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Research Article
Vol. 54, No. 15 / May 20 2015 / Applied Optics
Measurement system with high accuracy for laser beam quality YI KE,1 CILING ZENG,2 PEIYUAN XIE,2 QINGSHAN JIANG,1 KE LIANG,1 ZHENYU YANG,1
AND
MING ZHAO1,*
1
School of Optical and Electronic Information, Huazhong University of Science and Technology, Wuhan 430074, China State Grid Hunan Electric Power Corporation, Changsha 410007, China *Corresponding author: [email protected]
2
Received 4 February 2015; revised 9 April 2015; accepted 10 April 2015; posted 29 April 2015 (Doc. ID 233879); published 20 May 2015
Presently, most of the laser beam quality measurement system collimates the optical path manually with low efficiency and low repeatability. To solve these problems, this paper proposed a new collimated method to improve the reliability and accuracy of the measurement results. The system accuracy controlled the position of the mirror to change laser beam propagation direction, which can realize the beam perpendicularly incident to the photosurface of camera. The experiment results show that the proposed system has good repeatability and the measuring deviation of M2 factor is less than 0.6%. © 2015 Optical Society of America OCIS codes: (040.1490) Cameras; (120.1680) Collimation; (220.4830) Systems design; (350.5500) Propagation. http://dx.doi.org/10.1364/AO.54.004876
1. INTRODUCTION With the continuous development of laser technology and its wide applications in various fields [1–3], laser beams with high quality are desired. For different applications, there are some different evaluation criteria, such as far-field divergence angle, Strehl ratio [4], power in the bucket [5–7], and beam quality β-factor [7]. But these methods all have their own limitation. In the late 1980s, the M2 factor is presented which is a more scientific and reasonable evaluation criteria [7]. Now the M2 factor has become a hot research topic [8] and is widely used in beam quality evaluation. As the current M2 factor measurements are based on the paraxial beam [9], adjusting the optical path of the laser is necessary before the entire measurement process. Both the CCD imaging method and the blade scanning method can be used to measure the quality of the laser beam, but the collimation process of the optical path is often carried out manually with low accuracy, such as M2 -200 s developed by Ophir-Spiricon Inc. and the ModeScan1780 developed by Photon Inc. It is not only difficult to ensure high precision, but also time consumption. To solve the above problems, this paper proposed an improved laser beam quality measurement system which can collimate the optical path quickly with high accuracy. 2. THEORY A. System Setup
Figure 1 is a block diagram of the improved laser beam quality measurement system. First, the laser beam to be measured is attenuated to avoid saturation on camera. Then the beam is 1559-128X/15/154876-05$15/0$15.00 © 2015 Optical Society of America
reflected by a mirror and focused on the camera receiving plane by a spherical lens. The mirror space position can be changed through controlling the azimuth angle γ and horizontal angle α, to make sure that the beam normally incidents on the camera. Based on the accurate collimation, the camera then moves along the beam propagation direction to acquire continuous images. Then the system software can automatically calculate the M2 factor according to these images. B. M2 Calculation
The M2 factor is widely used to measure laser beam quality and it is also called the diffraction limit factor. M2
ω×θ π ωθ; ω0 × θ 0 λ
(1)
where λ, ω, and θ are the wavelength, waist radius, and far-field divergence angle of the laser beam, respectively. ω0 and θ0 are the waist radius and far-field divergence angle of ideal laser beam, respectively. Generally, the beam size of the laser is changed as a hyperbola in the propagation direction [10,11], so the ω and θ can be calculated through the beam propagation equation. The system can get the pictures of the beam spot at different propagation distances. So the center of gravity method can be used to calculate the spot center. With the laser beam propagating in space, the spot center x 0 ; y 0 of any cross section along the axis can be expressed by the first-order moments of the intensity distribution [12,13], but the system usually collected a series of discrete points during the actual measurement process, so the laser spot center can be expressed as Eqs. (2) and (3):
Research Article
Laser
Vol. 54, No. 15 / May 20 2015 / Applied Optics
Optical Box
Computer motorized translation stage
Attenuator
Lens
Two-Dimensional Manually Adjusting Platform Camera
Control azimuth angle Control horizontal angle α System circuit box
Fig. 1. System setup.
P I x ; y · x i ; x0 P i i I x i ; yi P I x ; y · yi ; y0 P i i I x i ; y i
(2)
(3)
where I x i ; y i is the light intensity at position x i ; y i of the cross section along the light axis. Then the spot size can be calculated by the second moment method [12,13]. In the Cartesian coordinate system, the second moment of energy density distribution function σz in laser beam propagation distance z can be expressed as Eqs. (4) and (5): P I x i ; yi · x i − x 0 2 2 P ; (4) σ x z I x i ; yi P
It is well known that the product of beam waist size and farfield divergence angle is a constant through an ideal aberrationfree optical system [10]. So the system can convert the beam through an aberration-free lens, so that to get the spot sizes near the beam waist, and result in a more accurate fitting result. C. Method of Collimation
Mirror
σ 2y z
4877
I x i ; y i · y i − y 0 2 P : I x i ; y i
(5)
So the spot diameter Dz can be expressed as Eqs. (6) and (7): Dx z 4σ x z;
(6)
Dy z 4σ y z:
(7)
During the measuring process, it is necessary for accurate measurement that the beam is always perpendicular with the photosurface of camera. Currently, most commercial measuring systems use a manual method to collimate the optical path. It not only cannot guarantee good collimation, but it also takes a lot of time. This paper puts forward a more accurate method to collimate the optical path through the spot center searching process. This system approximates the calculated beam deviation angle gradually by controlling the position of the mirror, so that to ensure a very small deviation of the spot center during the moving process of the camera. The calculation method of beam deviation angle is shown in Fig. 2. Assuming that the line OAB is the ideal situation that the laser beam perpendicularly shines to the photosurface of the camera, the line OA 0 B 0 is the actual beam situation, and point O is the beam reflected point in the mirror. The system considers the bottom-left corner of the camera picture as the coordinate origin, length of the picture as the X-axis, width as the Y-axis, and consider the beam propagation direction as the Z-axis. First, the camera detected the beam spot at the position of photosurface1, and the center coordinate of the spot is A 0 x 1 ; y1 . Then the camera was moved to the position of photosurface2 along the z direction, and detected the beam spot again. The center coordinate of the beam spot is B 0 x 2 ; y2 . So the beam azimuth angle γ and horizontal angle α can be calculated by the two coordinates and the distance d between photosurface1 and photosurface2:
Equations (2)–(4) are often used to deal with the unsaturated beam spots. For those saturated ones, we use Gaussian interpolation to fit the real intensity distribution of laser. Then according to the laser propagation equation [14], D2 z Az 2 Bz C;
(8)
the beam waist radius ω and far-field divergence angle θ can be expressed by the coefficients A, B, and C [10,15]. The waist radius ω is rffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 B2 (9) C− : ω 4A 2 The far-field divergence angle θ is pffiffiffiffi A : (10) θ 2 The laser beam quality can be obtained through putting Eqs. (9) and (10) into Eq. (1).
Fig. 2. Diagram of angle calculation.
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Research Article
Vol. 54, No. 15 / May 20 2015 / Applied Optics
Fig. 3. Diagram of collimating process.
x 2 − x 1 d tan α; y 2 − y 1 d tan γ:
11
where αmax and γ max are the maximal initial reflected angular deviations. For a fixed OB, x max and y max of the system, we cannot collimate the optical path if the beam angular deviations exceed the calculated initial angular deviations. Figure 3 shows a flowchart of the collimation, at first the system should be initialized: the emission direction of the laser beam is adjusted, so that the beam can shine to the photosurface of the camera. Then the system calculates beam deviation angle through the Eq. (11). If the beam azimuth angle and horizontal angle are both less than the predetermined threshold value (0.05° in this paper), it can be considered that the system has been collimated successfully. Then mark the current position of the beam spot. Position the lens in the optical path and make sure the position of the spot center incident to the photosurface is almost invariant. If the change of the beam azimuth angle or horizontal angle exceeds the predetermined threshold value, then according to the magnitudes and polarity of the angles, system control the mirror deflect half of the angles toward the corresponding direction, and then adjust the two-dimensional manually
Fig. 5. Beam cross section along the beam propagation direction: (a) 103 mm, (b) 108 mm, (c) 113 mm, (d) 118 mm, and (e) 123 mm.
adjusting platform to control the position of the camera so that the spot can shine to the center of the camera, then repeat the previous operation until the completion of the collimation. 3. EXPERIMENT A. Collimation Experiment Results
A He–Ne laser is used in the experiment and the threshold of collimation deviation is set at 0.05°. Figure 5 gives the changes of the beam deviation angle with the collimation steps. 1.6
2
Mx of system experiment 2
My of system experiment 2
Mx of commercial product experiment
1.4
2
My of commercial product experiment
2
From Fig. 2, after finishing the calculation of the angle, we need to adjust the laser beam propagation direction, and move the camera to the position of photosurface3 to detect the beam spot again. Assuming the largest movable distance of the camera in the X direction is x max and in the Y direction is y max , then the maximal initial angular deviations of the laser beam before reflecting αinitial and γ initial can be calculated as follows: x max 1 αinitail αmax 2 2 arctan OB ; 12 y max γ max 1 γ initail 2 2 arctan OB ;
M
1.2
1.0 1
2
3
4
Times
(a) 2.0 2
Mx of system experiment
3.5
My of system experiment 2
Mx of commercial product experiment
1.6
2
My of commercial product experiment
2
3.0
2
1.8
beam azimuth angle α beam horizontal angle γ
2.5
M
Beam Deviation Angle/degree
4.0
1.4
2.0 1.5
1.2
1.0
1.0
0.5
1
0.0
2
3
4
Times 1
2
3
Step Number
Fig. 4. Beam deviation angle of collimation.
4
5
(b) Fig. 6. Measured beam quality compared with the commercial product: (a) a He–Ne laser and (b) a 532 nm green laser.
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Vol. 54, No. 15 / May 20 2015 / Applied Optics
4879
Table 1. M2 Factor Measured with Different Lenses F 125 mm 1 2 3 4 ¯2 M
F 100 mm
F 75 mm
M2x
M2y
M2x
M2y
M2x
M2y
1.24482 1.24156 1.25051 1.24066 1.24439
1.23028 1.23865 1.24105 1.23748 1.23686
1.24666 1.24907 1.241 1.25039 1.24678
1.23514 1.24002 1.23387 1.23953 1.23714
1.31522 1.32071 1.31842 1.31731 1.31792
1.2592 1.26321 1.26062 1.26339 1.26161
B. M2 Factor Measurement Results
Table 2. Spot Waist Measured with Different Lenses F 125 mm F 100 mm F 75 mm
Dx ∕μm
D y ∕μm
166.338 135.824 106.676
160.791 129.031 100.527
It can be seen from Fig. 4 that the system just needs four steps to complete its collimation. After four collimation steps, the horizontal angle of the beam is 0.04° and the azimuth angle is 0.012° which are both less than the threshold value, and do not change any more. Figure 5 shows the spot image with the camera moving every 5 mm along the beam propagation direction. The spot center coordinate from Figs. 6(a)–6(e) is (56.02, 144.33), (56.45, 143.84), (57.01, 143.27), (57.53, 142.71), and (57.83, 142.16), respectively. It can be seen from the coordinate change that the spot center only moves 1.81 pixels (13 μm) in the X direction and 2.17 pixels (16.67 μm) in the Y direction with the camera moving 20 mm. So the system has completed the collimation of the optical path successfully.
First, in order to include more spot pixels for calculation to improve the measurement accuracy, we compared the measurement results of the lenses with different focal lengths F 125, 100, and 75 mm. A He–Ne laser is used in the experiments. The results are shown as Tables 1 and 2. It can be seen from Tables 1 and 2 that with the focal length increasing, the beam spot waist increases obviously, and the M2 factor has also been improved as expected. For the lens with F 75 mm, the spot sizes are too small and easy to be saturated. The system cannot get enough unsaturated data to fit the real beam spot with Gaussian interpolation, which will lead to major error with the results. In conclusion, the lens with longer focal length or higher resolution camera is recommended in the measurement. Second, the measurements of different laser beams compared with commercial product were carried out. The system designed by this paper uses a lens with a focal length of 125 mm. The commercial product is BeamScope-P7 which is produced by DataRay Inc. The latter uses the knife-edge method to measure spot diameters and its focal length of the lens is 85 mm. A He–Ne laser and a 532 nm green laser
Table 3. Measurement Data of the System Which Uses a He–Ne Laser Experiment 1 2 3 4 M2 σ
M2x
M2y
1.24482 1.24156 1.25051 1.24066 1.24439 0.5503%
1.23028 1.23865 1.24105 1.23748 1.23686 0.5031%
Commercial Product Ellipticity
M2x
M2y
Ellipticity
0.9887 0.9976 0.9924 0.9974 0.9948 0.43%
1.087 1.104 1.063 1.049 1.07575 2.4514%
1.028 1.012 1.028 1.032 1.02425 0.8869%
0.9457 0.9167 0.9671 0.9838 0.9533 2.90%
Table 4. Measurement Data of the System Which Uses a 532 nm Laser Experiment 1 2 3 4 M2 σ
M2x
M2y
1.15907 1.1554 1.16326 1.15913 1.15921 0.32%
1.35273 1.35876 1.35417 1.34815 1.35345 0.44%
Commercial Product Ellipticity
M2x
M2y
Ellipticity
0.8568 0.8503 0.8590 0.8598 0.8564 0.37%
1.186 1.148 1.135 1.192 1.165 2.80%
1.463 1.414 1.466 1.425 1.442 2.64%
0.8107 0.8119 0.7743 0.8365 0.8079 2.22%
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are used in this experiment. Figure 6 shows the measurement results of the two lasers, respectively. It can be seen from Fig. 6 that the laser beam qualities measured by the system and the commercial product are close, which means the system designed by this paper is available. The difference mainly results from the measurement method. The system designed by this paper uses Gaussian interpolation to fit the real beam spot. The commercial system uses the knifeedge method to measure diameter, which deals with light power directly. It also can be seen from Fig. 6 that the fluctuating of the measurements for the proposed system is less than the commercial product. As shown in Tables 3 and 4, the mean square root of the proposed system is less than 0.6%, which has a better stability compared with the commercial product whether using a He–Ne laser or a 532 nm laser. 4. CONCLUSIONS This paper presents a laser beam quality measurement system which can collimate the optical path quickly. The experiment results revealed that the system designed by this paper can well overcome the shortcomings of the time-consuming and the inaccuracy of manual collimation. The system could collimate the optical path quickly and the beam horizontal angle as well as the azimuth angle stayed less than 0.05° during the measuring process. Furthermore, it can get a more steady result, whose measuring deviations are less than 0.6%. During the measuring process, the system uses a spherical lens which may introduce some errors. Some special lenses such as the aplanatic lens can be used in the experiment. Fundamental Research Funds for the Central Universities (2014ZZGH008 and 2014TS045); National Natural Science Foundation of China (NSFC) (61475058); Open Fund of The State Key Laboratory of High Performance Complex Manufacturing (Kfkt2013-07). REFERENCES 1. F. Shmitt, B. Mehlmann, J. Gedicke, A. Olowinsky, A. Gillner, and R. Poprawe, “Laser beam micro welding with high brilliant fiber lasers,” J. Laser Micro Nanoeng. 5, 197–203 (2010).
Research Article 2. C. J. Chang and J. J. Chua, “Endovenous laser photocoagulation (EVLP) for varicose veins,” Lasers Surg. Med. 31, 257–262 (2002). 3. L. Quintino, A. Costa, R. Miranda, D. Yapp, V. Kumar, and C. J. Kong, “Welding with high power fiber lasers–a preliminary study,” Mater. Des. 28, 1231–1237 (2007). 4. V. N. Mahajan, “Strehl ratio for primary aberrations: some analytical results for circular and annular pupils,” J. Opt. Soc. Am. 72, 1258– 1266 (1982). 5. P. J. Wegner, M. A. Henesian, J. T. Salmon, L. G. Seppala, T. L. Weiland, W. H. Williams, and B. M. Van Wonterghem, “Wavefront and divergence of the beamlet prototype laser,” Proc. SPIE 3492, 1019–1030 (1999). 6. A. Siegman, “How to (maybe) measure laser beam quality,” in DPSS (Diode Pumped Solid State) Lasers: Applications and Issues, M. Dowley, ed. (Optical Society of America, 1998), vol. 17, 184–198. 7. A. E. Siegman, “New developments in laser resonators,” Proc. SPIE 1224, 2–14 (1990). 8. J. V. Sheldakova, A. V. Kudryashov, V. Y. Zavalova, and T. Y. Cherezova, “Beam quality measurements with Shack–Hartmann wavefront sensor and M2-sensor: comparison of two methods,” Proc. SPIE 6452, 645207 (2007). 9. J. M. Fleischer, “Laser beam width, divergence, and propagation factor: status and experience with the draft standard,” Proc. SPIE 1414, 2–11 (1991). 10. W. Caixia and L. Shuchang, “Design of embedded laser beam measurement system,” in International Conference on Mechatronics and Automation (ICMA) (IEEE, 2009), pp. 252–256). 11. T. F. Johnston, “Beam propagation (M2) measurement made as easy as it gets: the four-cuts method,” Appl. Opt. 37, 4840–4850 (1998). 12. A. Khizhnyak, M. Lopiitchouk, and I. Peshko, “Lens transformations of high power solid-state laser beams,” Opt. Laser Technol. 30, 341–348 (1998). 13. W. Xiaoman, Z. Gang, W. Caixia, and M. Dexin, “Study on high power laser beam quality measurement technology,” in Mechanic Automation and Control Engineering (MACE), (IEEE, 2010), pp. 3203–3206. 14. T. S. Ross, “Assigning error to an M2 measurement,” Proc. SPIE 6101, 610108 (2006). 15. W. Jing, W. Yang, X. Wang, and H. Jiang, “Research on solving laser beam quality factor M2 with normal equations,” in International Conference on Electrical and Control Engineering (ICECE), (IEEE, 2010), pp. 1765–1769.
Research Article
Vol. 54, No. 15 / May 20 2015 / Applied Optics
Measurement system with high accuracy for laser beam quality YI KE,1 CILING ZENG,2 PEIYUAN XIE,2 QINGSHAN JIANG,1 KE LIANG,1 ZHENYU YANG,1
AND
MING ZHAO1,*
1
School of Optical and Electronic Information, Huazhong University of Science and Technology, Wuhan 430074, China State Grid Hunan Electric Power Corporation, Changsha 410007, China *Corresponding author: [email protected]
2
Received 4 February 2015; revised 9 April 2015; accepted 10 April 2015; posted 29 April 2015 (Doc. ID 233879); published 20 May 2015
Presently, most of the laser beam quality measurement system collimates the optical path manually with low efficiency and low repeatability. To solve these problems, this paper proposed a new collimated method to improve the reliability and accuracy of the measurement results. The system accuracy controlled the position of the mirror to change laser beam propagation direction, which can realize the beam perpendicularly incident to the photosurface of camera. The experiment results show that the proposed system has good repeatability and the measuring deviation of M2 factor is less than 0.6%. © 2015 Optical Society of America OCIS codes: (040.1490) Cameras; (120.1680) Collimation; (220.4830) Systems design; (350.5500) Propagation. http://dx.doi.org/10.1364/AO.54.004876
1. INTRODUCTION With the continuous development of laser technology and its wide applications in various fields [1–3], laser beams with high quality are desired. For different applications, there are some different evaluation criteria, such as far-field divergence angle, Strehl ratio [4], power in the bucket [5–7], and beam quality β-factor [7]. But these methods all have their own limitation. In the late 1980s, the M2 factor is presented which is a more scientific and reasonable evaluation criteria [7]. Now the M2 factor has become a hot research topic [8] and is widely used in beam quality evaluation. As the current M2 factor measurements are based on the paraxial beam [9], adjusting the optical path of the laser is necessary before the entire measurement process. Both the CCD imaging method and the blade scanning method can be used to measure the quality of the laser beam, but the collimation process of the optical path is often carried out manually with low accuracy, such as M2 -200 s developed by Ophir-Spiricon Inc. and the ModeScan1780 developed by Photon Inc. It is not only difficult to ensure high precision, but also time consumption. To solve the above problems, this paper proposed an improved laser beam quality measurement system which can collimate the optical path quickly with high accuracy. 2. THEORY A. System Setup
Figure 1 is a block diagram of the improved laser beam quality measurement system. First, the laser beam to be measured is attenuated to avoid saturation on camera. Then the beam is 1559-128X/15/154876-05$15/0$15.00 © 2015 Optical Society of America
reflected by a mirror and focused on the camera receiving plane by a spherical lens. The mirror space position can be changed through controlling the azimuth angle γ and horizontal angle α, to make sure that the beam normally incidents on the camera. Based on the accurate collimation, the camera then moves along the beam propagation direction to acquire continuous images. Then the system software can automatically calculate the M2 factor according to these images. B. M2 Calculation
The M2 factor is widely used to measure laser beam quality and it is also called the diffraction limit factor. M2
ω×θ π ωθ; ω0 × θ 0 λ
(1)
where λ, ω, and θ are the wavelength, waist radius, and far-field divergence angle of the laser beam, respectively. ω0 and θ0 are the waist radius and far-field divergence angle of ideal laser beam, respectively. Generally, the beam size of the laser is changed as a hyperbola in the propagation direction [10,11], so the ω and θ can be calculated through the beam propagation equation. The system can get the pictures of the beam spot at different propagation distances. So the center of gravity method can be used to calculate the spot center. With the laser beam propagating in space, the spot center x 0 ; y 0 of any cross section along the axis can be expressed by the first-order moments of the intensity distribution [12,13], but the system usually collected a series of discrete points during the actual measurement process, so the laser spot center can be expressed as Eqs. (2) and (3):
Research Article
Laser
Vol. 54, No. 15 / May 20 2015 / Applied Optics
Optical Box
Computer motorized translation stage
Attenuator
Lens
Two-Dimensional Manually Adjusting Platform Camera
Control azimuth angle Control horizontal angle α System circuit box
Fig. 1. System setup.
P I x ; y · x i ; x0 P i i I x i ; yi P I x ; y · yi ; y0 P i i I x i ; y i
(2)
(3)
where I x i ; y i is the light intensity at position x i ; y i of the cross section along the light axis. Then the spot size can be calculated by the second moment method [12,13]. In the Cartesian coordinate system, the second moment of energy density distribution function σz in laser beam propagation distance z can be expressed as Eqs. (4) and (5): P I x i ; yi · x i − x 0 2 2 P ; (4) σ x z I x i ; yi P
It is well known that the product of beam waist size and farfield divergence angle is a constant through an ideal aberrationfree optical system [10]. So the system can convert the beam through an aberration-free lens, so that to get the spot sizes near the beam waist, and result in a more accurate fitting result. C. Method of Collimation
Mirror
σ 2y z
4877
I x i ; y i · y i − y 0 2 P : I x i ; y i
(5)
So the spot diameter Dz can be expressed as Eqs. (6) and (7): Dx z 4σ x z;
(6)
Dy z 4σ y z:
(7)
During the measuring process, it is necessary for accurate measurement that the beam is always perpendicular with the photosurface of camera. Currently, most commercial measuring systems use a manual method to collimate the optical path. It not only cannot guarantee good collimation, but it also takes a lot of time. This paper puts forward a more accurate method to collimate the optical path through the spot center searching process. This system approximates the calculated beam deviation angle gradually by controlling the position of the mirror, so that to ensure a very small deviation of the spot center during the moving process of the camera. The calculation method of beam deviation angle is shown in Fig. 2. Assuming that the line OAB is the ideal situation that the laser beam perpendicularly shines to the photosurface of the camera, the line OA 0 B 0 is the actual beam situation, and point O is the beam reflected point in the mirror. The system considers the bottom-left corner of the camera picture as the coordinate origin, length of the picture as the X-axis, width as the Y-axis, and consider the beam propagation direction as the Z-axis. First, the camera detected the beam spot at the position of photosurface1, and the center coordinate of the spot is A 0 x 1 ; y1 . Then the camera was moved to the position of photosurface2 along the z direction, and detected the beam spot again. The center coordinate of the beam spot is B 0 x 2 ; y2 . So the beam azimuth angle γ and horizontal angle α can be calculated by the two coordinates and the distance d between photosurface1 and photosurface2:
Equations (2)–(4) are often used to deal with the unsaturated beam spots. For those saturated ones, we use Gaussian interpolation to fit the real intensity distribution of laser. Then according to the laser propagation equation [14], D2 z Az 2 Bz C;
(8)
the beam waist radius ω and far-field divergence angle θ can be expressed by the coefficients A, B, and C [10,15]. The waist radius ω is rffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 B2 (9) C− : ω 4A 2 The far-field divergence angle θ is pffiffiffiffi A : (10) θ 2 The laser beam quality can be obtained through putting Eqs. (9) and (10) into Eq. (1).
Fig. 2. Diagram of angle calculation.
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Vol. 54, No. 15 / May 20 2015 / Applied Optics
Fig. 3. Diagram of collimating process.
x 2 − x 1 d tan α; y 2 − y 1 d tan γ:
11
where αmax and γ max are the maximal initial reflected angular deviations. For a fixed OB, x max and y max of the system, we cannot collimate the optical path if the beam angular deviations exceed the calculated initial angular deviations. Figure 3 shows a flowchart of the collimation, at first the system should be initialized: the emission direction of the laser beam is adjusted, so that the beam can shine to the photosurface of the camera. Then the system calculates beam deviation angle through the Eq. (11). If the beam azimuth angle and horizontal angle are both less than the predetermined threshold value (0.05° in this paper), it can be considered that the system has been collimated successfully. Then mark the current position of the beam spot. Position the lens in the optical path and make sure the position of the spot center incident to the photosurface is almost invariant. If the change of the beam azimuth angle or horizontal angle exceeds the predetermined threshold value, then according to the magnitudes and polarity of the angles, system control the mirror deflect half of the angles toward the corresponding direction, and then adjust the two-dimensional manually
Fig. 5. Beam cross section along the beam propagation direction: (a) 103 mm, (b) 108 mm, (c) 113 mm, (d) 118 mm, and (e) 123 mm.
adjusting platform to control the position of the camera so that the spot can shine to the center of the camera, then repeat the previous operation until the completion of the collimation. 3. EXPERIMENT A. Collimation Experiment Results
A He–Ne laser is used in the experiment and the threshold of collimation deviation is set at 0.05°. Figure 5 gives the changes of the beam deviation angle with the collimation steps. 1.6
2
Mx of system experiment 2
My of system experiment 2
Mx of commercial product experiment
1.4
2
My of commercial product experiment
2
From Fig. 2, after finishing the calculation of the angle, we need to adjust the laser beam propagation direction, and move the camera to the position of photosurface3 to detect the beam spot again. Assuming the largest movable distance of the camera in the X direction is x max and in the Y direction is y max , then the maximal initial angular deviations of the laser beam before reflecting αinitial and γ initial can be calculated as follows: x max 1 αinitail αmax 2 2 arctan OB ; 12 y max γ max 1 γ initail 2 2 arctan OB ;
M
1.2
1.0 1
2
3
4
Times
(a) 2.0 2
Mx of system experiment
3.5
My of system experiment 2
Mx of commercial product experiment
1.6
2
My of commercial product experiment
2
3.0
2
1.8
beam azimuth angle α beam horizontal angle γ
2.5
M
Beam Deviation Angle/degree
4.0
1.4
2.0 1.5
1.2
1.0
1.0
0.5
1
0.0
2
3
4
Times 1
2
3
Step Number
Fig. 4. Beam deviation angle of collimation.
4
5
(b) Fig. 6. Measured beam quality compared with the commercial product: (a) a He–Ne laser and (b) a 532 nm green laser.
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Table 1. M2 Factor Measured with Different Lenses F 125 mm 1 2 3 4 ¯2 M
F 100 mm
F 75 mm
M2x
M2y
M2x
M2y
M2x
M2y
1.24482 1.24156 1.25051 1.24066 1.24439
1.23028 1.23865 1.24105 1.23748 1.23686
1.24666 1.24907 1.241 1.25039 1.24678
1.23514 1.24002 1.23387 1.23953 1.23714
1.31522 1.32071 1.31842 1.31731 1.31792
1.2592 1.26321 1.26062 1.26339 1.26161
B. M2 Factor Measurement Results
Table 2. Spot Waist Measured with Different Lenses F 125 mm F 100 mm F 75 mm
Dx ∕μm
D y ∕μm
166.338 135.824 106.676
160.791 129.031 100.527
It can be seen from Fig. 4 that the system just needs four steps to complete its collimation. After four collimation steps, the horizontal angle of the beam is 0.04° and the azimuth angle is 0.012° which are both less than the threshold value, and do not change any more. Figure 5 shows the spot image with the camera moving every 5 mm along the beam propagation direction. The spot center coordinate from Figs. 6(a)–6(e) is (56.02, 144.33), (56.45, 143.84), (57.01, 143.27), (57.53, 142.71), and (57.83, 142.16), respectively. It can be seen from the coordinate change that the spot center only moves 1.81 pixels (13 μm) in the X direction and 2.17 pixels (16.67 μm) in the Y direction with the camera moving 20 mm. So the system has completed the collimation of the optical path successfully.
First, in order to include more spot pixels for calculation to improve the measurement accuracy, we compared the measurement results of the lenses with different focal lengths F 125, 100, and 75 mm. A He–Ne laser is used in the experiments. The results are shown as Tables 1 and 2. It can be seen from Tables 1 and 2 that with the focal length increasing, the beam spot waist increases obviously, and the M2 factor has also been improved as expected. For the lens with F 75 mm, the spot sizes are too small and easy to be saturated. The system cannot get enough unsaturated data to fit the real beam spot with Gaussian interpolation, which will lead to major error with the results. In conclusion, the lens with longer focal length or higher resolution camera is recommended in the measurement. Second, the measurements of different laser beams compared with commercial product were carried out. The system designed by this paper uses a lens with a focal length of 125 mm. The commercial product is BeamScope-P7 which is produced by DataRay Inc. The latter uses the knife-edge method to measure spot diameters and its focal length of the lens is 85 mm. A He–Ne laser and a 532 nm green laser
Table 3. Measurement Data of the System Which Uses a He–Ne Laser Experiment 1 2 3 4 M2 σ
M2x
M2y
1.24482 1.24156 1.25051 1.24066 1.24439 0.5503%
1.23028 1.23865 1.24105 1.23748 1.23686 0.5031%
Commercial Product Ellipticity
M2x
M2y
Ellipticity
0.9887 0.9976 0.9924 0.9974 0.9948 0.43%
1.087 1.104 1.063 1.049 1.07575 2.4514%
1.028 1.012 1.028 1.032 1.02425 0.8869%
0.9457 0.9167 0.9671 0.9838 0.9533 2.90%
Table 4. Measurement Data of the System Which Uses a 532 nm Laser Experiment 1 2 3 4 M2 σ
M2x
M2y
1.15907 1.1554 1.16326 1.15913 1.15921 0.32%
1.35273 1.35876 1.35417 1.34815 1.35345 0.44%
Commercial Product Ellipticity
M2x
M2y
Ellipticity
0.8568 0.8503 0.8590 0.8598 0.8564 0.37%
1.186 1.148 1.135 1.192 1.165 2.80%
1.463 1.414 1.466 1.425 1.442 2.64%
0.8107 0.8119 0.7743 0.8365 0.8079 2.22%
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are used in this experiment. Figure 6 shows the measurement results of the two lasers, respectively. It can be seen from Fig. 6 that the laser beam qualities measured by the system and the commercial product are close, which means the system designed by this paper is available. The difference mainly results from the measurement method. The system designed by this paper uses Gaussian interpolation to fit the real beam spot. The commercial system uses the knifeedge method to measure diameter, which deals with light power directly. It also can be seen from Fig. 6 that the fluctuating of the measurements for the proposed system is less than the commercial product. As shown in Tables 3 and 4, the mean square root of the proposed system is less than 0.6%, which has a better stability compared with the commercial product whether using a He–Ne laser or a 532 nm laser. 4. CONCLUSIONS This paper presents a laser beam quality measurement system which can collimate the optical path quickly. The experiment results revealed that the system designed by this paper can well overcome the shortcomings of the time-consuming and the inaccuracy of manual collimation. The system could collimate the optical path quickly and the beam horizontal angle as well as the azimuth angle stayed less than 0.05° during the measuring process. Furthermore, it can get a more steady result, whose measuring deviations are less than 0.6%. During the measuring process, the system uses a spherical lens which may introduce some errors. Some special lenses such as the aplanatic lens can be used in the experiment. Fundamental Research Funds for the Central Universities (2014ZZGH008 and 2014TS045); National Natural Science Foundation of China (NSFC) (61475058); Open Fund of The State Key Laboratory of High Performance Complex Manufacturing (Kfkt2013-07). REFERENCES 1. F. Shmitt, B. Mehlmann, J. Gedicke, A. Olowinsky, A. Gillner, and R. Poprawe, “Laser beam micro welding with high brilliant fiber lasers,” J. Laser Micro Nanoeng. 5, 197–203 (2010).
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