Optik 123 (2012) 34–39
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Optik journal homepage: www.elsevier.de/ijleo
Finite size panoramic optical system integrated design Hongyuan Wen Taizhou Institute of Science and Technology, Nanjing University of Science and Technology, Taizhou 225300, China
a r t i c l e
i n f o
Article history: Received 5 August 2010 Accepted 26 February 2011
Keywords: Target detection Panoramic optical system Integrated design Gaussian beams Lasers
a b s t r a c t Aiming at the present situation of the panoramic target detection field, one laser target panoramic optical system on finite size is designed. The laser transmission optical system proposes a partition beam layout method, namely 360◦ omnidirectional detection can be realized by 6 fan-shaped light beams with 60◦ × 1◦ field angle. The receiving system position and size can be determined based on calculation the transformation of the Gaussian beam through the lens. After the computing and optimizing the lens curvature radius and other optical parameters, the integrated design of the transmission and receiving optical system is completed. The system echo signal experiment is carried out, and the experimental results show the error of the actual value and theoretical value is less than 4.8%. The system works stably and the anticipated design effect is achieved. © 2011 Elsevier GmbH. All rights reserved.
1. Introduction
2. System design requirement
In the panoramic target detection field, such as the search and rescue, aerospace, robots, communication, war, security, and unmanned vehicles, the international commonly used detection system is the radio detection system, infrared detection system and laser detection system [1–3]. Because of many adverse target detection environment and strong electromagnetic interference, the radio detection system cannot work stably and normally [4,5]. The infrared detection system has many applications in the panoramic target detection fields, but it unable to realize the target detection effectively in complex landform, weather and other unpredictable conditions [6,7]. The laser detection system has the strong antijamming and target accurate control ability, and in some developed countries it is widely used in the military field at present [8–10]. However, it is difficulty to promote to civil field with the big equipment, expensive cost, some secret technology and other reasons. Therefore, it needs to design a low cost, small volume, high reliability, accurate orientation and quick response detection system in the world related civil field urgently. Aiming at the above problems, a laser target panoramic optical system on finite size was designed and the experimental results show the system echo signal error is small. The design idea, method and product in this paper have some extension value.
Based on the panoramic target detection project demand in the civil field, the research is carried out, which plans to design the system and realize the active panoramic detection in a cylinder structure with 100 mm diameter and some axial length. The system should have high time sensitivity, and the effective detection range is in 15 m. The structure should be simple, firm and work well in the great acceleration environment. The active laser detection system includes the laser transmission optical system, receiving optical system and circuit system. Due to the finite size, the semiconductor laser is chose in this research. The transmission optical system should insure the emission beam has the appropriate optical path angle and beam field angle. In the receiving optical system, the detector device could have the certain detecting directivity and field angle, and get the target reflected laser beam to improve the detection signal-to-noise ratio with big light pass aperture. Therefore, the research must consider the target detection matching and the system space beam layout method. In this paper, the circuit system is not discussed. Considering the above requirements, the detection system should be designed to achieve the following functions:
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(1) Taking the system axis as the center, the laser transmission system emits laser beams to the 360◦ space, which form an “umbrella” shape. These laser beams is the “umbrella surface”. If the distance between the target and the transmission system is less than a certain space range, the laser beam will detect the target and form the scattering. (2) The angle of the umbrella surface and the axis can be changed from 60◦ to 90◦ depend on the actual demand.
H. Wen / Optik 123 (2012) 34–39
35
1
F
f
B
b
B
O e
c
E 5
2
d D
C
H
A
D=100m
6
A a
Laser source Cylinder structure
3
4
O
(a) Laser source position set
Fig. 1. Partition beam layout method.
(3) The receiving system is composed of optical receiving components and the corresponding wave length photoelectric detectors. The detector device could get the scatting signal from the 6 to 8 same angle space areas and estimate the target orientation.
F
B
G
A
H
O
C
3. Panoramic optical system layout designs
E
D
3.1. Laser beam layout method
(b) Field angle calculation inscribed hexagon Considering the low cost and finite size, the partition detection method is proposed based on the existing research condition and project demand. The partition method divides the space into 4–8 area, and each area could realize the light source emission and echo signal receiving by the independent detector unit. In order to cover the entire circumference without non-blind area, these area boundaries could superpose or have small overlapping. The detector unit is an integrated transmission and receiving optical system and it will be discussed in the following paragraph. Two questions should be considered before design. Firstly, the laser beam energy distribution characteristic is Gaussian distribution characteristic and the oversize field angle laser light source is not suitable. Secondly, considering the existing common laser product’s size, the 100 mm diameter is quite small to ensure the beam emission direction and install several lasers, especially for columnar structure. Compromising the two points, the circumference is divided into 6 areas; each area has an independent detector unit to realize the light beam emission and echo signal receiving. The single light source field angle is not so big and the lasers could be installed in the finite size based on the partition beam layout method. Under the high-speed detection condition, the detector reaction rate is the key to realize the system function. In order to make the response promptly, the research choose the high reaction rate detector and propose a new mechanism – an “umbrella” shape beam design to help the system discover the target early, which is shown in Fig. 1. In Fig. 1, the symbol a–f stands for the laser source in the system respectively; the symbol 1–6 represents the laser beam detection field angle on the 360◦ circumference; the symbol O is the intersection point of the laser sources on the system axis and the symbol A–F stands for the vertex on the cycle. 3.2. Calculate the laser source The linear beam laser is chosen to cover the single area, whose field angle in one direction is 30–90◦ and in the vertical direction is less than 1◦ . This kind laser has the more possibility to satisfy the regional coverage and the echo signal power density. The laser panoramic system is different with the remote lidar system, the
Fig. 2. Laser source position establishment and field angle calculation inscribed hexagon. (a) Laser source position set and (b) field angle calculation inscribed hexagon.
former’s operating range is short and the target surface is complex, therefore the laser is not reflected from the target surface by the pointolite way. First step: calculate the laser energy threshold. If the target has the diffuse reflection characteristic and the laser power is PT , the received echo power Pt is [11] Pt = 4PT
At AT T R 02 2 R4
(1)
where T , R , 0 and are the emission optical system transmittance, the receiving optical system transmittance, the unidirectional propagation path transmittance, and the target reflectivity respectively, and At is the detector effective aperture area. If the laser beams cover the target completely, then the presented target area is AT =
2 R2 4
(2)
where R is the operating range and is the emission beam plane angle. Due to the system operating range is not long, the atmospheric transmission attenuation could be ignore, that is 0 = 1. Pt can be written as Pt = PT
At T r R2
(3)
Second step: estimate the laser source position and calculate the field angle. Fig. 2 shows the laser source position establishment and the field angle calculation inscribed hexagon structure. A–F is the hexagon vertex and O is some point on the system axis which is the identical point in Fig. 1. The symbol H is the inscribed hexagon center, and the symbol G is the center of line segment AB. In this design requirement ∠GOH is 60◦ , and ∠AOB is about 53.13◦ after calculation. Then the field angle can be set as 55◦ . Once the laser
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field angle on one direction is bigger than 55◦ , and then the 360◦ omnidirectional detection will be realized. The diffraction spot size on 10 m detection distance is 0.087 m, which meets the field angle on the other direction less than 1◦ requirement. One question is worthy to consider, that is the whole laser component size should be installed in the limited space size to realize the emission, receiving and detection function. In the view of simple and convenient, as long as the detector unit can be set in the hexagonal pyramid with O as the vertex, it will be suitable for the system. 4. Integrated designs of the panoramic transmission and receiving optical system In order to obtain the best detection performance, the laser and detector coaxial design method is adopted in this research, which is the integrated design of the transmission and receiving optical system in fact. The detector unit also includes the detector equipment besides the laser source. The detector field angle should be at least 60◦ , and 6 same detectors can realize the panoramic target detection. In view of the low cost and the detector only need to receive the echo signal energy, the simple lens is selected in the system design. The lens not only causes the echo signal imaging on the detector, but also is the shaping lens on beam least significant end. The laser beam through the lens should be discussed in detail.
Without considering the lens curvature radius and aperture size, the transformation of the beam through the lens should be calculated at first, and then makes the further adjustment. The laser intensity distribution on beam cross section is uneven. The relation between the amplitude A and the beam cross section radius r is A = A0 e
(4)
where A0 is the beam cross section center amplitude and w is a parameter related with r. So the laser beam is one kind of Gaussian beams. This kind Gaussian beam has the following transformation: Let z and w0 be the waist position and waist radius of the Gaussian beam before the lens respectively. By some transformation method, the waist position z and waist radius w0 of the Gaussian beam after the lens can be written as: z = f
z(f + z) + (w02 /) 2
2
(f + z) + (w02 /)
2
(5)
2
w 0 =
f w02
2
2
(f + z) + (w02 /)
(6)
When the beam waist position is far away from the lens, the waist position can be calculated by the paraxial optics image equation, namely
(f + z)
w02
2
(7)
and there is the equation z f +z
(8)
1 1 1 − = z z f
(9)
z ≈ f
w0 = f
If the beam waist position is on the lens front focal plane, another data will be obtained. That is once z = −f , z = f . It indicates when the Gaussian beam waist is on the lens object focal plane, the beam
w0
(10)
The Eq. (10) indicates when z = −f , the emission beam will have the beam waist radius maximum. 4.2. The transformation of laser beam divergence angle through the simple lens Let the Gaussian beam divergence angle before and after the simple lens is and . The equation derivation of Gaussian beam divergence angle on meridian plane is as follows: From the concept of the Gaussian beam aperture angle, w0 =
//
(11)
and the Gaussian beam section radius is
w(z) = w0 1 +
z
2 1/2
w02
(12)
Similarly w0 =
4.1. Gaussian beams and transformation
−r 2 /w2
waist position will be on the image focal plane after the lens transformation, which is completely different with the imaging concept of the geometric optics. The beam waist radius can be written as
//
(13)
So // · // =
f
(14)
On the sagittal plane there is · ⊥ = ⊥
f
(15)
Eqs. (14) and (15) show the product of the beam divergence angle in the same direction before and after the simple lens is a constant, which will be used in the following design. 4.3. The detector unit double lens structure design Based on the above conclusion, we design the double lens structure of the detector unit. If the laser beams with 60◦ × 1◦ field angle through the double lens, the transmission can be shown in Fig. 3. In order to see the laser beam clearly, the beam is enlarged in Fig. 3. The laser beam divergence angle has changed greatly through one simple lens (lens1), whose focal length is f1 (f1 = f), so another simple lens (lens2) is required to return the Gaussian beam to original state, whose focus is just the emission beam waist position. Actually this is a simple and ingenious symmetric transformation design, lens2 focal length is f2 , namely f1 = f2 = f. Such design result is a 4f system in fact, the laser beam changes through Lens1 and returns to 60◦ × 1◦ field angle through lens2 by the reverse transform. In Fig. 3 the symbol 4 stands for the transformation of the laser beam through lens1 (or lens2). The Gaussian beam emits on a random object, and the echo signal reflected by the object is the Gaussian beam. That is, the laser beams with 60◦ × 1◦ field angle through the double lens and the echo signal is the laser beams with 60◦ × 1◦ field angle. So the transformation of the laser beam through lens1 (from the laser source) and lens2 (from the echo signal) has the same result, which can be calculated by the above equations. The symbol 7 is the detector equipment, established between lens1 and lens2, and it can receive the echo signal, whose power is smaller
H. Wen / Optik 123 (2012) 34–39
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Table 1 Beam divergence angle and waist radius transformation through the lens. Optical parameters
Original laser beam
Beam through lens 1
Beam through lens 2
Meridian plane divergence angle Sagittal plane divergence angle Meridian plane beam waist radius Sagittal plane beam waist radius
/6 /360 359.152 × 10−9 m 23,709.157 × 10−9 m
28.2252 × 10-6 rad 1693.5112 × 10-6 rad 7.3304 × 10-3 m 0.122 × 10-3 m
/6 /360 359.152 × 10−9 m 23709.157 × 10−9 m
2
Table 2 ZEMAX lens design results.
5
3
6
4
8
1
7 Lens2
Lens1
Surf
Type
Radius
Thickness
OBJ STO 2 3 IMA
STANDARD STANDARD STANDARD STANDARD STANDARD
Infinity 11.88 −79.18022 Infinity Infinity
Infinity 2 0 16.97
Glass K9
Diameter 0 12 11.94327 11.78776 0.08549003
(a) Laser beam divergence angle through the double lens 3
5 9
4
8
1
7 Lens1
Lens2
(b) Detect the echo signal 1: Laser light source 2: Laser beam with 60°×1° field angle 3: Lens1 4: Transformation of Beam through lens1 (or lens2) 5: Lens2 6: Transformation of Beam through lens2 with field angle 60°×1° 7: Detector equipment 8: Detection target 9: The echo signal with 60°×1° field angle Fig. 3. Transformation of laser beam divergence angle through the double lens structure. (a) Laser beam divergence angle through the double lens and (b) detect the echo signal. 1: Laser light source. 2: Laser beam with 60◦ × 1◦ field angle. 3: Lens1. 4: Transformation of beam through lens1 (or lens2). 5: Lens2. 6: Transformation of beam through lens2 with field angle 60◦ × 1◦ . 7: Detector equipment. 8: Detection target. 9: The echo signal with 60◦ × 1◦ field angle.
divergence angle and beam waist radius through the lens by the above conclusions and correlation equations.Refers to the above data, selects small aperture D under the feasible premise, which meets requirements of the light pass aperture size and the minimum relative aperture, and then D ≥ 8 mm. As seen from Table 1, the beam divergence angle is small and the beam waist radius big, where the detector equipment can be placed. So long as the reservation space is bigger than the beam waist light spot size, the coaxial design of the emission optical system and the receiving optical system will be realized. The symbol 7 is the detector equipment in Fig. 3. In the design, the reservation space length and width are 15 mm and 1 mm respectively, and the detector equipment can be placed in the rest position to realize the big field detection. The simple lens system is selected in the finite size, and it does no need to rectify some high order aberration, only needs to rectify the spherical aberration at a certain extent. The lens selects the most common K9 glass to reduce cost and the curvature radius r equation is: r1 = −r2 =
2(n − 1) ˚
(16)
than the emission laser. The detector equipment size is calculated in the following section.
where ˚ is the lens focal power and n is the refractive index. The lens thickness d can be calculated by Eq. (17) [12] with the known parameters:
4.4. Calculate and optimize the double lens parameters
f = −f =
The Gaussian beam returns to original state through the double lens system, which is shown in Fig. 4. Some lens parameters should be calculated; i.e., the aperture size, the focal length, the lens curvature radius, and the detector equipment size should be explained. Considering the two same focal length lens are placed in the system and the first lens field angle is about 60◦ , the lens focal length maximum is 25 × 31/2 /3 = 14.43 mm. The laser size is 30 × 14 mm with 650 nm working wavelength and the lens focal length is 14 mm in this research. Table 1 represents the transformation of the beam D=100
The double lens and detector equipment
Mirror Cylinder structure Laser source
Fig. 4. Reflex optical path method.
nr1 r2 (n − 1)[n(r2 − r1 ) + (n − 1)d]
(17)
The initial structure data is input ZEMAX to optimize after calculating. The main purpose is to control the single lens’ spherical aberration and effective focal length, and the final results are shown in Table 2. 4.5. The detector unit structure design According to the calculated data, a question should be considered, that is 6 detector units cannot be placed in the finite size system with the 100 diameter, which includes the laser and double lens system, because a single detector unit length is about 70 mm. A reflex optical path method is presented in this research as shown in Fig. 4. Each detector unit’s laser is placed in the system axis center position concentratively, and a mirror is placed in the corresponding position, which could reflect the laser beam to the detector equipment. The angle between the mirror and the system axis is 60◦ . The laser beam from the laser source emits on lens1 directly in Fig. 3, while in Fig. 4 it has depend on the mirror to emit on lens1. The laser beams before and after the mirror is the same Gaussian beam. There is not any difference between the reflex optical path method and the direct optical path method which is shown in Fig. 3 except
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H. Wen / Optik 123 (2012) 34–39
(a) Top view The double lens and detector equipment Fig. 7. The distribution graph of the echo signal theoretical and actual measured value.
Laser source
(b) Front view Fig. 5. Panoramic optical system structure. (a) Top view and (b) front view.
for the loss energy. Comparing with the suitable establishment of detector unit in the finite size system, the inevitable loss energy is acceptable. 4.6. Panoramic optical system product and experiment results In view of the effective detector distance and other reasons, the technical parameters of the custom-order linear laser are as follows: the size is 14 × 30 mm, the wavelength is 650 nm, the LD power is 100 mw, the output power is 50 mw, and the field angle is 60◦ × 1◦ , the big angle is realized by using a triangle prism. Open the radial holes in the cylinder structure with 100 mm diameter, as shown in Fig. 5, these holes are arranged in the system panoramic detection uniformly, where the position of the laser source and the detector equipment overlaps. The integrated design of the transmission and receiving optical system is completed, and the panoramic optical system product is shown in Fig. 6. As seen in Fig. 6, the transmission system (laser source and related circuit system) is arranged in the panoramic optical system under hole, and the double lens and detector equipment is placed in the upper hole.
Fig. 6. Panoramic optical system product.
In order to test the working performance of the system product, the echo signal experiment is carried out under the laboratory environment. In this experiment, an assumed detection target is placed in a certain space position. Set the most distance between the detection target and the panoramic optical system is 15 m. Taking the target as the center, the panoramic optical system can go forwards or backwards while rotate randomly in the circle area, and the system mechanical movement is not discussed here. So the angle between the system axis and the detection target center is the random value. Known from the above discussion, the transmission system will emit laser beams to the 360◦ space and the detector equipments will obtain some echo signals reflected by the detection target. The echo signal power received by the detector equipments is different. The direction of the echo signal with the biggest power is the target space region and the maximum power is obtained by the nearest detector equipment. The distance between the detection target and that nearest detector equipment is defined as the shortest detection range. The theoretical value of the echo signal can be calculated by the above correlation equations. The actual measured value of the echo signal and the theoretical value of the echo signal are shown in Fig. 7. Although there is certain error between the actual value and the theoretical value, but the error is very small as seen in the graph. The maximum error is about the 4.8% of the echo signal power theoretical value by calculation. The experiment results show the system works stably and meets the requirement anticipated design purpose. 5. Conclusions A laser target panoramic optical system is designed in this paper, considering the finite size detection system, the partition beam layout method is proposed. The transformation of the Gaussian beam through the lens is discussed and the integrated design of the coaxial transmission and receiving system after calculating and optimizing the lens parameters. Under the existing laboratory condition, the echo signal experiment is carried out to test the working performance of the system product. The experiment results show the system achieves the anticipated goal with low cost and small volume. The design idea, method and product in this paper have some extension value. Future work can be improved by the following points: (1) The laser produces the reflection may form the noise disturbance when passing through the lens, and the problem is considered to be solved by the coating. As a result the reflected laser may be received by the detector equipment and it may interrupt the detection precision, which is caused by the lens
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film surface, the corresponding experiment will be carried out in the future work. (2) At present, the system product working performance is only tested under the laboratory condition with −20 ◦ C to 100 ◦ C temperature and ≤80% humidity. The system stability should be verified in the adverse target detection environment. References [1] W.J. Yue, B.Y. Zheng, Spectrum sensing algorithms for primary detection based on reliability in cognitive radio systems, Comput. Electr. Eng. 36 (3) (2010) 469–479. [2] C. Bjork, W. Wan, Mid-wave infrared (MWIR) panoramic sensor for various applications, Proc. SPIE 7660 (2010), 76600B-1–76600B-9. [3] A. Baba, R. Chatila, Data fusion of panoramic images and laser scans for dynamic targets detection, in: Proceedings of the International Conference on Information and Communication Technologies from Theory to Applications, vol. 29, 2008, pp. 1853–1858.
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