- Email: [email protected]
Real-time adjustment of optical transmitter by laser beam parameter measurement based on two linear array CCD scanning imaging
G Model IJLEO-54446; No. of Pages 5
ARTICLE IN PRESS Optik xxx (2014) xxx–xxx
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Real-time adjustment of optical transmitter by laser beam parameter measurement based on two linear array CCD scanning imaging Jing Xie a,b , Haiqing Chen b , Zuojun Tan a,∗ , Dejia Hou a , Xianfeng Wang a a b
College of Sciences, Huazhong Agricultural University, 430070 Wuhan, PR China Optical and Electronic Information, Huazhong University of Science and Technology, 430070 Wuhan, PR China
a r t i c l e
i n f o
Article history: Received 29 July 2013 Accepted 26 January 2014 Available online xxx Keywords: Optical transmitter Relative intensity distribution curve Beam divergence angle curve Pitching angle curve Beam intensity distribution
a b s t r a c t In this paper, we present a real-time measurement and adjustment method, based on scanning imaging, for optical transmitter which emits 90◦ × 2◦ linear laser beam. This novel optical arrangement consists of an area array CCD and two linear array CCDs. According to the relationship between the positions, angles of transmitter optical components and the beam parameters of emergent laser, the system can help us to decide the real-time adjustment of optical transmitter by measuring the related beam parameters. In order to improve the measurement speed, avoid occlusion and ensure simultaneous measurement, the two linear array CCDs are placed at near field, far field and separated by a definite angle to acquire the beam intensity distribution through suitable nonlinear correction during the process of scanning. After a complete scanning, the beam parameters and the spot image are acquired by continuous measurement. The proof-of-principle experiments showed that the measurement results were in agreement with the analysis. The presented method was applied to direct fast adjustment for higher quality on the assembly of the optical transmitter. The presented procedure is highly advantageous for diverse laser beam emitted from the optical transmitter, such as elliptic, linear and so on. © 2014 Elsevier GmbH. All rights reserved.
1. Introduction Laser optical transmitter [1] is a crucial component of instruments such as lidar, laser fuze and laser range finder. After passing through an optical system, the divergent laser beam emitted from pulse semiconductor laser is transformed into the required beam with small divergence angle and large section. Meanwhile, the collimation and aberration correction of the laser beam are accomplished. And then, the emergent laser beam must meet the requirements of uniformity, directivity and horizontality, which are directly influenced by the internal structure of optical transmitter. Therefore, it needs higher quality on the assembly of optical transmitter. Especially, it is important to achieve fast, real-time adjustment and judge whether the optical transmitter reaches assembly requirements. Up to now, many automatic measurement systems [2,3] for evaluating the performance of laser optical transmitter have been developed. In these systems, comprehensive measurement of laser parameters was carried to evaluate the performance of optical
transmitter. Nevertheless, these automatic measurement systems were only suitable for the laser beam with elliptic spot, which has small divergence angle in the vertical and horizontal directions. In addition, it is impossible to adjust the internal structure of optical transmitter due to the results in real-time measurement. In this paper, according to the characteristics of new optical transmitter which emits 90◦ × 2◦ linear laser beam, we discussed the relationship between the position, angle of transmitter optical components and the beam parameters of emergent laser. A realtime measurement and adjustment method based on two linear array CCDs scanning imaging is proposed. The two linear array CCDs are placed at near field, far field and separated by a definite angle. The beam parameters, including the relative intensity distribution, beam divergence angle and pitching angle in view direction, are analyzed by near field and far field light beam distribution. These parameters help us to adjust the optical transmitter efficiently, such as the position or the deflection angle of the internal optical components.
2. Design principle analysis ∗ Corresponding author. Tel.: +86 13971372622. E-mail address: [email protected] (Z. Tan).
Assembled optical transmitter [4] consists of a pulse semiconductor array laser, an aspheric lens and a group of semi-cylindrical
http://dx.doi.org/10.1016/j.ijleo.2014.01.145 0030-4026/© 2014 Elsevier GmbH. All rights reserved.
Please cite this article in press as: J. Xie, et al., Real-time adjustment of optical transmitter by laser beam parameter measurement based on two linear array CCD scanning imaging, Optik - Int. J. Light Electron Opt. (2014), http://dx.doi.org/10.1016/j.ijleo.2014.01.145
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IJLEO-54446; No. of Pages 5
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2
Fig. 2. Beam expansion system of the cylindrical group mirror.
Fig. 1. The composition block diagram of optical transmitter.
mirrors (V type), as shown in Fig. 1. The aspheric lens compresses and collimates the laser beam emitted from the pulse semiconductor array laser. It also can correct spherical aberration. A group of semi-cylindrical mirrors, which are glued on a V-groove substrate side by side, expands the collimated laser beam in the sagittal direction. We call it cylindrical group mirror. The pulse semiconductor array laser emits Hermite-Graussian (HG) beam TEMmn with the beam width [5]:
∞ ⎧ √ ⎪ 2 4 x2 Hm ( 2x/ω(z)) exp(−2x2 /ω2 (z)) dx ⎪ ⎪ ⎪ ⎪ −∞ 2 ⎪ ωm = (2m + 1)ω2 (z) (z) = ∞ ⎪ ⎪ √ ⎪ 2 ⎪ Hm ( 2x/ω(z)) exp(−2x2 /ω2 (z)) dx ⎨ −∞ ∞ √ ⎪ ⎪ 4 x2 Hn2 ( 2x/ω(z)) exp(−2x2 /ω2 (z))dx ⎪ ⎪ ⎪ −∞ ⎪ = (2n + 1)ω2 (z) ⎪ ωn2 (z) = ∞ ⎪ ⎪ √ ⎪ 2 2 2 ⎩ Hn ( 2x/ω(z)) exp(−2x /ω (z)) dx
(1)
−∞
where ωm (z) and ωn (z) are respectively the beam width in the xdirection (sagittal) and y-direction (meridian). ω(z) denotes the beam width of Gaussian beam TEM00 , reads as:
ω(z) = ω0
1+
z
2 (2)
ω02
where is the wavelength and ω0 is the waist radius of beam. The beam divergence angle [6] is expressed as a full angle measured for the increase of the beam width with increasing distance from the beam waist location, given by:
⎧ 2 ωm (z)
⎪ ⎨ m = lim z = 2m + 1 ω z→∞ 0
⎪ ⎩ n = lim ωn (z) = 2n + 1 2 z→∞
z
position and deflection directly affect the beam quality, especially the distance between the cylindrical group mirror and the aspheric lens, the deflection angle of the cylindrical group mirror. 2.1. The relative intensity distribution in view direction The relative intensity distribution in view direction means energy distribution curve of the laser beam emitted from optical transmitter. It shows the uniformity of radiation energy in the whole view field. The collimated laser beam is expanded after two refractions through the cylindrical group mirror. The light path of the center cylindrical lens [9] is depicted in Fig. 2(a). Z-direction is the main optical axis. ˛ and i1 are respectively the incident angle and refracted angle of incident ray on the half cylinder. i2 and ˇ are respectively the incident angle and refracted angle of emergent ray on the flat substrates. n0 is the refractive index of air and n1 is the refractive index of the cylindrical group mirror. From Snell’s law, we obtain that:
n0 sin ˛ = n1 sin i1
Considering geometric relations in Fig. 2(a), i2 is given as: i2 = ˛ − i1
(6)
Combining Eq. (5) with Eq. (6), ˇ can be described as:
(3)
(5)
n1 sin i2 = n0 sin ˇ
ˇ = f (˛) = arcsin
n1 sin ˛ n0
1−
2
n0 sin ˛ n1
− sin ˛
2
1 − sin
˛
(7)
ω0
where m and n are respectively the beam divergence angle in the x-direction and y-direction. According to the imaging principle and transformation law of Gaussian beam [7], the divergence angle of the emergent beam through aspheric lens [8] is expressed as:
⎧ 2 1 ω 2
⎪ √ 1 2 l ⎪ 0 = 2m + 1 ⎪ m = 2m + 1 1 − + 2 ⎪ ⎨ ω0 f f ω02 ⎪ 2 1 ω 2
⎪ √ 2 l 1 ⎪ 0 ⎪ n = 2n + 1 = 2n + 1 1 − + 2 ⎩ 2 ω f 0
ω0
f
(4) where f is the focal length and l denotes the distance between the light source and the aspheric lens. As demonstrated in Eq. (4), the divergence angle reaches its minimum if l = f. In other words, the best collimation effect is achieved while the emergent beam waist lies in the focal plane of the lens, as shown in Fig. 1. Then, the collimated laser beam is expanded in the sagittal direction by multiple semi-cylinder after the cylindrical group mirror, the beam is shaped into a narrow light band of 90◦ × 2◦ . Hence, its
In order to understand the relationship between ˛ and ˇ, we take the derivative of f(˛). Observe now that the conditions ˛ ∈ (0◦ , 90◦ ), f (˛) > 0. This means that the refracted angle ˇ increases with the increase of the incident angle ˛ or the beam width on the original surface of the cylindrical group mirror. In terms of Fig. 2(b), the light ray after two refractions is simultaneously deviated from both directions (upward and downward). Almost half of the light ray is expanded near the main optical axis. Therefore, the smaller beam width can ensure the uniformity of energy distribution. A portion of the central light energy complements the edge. Thus, the cylindrical group mirror should be placed on the position B of Fig. 1. If it is placed on the left or right side, energy stacking is produced near the main optical axis, as shown in Fig. 3. The energy near the main optical axis is more than the top and bottom edge. A Gaussian-like energy distribution is formed. This phenomenon makes laser beam to be poor energy uniformity and small view angle. Hence, we can use the parameter to decide coarse adjustment of the distance between the cylindrical group mirror and the aspheric lens. The relative value of the intensity for the optical transmitter demands ≥50%.
Please cite this article in press as: J. Xie, et al., Real-time adjustment of optical transmitter by laser beam parameter measurement based on two linear array CCD scanning imaging, Optik - Int. J. Light Electron Opt. (2014), http://dx.doi.org/10.1016/j.ijleo.2014.01.145
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Intensity(Energy)
10
x 10
3
6
8
Energy stacking
6
4
Main optical axis
2 Fig. 5. Measurement schematic diagram of pitching angle.
0
X-direction -50
0
50
Rotation angle
2.3. The pitching angle in view direction
Fig. 3. Energy distribution curve (contained energy stacking).
2.2. The beam divergence angle in view direction The beam divergence angle in view direction is available for evaluating the collimated degree which represents the longdistance transmission characteristics of optical transmitter. According to the principle of beam expansion through the cylindrical group mirror [10], the divergence angle of the emergent laser beam in the y-direction remains the same, reads as: n
=
n
=
2 2n + 1 ω0
(8)
Hence, the cylindrical group mirror should be placed on the emergent beam waist to acquire the minimum value of the divergence angle. Approximately, we assume that beam width conforms to linear equation in the far field. Then the method of linear fitting by two points is adopted to measure the divergence angle in Fig. 4. It is expressed as: n ≈ ˛ = 2arg tan
d2 − d1 d2 − d1 ≈ z2 − z1 2(z2 − z1 )
(9)
where d1 and d2 are respectively the beam width of the position z1 and z2 , Z is the distance difference. While the cylindrical group mirror is placed on the position B of the emergent beam waist in Fig. 1, the divergence angle has the minimum with the condition of d2 ≈ d1 . If it is placed on the position A, the divergence angle has the negative value with d2 < d1 . On the contrary, if it is placed on the position C, the divergence angle has the positive value with d2 > d1 . Therefore, we can use it to decide fine adjustment of the distance between the cylindrical group mirror and the aspheric lens. The measurement values of the divergence angle for optical transmitter are limited within ±30 .
Fig. 4. Measurement schematic diagram of beam divergence angle.
The pitching angle in view direction means the inclination angle between laser beam and the datum plane of optical transmitter. It can evaluate the levelness of the laser beam. Fig. 5 illustrates that it is expressed as the angle between the beam center and the horizontal axis. As the geometrical relationship in Fig. 5 show: ϕ = arctg
h − h 2 1 Z
≈
h2 − h1 Z
(10)
where h1 and h2 are respectively the beam center of the position z1 and z2 . By means of the formula with beam intensity barycenter [11], hi is found by calculating its center of mass using a first-order moment method, given by: hi =
ipIi i I i i
(11)
where Ii is the intensity of the ith pixel and p is the size of the ith pixel. According to the process technology and imaging principle [12], the cylindrical group mirror transforms a parallel laser beam with elliptic spot into a linear laser beam along certain direction. This direction is perpendicular to the generatrix of the cylindrical group mirror. Hence, the levelness of the laser beam is optimum with the condition that the generatrix is parallel to the vertical axis, as shown in the position B of Fig. 6(a). While the generatrix has a left deflection from the vertical axis, the emergent laser beam is upward sloping and the pitching angle curve in view direction has positive slope. On the contrary, the laser beam is downward sloping and the curve has negative slope. Therefore, we can use the parameter to adjust the deflection angle of the cylindrical group mirror. The difference value of the pitch angle for the optical transmitter demands ≤30 .
Fig. 6. Schematic diagram of the deflection angle with cylindrical group mirror.
Please cite this article in press as: J. Xie, et al., Real-time adjustment of optical transmitter by laser beam parameter measurement based on two linear array CCD scanning imaging, Optik - Int. J. Light Electron Opt. (2014), http://dx.doi.org/10.1016/j.ijleo.2014.01.145
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Fig. 8. Comparison of the relative intensity distribution curve and corresponding scanning spot before and after the coarse adjustment. Fig. 7. Scheme of measurement setup.
3. Measurement setup The optical setup in Fig. 7 consists of the control module, the imaging system and the data processor. It can help us to decide the real-time adjustment of optical transmitter by measuring the related beam parameters, including the relative intensity distribution, beam divergence angle and pitching angle in view direction. Because the optical transmitter emits 90◦ × 2◦ linear laser beam, a real-time measurement and adjustment method based on two linear array CCDs scanning imaging is proposed. The control module including motion controller, rotary stage and goniometer and translation stage controls the optical transmitter to rotate with a certain speed. The linear array CCD acquires the beam intensity distribution and the area array CCD observes the laser beam during the process of scanning. The optical filter eliminates parasitic light. In order to improve the measurement speed, the two linear array CCDs are respectively placed on the position z1 of the near field and the position z2 of the far field. Meanwhile, they are separated by an angle to avoid occlusion and ensure simultaneous measurement. Finally, the beam parameters and the spot image are obtained by image acquisition and data processing after the scanning completes. 4. Results and discussion In the present experiment, the linear array CCD is a TCD1501D model product of Toshiba Company. It has 5000 photosensitive pixels, each pixel size is 7 m × 7 m. The positions of the two linear array CCDs are: z1 = 0.337 m, z2 = 0.545 m. Moreover, they are separated by = 30◦ . When the optical transmitter rotates around the y-axis with the view angle of 110◦ , the emergent laser beam sweeps over each linear array CCD. The intensity distribution curves of the position z1 and z2 in the y-direction are obtained for every degree through suitable nonlinear correction [13]. Since the beam width is defined by the transverse size while the beam intensity is decreased to the 1/e2 of peak value. Using Eqs. (9) and (10), the values of the divergence angle and pitching angle can be calculated. After a complete scanning, the relative intensity distribution curve, beam divergence angle curve and pitching angle curve in view direction are acquired by continuous measurement. We can use these curves to direct the real-time adjustment of the optical transmitter. The results for the measurement of the relative intensity distribution in view direction before and after the coarse adjustment are compared in Fig. 8. As can be seen from the figure, the uniformity of laser beam energy is very poor before the coarse adjustment. Energy stacking is formed in the range of 25–35◦ . After the left or right shift of the cylindrical group mirror, the energy distribution of the laser beam is more uniform and the curve becomes smoother. The relative value of 60% satisfies the request. However, this parameter only can determine the approximate position. The cylindrical
Fig. 9. Comparison of the beam divergence angle curve and corresponding scanning spot before and after the further fine adjustment.
group mirror needs to be placed accurately at the waist position. The optical transmitter needs further fine adjustment. The results for the measurement of the beam divergence angle in view direction before and after the further fine adjustment are compared in Fig. 9. The maximum, average and minimum values are selected and analyzed to test the accurate position of the cylindrical group mirror. From Fig. 9, we can see that the values of the blue curve are relatively large and the corresponding scanning spot is wider in y-direction. This means that the cylindrical group mirror is a little far away from the aspheric lens. It needs to be pushed slightly. Hence, all values of the red curve are within the acceptable range and satisfy the request. The average value of 0.963 denotes the perfect position of the cylindrical group mirror. Nevertheless, the above two parameters are unable to adjust the deflection angle of the cylindrical group mirror. It needs independent adjustment. The pitching angle curve is identical with the laser beam in tilt direction which guides the adjustment direction. The difference value between the maximum and the minimum indicates the gradient. The results for the measurement of the pitching angle in view direction before and after the deflection angle adjustment are compared in Fig. 10. The blue curve has positive slope and the corresponding scanning spot is upward sloping. This means that the cylindrical group mirror has a left deflection. It needs to be rotated with clockwise direction. Hence, the difference value of the red curve is 2.768 , which denotes the good levelness of the laser beam.
Fig. 10. Comparison of the pitching angle curve and corresponding scanning spot before and after the deflection angle adjustment.
Please cite this article in press as: J. Xie, et al., Real-time adjustment of optical transmitter by laser beam parameter measurement based on two linear array CCD scanning imaging, Optik - Int. J. Light Electron Opt. (2014), http://dx.doi.org/10.1016/j.ijleo.2014.01.145
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In all analyzed cases, the results demonstrate the functionality of the method, especially in real-time adjustment of transmitter components.
5
Fundamental Research Funds for the Central Universities (Grant No. 2014QC013, No. 2014JC008). References
5. Conclusion We introduced a real-time measurement and adjustment method for optical transmitter based on scanning imaging using two linear array CCDs. We demonstrated the feasibility by analyzing the relationship between the beam parameters and the internal structure of the optical transmitter. The relative intensity distribution curve and beam divergence angle curve in view direction can reflect the position of the cylindrical group mirror. Moreover, the pitching angle curve in view direction can reflect the deflection angle of the cylindrical group mirror. The presented method was applied to direct fast adjustment for higher quality on the assembly of the optical transmitter. The proof-of-principle experiments showed that the measurement results were in agreement with the analysis. The experiment results demonstrated the feasibility and accuracy of this method. We conclude that this method can provide an experimentally simple possibility to accomplish real-time adjustment quickly. The presented procedure is highly advantageous for diverse laser beam emitted from the optical transmitter, such as elliptic, linear and so on. Acknowledgements This work was partly supported by National Natural Science Foundation of China (Grant No. 31000848, No. 41201364), the
[1] O. Liam, D. Kapil, Y.G. Frederic, S. Andreas, T. Emel, et al., Scalable optical transmitter and receiver based on cascaded nanoresonator modulators and multiwavelength laser, in: Proc. SPIE 8630, Optoelectronic Interconnexts XIII, 86300P, 2013, http://dx.doi.org/10.1117/12.2004841. [2] Q.Q. Wang, J. Liu, Z. Peng, L. Liu, Measurement system for laser divergence angle based on labview, Chin. J. Lasers 39 (2012) 1108005. [3] D.Y. Zheng, Research on Emission System of LD Laser Fuze, Changchun University of Science and Technology, Changchun, 2011. [4] X.J. Wang, A laser beam shaping optical system for laser fuze, Aero Weaponry 10 (2012) 56–60. [5] S. Orazio, Principles of Lasers, 4th ed., Springer-Verlag New York Inc., 2010. [6] ISO 11146-1, Test methods for laser beam widths, divergence angles and beam propagation ratios, 2005. [7] H.Y. Li, Q. Li, Z.W. Xia, Y.P. Zhao, D.Y. Chen, Q. Wang, Influence of Gaussian Beam on terahertz radar cross section of a conducting sphere, J. Infrared Millimeter Terahertz Waves 34 (2013) 88–96. [8] Z.M. Fan, Z. Li, L.X. Qian, Aspherical lens laser beam shaping system, Infrared Laser Eng. 41 (2012) 353–357. [9] C.J.R. Sheppard, Cylindrical lenses-focusing and imaging: a review, Appl. Opt. 52 (2013) 538–545. [10] Y. Li, Y.F. Liu, Q. Li, S.T. Wu, Polarization independent blue-phase liquid crystal cylindrical lens with a resistive film, Appl. Opt. 51 (2012) 2568–2572. [11] Z.Y. Ye, H.P. Song, L. Wang, et al., Measurement of far-field beam quality parameters of high power laser, High Power Laser Particle Beams 23 (2011) 87–91. [12] D.X. Chen, Optical processing technique of small-radius cylindrical lens, J. Appl. Opt. 33 (2012) 580–583. [13] Y.X. He, X.Y. Li, Analysis of influence of CCD’s nonlinear response characterization on measurement results of focal spot and beam quality, Chin. J. Lasers 39 (2013) 1–8.
Please cite this article in press as: J. Xie, et al., Real-time adjustment of optical transmitter by laser beam parameter measurement based on two linear array CCD scanning imaging, Optik - Int. J. Light Electron Opt. (2014), http://dx.doi.org/10.1016/j.ijleo.2014.01.145
ARTICLE IN PRESS Optik xxx (2014) xxx–xxx
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Real-time adjustment of optical transmitter by laser beam parameter measurement based on two linear array CCD scanning imaging Jing Xie a,b , Haiqing Chen b , Zuojun Tan a,∗ , Dejia Hou a , Xianfeng Wang a a b
College of Sciences, Huazhong Agricultural University, 430070 Wuhan, PR China Optical and Electronic Information, Huazhong University of Science and Technology, 430070 Wuhan, PR China
a r t i c l e
i n f o
Article history: Received 29 July 2013 Accepted 26 January 2014 Available online xxx Keywords: Optical transmitter Relative intensity distribution curve Beam divergence angle curve Pitching angle curve Beam intensity distribution
a b s t r a c t In this paper, we present a real-time measurement and adjustment method, based on scanning imaging, for optical transmitter which emits 90◦ × 2◦ linear laser beam. This novel optical arrangement consists of an area array CCD and two linear array CCDs. According to the relationship between the positions, angles of transmitter optical components and the beam parameters of emergent laser, the system can help us to decide the real-time adjustment of optical transmitter by measuring the related beam parameters. In order to improve the measurement speed, avoid occlusion and ensure simultaneous measurement, the two linear array CCDs are placed at near field, far field and separated by a definite angle to acquire the beam intensity distribution through suitable nonlinear correction during the process of scanning. After a complete scanning, the beam parameters and the spot image are acquired by continuous measurement. The proof-of-principle experiments showed that the measurement results were in agreement with the analysis. The presented method was applied to direct fast adjustment for higher quality on the assembly of the optical transmitter. The presented procedure is highly advantageous for diverse laser beam emitted from the optical transmitter, such as elliptic, linear and so on. © 2014 Elsevier GmbH. All rights reserved.
1. Introduction Laser optical transmitter [1] is a crucial component of instruments such as lidar, laser fuze and laser range finder. After passing through an optical system, the divergent laser beam emitted from pulse semiconductor laser is transformed into the required beam with small divergence angle and large section. Meanwhile, the collimation and aberration correction of the laser beam are accomplished. And then, the emergent laser beam must meet the requirements of uniformity, directivity and horizontality, which are directly influenced by the internal structure of optical transmitter. Therefore, it needs higher quality on the assembly of optical transmitter. Especially, it is important to achieve fast, real-time adjustment and judge whether the optical transmitter reaches assembly requirements. Up to now, many automatic measurement systems [2,3] for evaluating the performance of laser optical transmitter have been developed. In these systems, comprehensive measurement of laser parameters was carried to evaluate the performance of optical
transmitter. Nevertheless, these automatic measurement systems were only suitable for the laser beam with elliptic spot, which has small divergence angle in the vertical and horizontal directions. In addition, it is impossible to adjust the internal structure of optical transmitter due to the results in real-time measurement. In this paper, according to the characteristics of new optical transmitter which emits 90◦ × 2◦ linear laser beam, we discussed the relationship between the position, angle of transmitter optical components and the beam parameters of emergent laser. A realtime measurement and adjustment method based on two linear array CCDs scanning imaging is proposed. The two linear array CCDs are placed at near field, far field and separated by a definite angle. The beam parameters, including the relative intensity distribution, beam divergence angle and pitching angle in view direction, are analyzed by near field and far field light beam distribution. These parameters help us to adjust the optical transmitter efficiently, such as the position or the deflection angle of the internal optical components.
2. Design principle analysis ∗ Corresponding author. Tel.: +86 13971372622. E-mail address: [email protected] (Z. Tan).
Assembled optical transmitter [4] consists of a pulse semiconductor array laser, an aspheric lens and a group of semi-cylindrical
http://dx.doi.org/10.1016/j.ijleo.2014.01.145 0030-4026/© 2014 Elsevier GmbH. All rights reserved.
Please cite this article in press as: J. Xie, et al., Real-time adjustment of optical transmitter by laser beam parameter measurement based on two linear array CCD scanning imaging, Optik - Int. J. Light Electron Opt. (2014), http://dx.doi.org/10.1016/j.ijleo.2014.01.145
G Model
ARTICLE IN PRESS
IJLEO-54446; No. of Pages 5
J. Xie et al. / Optik xxx (2014) xxx–xxx
2
Fig. 2. Beam expansion system of the cylindrical group mirror.
Fig. 1. The composition block diagram of optical transmitter.
mirrors (V type), as shown in Fig. 1. The aspheric lens compresses and collimates the laser beam emitted from the pulse semiconductor array laser. It also can correct spherical aberration. A group of semi-cylindrical mirrors, which are glued on a V-groove substrate side by side, expands the collimated laser beam in the sagittal direction. We call it cylindrical group mirror. The pulse semiconductor array laser emits Hermite-Graussian (HG) beam TEMmn with the beam width [5]:
∞ ⎧ √ ⎪ 2 4 x2 Hm ( 2x/ω(z)) exp(−2x2 /ω2 (z)) dx ⎪ ⎪ ⎪ ⎪ −∞ 2 ⎪ ωm = (2m + 1)ω2 (z) (z) = ∞ ⎪ ⎪ √ ⎪ 2 ⎪ Hm ( 2x/ω(z)) exp(−2x2 /ω2 (z)) dx ⎨ −∞ ∞ √ ⎪ ⎪ 4 x2 Hn2 ( 2x/ω(z)) exp(−2x2 /ω2 (z))dx ⎪ ⎪ ⎪ −∞ ⎪ = (2n + 1)ω2 (z) ⎪ ωn2 (z) = ∞ ⎪ ⎪ √ ⎪ 2 2 2 ⎩ Hn ( 2x/ω(z)) exp(−2x /ω (z)) dx
(1)
−∞
where ωm (z) and ωn (z) are respectively the beam width in the xdirection (sagittal) and y-direction (meridian). ω(z) denotes the beam width of Gaussian beam TEM00 , reads as:
ω(z) = ω0
1+
z
2 (2)
ω02
where is the wavelength and ω0 is the waist radius of beam. The beam divergence angle [6] is expressed as a full angle measured for the increase of the beam width with increasing distance from the beam waist location, given by:
⎧ 2 ωm (z)
⎪ ⎨ m = lim z = 2m + 1 ω z→∞ 0
⎪ ⎩ n = lim ωn (z) = 2n + 1 2 z→∞
z
position and deflection directly affect the beam quality, especially the distance between the cylindrical group mirror and the aspheric lens, the deflection angle of the cylindrical group mirror. 2.1. The relative intensity distribution in view direction The relative intensity distribution in view direction means energy distribution curve of the laser beam emitted from optical transmitter. It shows the uniformity of radiation energy in the whole view field. The collimated laser beam is expanded after two refractions through the cylindrical group mirror. The light path of the center cylindrical lens [9] is depicted in Fig. 2(a). Z-direction is the main optical axis. ˛ and i1 are respectively the incident angle and refracted angle of incident ray on the half cylinder. i2 and ˇ are respectively the incident angle and refracted angle of emergent ray on the flat substrates. n0 is the refractive index of air and n1 is the refractive index of the cylindrical group mirror. From Snell’s law, we obtain that:
n0 sin ˛ = n1 sin i1
Considering geometric relations in Fig. 2(a), i2 is given as: i2 = ˛ − i1
(6)
Combining Eq. (5) with Eq. (6), ˇ can be described as:
(3)
(5)
n1 sin i2 = n0 sin ˇ
ˇ = f (˛) = arcsin
n1 sin ˛ n0
1−
2
n0 sin ˛ n1
− sin ˛
2
1 − sin
˛
(7)
ω0
where m and n are respectively the beam divergence angle in the x-direction and y-direction. According to the imaging principle and transformation law of Gaussian beam [7], the divergence angle of the emergent beam through aspheric lens [8] is expressed as:
⎧ 2 1 ω 2
⎪ √ 1 2 l ⎪ 0 = 2m + 1 ⎪ m = 2m + 1 1 − + 2 ⎪ ⎨ ω0 f f ω02 ⎪ 2 1 ω 2
⎪ √ 2 l 1 ⎪ 0 ⎪ n = 2n + 1 = 2n + 1 1 − + 2 ⎩ 2 ω f 0
ω0
f
(4) where f is the focal length and l denotes the distance between the light source and the aspheric lens. As demonstrated in Eq. (4), the divergence angle reaches its minimum if l = f. In other words, the best collimation effect is achieved while the emergent beam waist lies in the focal plane of the lens, as shown in Fig. 1. Then, the collimated laser beam is expanded in the sagittal direction by multiple semi-cylinder after the cylindrical group mirror, the beam is shaped into a narrow light band of 90◦ × 2◦ . Hence, its
In order to understand the relationship between ˛ and ˇ, we take the derivative of f(˛). Observe now that the conditions ˛ ∈ (0◦ , 90◦ ), f (˛) > 0. This means that the refracted angle ˇ increases with the increase of the incident angle ˛ or the beam width on the original surface of the cylindrical group mirror. In terms of Fig. 2(b), the light ray after two refractions is simultaneously deviated from both directions (upward and downward). Almost half of the light ray is expanded near the main optical axis. Therefore, the smaller beam width can ensure the uniformity of energy distribution. A portion of the central light energy complements the edge. Thus, the cylindrical group mirror should be placed on the position B of Fig. 1. If it is placed on the left or right side, energy stacking is produced near the main optical axis, as shown in Fig. 3. The energy near the main optical axis is more than the top and bottom edge. A Gaussian-like energy distribution is formed. This phenomenon makes laser beam to be poor energy uniformity and small view angle. Hence, we can use the parameter to decide coarse adjustment of the distance between the cylindrical group mirror and the aspheric lens. The relative value of the intensity for the optical transmitter demands ≥50%.
Please cite this article in press as: J. Xie, et al., Real-time adjustment of optical transmitter by laser beam parameter measurement based on two linear array CCD scanning imaging, Optik - Int. J. Light Electron Opt. (2014), http://dx.doi.org/10.1016/j.ijleo.2014.01.145
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Intensity(Energy)
10
x 10
3
6
8
Energy stacking
6
4
Main optical axis
2 Fig. 5. Measurement schematic diagram of pitching angle.
0
X-direction -50
0
50
Rotation angle
2.3. The pitching angle in view direction
Fig. 3. Energy distribution curve (contained energy stacking).
2.2. The beam divergence angle in view direction The beam divergence angle in view direction is available for evaluating the collimated degree which represents the longdistance transmission characteristics of optical transmitter. According to the principle of beam expansion through the cylindrical group mirror [10], the divergence angle of the emergent laser beam in the y-direction remains the same, reads as: n
=
n
=
2 2n + 1 ω0
(8)
Hence, the cylindrical group mirror should be placed on the emergent beam waist to acquire the minimum value of the divergence angle. Approximately, we assume that beam width conforms to linear equation in the far field. Then the method of linear fitting by two points is adopted to measure the divergence angle in Fig. 4. It is expressed as: n ≈ ˛ = 2arg tan
d2 − d1 d2 − d1 ≈ z2 − z1 2(z2 − z1 )
(9)
where d1 and d2 are respectively the beam width of the position z1 and z2 , Z is the distance difference. While the cylindrical group mirror is placed on the position B of the emergent beam waist in Fig. 1, the divergence angle has the minimum with the condition of d2 ≈ d1 . If it is placed on the position A, the divergence angle has the negative value with d2 < d1 . On the contrary, if it is placed on the position C, the divergence angle has the positive value with d2 > d1 . Therefore, we can use it to decide fine adjustment of the distance between the cylindrical group mirror and the aspheric lens. The measurement values of the divergence angle for optical transmitter are limited within ±30 .
Fig. 4. Measurement schematic diagram of beam divergence angle.
The pitching angle in view direction means the inclination angle between laser beam and the datum plane of optical transmitter. It can evaluate the levelness of the laser beam. Fig. 5 illustrates that it is expressed as the angle between the beam center and the horizontal axis. As the geometrical relationship in Fig. 5 show: ϕ = arctg
h − h 2 1 Z
≈
h2 − h1 Z
(10)
where h1 and h2 are respectively the beam center of the position z1 and z2 . By means of the formula with beam intensity barycenter [11], hi is found by calculating its center of mass using a first-order moment method, given by: hi =
ipIi i I i i
(11)
where Ii is the intensity of the ith pixel and p is the size of the ith pixel. According to the process technology and imaging principle [12], the cylindrical group mirror transforms a parallel laser beam with elliptic spot into a linear laser beam along certain direction. This direction is perpendicular to the generatrix of the cylindrical group mirror. Hence, the levelness of the laser beam is optimum with the condition that the generatrix is parallel to the vertical axis, as shown in the position B of Fig. 6(a). While the generatrix has a left deflection from the vertical axis, the emergent laser beam is upward sloping and the pitching angle curve in view direction has positive slope. On the contrary, the laser beam is downward sloping and the curve has negative slope. Therefore, we can use the parameter to adjust the deflection angle of the cylindrical group mirror. The difference value of the pitch angle for the optical transmitter demands ≤30 .
Fig. 6. Schematic diagram of the deflection angle with cylindrical group mirror.
Please cite this article in press as: J. Xie, et al., Real-time adjustment of optical transmitter by laser beam parameter measurement based on two linear array CCD scanning imaging, Optik - Int. J. Light Electron Opt. (2014), http://dx.doi.org/10.1016/j.ijleo.2014.01.145
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Fig. 8. Comparison of the relative intensity distribution curve and corresponding scanning spot before and after the coarse adjustment. Fig. 7. Scheme of measurement setup.
3. Measurement setup The optical setup in Fig. 7 consists of the control module, the imaging system and the data processor. It can help us to decide the real-time adjustment of optical transmitter by measuring the related beam parameters, including the relative intensity distribution, beam divergence angle and pitching angle in view direction. Because the optical transmitter emits 90◦ × 2◦ linear laser beam, a real-time measurement and adjustment method based on two linear array CCDs scanning imaging is proposed. The control module including motion controller, rotary stage and goniometer and translation stage controls the optical transmitter to rotate with a certain speed. The linear array CCD acquires the beam intensity distribution and the area array CCD observes the laser beam during the process of scanning. The optical filter eliminates parasitic light. In order to improve the measurement speed, the two linear array CCDs are respectively placed on the position z1 of the near field and the position z2 of the far field. Meanwhile, they are separated by an angle to avoid occlusion and ensure simultaneous measurement. Finally, the beam parameters and the spot image are obtained by image acquisition and data processing after the scanning completes. 4. Results and discussion In the present experiment, the linear array CCD is a TCD1501D model product of Toshiba Company. It has 5000 photosensitive pixels, each pixel size is 7 m × 7 m. The positions of the two linear array CCDs are: z1 = 0.337 m, z2 = 0.545 m. Moreover, they are separated by = 30◦ . When the optical transmitter rotates around the y-axis with the view angle of 110◦ , the emergent laser beam sweeps over each linear array CCD. The intensity distribution curves of the position z1 and z2 in the y-direction are obtained for every degree through suitable nonlinear correction [13]. Since the beam width is defined by the transverse size while the beam intensity is decreased to the 1/e2 of peak value. Using Eqs. (9) and (10), the values of the divergence angle and pitching angle can be calculated. After a complete scanning, the relative intensity distribution curve, beam divergence angle curve and pitching angle curve in view direction are acquired by continuous measurement. We can use these curves to direct the real-time adjustment of the optical transmitter. The results for the measurement of the relative intensity distribution in view direction before and after the coarse adjustment are compared in Fig. 8. As can be seen from the figure, the uniformity of laser beam energy is very poor before the coarse adjustment. Energy stacking is formed in the range of 25–35◦ . After the left or right shift of the cylindrical group mirror, the energy distribution of the laser beam is more uniform and the curve becomes smoother. The relative value of 60% satisfies the request. However, this parameter only can determine the approximate position. The cylindrical
Fig. 9. Comparison of the beam divergence angle curve and corresponding scanning spot before and after the further fine adjustment.
group mirror needs to be placed accurately at the waist position. The optical transmitter needs further fine adjustment. The results for the measurement of the beam divergence angle in view direction before and after the further fine adjustment are compared in Fig. 9. The maximum, average and minimum values are selected and analyzed to test the accurate position of the cylindrical group mirror. From Fig. 9, we can see that the values of the blue curve are relatively large and the corresponding scanning spot is wider in y-direction. This means that the cylindrical group mirror is a little far away from the aspheric lens. It needs to be pushed slightly. Hence, all values of the red curve are within the acceptable range and satisfy the request. The average value of 0.963 denotes the perfect position of the cylindrical group mirror. Nevertheless, the above two parameters are unable to adjust the deflection angle of the cylindrical group mirror. It needs independent adjustment. The pitching angle curve is identical with the laser beam in tilt direction which guides the adjustment direction. The difference value between the maximum and the minimum indicates the gradient. The results for the measurement of the pitching angle in view direction before and after the deflection angle adjustment are compared in Fig. 10. The blue curve has positive slope and the corresponding scanning spot is upward sloping. This means that the cylindrical group mirror has a left deflection. It needs to be rotated with clockwise direction. Hence, the difference value of the red curve is 2.768 , which denotes the good levelness of the laser beam.
Fig. 10. Comparison of the pitching angle curve and corresponding scanning spot before and after the deflection angle adjustment.
Please cite this article in press as: J. Xie, et al., Real-time adjustment of optical transmitter by laser beam parameter measurement based on two linear array CCD scanning imaging, Optik - Int. J. Light Electron Opt. (2014), http://dx.doi.org/10.1016/j.ijleo.2014.01.145
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In all analyzed cases, the results demonstrate the functionality of the method, especially in real-time adjustment of transmitter components.
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Fundamental Research Funds for the Central Universities (Grant No. 2014QC013, No. 2014JC008). References
5. Conclusion We introduced a real-time measurement and adjustment method for optical transmitter based on scanning imaging using two linear array CCDs. We demonstrated the feasibility by analyzing the relationship between the beam parameters and the internal structure of the optical transmitter. The relative intensity distribution curve and beam divergence angle curve in view direction can reflect the position of the cylindrical group mirror. Moreover, the pitching angle curve in view direction can reflect the deflection angle of the cylindrical group mirror. The presented method was applied to direct fast adjustment for higher quality on the assembly of the optical transmitter. The proof-of-principle experiments showed that the measurement results were in agreement with the analysis. The experiment results demonstrated the feasibility and accuracy of this method. We conclude that this method can provide an experimentally simple possibility to accomplish real-time adjustment quickly. The presented procedure is highly advantageous for diverse laser beam emitted from the optical transmitter, such as elliptic, linear and so on. Acknowledgements This work was partly supported by National Natural Science Foundation of China (Grant No. 31000848, No. 41201364), the
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Please cite this article in press as: J. Xie, et al., Real-time adjustment of optical transmitter by laser beam parameter measurement based on two linear array CCD scanning imaging, Optik - Int. J. Light Electron Opt. (2014), http://dx.doi.org/10.1016/j.ijleo.2014.01.145