The materials used in the first group of double gluing are ZF2 and K4, and those of the second group of double gluing are K9 and ZF2. To eliminate stray light, we use a secondary imaging optical system, which can be placed near the primary imaging surface to reduce stray light [9]. The optical system’s structure is shown in Fig. 2.

Figure 2. Structure of the optical system.

Then Zemax software (Zemax, WA, USA) is utilized to optimize the optical system. The system’s Modulation Transfer Function (MTF) curves are shown in Figs. 3 and 4. At the Nyquist frequency, when the wavelength is within 486–656 nm the modulation transfer function (MTF) value is 0.82 (25 lp/mm), which is close to the diffraction limit, and when the wavelength is within 1000–1100 nm the MTF value is 0.42 (25 lp/mm), which meets the imaging requirements. In this system we need to measure the light spot and the center of mass of the target plate, so the system has strict requirements for distortion. The optical system’s distortion is shown in Fig. 5; the full-field distortion is less than 0.18%. The spot diagrams for the optical system are shown in Figs. 6 and 7; it can be seen that the maximum root-mean-square radius of the visible-wave-band spot diagram is 3.162 μm, while that of the infrared-wave-band spot diagram is 16.228 μm. The energy-concentration curve is shown in Fig. 8, which shows that the energy concentration in the enclosing circle with a radius of 10 μm reaches about 90%, which can meet the system’s requirements.

Figure 3. MTF of the visible-light optical system.

Figure 4. MTF of the infrared-band optical system.

Figure 5. Distortion of the optical system.

Figure 6. Spot diagram of the visible-light optical system.

Figure 7. Spot diagram of the infrared-band optical system.

Figure 8. Energy-concentration curve for the system.

2.5. Methods of Eliminating Stray Light

Generally, stray light in a Cassegrain system has a great impact on the imaging of the system. To prevent stray light from entering the optical system, an outer baffle is added between the primary and secondary mirrors. To eliminate stray light in the lens barrel, we add a vane to the inner wall of the outer baffle to add an inner baffle to the primary imaging surface, and roughen the inner wall of the cone lens barrel, and paint the inner wall of the lens barrel black [10]. The mechanical structure of the optical system of the laser-irradiation-accuracy test system is shown in Fig. 7.

3.1. Principle of Measurement

As the target plate under test is moving, the measuring equipment must be installed on a turntable to track the target as the turntable rotates. To facilitate tracking, the target plate is always imaged on the CCD, and the imaging surface of the target plate is designed to occupy only 1/6 of the CCD’s area. The light spot occupies about 1/20 of the CCD. The target plate and the spot are imaged on the CCD at the same time. The CCD camera converts the optical image into image data and transmits them to the data-processing system. After digital image processing, the center of gravity of the spot and the center of mass of the target are extracted. The irradiation accuracy can be measured and analyzed in real time, and output to the industrial computer for real-time image display and data archiving.

3.2. Error Analysis

In the test of hit accuracy, the measurement accuracy is determined by the accidental error of several-pixel energy center of gravity, and the discrimination error of the center of mass.

3.2.1. Error analysis of accidental multipixel energy center of gravity test

The occasional errors that affect the accuracy of a single-pixel energy density test are: consistency accuracy of camera pixels, linearity accuracy of camera-pixel energy response, and consistency accuracy of diffuse reflectance of a diffuse target. The accidental error s₀ = 9.2% of the measurement precision of the energy density of a single pixel is obtained by analysis. To ascertain the effect of multiple pixels on the measurement accuracy of the center of gravity of the spot, one needs to know the number of pixels in the area covered by the spot. It is known that the spot’s diameter is 1.5 m at 1 km, and the width of the corresponding image on the CCD is 0.81 mm, which accounts for about 40 × 40 pixels. The impact on the entire center-of-gravity judgment is

Assuming that this uncertainty is applied to both ends of the spot pattern, the center of gravity’s deviation is

3.2.2. Analysis of the discrimination accuracy of the center of mass

When the focal length is f ̍ = 540 mm, the Airy spot diameter of the visible-light optical system is

and the Airy spot diameter of the near-infrared optical system is

The Airy spot diameters of the visible-light and near-infrared optical systems are both smaller than the pixel size of the CCD. Thus, the design is reasonable.

For the target plate, the discrimination accuracy of the CCD is

The corresponding target size is

For the light spot, the discrimination accuracy of the CCD is

The corresponding target size is

According to the accidental error of the measured energy center of gravity of the pixel and the discriminant error of the centroid [11], the accuracy that the energy center of gravity measurement can achieve is

The design meets the system indicators with a sufficient margin.

4.1. Equipment Calibration

The test equipment should be calibrated accurately before use, and the target plate and spot centers of mass should be calibrated respectively. The calibration of the target plate is to directly measure the center of mass of the crosshair of the target plate and compare it to the real coordinates of the crosshair. The calibration of the light spot uses a paper target with a circular Gaussian distribution pattern marked with the position of the center of gravity to measure the light spot, and compares that to the actual coordinates to verify the measurement accuracy. The specific measurement results are shown in Tables 2 and 3.

TABLE 2. Measuring the board’s deviation.

	X direction	Y direction
Actual value (cm)	230	115
Measured value (cm)	227.8	113.5
Deviation (cm)	2.2	1.5

TABLE 3. Measuring the Facular deviation.

	X direction	Y direction
Actual value (cm)	200	100
Measured value (cm)	196.2	101.8
Deviation (cm)	3.8	1.8

The target-plate centroid measurement deviation is 2.66 cm. The measurement deviation of the spot’s center of gravity is 4.2 cm.

4.2. Test Results

The measurement deviation of the target plate and the light spot can be eliminated as a systematic error; that is, a correction value is added to the measurement result to eliminate it. The actual measurement results after culling are shown in Table 4. Fig. 9 shows the coordinates of the actual measurement target.

TABLE 4. Measured data.

Index	Value
Frame number	1	2	3	4	5	6	7	8
Target centroid X coordinate	164	204	311	331	265	102	412	212
Target centroid Y coordinate	62	86	195	182	201	45	103	121
Facula barycenter X coordinate	170	196	315	320	271	109	406	219
Facula barycenter Y coordinate	70	81	196	178	196	51	108	126
X-direction total offset	6	8	4	11	6	7	6	7
Y-direction total offset	8	5	1	3	5	6	5	5
Total offset (number of pixels)	10	9.4	4.1	11.4	7.8	9.2	7.8	8.6
X-direction total offset (cm)	22.2	29.6	14.8	40.7	22.2	25.9	22.2	25.9
Y-direction total offset (cm)	29.6	18.5	3.7	11.1	18.5	22.2	18.5	18.5
Total offset (cm) (Offset of the exposure position)	37	34.8	15.2	42.2	28.9	34	28.9	31.8

Figure 9. Coordinate display of bull’s eye and centroid.

In this study, we use a catadioptric optical system to image a visible target plate and near-infrared spot, and the position deviation is obtained through image processing. Compared to a spectroscopic optical system in which the visible target plate and near-infrared spot are separately imaged and then fused, our design does not feature a two-image fusion process and a two-coordinate conversion process, which can reduce errors and increase the speed of processing data. Since only one camera is used, the mechanical weight is also reduced, as well as cost. According to the analysis in this article, the optical system’s design is reasonable and meets the project requirements.

In the proposed system, an improved Cassegrain system is used. Both the primary and secondary mirrors are spherical, which reduces processing difficulties. A front correction group and rear correction group are placed before and after the primary and secondary mirrors respectively, to increase the field of view and reduce aberrations. The methods of secondary imaging and placing an inner baffle on the primary imaging surface are used, greatly reducing the stray light that strongly affects the Cassegrain system. The actual test results show that when the test distance is 1 km, the measurement accuracy of the irradiation hit ratio is better than 50 mm, which is better than the required accuracy of 100 mm/km.

The authors gratefully acknowledge the support of the Changchun University of Science and Technology Foundation (No. XQNJJ-2018-08).