Design of an omnidirectional optical antenna for ultraviolet communication Xuebin Zhang, Yi Tang,* Heqing Huang, Lijun Zhang, and Tingzhu Bai Key Laboratory of Photoelectronic Imaging Technology and System, Ministry of Education of China, School of Optoelectronics, Beijing Institute of Technology, Beijing 100081, China *Corresponding author: [email protected] Received 3 January 2014; revised 8 April 2014; accepted 12 April 2014; posted 15 April 2014 (Doc. ID 203359); published 14 May 2014
In this paper we propose an omnidirectional large field-optical antenna with a dual-mirror structure and field devices and demonstrate its utilization in ultraviolet (UV) communications. Theoretical analysis shows that it is suitable for short-range UV communication. Simulation indicates that the optical gain is 32, and the system has a good spot uniformity. Additionally, incident angles of incident ray meet the requirement of the interference filter (10°). Outdoor experiments show that the angle of FOV ~ is in the range of 20°80° and a SNR increase of 31 dB compared with bare tube is observed, demonstrating the effectiveness of the omnidirectional optical antenna structure for free-space UV communication. © 2014 Optical Society of America OCIS codes: (120.4570) Optical design of instruments; (220.0220) Optical design and fabrication; (060.4510) Optical communications. http://dx.doi.org/10.1364/AO.53.003225
1. Introduction
Scattering of ultraviolet (UV) radiation makes it possible to establish a free-space nonline-of-sight (NLOS) communication link and the strong absorption in solar-blind band provides a low-noise background for high-quality communication [1]. Thus, the NLOS UV communication has been considered an effective supplement to conventional wireless communication with potential advantages of no interference and high security [2,3]. It is one of the most promising schemes for addressing the “last mile” bottleneck in the emerging broadband access markets [4]. Researchers are continuously looking for effective methods to improve the transmission performance of the optical system [5–8]. An omnidirectional optical antenna using two convex mirrors was introduced in 2003 [5], its FOV is considerably large (11°–70°). In 2010 [6] researchers proposed to use compound 1559-128X/14/153225-08$15.00/0 © 2014 Optical Society of America
parabolic concentrator combined with a hemispherical lens in scattering optical communication as a receiving antenna since it can gather feeble signals and increase communication distance. An off-axis catadioptric fisheye optical receiver, whose FOV is 30°, in [8] was addressed later in 2012, and it can mitigate optical aberrations to improve the tracking accuracy for free-space optical communication systems in turbulent atmosphere. Although there has been considerable activity on optical systems, comparatively less has been done on optical system design for NLOS UV communication. The optical antenna for NLOS UV communication is different from the optical systems that use other wavelengths. First of all, the optical antenna demands an FOV as large as possible in order to increase the scattering receiving area of UV signal. Since the relative positions of the transmitter and the receiver may change constantly, it is important to design an omnidirectional large field-optical antenna [9]. But there is a contradiction between small photo-surface and large FOV, so it is impending and important to find an optimum FOV for the antenna. 20 May 2014 / Vol. 53, No. 15 / APPLIED OPTICS
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At the same time, in order to improve the SNR, noise reduction also has to be taken into consideration when the optical system is designed. Based on analysis and simulation, we designed an omnidirectional optical antenna with large FOV, which consists of a dual-mirror structure and a secondary optical system. This is the first time, to the best of our knowledge, that the dual-mirror structure is used for NLOS UV communication, which has a large FOV and works omnidirectionally, while maintaining high optical gain. Related analyses and experiments were conducted on the performance of the antenna. Experimental results show that the ~ SNR has a 31 dB inFOV is approximately 20°80°, crease compared to a bare PMT reception, and the system has the desired spot uniformity. With these features the antenna significantly improves the performance of free-space NLOS UV communication. The organization of this paper is as follows. In Section 2 we introduce the basic structure of the optical system. Detailed design and analysis are given in Section 3. In Section 4 the application and experimental results of the omnidirectional antenna are given. Finally, Section 5 is the conclusion.
signal
Quartz glass cover noise
Solar suppression
Curved mirrors
Field optical devices UV filter UV sensor
Fig. 1. Schematic diagram of the omnidirectional large fieldoptical antenna.
Secondary mirror
UV signal light in each FOV
UV signal light in each FOV
2. Theoretical Analysis A.
Structure of Antenna
Although the UV communication systems work in solar-blind UV, the UV sensors still have response beyond the solar-blind wavelength, which is called background noise. The SNR can be greatly improved by reducing the background noise from the sun. The typical spectrum-selective components used in UV communications are UV interference filters. The interference filter has a drawback: it is very sensitive to the incidence angle of the light, and the effectiveness of the filter will reduce dramatically when the angle exceeds 10° [10], for which the FOV of UV communication is seriously limited. Our purpose is to design an optical antenna with large FOV. If the interference filter is to be used, the incidence angle of interference filters should meet the requirement. So we propose a two-mirror structure to narrow down the incidence angle of the interference filter and the total FOV of the antenna remains large at the same time. The schematic diagram of the omnidirectional antenna is shown in Fig. 1. This system consists of two curved mirrors, field-optical devices, a UV filter and a UV sensor. In addition to using UV filters, UV-reflective filter membrane is coated on the two mirrors. By doing so the background noise will be seriously weakened and SNR will be improved in turn. The quartz glass cover is the protective cover for the antenna. Since the UV commutations system communicates by receiving the scattering UV light in the atmosphere, to make sure the optical antenna can effectively receive scattering signals from different 3226
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Primary mirror Sensor Fig. 2. Optical path of omnidirectional optical antenna.
directions the crucial parameter is large FOV. If the primary mirror is a concave one similar to the Cassegrain system, then the FOV would be too small, and the main field angle is focused at near 0°. So that convex mirror [6] is a better choice of the primary mirror. To make the entire field angle narrow down to a certain range, a secondary mirror with strong ability to alter the optical path, i.e., a concave mirror is chosen. Based on the considerations above, we proposed an omnidirectional optical system composed of two mirrors, and its structure is shown in Fig. 2: B. Design of Mirrors’ Shapes
For the optical antenna design in this paper, its initial design is focused on choosing the surface type and the radius of curvature of the primary and secondary mirrors. To simplify the calculation both surfaces are assumed to be spherical, and the ray trace radius should be small enough to keep the rays within the paraxial region so that the spherical and aspherical errors can be controlled within allowable range. Figure 3(a) shows the schematic diagram of the secondary mirror, and the origin O denotes the first principal point of the lens. Point M 1 and M 2 denote the inner and the outer periphery of the primary mirror, respectively. Point S1 and S2 denote the inner and the outer periphery of the secondary mirror,
The Secondary Mirror z S2
z P2
S1
f2(x)
N2 C
N1
A f1(x)
min max
M2
M1 O
x
(a)
M1
P1
O
x
(b)
Fig. 3. (a) Schematic diagram of secondary mirror. (b) Schematic diagram of primary mirror calculation.
respectively. By calculating the edge ray in maximum and minimum FOV, we can determine the scope of the secondary mirror. Figure 3(b) is a schematic diagram of primary mirror calculation. P1 is the point of intersection of incident ray and the primary mirror, P2 is the point of intersection of the first reflected ray and the secondary mirror, θ is the angle of incident ray coming into the system, and Φ represents the incident angle of the second reflected ray. So (θmax − θmin ) represents the range of incident angle of the first mirror, (Φmax − Φmin ) represents the range of incident angle of the second reflected ray. According to geometrical optics, the following restrictive conditions can be acquired from Fig. 4 [5,11]: (1) The range of the incident angle (θmax − θmin ) limits that of the second reflected ray (Φmax − Φmin ). The two incident angles θ and Φ have a relationship of θ
First we shall come up with a ray tracing formula as shown in Fig. 3(b). Suppose A is the unit vector of the incident ray, B is the unit vector of the first reflected ray, and C is the unit vector of the second reflected ray, N 1 and N 2 , respectively, represent the unit normal vector of the primary mirror at point P1 x1 ; z1 and the secondary mirror at point P2 x2 ; z2 , then vectors listed above have following relations:
θmax − θmin tan ϕ − tan ϕmin θmin : tan ϕmax − tan ϕmin (1)
(2) The surface types of primary and secondary mirrors can be express as for the primary mirror, z1 f 1 x, and the secondary mirror, z2 f 2 x. (3) The positions of M 1 and M 2 are related to the surface type of primary mirror and its incident angle.
A − sin θ; − cos θ;
(2)
B x1 − x2 ; z1 − z2 ;
(3)
C −x2 ; −z2 ;
(4)
N 1 −f 01 x1 ; 1;
(5)
N 2 f 02 x2 ; −1:
(6)
In the formula, f 01 x1 is the derivative of x1 at the primary mirror. f 02 x2 is the derivative of x2 at the secondary mirror. According to law of reflection, we have the formulas [12] B A ; N 1 0; jBj
B C ;N jBj jCj 2
0:
(8)
Formulas above are the basis of the initial design. A simplified method to calculate the curvature is shown in Fig. 4 where a is the diaphragm, b is the primary mirror, and c is the secondary mirror. The ray paths of minimum field are marked with dashed lines, and P1 , P2 , P3 , respectively, represent points of intersection on the edge of the diaphragm, the secondary mirror, and the primary mirror. The corresponding coordinates are P1 x1 ; z1 , P2 x2 ; z2 , and P3 x3 ; 0. Taking the distance between the primary mirror and the secondary mirror as 100 mm, and the diaphragm’s diameter is ≤22 mm, which is the same as the diameter of the sensor, the curve equations of the primary mirror, and the secondary mirror are q R21 − x2 − R1 ;
(9)
q R22 − x2 100 R2 :
(10)
z1 f 1 x
z2 f 2 x
Fig. 4. Calculation method of optical path.
(7)
From the ray path in Fig. 4 P1 should be at the edge of diaphragm, P3 should be as close to the origin point as possible, and the abscissa of P2 should be 20 May 2014 / Vol. 53, No. 15 / APPLIED OPTICS
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between the P1 and P3 . So x1 11, 3 ≤ x2 ≤ 5, x3 is close to 0. In Fig. 4 O is the center of the primary mirror, θ1 is the included angle of incident ray and z axial, and θ3 is the included angle of normal (at P1 ) and z axial. θ4 and θ5 are the incidence angle and the exit angle at P1 . According to the geometrical relationship and reflection law we can see that θ4 θ5 θ1 θ3 ;
(11)
θ4 θ5 θ1 θmin 2θ1 θ3 :
(12)
We also assume θmin is 15°, x1 11, so we can get θ1 15° − 2 arcsin11∕R1 :
(13)
Then we can get x2 , q i h x2 ≈ 11∕ tanθ1 − 100 − R21 − 112 R1 tanθ1 (14) Similarly, we can get the included angle of the reflected ray and the z axial: θ2 2 arcsinx2 ∕R2 − θ1 :
(15)
Then x3 , qi h x3 ≈ x2 ∕ tanθ2 100 R2 − R22 − x22 tanθ2 : (16) According to the boundary conditions (1) 3 ≤ x2 ≤ 5, (2) x3 is as close to 0 as possible. We can therefore get R1 103 mm, R2 50 mm.
3. Design Results and Simulation Analyses A. Design Example
The ray is often deflected severely for large FOV, which is caused by spherical aberration, coma, astigmatism, and other factors. On the other hand, hyperboloid should not be an issue for the surface of the primary mirror. By using ZEMAX, the mirrors’ curvature, cone coefficient, and the distance between the mirrors can be optimized based on boundary conditions listed below: (1) Center ray of each FOV should converge on the center of diaphragm after two reflections. (2) The intersection point’s ordinate of the incident light and the primary mirror at minimum edge FOV (15°) should be bigger than 11 mm. (3) The intersection point’s ordinate of the incident light and the primary mirror at maximum edge FOV (80°) should be less than 75 mm. (4) The distance between the two mirrors is between 90–150 mm. The optical structure is shown in Fig. 5(a), a fieldoptical device is added to the dual-mirror structure. Since the sensing optical system often has contradiction between the small sensing area and large FOV, in order to increase the FOV of the system without increasing the sensing area we propose using field-optical devices to enhance performance of the antenna. Such field-optical devices mainly include a field lens, a light cone, and an immersion lens [13]. As the diameter of the sensor is close to the diameter of the diaphragm, the main function of field-optical devices is to improve the SNR and increase the FOV, so we decide to choose a field lens as the secondary system. The main function of the field lens is to eliminate stray light, improve the SNR, reduce the sensing area, and enhance the sensitivity of the system. A field lens is placed near the focal plane of the antenna. In actual design we use
Stray light
Secondary light blocking mirror diaphragm
Secondary mirror
UV signal light in each FOV
UV signal light in each FOV
Primary mirror
UV signal light in each FOV
UV signal light in each FOV
Primary mirror
Field lens
Sensor Sensor
(a)
(b)
Fig. 5. Final simulation results, (a) without the secondary optical system and (b) exist with the secondary optical system. 3228
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ray tracing and spot diagram comparison. And the design criterion is as follows. First the spot diameter in the spot diagram of each FOV should be less than 22 mm (which is the diameter of the UV sensor). Then, the spot illuminance distribution of each FOV should be uniform, and the receiving efficiency should higher than 70%, which defines FOV of the optical antenna. The last criterion is that the field-optical system should reduce the stray light effectively. A designed structure of an antenna is shown in Fig. 5(b). The field diaphragm’s diameter is a function of FOV, especially when the FOV value is small. As can be seen in Fig. 5(b), if the field diaphragm becomes larger the incident light in the smallest FOV case will not be reflected by the primary mirror, and the antenna FOV will become small, SNR of the system will decrease. If the field diaphragm becomes too small, part of the light spot after the field diaphragm will be larger than the field diaphragm diameter, which may also deteriorate the SNR. There would be a trade-off between the SNR and the FOV (in this system is 24 mm). As shown in Fig. 5(b) most stray light, which can enter the field-optical system directly, has been blocked by a light-blocking diaphragm, and the rest is refracted out of the sensor by a field lens. With the light-blocking diaphragm and a field-optical system, the stray light has been weakened dramatically without affecting the signal light, thus the SNR is improved. A prototype of the design is demonstrated in Fig. 6. The diameter of the prototype is 18 cm, and the height is 25 cm. The antenna is enclosed in a quartz cover to protect the antenna. The quartz cover has a UV transmittance of over 85%. B.
In Eq. (17), n is the internal refractive index, ψ c ≤ π∕2 is the FOV. As for this antenna, the optical gain is 32. Figure 7 shows the contrast of the illuminance distribution, illumination distribution curve in tangential plane, and flattened Gaussian distribution curve. The sensing area is on the image surface. In Fig. 7 the spot diameter is approximately 20 mm, and the sensor can receive most of the energy within its FOV. By comparison of Figs. 7(b) and 7(c), we can see the curve shape agrees to flattened the Gaussian distribution curve, and the only difference is in the waist radius of the flattened Gaussian distribution. So the design has reached a relatively ideal condition, and the uniformity of the received spot will not interfere the receiving efficiency of the system.
(a)
System Simulation Analysis
In the simulation, FOV varies to meet the requirement for suppressing the stray light and limiting the size of the primary mirror. In the final design, ~ the FOV angle is 20°80°. For a large field-optical antenna, the optical gain is defined as [4] n2 sin2 ψ c
0
0 ≤ ψ ≤ ψ c; : ψ > ψc
1
(17)
Relative Illumination
gψ
(b)
0.8 0.6 0.4 0.2 0 -11
-8.8
-6.6
-4.4
-2.2
0
2.2
4.4
6.6
8.8
11
Image coordinate in millimeters
(c)
Fig. 6. Omnidirectional large field-optical antenna.
Fig. 7. (a) Illuminance distribution, (b) illumination distribution curve in tangential plane, and (c) flattened Gaussian distribution curve. 20 May 2014 / Vol. 53, No. 15 / APPLIED OPTICS
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50
Results of each Field Ray Tracing
FOV(°)
tan ϕ−1
tan ϕ1
ϕ−1 (°)
ϕ1 (°)
20 40 60 80
−0.1202 −0.1185 −0.1247 −0.1728
0.0637 0.0051 −0.0646 −0.1594
−6.86 −6.76 −7.11 −9.81
3.65 0.29 −3.69 −9.06
In order to ensure the effectiveness of the interference filter, the incident angle should satisfy the requirement of the interference filter, i.e., < 10°. In ZEMAX, we can use the ray-tracing method to trace the light beam at different FOV. Table 1 show the tracing results and the conversed angle results where φ is incidence angle, the subscript “−1” represents the lower boundary of the light beam, and “1” represents the upper boundary of the light beam. Since the incident angle of each FOV does not exceed the valid range of interference filter, the interference filter should decrease the noise effectively and in turn increase the SNR of the system. 4. Outdoor Experiments
Since optical gain and large field are important indicators for an omnidirectional antenna, we test the antenna against these parameters at different angles of the transmitter. A.
Optical Gain
According to the Planck’s law, each photon carries energy hc∕λ, where c is the speed of light and h is the Planck’s constant. Assume the PR is the received optical power in the free space, δs is the system transmission coefficient, ψ r and M are the system quantum efficiency and gain, respectively. For direct detection by an on–off keying modulation system, the output signal optical current is [14] ir M
eψ r δs n2 eψ r δs PR : PR hv sin2 ψ c hv
(18)
30
0
-10 2
n δs ψ r 4K S T B PR 4 RL sin ψ c hv
1∕2
:
(19)
Where B is the bandwidth, K S is the Boltzmann constant, and T is the effective noise temperature. Assume hPR i is the mean signal optical power, then the mean output SNR is
3
4
5
6
7
8
9
10
11
12
Range(m)
Fig. 8. Comparison of received power between with and without the antenna.
Base on Eq. (20) we can compare the SNR of the PMT and the antenna. In the experiment the transmitter (a UV source) is placed horizontally with the power of 1 W; a naked PMT and a receiver with an antenna are used to collect the scattering UV photons simultaneously. The results are shown in Fig. 8. From Fig. 8, the SNR of the antenna with a filter is 31 dB greater than that of the naked PMT. The increased SNR derives from not only the optical gain of the antenna but also the decease of the background noise along the solar blind UV wavelength. B. Field Angle
The curves in Fig. 9 are the SNR versus pitch angles at different measuring points. When the UV source is placed horizontally, the pitch angle of optical antenna is the field angle of center ray where the light source is emitted. It can be seen that the SNR is drastically decreased when the pitch angle is above 80°, between 20° and 80° SNR is plateaued. The SNR
50 40 30
SNR(dB)
in 2e2 B
4
20
10
Assume that the random fluctuations observed in the sensor (photon multiplier tube) output are derived from the shot noise due to the signal optical current and the thermal noise associated with the output resistance RL . Then, the total noise is [14]
Without antenna Antenna without filter Antenna with filter
40
SNR(dB)
Table 1.
20 10
Simulation at 6 m 0
Experiment at 2 m Experiment at 6 m
-10
Experiment at 12 m
hSNRi
2
hir i hPR i : 4K s TB sin2 ψ c hv 2 2 hvB i2n hP i R δs ψ r RL n2 eδ ψ s
3230
-20
2
r
APPLIED OPTICS / Vol. 53, No. 15 / 20 May 2014
(20)
0
20
40
60
80
100
Pitch angle(°) Fig. 9. SNR changes with pitch angles.
120
variation trend from 20° to 80° fits the field angle of the optical antenna, which is 20°–80° and the variation trend of the simulation at 6 m is broadly in line with the experimental results. The simulation results are greater than the experimental results because the atmospheric attenuation is not considered in the simulation, and the SNR will change at different measuring points as the atmospheric attenuation. C.
(a)
(b)
Elevation of the Transmitting Angle
We still test the receiving characteristics of the antenna while the transmitting angle varies, which shows the ability for mobile use. The antenna is placed 12 m away from the UV source, and the transmitting angle of the UV source changes from 30° to 90°. It can be seen from the experimental results in Table 2 and the data in Fig. 10 that the SNR is highest when the transmitting elevation is 30°, where the signal inception is best. As shown in Fig. 11, the overlap between the transmitting angle and the antenna receiving angle is where the antenna can receive a scattered light beam. Even if the overlap area is much bigger when the UV source elevation becomes larger, the SNR may not increase with a larger UV source elevation. The reason is that when the light-source elevation exceeds a certain angle (such as 30° in this experiment), atmospheric attenuation will also increase.
Table 2.
Experimental Results of Different Light Source Elevations
Light Source Elevation (°)
Signal Power (dB)
Noise Power (dB)
SNR (dB)
0 (placed horizontally) 30 45 60 90
28.4
4.8
23.6
29.0 28.3 27.8 26.0
3.3 5.8 6.7 8.4
25.7 22.5 21.1 17.6
The antenna
26
Scattered light transmission area
(c) Fig. 11. Scatter communication receive area. Light source elevation (a) 0°, (b) 30°, and (c) 45°.
5. Conclusion
In this paper, an omnidirectional large field-optical antenna for free-space UV communication has been designed and theoretically analyzed. In contrast to field-optical devices, we selected a field lens as the secondary optical system, and designed an omnidirectional large field-optical antenna for free-space UV communication. We calculated the optical gain, and did simulation analysis on the receiving spot uniformity and the UV incidence angle at the interference filter. Simulation indicates that the optical gain is 32, the angle of FOV is in the range of ~ 20°80°. We also constructed a prototype antenna and experimentally verified the optical-gain field angle at different UV source radiation angles. Experimental data show that the omnidirectional large field-optical antenna has significantly improved performance and is suitable for wireless UV communication. This work is sponsored by the National Key Basic Research Program 973 project (No. 2013CB329202) and Basic Industrial Technology Project (No. J312012B002). References
24
SNR (dB)
The scattered light receiving region
22
20
18
16 0
10
20
30
40
50
60
70
80
90
Source angle (°) Fig. 10. SNR curve of different light source elevations.
100
1. G. A. Shaw, A. M. Siegel, and M. L. Nischan, “Extending the range and performance of non-line-of-sight ultraviolet communication links,” Proc. SPIE 6231, 62310C (2006). 2. Z. Xu and B. M. Sadler, “Ultraviolet communication: potential and state-of-art,” IEEE Commun. Mag. 46(5), 67–73 (2008). 3. Y. Zuo, H. Xiao, and J. Wu, “Effect of atmospheric turbulence on non-line-of-sight ultraviolet communications,” in IEEE 23rd International Symposium on Personal Indoor and Mobile Radio Communications (PIMRC), 2012, pp. 1682–1686. 4. Z. Ghassemlooy, W. Popoola, and S. Rajbhandari, Optical Wireless Communications: System and Channel Modelling with MATLAB (CRC Press, 2012). 5. N. Takato, N. Okada, G. Kosugi, M. Suganuma, A. Miyashita, and F. Uraguchi, “All-sky 10 μm cloud monitor on Mauna Kea,” Proc. SPIE 4837, 786 (2003). 20 May 2014 / Vol. 53, No. 15 / APPLIED OPTICS
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6. J. Fang, H. Zhang, and H. Jia, “Compound parabolic concentrator applied as receiving antenna in scattering optical communication,” Chin. Opt. Lett. 8, 5–8 (1991). 7. X. Ma, H. Yang, and B. Wang, “An optimum structure design for Cassegrain optical system,” Optik 125, 1423–1426 (2014). 8. P. Deng, X. Yuan, and M. Kavehrad, “Off-axis catadioptric fish eye wide field-of-view optical receiver for free space optical communications,” Opt. Eng. 51, 063002 (2012). 9. P. Tian, P. Wang, and H. Wang, “Research of receiver technology in NLOS ultraviolet communication,” Chin. Opt. Commun. Technol. 9, 62–64 (2006).
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10. G. A. Shaw, A. M. Siegel, and M. L. Nischan, “Demonstration system and applications for compact wireless ultraviolet communication,” Proc. SPIE 5071, 241 (2003). 11. A. Takeya, T. Kuroda, K. Nishiguchi, and A. Ichikawa, “Omnidirectional vision system using two mirrors,” Proc. SPIE 3430, 50 (1998). 12. J. Pan, The Design, Manufacture and Test of the Aspherical Optical Surfaces (Suzhou University, 2004). 13. W. He, “Study of wide-FOV optical system with optical gain,” Ph.D. thesis, (University of Electronic Science and Technology, 2006). 14. L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE, 2001).
In this paper we propose an omnidirectional large field-optical antenna with a dual-mirror structure and field devices and demonstrate its utilization in ultraviolet (UV) communications. Theoretical analysis shows that it is suitable for short-range UV communication. Simulation indicates that the optical gain is 32, and the system has a good spot uniformity. Additionally, incident angles of incident ray meet the requirement of the interference filter (10°). Outdoor experiments show that the angle of FOV ~ is in the range of 20°80° and a SNR increase of 31 dB compared with bare tube is observed, demonstrating the effectiveness of the omnidirectional optical antenna structure for free-space UV communication. © 2014 Optical Society of America OCIS codes: (120.4570) Optical design of instruments; (220.0220) Optical design and fabrication; (060.4510) Optical communications. http://dx.doi.org/10.1364/AO.53.003225
1. Introduction
Scattering of ultraviolet (UV) radiation makes it possible to establish a free-space nonline-of-sight (NLOS) communication link and the strong absorption in solar-blind band provides a low-noise background for high-quality communication [1]. Thus, the NLOS UV communication has been considered an effective supplement to conventional wireless communication with potential advantages of no interference and high security [2,3]. It is one of the most promising schemes for addressing the “last mile” bottleneck in the emerging broadband access markets [4]. Researchers are continuously looking for effective methods to improve the transmission performance of the optical system [5–8]. An omnidirectional optical antenna using two convex mirrors was introduced in 2003 [5], its FOV is considerably large (11°–70°). In 2010 [6] researchers proposed to use compound 1559-128X/14/153225-08$15.00/0 © 2014 Optical Society of America
parabolic concentrator combined with a hemispherical lens in scattering optical communication as a receiving antenna since it can gather feeble signals and increase communication distance. An off-axis catadioptric fisheye optical receiver, whose FOV is 30°, in [8] was addressed later in 2012, and it can mitigate optical aberrations to improve the tracking accuracy for free-space optical communication systems in turbulent atmosphere. Although there has been considerable activity on optical systems, comparatively less has been done on optical system design for NLOS UV communication. The optical antenna for NLOS UV communication is different from the optical systems that use other wavelengths. First of all, the optical antenna demands an FOV as large as possible in order to increase the scattering receiving area of UV signal. Since the relative positions of the transmitter and the receiver may change constantly, it is important to design an omnidirectional large field-optical antenna [9]. But there is a contradiction between small photo-surface and large FOV, so it is impending and important to find an optimum FOV for the antenna. 20 May 2014 / Vol. 53, No. 15 / APPLIED OPTICS
3225
At the same time, in order to improve the SNR, noise reduction also has to be taken into consideration when the optical system is designed. Based on analysis and simulation, we designed an omnidirectional optical antenna with large FOV, which consists of a dual-mirror structure and a secondary optical system. This is the first time, to the best of our knowledge, that the dual-mirror structure is used for NLOS UV communication, which has a large FOV and works omnidirectionally, while maintaining high optical gain. Related analyses and experiments were conducted on the performance of the antenna. Experimental results show that the ~ SNR has a 31 dB inFOV is approximately 20°80°, crease compared to a bare PMT reception, and the system has the desired spot uniformity. With these features the antenna significantly improves the performance of free-space NLOS UV communication. The organization of this paper is as follows. In Section 2 we introduce the basic structure of the optical system. Detailed design and analysis are given in Section 3. In Section 4 the application and experimental results of the omnidirectional antenna are given. Finally, Section 5 is the conclusion.
signal
Quartz glass cover noise
Solar suppression
Curved mirrors
Field optical devices UV filter UV sensor
Fig. 1. Schematic diagram of the omnidirectional large fieldoptical antenna.
Secondary mirror
UV signal light in each FOV
UV signal light in each FOV
2. Theoretical Analysis A.
Structure of Antenna
Although the UV communication systems work in solar-blind UV, the UV sensors still have response beyond the solar-blind wavelength, which is called background noise. The SNR can be greatly improved by reducing the background noise from the sun. The typical spectrum-selective components used in UV communications are UV interference filters. The interference filter has a drawback: it is very sensitive to the incidence angle of the light, and the effectiveness of the filter will reduce dramatically when the angle exceeds 10° [10], for which the FOV of UV communication is seriously limited. Our purpose is to design an optical antenna with large FOV. If the interference filter is to be used, the incidence angle of interference filters should meet the requirement. So we propose a two-mirror structure to narrow down the incidence angle of the interference filter and the total FOV of the antenna remains large at the same time. The schematic diagram of the omnidirectional antenna is shown in Fig. 1. This system consists of two curved mirrors, field-optical devices, a UV filter and a UV sensor. In addition to using UV filters, UV-reflective filter membrane is coated on the two mirrors. By doing so the background noise will be seriously weakened and SNR will be improved in turn. The quartz glass cover is the protective cover for the antenna. Since the UV commutations system communicates by receiving the scattering UV light in the atmosphere, to make sure the optical antenna can effectively receive scattering signals from different 3226
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Primary mirror Sensor Fig. 2. Optical path of omnidirectional optical antenna.
directions the crucial parameter is large FOV. If the primary mirror is a concave one similar to the Cassegrain system, then the FOV would be too small, and the main field angle is focused at near 0°. So that convex mirror [6] is a better choice of the primary mirror. To make the entire field angle narrow down to a certain range, a secondary mirror with strong ability to alter the optical path, i.e., a concave mirror is chosen. Based on the considerations above, we proposed an omnidirectional optical system composed of two mirrors, and its structure is shown in Fig. 2: B. Design of Mirrors’ Shapes
For the optical antenna design in this paper, its initial design is focused on choosing the surface type and the radius of curvature of the primary and secondary mirrors. To simplify the calculation both surfaces are assumed to be spherical, and the ray trace radius should be small enough to keep the rays within the paraxial region so that the spherical and aspherical errors can be controlled within allowable range. Figure 3(a) shows the schematic diagram of the secondary mirror, and the origin O denotes the first principal point of the lens. Point M 1 and M 2 denote the inner and the outer periphery of the primary mirror, respectively. Point S1 and S2 denote the inner and the outer periphery of the secondary mirror,
The Secondary Mirror z S2
z P2
S1
f2(x)
N2 C
N1
A f1(x)
min max
M2
M1 O
x
(a)
M1
P1
O
x
(b)
Fig. 3. (a) Schematic diagram of secondary mirror. (b) Schematic diagram of primary mirror calculation.
respectively. By calculating the edge ray in maximum and minimum FOV, we can determine the scope of the secondary mirror. Figure 3(b) is a schematic diagram of primary mirror calculation. P1 is the point of intersection of incident ray and the primary mirror, P2 is the point of intersection of the first reflected ray and the secondary mirror, θ is the angle of incident ray coming into the system, and Φ represents the incident angle of the second reflected ray. So (θmax − θmin ) represents the range of incident angle of the first mirror, (Φmax − Φmin ) represents the range of incident angle of the second reflected ray. According to geometrical optics, the following restrictive conditions can be acquired from Fig. 4 [5,11]: (1) The range of the incident angle (θmax − θmin ) limits that of the second reflected ray (Φmax − Φmin ). The two incident angles θ and Φ have a relationship of θ
First we shall come up with a ray tracing formula as shown in Fig. 3(b). Suppose A is the unit vector of the incident ray, B is the unit vector of the first reflected ray, and C is the unit vector of the second reflected ray, N 1 and N 2 , respectively, represent the unit normal vector of the primary mirror at point P1 x1 ; z1 and the secondary mirror at point P2 x2 ; z2 , then vectors listed above have following relations:
θmax − θmin tan ϕ − tan ϕmin θmin : tan ϕmax − tan ϕmin (1)
(2) The surface types of primary and secondary mirrors can be express as for the primary mirror, z1 f 1 x, and the secondary mirror, z2 f 2 x. (3) The positions of M 1 and M 2 are related to the surface type of primary mirror and its incident angle.
A − sin θ; − cos θ;
(2)
B x1 − x2 ; z1 − z2 ;
(3)
C −x2 ; −z2 ;
(4)
N 1 −f 01 x1 ; 1;
(5)
N 2 f 02 x2 ; −1:
(6)
In the formula, f 01 x1 is the derivative of x1 at the primary mirror. f 02 x2 is the derivative of x2 at the secondary mirror. According to law of reflection, we have the formulas [12] B A ; N 1 0; jBj
B C ;N jBj jCj 2
0:
(8)
Formulas above are the basis of the initial design. A simplified method to calculate the curvature is shown in Fig. 4 where a is the diaphragm, b is the primary mirror, and c is the secondary mirror. The ray paths of minimum field are marked with dashed lines, and P1 , P2 , P3 , respectively, represent points of intersection on the edge of the diaphragm, the secondary mirror, and the primary mirror. The corresponding coordinates are P1 x1 ; z1 , P2 x2 ; z2 , and P3 x3 ; 0. Taking the distance between the primary mirror and the secondary mirror as 100 mm, and the diaphragm’s diameter is ≤22 mm, which is the same as the diameter of the sensor, the curve equations of the primary mirror, and the secondary mirror are q R21 − x2 − R1 ;
(9)
q R22 − x2 100 R2 :
(10)
z1 f 1 x
z2 f 2 x
Fig. 4. Calculation method of optical path.
(7)
From the ray path in Fig. 4 P1 should be at the edge of diaphragm, P3 should be as close to the origin point as possible, and the abscissa of P2 should be 20 May 2014 / Vol. 53, No. 15 / APPLIED OPTICS
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between the P1 and P3 . So x1 11, 3 ≤ x2 ≤ 5, x3 is close to 0. In Fig. 4 O is the center of the primary mirror, θ1 is the included angle of incident ray and z axial, and θ3 is the included angle of normal (at P1 ) and z axial. θ4 and θ5 are the incidence angle and the exit angle at P1 . According to the geometrical relationship and reflection law we can see that θ4 θ5 θ1 θ3 ;
(11)
θ4 θ5 θ1 θmin 2θ1 θ3 :
(12)
We also assume θmin is 15°, x1 11, so we can get θ1 15° − 2 arcsin11∕R1 :
(13)
Then we can get x2 , q i h x2 ≈ 11∕ tanθ1 − 100 − R21 − 112 R1 tanθ1 (14) Similarly, we can get the included angle of the reflected ray and the z axial: θ2 2 arcsinx2 ∕R2 − θ1 :
(15)
Then x3 , qi h x3 ≈ x2 ∕ tanθ2 100 R2 − R22 − x22 tanθ2 : (16) According to the boundary conditions (1) 3 ≤ x2 ≤ 5, (2) x3 is as close to 0 as possible. We can therefore get R1 103 mm, R2 50 mm.
3. Design Results and Simulation Analyses A. Design Example
The ray is often deflected severely for large FOV, which is caused by spherical aberration, coma, astigmatism, and other factors. On the other hand, hyperboloid should not be an issue for the surface of the primary mirror. By using ZEMAX, the mirrors’ curvature, cone coefficient, and the distance between the mirrors can be optimized based on boundary conditions listed below: (1) Center ray of each FOV should converge on the center of diaphragm after two reflections. (2) The intersection point’s ordinate of the incident light and the primary mirror at minimum edge FOV (15°) should be bigger than 11 mm. (3) The intersection point’s ordinate of the incident light and the primary mirror at maximum edge FOV (80°) should be less than 75 mm. (4) The distance between the two mirrors is between 90–150 mm. The optical structure is shown in Fig. 5(a), a fieldoptical device is added to the dual-mirror structure. Since the sensing optical system often has contradiction between the small sensing area and large FOV, in order to increase the FOV of the system without increasing the sensing area we propose using field-optical devices to enhance performance of the antenna. Such field-optical devices mainly include a field lens, a light cone, and an immersion lens [13]. As the diameter of the sensor is close to the diameter of the diaphragm, the main function of field-optical devices is to improve the SNR and increase the FOV, so we decide to choose a field lens as the secondary system. The main function of the field lens is to eliminate stray light, improve the SNR, reduce the sensing area, and enhance the sensitivity of the system. A field lens is placed near the focal plane of the antenna. In actual design we use
Stray light
Secondary light blocking mirror diaphragm
Secondary mirror
UV signal light in each FOV
UV signal light in each FOV
Primary mirror
UV signal light in each FOV
UV signal light in each FOV
Primary mirror
Field lens
Sensor Sensor
(a)
(b)
Fig. 5. Final simulation results, (a) without the secondary optical system and (b) exist with the secondary optical system. 3228
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ray tracing and spot diagram comparison. And the design criterion is as follows. First the spot diameter in the spot diagram of each FOV should be less than 22 mm (which is the diameter of the UV sensor). Then, the spot illuminance distribution of each FOV should be uniform, and the receiving efficiency should higher than 70%, which defines FOV of the optical antenna. The last criterion is that the field-optical system should reduce the stray light effectively. A designed structure of an antenna is shown in Fig. 5(b). The field diaphragm’s diameter is a function of FOV, especially when the FOV value is small. As can be seen in Fig. 5(b), if the field diaphragm becomes larger the incident light in the smallest FOV case will not be reflected by the primary mirror, and the antenna FOV will become small, SNR of the system will decrease. If the field diaphragm becomes too small, part of the light spot after the field diaphragm will be larger than the field diaphragm diameter, which may also deteriorate the SNR. There would be a trade-off between the SNR and the FOV (in this system is 24 mm). As shown in Fig. 5(b) most stray light, which can enter the field-optical system directly, has been blocked by a light-blocking diaphragm, and the rest is refracted out of the sensor by a field lens. With the light-blocking diaphragm and a field-optical system, the stray light has been weakened dramatically without affecting the signal light, thus the SNR is improved. A prototype of the design is demonstrated in Fig. 6. The diameter of the prototype is 18 cm, and the height is 25 cm. The antenna is enclosed in a quartz cover to protect the antenna. The quartz cover has a UV transmittance of over 85%. B.
In Eq. (17), n is the internal refractive index, ψ c ≤ π∕2 is the FOV. As for this antenna, the optical gain is 32. Figure 7 shows the contrast of the illuminance distribution, illumination distribution curve in tangential plane, and flattened Gaussian distribution curve. The sensing area is on the image surface. In Fig. 7 the spot diameter is approximately 20 mm, and the sensor can receive most of the energy within its FOV. By comparison of Figs. 7(b) and 7(c), we can see the curve shape agrees to flattened the Gaussian distribution curve, and the only difference is in the waist radius of the flattened Gaussian distribution. So the design has reached a relatively ideal condition, and the uniformity of the received spot will not interfere the receiving efficiency of the system.
(a)
System Simulation Analysis
In the simulation, FOV varies to meet the requirement for suppressing the stray light and limiting the size of the primary mirror. In the final design, ~ the FOV angle is 20°80°. For a large field-optical antenna, the optical gain is defined as [4] n2 sin2 ψ c
0
0 ≤ ψ ≤ ψ c; : ψ > ψc
1
(17)
Relative Illumination
gψ
(b)
0.8 0.6 0.4 0.2 0 -11
-8.8
-6.6
-4.4
-2.2
0
2.2
4.4
6.6
8.8
11
Image coordinate in millimeters
(c)
Fig. 6. Omnidirectional large field-optical antenna.
Fig. 7. (a) Illuminance distribution, (b) illumination distribution curve in tangential plane, and (c) flattened Gaussian distribution curve. 20 May 2014 / Vol. 53, No. 15 / APPLIED OPTICS
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50
Results of each Field Ray Tracing
FOV(°)
tan ϕ−1
tan ϕ1
ϕ−1 (°)
ϕ1 (°)
20 40 60 80
−0.1202 −0.1185 −0.1247 −0.1728
0.0637 0.0051 −0.0646 −0.1594
−6.86 −6.76 −7.11 −9.81
3.65 0.29 −3.69 −9.06
In order to ensure the effectiveness of the interference filter, the incident angle should satisfy the requirement of the interference filter, i.e., < 10°. In ZEMAX, we can use the ray-tracing method to trace the light beam at different FOV. Table 1 show the tracing results and the conversed angle results where φ is incidence angle, the subscript “−1” represents the lower boundary of the light beam, and “1” represents the upper boundary of the light beam. Since the incident angle of each FOV does not exceed the valid range of interference filter, the interference filter should decrease the noise effectively and in turn increase the SNR of the system. 4. Outdoor Experiments
Since optical gain and large field are important indicators for an omnidirectional antenna, we test the antenna against these parameters at different angles of the transmitter. A.
Optical Gain
According to the Planck’s law, each photon carries energy hc∕λ, where c is the speed of light and h is the Planck’s constant. Assume the PR is the received optical power in the free space, δs is the system transmission coefficient, ψ r and M are the system quantum efficiency and gain, respectively. For direct detection by an on–off keying modulation system, the output signal optical current is [14] ir M
eψ r δs n2 eψ r δs PR : PR hv sin2 ψ c hv
(18)
30
0
-10 2
n δs ψ r 4K S T B PR 4 RL sin ψ c hv
1∕2
:
(19)
Where B is the bandwidth, K S is the Boltzmann constant, and T is the effective noise temperature. Assume hPR i is the mean signal optical power, then the mean output SNR is
3
4
5
6
7
8
9
10
11
12
Range(m)
Fig. 8. Comparison of received power between with and without the antenna.
Base on Eq. (20) we can compare the SNR of the PMT and the antenna. In the experiment the transmitter (a UV source) is placed horizontally with the power of 1 W; a naked PMT and a receiver with an antenna are used to collect the scattering UV photons simultaneously. The results are shown in Fig. 8. From Fig. 8, the SNR of the antenna with a filter is 31 dB greater than that of the naked PMT. The increased SNR derives from not only the optical gain of the antenna but also the decease of the background noise along the solar blind UV wavelength. B. Field Angle
The curves in Fig. 9 are the SNR versus pitch angles at different measuring points. When the UV source is placed horizontally, the pitch angle of optical antenna is the field angle of center ray where the light source is emitted. It can be seen that the SNR is drastically decreased when the pitch angle is above 80°, between 20° and 80° SNR is plateaued. The SNR
50 40 30
SNR(dB)
in 2e2 B
4
20
10
Assume that the random fluctuations observed in the sensor (photon multiplier tube) output are derived from the shot noise due to the signal optical current and the thermal noise associated with the output resistance RL . Then, the total noise is [14]
Without antenna Antenna without filter Antenna with filter
40
SNR(dB)
Table 1.
20 10
Simulation at 6 m 0
Experiment at 2 m Experiment at 6 m
-10
Experiment at 12 m
hSNRi
2
hir i hPR i : 4K s TB sin2 ψ c hv 2 2 hvB i2n hP i R δs ψ r RL n2 eδ ψ s
3230
-20
2
r
APPLIED OPTICS / Vol. 53, No. 15 / 20 May 2014
(20)
0
20
40
60
80
100
Pitch angle(°) Fig. 9. SNR changes with pitch angles.
120
variation trend from 20° to 80° fits the field angle of the optical antenna, which is 20°–80° and the variation trend of the simulation at 6 m is broadly in line with the experimental results. The simulation results are greater than the experimental results because the atmospheric attenuation is not considered in the simulation, and the SNR will change at different measuring points as the atmospheric attenuation. C.
(a)
(b)
Elevation of the Transmitting Angle
We still test the receiving characteristics of the antenna while the transmitting angle varies, which shows the ability for mobile use. The antenna is placed 12 m away from the UV source, and the transmitting angle of the UV source changes from 30° to 90°. It can be seen from the experimental results in Table 2 and the data in Fig. 10 that the SNR is highest when the transmitting elevation is 30°, where the signal inception is best. As shown in Fig. 11, the overlap between the transmitting angle and the antenna receiving angle is where the antenna can receive a scattered light beam. Even if the overlap area is much bigger when the UV source elevation becomes larger, the SNR may not increase with a larger UV source elevation. The reason is that when the light-source elevation exceeds a certain angle (such as 30° in this experiment), atmospheric attenuation will also increase.
Table 2.
Experimental Results of Different Light Source Elevations
Light Source Elevation (°)
Signal Power (dB)
Noise Power (dB)
SNR (dB)
0 (placed horizontally) 30 45 60 90
28.4
4.8
23.6
29.0 28.3 27.8 26.0
3.3 5.8 6.7 8.4
25.7 22.5 21.1 17.6
The antenna
26
Scattered light transmission area
(c) Fig. 11. Scatter communication receive area. Light source elevation (a) 0°, (b) 30°, and (c) 45°.
5. Conclusion
In this paper, an omnidirectional large field-optical antenna for free-space UV communication has been designed and theoretically analyzed. In contrast to field-optical devices, we selected a field lens as the secondary optical system, and designed an omnidirectional large field-optical antenna for free-space UV communication. We calculated the optical gain, and did simulation analysis on the receiving spot uniformity and the UV incidence angle at the interference filter. Simulation indicates that the optical gain is 32, the angle of FOV is in the range of ~ 20°80°. We also constructed a prototype antenna and experimentally verified the optical-gain field angle at different UV source radiation angles. Experimental data show that the omnidirectional large field-optical antenna has significantly improved performance and is suitable for wireless UV communication. This work is sponsored by the National Key Basic Research Program 973 project (No. 2013CB329202) and Basic Industrial Technology Project (No. J312012B002). References
24
SNR (dB)
The scattered light receiving region
22
20
18
16 0
10
20
30
40
50
60
70
80
90
Source angle (°) Fig. 10. SNR curve of different light source elevations.
100
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