I. INTRODUCTION
Recently, there has been a need to develop a technology to obtain three-dimensional (3D) image information at high speeds, while processing and tracking image information in real time. 3D image sensors, which are a core component of LADAR (Laser Radar) systems, have been developed from single-pixel detectors to focal-plane arrays (FPAs). Because LADAR sensors have high spatial resolution and can provide high resolution, they have the advantage of enabling the identification of even hidden objects, by acquiring and processing 3D images in many directions[1-3]. LADAR sensors can be used in the application ofLADAR to aviation [4]. LADAR systems are being developed for the acquisition and fusion of 3D LADARimages with 2D CCD camera images, or infrared camera images [5, 6]. Optical systems that use a combination of LADAR sensors, CCD sensors, and infrared sensors are being developed as common optical systems for high-speed operation and downsizing. LWIR (Long WavelengthInfrared) sensors are non cooling types, and have advantages for downsizing and weight reduction; moreover, target identification is possible day or night.
When optical systems using LADAR sensors are designed, the detection-range analysis should be considered first. The detection range is determined by the laser output power, ambient conditions, and detector and optical system specifications. The ambient conditions should be considered during system design because they affect the detection range and laser pointing errors of the LADARsystem. For a LADAR optical system, the optimum diameter of the entrance pupil can be determined by analyzing the detection range of the pupil, considering the operating conditions of the LADAR system. When a common optical system using both LADAR and infrared sensors is designed, the specifications for the LADAR camera should be determined first, because the target detection performance of a LADAR camera is lower than that of an infrared camera. In particular, the entrance pupil of the LADAR optical system is a parameter that becomes a standard when a common optical system is designed.In the present study, the LADAR detector was analyzed,to obtain the minimum detectable signal of the 3D-image capturing LADAR detector; the refractive-index structure was calculated, to analyze the ambient conditions; and the detection range of the LADAR sensor was analyzed, to obtain the diameter of the entrance pupil of the LADARoptical system. Using the results of analysis and calculation,a common optical system using LADAR sensors and LWIRsensors was design and analyzed.
II. ATMOSPHERIC-CONDITION ANALYSIS
When a laser beam passes through the atmosphere, it is attenuated or its optical path changes depending on the atmospheric air conditions. The refractive-index structure function was analyzed, to determine changes in the path of the laser beam due to atmospheric air turbulence. The refractive-index structure function was obtained by analyzing the Hufnagel-Valley model and the Miller-Zieske model.The Hunfnagel-Valley model is expressed as a refractive index structure function, as shown by the following formula [7].
\(C_{\mathrm{m}}^{2}(h)=5.9 \mathrm{d} \times 10^{-23} e^{-\mathrm{h}}\left(\frac{W}{27}\right)+2.7 \times 10^{-16} \mathrm{e}^{-2 \mathrm{h} / 3}+1.7 \times 10^{-14} \mathrm{e}^{-10 \mathrm{h}}\)(1)
where h is the altitude and W is an adjustable wind correlating parameter of 21 [8].
The Miller-Zieske model is expressed as a refractiveindex structure function for the daytime model Eq. (2)and the night model Eq. (3) as shown in the followingformulas [9].
\(\begin{array}{rl} C_{n}^{2}(h)=1.7 \times 10^{-14} & 0 (2)
\(\begin{aligned} C_{n}^{2}(h) &=8.4 \times 10^{-15} & & 0 (3)
where h represents the altitude.
Figure 1 shows the refractive-index structures for the atmospheric air models, for different altitudes. When the LADAR sensor is used as a LADAR navigator, the effects of atmospheric air on the altitude must be considered. In general, the LADAR navigator has been reported to be operated at an altitude of 200 m [10] and a slant range of1,000 m [11]. As shown in Fig. 1, the refractive-index structure shows a tendency to increase as the altitude decreases, which generates the beam-wander effect. When the laser beam penetrates the atmosphere, the optical path is affected by the beam-wander effect so that the laser beam irradiates several points instead of one point on the target. At an altitude of 200 m, the refractive-index structure function was calculated as 2.54 × 10-15 m-2/3 when the Hufnagel-Valley model was applied, and as 1.20 ×10-15 m-2/3 and 2.5 × 10-16 m-2/3 for daytime and nighttime in the Miller-Zieske model respectively. According to the literature, the refractive-index structure is divided according to atmospheric air conditions (turbulence strength) into 5 ×10-14 m-2/3 under strong conditions, 1 × 10-14 5 × 10-15 m-2/3under moderate conditions, and 1 × 10-15 m-2/3 or lower under weak conditions. When calculating the detection range,the refractive-index structure was set to 5 × 10-15 m-2/3, considering the calculated values and the literature [12].
FIG. 1. Refractive-index structures for the atmospheric airmodels, in relation to the altitude.
III. LADAR SENSOR DETECTION-RANGEANALYSIS
Detectors intended to satisfy the required performance of LADAR basically use linear-mode avalanche photodiodes(LMAPD) or Geiger-mode avalanche photodiodes (GMAPD)[13]. The LMAPD operates at a bias voltage that is lower than the breakdown voltage, and is used together with a current-amplifying stage. The GMAPD is used at a bias voltage that is not lower than the breakdown voltage, and can detect weak signals at the level of a single photon; however, it has a characteristic of responding to photons only once during the detection time. Applying the GMAPDin LADAR systems is advantageous in securing the maximum detection-range performance, because its photon sensitivity is higher than that of the LMAPD. However, itis vulnerable to various types of noise, and cannot easily distinguish materials based on reflectivity, because it measures only the time to return after being reflected. TheLMAPD has strong noise characteristics, plus the advantage of relatively easy image implementation, because it can measure the pulse shape and intensity of the laser being reflected [14]. In the present study, the performance specification of the OptoGration Co.’s (In,Ga)As-(In,Al)As-based LMAPD was applied, to consider laser wavelengths and enhance the detected target tracking performance. The LADAR detector specification is provided in Table 1. The detector can amplify signals 10 times at a voltage of 0.55V; in this case, the responsivity is 6.1 A/W, and the dark current is not higher than 25 nA. The noise equivalent power (NEP) is 4.1 nW. When the threshold value for recognition of laser signals as pulses by the system is assumed to be five times the noise-equivalent power, to stably detect the laser signals reflected by the target, the minimum detectable signal at the LADAR system applied with the detector is calculated as 20.5 nW. The applied specification is a result of fabrication of 100 pixels percm2, and lower dark-current specifications are expected tobe implemented when APD sensors with 128 × 128 pixels and 100 µm pitch are fabricated.
TABLE 1. LADAR sensor specification
To determine the parameters for the design of a common optical system, the detection range of the LADAR sensor should be evaluated. As the pulsed laser beam generated by the laser light source passes through the atmospheric air, its peak output power is reduced. The laser beam incident on the target is reflected only partially, depending on the size of the target and the angle of incidence and reflectivity of the laser beam. Out of the reflected laser beam, only the quantity of light corresponding to the size of the entrance pupil of the LADAR optical system is received by the LADAR sensor. The LADAR sensor processes signals only when laser signals exceeding several times the circuit noise have been received, and recognizes the target thereafter through the algorithm. The detection range can be calculated using Eq. (4) [15].
Current Optics and Photonics, Vol. 3, No. 1, February 2019
where \(E_{\text {Pulse }}\) is the energy per laser pulse, ∆t is the laser pulse width, \(T_{T z}\) is the transmissivity of the laser designator,\(\alpha_1\) is the atmospheric air’s extinction coefficient between the laser designator and the target, \(R_1\) is the distance between the laser designator and the target, \(\rho\) is the target’s reflectivity, \(\theta\) is the angle between the laser designator and the camera, H is the height of the footprint, W is the width of the footprint, \(u_{B S}\) is the bore-sight error, \(\alpha_2\) is the atmospheric air’s extinction coefficient between the target and the receiving part, \(R_2\)is the distance between the target and the receiving part, \(D_{R{x}}\) is the diameter of the entrance pupil of the receiving part’s optical system, \(\tau_{R x}\) is the transmissivity of the receiving part’s optical system, \(\delta_b\) is the laser beam’s divergence angle, \(\delta_j\) is the jitter of the laser designator, \(\lambda\) is the laser’s wavelength,and \(C_{n}^{2}\) is the refractive-index structure function.
Table 2 shows the parameters used for calculating the detection range of the LADAR sensor. For the laser designator, a laser with 1540 nm wavelength was selected, considering laser eye safety. The laser beam’s divergence angle was set to 4°, identical to the field of view of the optical system. It was assumed that there is no alignment error between the laser designator and the camera. The jitter of the laser designator was set to 50 µrad, which is a general value. The atmospheric air’s extinction coefficient of 0.057 km-1 is a value corresponding to a visibility of 15km, derived using the commercial software PcModwin 4.0.The refractive-index structure function was set to 5 × 10-15m-2/3, as shown in Fig. 1. The target’s size is identical to the laser beam’s size at a point 1000 m from the laser designator, and this indicates that the transverse mode of the laser beam is square. The target’s reflectivity was set to 30%, which is a general condition. The laser designator and camera were assumed to have been installed in the same equipment, and the LOS (line of sight) angle was setto 0°. The distance between the laser designator and the target of the LADAR sensor was set to 1000 m or less.To analyze the quantity of light received according to the diameter of the entrance pupil, the quantity of light was calculated for entrance pupils with diameters of 5, 7, 10,12, and 15 cm. The laser designator and camera were assumed to have no optical loss.
TABLE 2. Detection-range calculation parameters
Figure 2 shows the quantity of laser light received per pixel of the LADAR sensor, according to the entrance-pupil diameter of the optical system in relation to the distance.The calculation was conducted using Eq. (4) and the parameter values shown in Table 2. The received quantity of laser light shows a tendency to decrease as the target range increases, and at a given distance, a larger quantity of laser light is received when the diameter of the entrance pupil is larger. At the maximum detection range of 1000 m, when the diameter of the entrance pupil was 5, 7, 10, 12,and 15 cm, the quantity of light received per pixel of the LADAR detector was calculated as 2.5, 4.8, 9.9, 14.2, and22.3 nW respectively. The target can be detected even when diameter of the entrance pupil is 15 cm, because the quantity of light received is larger than the minimum detectable signal of 20.5 nW. However, for the diameter of the entrance pupil, atmospheric air attenuation under various conditions should be considered.
FIG. 2. The quantity of laser light received per pixel of the LADAR detector, as a function of target range, for several diameters of the entrance pupil of the optical system.
Figure 3 shows the quantity of laser light received per pixel of the LADAR detector versus the diameter of the entrance pupil, for different atmospheric extinction coefficients. The calculation was conducted using Eq. (4)and the parameter values shown in Table 2. The received quantity of laser light shows a tendency to increase as the diameter of the entrance pupil’s target range becomes larger, and at a given diameter of the entrance pupil, a larger quantity of light of laser is received when the atmospheric air’s extinction coefficient is smaller. According to the results of the LADAR detector analysis, when the SNR is not smaller than 5, laser signals can be detected in cases where the quantity of laser light received is at least20.5 nW. In cases where the diameter of the entrance pupil was 15.7 cm, when the atmospheric air’s extinction coefficient value was 0.140, 0.081, and 0.039 km-1, the quantity of light received per pixel of the LADAR detector was calculated as 20.7, 23.3, and 25.3 nW respectively.The analysis indicates that to obtain detection ranges not shorter than 1000 m, the diameter of the entrance pupil should be at least 15.7 cm, regardless of the atmospheric airs extinction coefficient. The diameters of the entrance pupil shown in Fig. 3 are applied when the common optical system is designed, which will be explained in the following chapter.
FIG. 3. The quantity of laser light received per pixel of the LADAR detector, as a function of diameter of the entrance pupil, for several extinction coefficients.
Figure 4 shows the pointing error versus target range,according to refractive-index structure. Pointing errors are caused by laser-beam divergence angles, laser-beam jitter,and refractive-index structure. Although the laser-beam divergence angles and jitter are output-power characteristics of the laser light source, the refractive-index structure differs depending on the ambient conditions. The laser pointing error was calculated using Eq. (4). At the target range of 1000 m, when the refractive-index structure increases to 1 × 10-15, 5 × 10-15, 1 × 10-14 and 5 × 10-14 m-2/3,the pointing error also increases to 3.9, 10.3, 15.7, and41.1 µrad respectively. That is, at the target range of 1000m, the laser beam irradiated to the target varies by 4.1 cmat most, because of the beam-wander effect. In the case where the field of view of the optical system is assumed to be 4 degrees and the measurement resolution for 1 pixel of the LADAR detector is assumed to be 54.6 cm at the target range of 1,000 m, the laser pointing error due to refractive-index structure is identified to be 7.5%.
FIG. 4. Turbulence contributions to target range, according to refractive-index structure function.
IV. DESIGN OF A COMMON OPTICAL SYSTEM
Figure 5 shows the ray tracing and layout of the designed common optical system. The common optical system was composed of a LADAR optical system and aLWIR optical system, to receive the energy reflected and radiated by the target. The energy of the target enters the optical system through the common lens group, and is split into the LADAR wavelength band (1.54 µm) and the LWIR wavelength band (7.75~12.77 µm) by the beamsplitter. The LADAR wavelength band penetrates the beamsplitter to progress, and is concentrated on the LADARsensor face through the LADAR lens group. The LWIRwavelength band was designed to be reflected by the beamsplitter and concentrated on the LWIR sensor face through the LWIR lens group. From the results of the detection range analysis, the diameter of the entrance pupil of the LADAR optical system was designed as 15.7 cm, and ata target range of 1000 m the ground spot diameter is69.81 × 69.81 m. The optical system’s design specification is provided in Table 3.
FIG. 5. Ray tracing and layout of the designed common optical system
TABLE 3. Optical system design specification
Table 4 shows the lens data for the LADAR optical system. Table 5 shows the lens data for the LWIR optical system. For the common lens group, zinc sulfide was selected as the lens material, so that the LADAR and LWIRwavelength band energies would penetrate simultaneously.The common lens group consists of two ZnS lenses. The first lens was selected to have positive refractive power,while the second lens was selected to have negative refractive power. To minimize sensitivity to fabrication and assembly, all of the common lenses were made to have spherical surfaces, rather than aspherical. The beam splitter plays the role of allowing the LWIR wavelength band to penetrate, while reflecting the LADAR band. The transmission and reflection performances could be optimized through multilayer-thin-film technology. The beam splitter is tilted 45 degrees to reflect the LADAR energy. The LADAR lens group plays the role of minimizing the residual aberration of the rays that have penetrated through the common optical system. This lens group was composed of three ZnS lenses and a band-pass filter, and included one or more aspherical surfaces. For the band-pass filter,a half-width of 100 nm was selected to obtain high transmissivity. The LWIR lens group was also composed ofthree germanium lenses, to minimize the residual aberrations of the rays that have penetrated through the common optical system, and it included one aspherical surface.
TABLE 4. LADAR optical system lens data
Figure 6 shows the results of the spot diagram andMTF analysis by field, conducted through LADAR optical system ray tracing. The spot diagram in Fig. 6(a) shows that the root-mean-square (RMS) geometric spot size is 2.2µm and the total geometric spot size is 4.2 µm, based on zero field; this indicates that the pitch of 1 pixel is 100µm or less. As shown in Fig. 6(b), the MTF of all fields is 98.8% of the MTF of the diffraction limit, at the spatial frequency of 5 cycles per millimeter.
FIG. 6. (a) Spot diagrams and (b) MTFs of the LADAR optical system, according to the field.
Figure 7 shows the results of analyses of the spot diagrams and MTFs of the LWIR optical system. The spot diagram in Fig. 7(a) shows that the RMS geometric spot size is 9.4 µm and the total geometric spot size is 16.6µm, based on zero field; this indicates that the pitch of 1pixel is 17 µm or less. As shown in Fig. 7(b), the MTF of all fields is 92.4% of the MTF of the diffraction limit, at the spatial frequency of 29 cycles per millimeter.
FIG. 7. (a) Spot diagrams and (b) MTFs of the LWIR optical system, according to the field.
Figure 8 shows the probabilities of detection, recognition,and identification by the LWIR optical system, according to distance. To analyze the detection performance of the designed LWIR, the commercial software Night VisionThermal Imaging Systems Performance Model (NVTherm 2002) was used; Table 6 shows the parameters used in the performance analysis. The optical system’s parameters are reflected in the LWIR optical system’s design specification.The transmissivity values for one lens, the beam splitter,and the detector window were calculated as 97%, 80%,and 95% respectively. For the detector, the specification ofa commercial detector with 640 × 480 pixels was reflected.The atmospheric air’s transmissivity was calculated on the basis of 15 km of visibility under good weather conditions,and atmospheric turbulence was assumed to be moderate.The temperature difference between target and background is 2 K, and the target size is 6.5 × 6.5 m. The criteria for detection, recognition, and identification according to distance were set to 3, 6, and 9 cycles. Analysis of the LWIRoptical system as a function of distance showed that the detection range is 5.14 km, recognition distance is 2.82 km, identification distance is 1.96 km, based on a probability of 50%.
FIG. 8. Probabilities of detection, recognition, and identification for the LWIR optical system, according to distance.
TABLE 6. Parameters for LWIR optical system detectionrange analysis
V. CONCLUSION
In the present study, a common optical system was investigated for the acquisition and fusion of 3D LADARimages together with infrared-camera images. The therefractive-index structure has been observed to have larger beam-wander effects as the altitude decreases, and the maximum beam-wander effect of 2.54 × 10-15 m-2/3 was identified at an altitude of 200 m. An analysis of the pointing error by refractive-index structure of the target range revealed that the maximum variation is 4.1 cm at a target range of 1000 m. An array detector using 128 ×128-pixel linear-mode avalanche photodiodes capable of implementing large-area images was analyzed. The minimum detectable signal necessary for the LADAR system to stably detect the laser signal reflected from the target was calculated to be 20.5 nW. Analysis of the detection range of the LADAR sensor revealed that the diameter of the entrance pupil should be greater than 15.7 cm to detect the target at a range of 1000 m, regardless of the atmospheric air attenuation. A common optical system using LADARsensors and LWIR sensors was designed and analyzed. For the LADAR optical system, the MTF of all fields was shown to be 98.8% at a spatial frequency of 5 cycles per millimeter. For the LWIR optical system, the MTF of all the fields was shown to be 92.4% at a spatial frequency of 29 cycles per millimeter. The detection, recognition, and identification distances of the LWIR optical system were found to be 5.14, 2.82, and 1.96 km respectively, at a probability of 50%. In the future, the optical system using LADAR sensors and LWIR sensors will be useful for the take-off and landing of drones or unmanned air vehicles, and can be used to prevent the collision of helicopters or drones.
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