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The detector in a highly accurate and high-definition scanning 3D imaging lidar system requires high frequency bandwidth and sufficient photosensitive area. To solve the problem of small photosensitive area of an existing indium gallium arsenide detector with a certain frequency bandwidth, this study proposes a method for increasing the receiving field of view (FOV) and enlarging the effective photosensitive aperture of such detector through hexagonal prism beam splitting. The principle and construction of hexagonal prism beam splitting is also discussed in this research. Accordingly, a receiving optical system with two hexagonal prisms is provided and the splitting beam effect of the simulation experiment is analyzed. Using this novel method, the receiving optical system’s FOV can be improved effectively up to ±5°, and the effective photosensitive aperture of the detector is increased from 0.5 mm to 1.5 mm.
© 2016 Optical Society of America
1. Introduction
A scanning direct-detection 3D imaging lidar system with a wavelength of 1550 nm often operates in monostatic [1–5] or bistatic model [6–10]. For the monostatic model, the instantaneous receiving field of view (FOV) varies as the scanning mirror, is considerably small, and the return signal intensity is relatively weak. For the bistatic model, the stationary receiving FOV is required to be large enough for covering all the desired scanning areas, so the relatively large receiving FOV, compared to that of monostatic model, allows the return beam scattered from target to be collected onto the photosensitive area of a detector within a certain range of scattering angle, resulting in a strong return signal. Thus, a high-speed and high-definition 3D imaging lidar system operating under the bistatic model can obtain the desired signal intensity and signal-to-noise ratio.
However, the frequency bandwidth and photosensitive area of a detector are important factors in obtaining high speed and high definition for the imaging lidar. First, the frequency bandwidth of the detector should be considerably high. If the bandwidth is insufficient, then the less steep rising edge of the response pulse will affect the speed of time distinction, thereby decreasing the frame rate. Second, the photosensitive area of the detector should be substantially large to obtain a considerably large receiving FOV, as well as to receive additional return signal. Otherwise, collecting the return signal in a large receiving FOV onto the small photosensitive area of the detector is necessary. However, the corresponding receiving optical system is considerably complex to design; hence, researchers and lidar designers expect to find detectors with large photosensitive area with high frequency bandwidth. In the existing single-channel indium gallium arsenide (InGaAs) positiveintrinsicnegative (PIN) diode or avalanche photodiode (APD) detector that is suitable for 1550 nm, the one with a high-speed response has a small effective photosensitive area (with a of magnitude of 50 μm for the response bandwidth over 1 GHz). The photosensitive area of detectors with low bandwidth can have a magnitude of 1 mm. The bandwidth and photosensitive area of a detector are two opposite restrictions. By contrast, the PIN detector has a larger photosensitive area than the APD detector. The photosensitive aperture of the existing InGaAs PIN detector with bandwidth of over 500 MHz is approximately 0.3 mm (whereas the active area is 0.5 mm for 300 MHz).
The InGaAs detector array, can be large photosensitive area, that mainly comprises 64×64 and 128×128 pixels. For example, the total areas of the detector arrays are 3.2 mm×3.2 mm and 6.4 mm×6.4 mm. The linear detector array can be 1 ×N(N = 2, 4,···40) with the unit pixel at 70 μm. The linear array detector for 1550 nm in the experimental stage can be 256×1 components [11]. However, the disadvantages of this detector include high price and considerably complex signal processing. Furthermore, the detector array is mainly used in a flash lidar system, in which the current range measurement performance is still inferior to the performance of a single-channel detector [12]. By contrast, the single-channel detector has the advantages of low cost and relatively easy subsequent signal processing. Therefore, the single-channel detector is our preference for the current experiment.
To obtain high speed in a bistatic lidar system, as well as significant intensity of the return signal in certain receiving FOV, we preferred the single InGaAs PIN detector with a bandwidth of 300 MHz (the corresponding rising time is approximately 1.17 ns) and an active area of 0.5 mm. However, the detector with a photosensitive area of 0.5 mm is still limited in covering the return signal receiving FOV. Hence, this study proposed a method for increasing the receiving FOV and effective aperture of the detector in a 3D imaging lidar system with wavelength of 1550 nm, which is in a bistatic model and scanning type for direct detection. We used seven single-channel PIN detectors to construct a hexagonal detector lattice that is equivalent to enlarging the photosensitive aperture from 0.5 mm to 1.5 mm.
2. Principle of enlarging the detector′s effective aperture
Assuming that the spot of the laser emitted from the pulse laser is approximately 3.5 mm, this spot increases to 7.0 mm after being expanded twice and projected onto the target thereafter. The return laser beam from the target is collected onto a detector for time-of-flight measurement. The entrance aperture of the receiving optical system is designed to be 15 mm. To focus the return beam onto the photosensitive area of the detector, the receiving optical system needs to reduce the spot aperture of the return beam by at least 30 times, which is considerably complex and difficult in terms of optical design. Even if this process involved two steps, that is, focusing thrice initially and 10 times thereafter, completing the optical system design is still difficult. An alternative method is splitting the back beam into n equal components in which each component projects onto the detector (i.e., n portions correspond to n detectors). This process will make the optical design easy to complete. Note that the parameter n should not be large; otherwise, the optical system will be bulky and complex. Accordingly, we opted for n = 6 + 1 in our design.
Figure 1 shows that the receiving optical system mainly includes four components: telescope beam expander (not shown in Fig. 1), beam splitting, beam focusing, and a detector array constructed using seven single-channel InGaAs PIN detectors. The designed receiving FOV is ±5° (i.e., the sub-picture in Fig. 1 denoted as FOV of the incident beam, which illustrates seven different incident azimuths), the entire receiving FOV of 10° is divided into seven regions, and the center corresponds to 0°. The spot of each FOV region is designed to be 15 mm. After being divided into seven components, the incident beam becomes a hexagonal arrangement in space. By considering the size of the follow-up optical system, a twice expander lens is added in front of the hexagonal prisms. The reason for adding this lens is that when the incident angle of the beam θ is below 10°, the following relationship is established: [13]
where θ1, θ2 are the incident and emergent angles, respectively, of the expander system; and m is the expander magnification. Thus, FOV of the beam entering the hexagonal prisms is reduced to ±2.5°, which is half of the original FOV. Therefore, each of the seven components is equivalent to a beam with aperture of 10 mm. Thereafter, this beam is reduced 20 times and focused by the aspheric lens onto the photosensitive surface of the PIN detector with aperture of 0.5 mm. In the subsequent signal processing, the electrical signal from the seven detectors are added to produce a total signal. Hence, this process will achieve the goals of enhancing the detected signal intensity and increasing the receiving FOV to ±5°.Each FOV region experienced the beam splitting system and its laser signal can be obtained in all seven detectors. However, only the beam intensity received by the detectors varies with the FOV azimuths. The numbers marked in the detectors (see Fig. 1) refer to the detectors that will receive the strongest signal intensity of the return beams when the beam enters the hexagonal prisms in the corresponding FOV azimuths. For example, the number 1 means that the detector in the center will receive the major part of the return beam when the incident angle of the back signal is 0°.
2.1. One beam split into seven by a pair of hexagonal prisms
Figure 2 shows the hexagonal prisms, where a1 is the aperture of the small end face, h1 is the height, α0 = 45° is the angle between the lateral edge and bottom surface, and θ = 49.11° is the angle between the lateral face and bottom surface. A pair of hexagonal prisms can realize the beam split from one to seven because of symmetry (see Fig. 3(a)) for the case of the 0° incident angle. Figures 3(b) and 3(c) show the incident and emergent beam patterns, respectively.
Fig. 3 Simulation results of the beam splitting the hexagonal prism when the incident beam enters at an angle of 0°: (a) splitting optical path, (b) incident spot pattern, and (c) emergent beam spot patterns.
2.2. Arrangement of the aspheric lens array
As the beam has been split into seven parts, seven aspheric lenses are configured to focus them onto the detectors. The interval between the split beams is affected by the relative position of the two hexagonal prisms, as well as determines the ideal aperture of the aspheric lens. Furthermore, the interval influences the configuration of the aspheric lenses. To determine the aperture of the aspheric lens, discussing the distance (denoted as R) between the z-axis and the spot center of the emergent beams is necessary when moving away from the two hexagonal prisms.
Calculation is performed in the case of the 0° incident beam. Figure 4 shows that the distance R is associated with the position parameter of the incident beam on prism R0, the apertures of the two end faces of the prisms a1, and a2, the angle between the lateral surface and bottom surface θ, the height of the two hexagonal prisms h1 and h3, and the air interval h2. This relationship can be expressed as follows:
where α2 and γ2 are the incident and refraction angles of the beam, respectively, when traveling through the bottom surface of the prism; and tanθ = tanα = 1.155.Fig. 4 Schematic diagrams of the aspheric lens array: (a) relative position of the two hexagonal prisms and (b) configuration of the aspheric lens array.
Snell’s law states the existence of n0 sinθ = n1 sinγ and n1 sinθ2 = n0 sinγ2; and n1 = 1.458 is the refractive index of the F_SILICA, where n0 = 1 is the refractive index of air and parameter α2 that satisfies α2 = θ − γ. In our design, the relative parameters are selected as follows: R0 = 10mm, a1 = 15mm, a2 = 25.4mm, and R0 = 10mm, a1 = 15mm, a2 = 25.4mm. Substituting the equation tanθ = 1.155 into Eqs. (3) and (4), we can easily obtain tanα2 = 0.323 and tanγ2 = 0.5014. Thus, the relationship between the distance R and the h2 complies with
when h2 = 30.690mm, the distance R = 25.4mm; hence, the maximum radius of the aspheric lens should be 25.4mm. The aspheric lenses are arranged to maximize the use of space in receiving the return signal (see Fig. 4(b)). The same is true for the immersion lenses and detectors, with the distance between each adjacent array unit at 25.4mm (see Fig. 4(b)).2.3. Influence of reflection on the two hexagonal prisms
The reflectivity of a non-polarized light ρ is provided as follows: [14]
where θi and θt are the incident and refraction angles, respectively, with respect to the interface. Before leaving the hexagonal prisms, the return beam passes through four interfaces that are marked in Fig. 4(a). The total transmittance of the return beam in the optical path between two hexagonal prisms is as follows: where ρ1 and ρ2 are the reflectivity of the first and second surfaces, respectively, and T is the transmittance. when the incident angle θ = 49.11°, Eqs. (3), (4) and (6) easily obtain ρ1 = 0.05 and ρ2 = 0.0358, respectively, and reflectivity R = 1 − T = 16.1%. This result is due to an incident angle of 0°.In considering all the desired receiving FOV (i.e., the incident angle of the return beam θ1 varies from 0° to 5°), the relationship between the reflectivity of the two hexagonal prisms and the incident angle θ2 is shown in Fig. 5, where the incident angle θ2, which is half of θ1 based on Eq. (1), is with respect to the z-axis of the optical system. The curve shown in Fig. 5 implies a small percentage of energy loss because of the reflection among the prism surfaces, although the influence is not considerable. As the incident angle of the return beam increases, the reflectivity gradually decreases. In general, transmittance exceeds 83.9% in all the designed receiving FOV. To reduce the influence of reflection on energy transmission, the prism surfaces can be coated with infrared C-band anti-reflective coating for the working wavelength of 1550 nm.
3. Simulation experiment of the receiving optical system
3.1. Design of the receiving optical system
We designed a receiving optical system, including hexagonal prisms for beam splitting, by employing Zemax, an optical design software [15]. The wavelength is 1550 nm, FOV of the incident beam is set at ±5° in seven directions in the xy-plane: (0°, 0°), (5°, 0°), (2.5°, 4.33°), (−2.5°, 4.33°), (−5°, 0°), (−2.5°, −4.33°) and (2.5°, −4.33°). The entire receiving optical system designed by Zemax is shown in Fig. 6. This system comprises four components, namely, two expender lenses, a pair of hexagonal prisms, seven focusing aspheric lenses array, and seven hyper-hemispheric submersed lenses arrays with each of them attached with a detector. The hexagonal prisms are the key components. The interval of the two hexagonal prisms determines the interval of the seven split beams. The system aperture is approximately 80 mm. The beam moving away from the hexagonal prisms is pre-focused by the aspheric lenses and further focused by the hyper-hemispheric submersed lenses onto the detectors. The different receiving FOVs are distinguished by color. Tables 1 and 2 list the corresponding parameters of the lenses.
Table 1. The corresponding parameters of the 2X collimating lens and immersion lenses designed in ZEMAX for the receiving optical system.
Table 2. The parameters of the seven aspheric lens.
3.2. Spot size verification of the simulation
Assessing the distribution shape and size of the beam spot in the designed receiving optical system is necessary. The return beam from a target in one direction can be detected in all the seven detectors on the detector array plane when it enters the receiving system. Figures 7(a) to 7(g) show the spot distribution patterns on the detector array plane comprising seven detectors when the return beam entered the receiving optical system from seven azimuth angles.
Fig. 7 Spot distribution of beams from different incident directions detected by seven detectors in the array plane, where the aperture of the incident beam is set at 15 mm; the different receiving azimuths are distinguished by colors; and the sub-pictures (a), (b), (c), (d), (e), (f), and (g) present the azimuth angles (θx, θy), that is, (0°, 0°), (2.5°, 4.33°), (−2.5°, 4.33°), (−5°, 0°), (−2.5°, −4.33°), (2.5°, −4.33°), and (5°, 0°), respectively.
The beam spots on the detectors located at the hexagon vertexes are completely symmetrical when the incident beam enters the system at 0°. For the other side receiving FOV at different azimuths within ±5°, the spot distribution on the detectors has a corresponding deviation. Thus, every receiving azimuth among the seven directions corresponds to a main detector. By contrast, the rest of the detectors can also receive a relatively weak part, and every detector is responsible for a direction of the return beam within an FOV of 5°.
The spot size on the photosensitive area of the detector is an important metric. The spot size shown in Fig. 8 reveals that when the angle of incidence of the received beam is 0°, the spot size of the central detector is 0.527 mm. By contrast, all the spot sizes of the surrounding six detectors are 0.589 mm. This result means that the PIN detector with a photosensitive area of 0.5 mm can be used for the proposed system. Although a few edges of the beam are outside of a detector in the array, it can still be detected by the detector in the center.
We also consider the cases where the receiving FOV are below ±5°. Accordingly, the spot sizes on the detectors are nearly 0.50 mm. Figure 9 illustrates that the spot aperture of the detector Φspotsize varies with the receiving FOV β, including both the one in center and the other surrounding six in the detector plane. Hence, the smaller FOV is, the smaller the spot size tends to be and the better the result of the system. In addition, the beam diverges slowly if the receiving FOV is over 5°.
4. Discussion
This method is applicable in direct-detection lidar systems operating in bistatic models, in which laser pulses are emitted from a high-stability laser. The optical receiving system proposed in this study is for a wavelength of 1550 nm, whereas the parameters of the optical receiving system for other infrared wavelengths must be reset. However, the principle is similar.
In order to enlarge the receiving FOV and increase the limited aperture of the detector, the light condensing part can be substituted with optical fiber taper. In general, the small end of the fiber taper is connected to the detector. The numerical aperture of the small end is relatively large, thereby causing the outgoing beam to diverge poorly; thus, a focus lens or lens group is necessary between the small end of the fiber taper and detector to focus the beam onto the detector with a limited aperture. Accordingly, a few technical problems remain unsolved. Hence, the proposed method is currently a superior choice compared to the substitution method.
5. Conclusion
This study proposes the method of beam splitting by a pair of hexagonal prisms by employing two hexagonal prisms. The incident beam can be split into seven portions. Each portion is focused and collected onto the photosensitive area of a detector with an aperture of 0.50 mm and frequency bandwidth of 300 MHz. The detectors comprise a hexagon array in a plane, which is equivalent to enlarging the photosensitive area of a detector from 0.5 mm to 1.5 mm, with the exception of the central detector. Every detector is associated with a receiving direction within 5°, thereby improving the receiving FOV to nearly 10°.
Funding
This work was sponsored by the Natural National Scient Foundation of China (NSFC) (61575054).
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