- Email: [email protected]
Aberration compensation of laser mode unging a novel intra-cavity adaptive optical system
G Model IJLEO-52001; No. of Pages 4
ARTICLE IN PRESS Optik xxx (2012) xxx–xxx
Contents lists available at SciVerse ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Aberration compensation of laser mode unging a novel intra-cavity adaptive optical system Jie Li a,∗ , Xiqu Chen b a b
Department of Electrical and Information Engineering, Wuhan Polytechnic University, Wuhan, China Department of Mathematics and Physics, Wuhan Polytechnic University, Wuhan, China
a r t i c l e
i n f o
Article history: Received 12 July 2011 Accepted 19 November 2011 Available online xxx Keywords: Adaptive optics Deformable micro-mirror Laser aberration compensation
a b s t r a c t Thermally induced optically distortion effects are one of the main impediments to be overcome in developing high power solid-state lasers. To compensate the dynamic aberration of laser beam, an intra-cavity adaptive optical system was developed. A beaconing light was introduced to measure the wavefront aberration of intracavity laser beam and a MEMS deformable mirror was used to improve the wavefront aberration and output power of the laser. A genetic algorithm was used to adjust the control voltages of 37 independent electrodes to vary the shape of the deformable mirror surface such that the aberration of laser beam can be compensated. The experimental result showed that the output power was increased nearly 3 times and the beam quality was improved obviously by closed loop automatic control of the adaptive optical system. © 2011 Elsevier GmbH. All rights reserved.
1. Introduction
1.1. The effect of Zernike aberrations on Gaussian beams
High-power lasers with excellent spectral- and spatial-mode properties are required for applications such as laser machining, medicine, quantum optics, nonlinear optics, and fusion [1]. But high power laser often suffers from reduced beam quality due to thermally induced aberrations [2]. These problems of obtaining a good transverse mode oscillation from high average power lasers are related to the heat load induced by the high pump powers deposited into the gain medium. Performance is degraded due to thermally induced birefringence and lensing in the gain material. There are a variety of ways of removing aberrations from a beam of light. Some pieces of glass can be shaped to provide a phase shift that cancels out the aberrations. But these pieces of glass only work well for static aberration. Adaptive optics has been developed over the last several decades to compensate the dynamical aberrations [3]. The concept of adaptive optics was invented by the astronomy community to provide engineering control over the spatial phase of a beam of light for obtaining high quality images through the rapidly fluctuating atmospheric aberrations. With an adaptive optics system, an aberrated laser beam can be compensated and returned to the TEM00 spatial mode [4]. In this paper, we describe a novel intra-cavity adaptive optical system based on the combination of a MEMS deformable mirror and a genetic algorithm.
The Hermite–Gauss laser modes are introduced here to help determine the effect of aberrations on laser beam. The effect of an aberration on TEM00 laser is to convert light from the TEM00 mode into higher order Hermite–Gauss modes. The fraction of light coupled to the higher-order Hermite–Gauss modes provides one way to evaluate laser beam quality. From the theory of modal coupling coefficients, we can get that:
∗ Corresponding author. E-mail addresses: [email protected] (J. Li), [email protected] (X. Chen).
cx,y (
aberrated ,
m,n )
+∞
=
+∞ m,n (x, y) ·
dy −∞
−∞
∗ (x, y)dx aberrated
(1)
where aberrated (x, y) is the electric field distribution of aberrated beam, m,n (x, y) is the electric field distribution of a two-dimensional Hermite–Gaussian modes, cx,y ( aberrated , m,n ) is the amplitude coupling of an aberrated beam with an electric field aberrated (x, y) to two-dimensional Hermite–Gaussian modes m,n (x, y). The power coupled from an incoming beam to an outgoing TEM00 mode beam, k, is the product of the two-dimensional electric field coupling coefficient to TEM00 two-dimensional Hermite–Gaussian modes and its complex conjugate:
k = cx,y (
aberrated ,
∗ 0,0 ) · cx,y (
aberrated ,
0,0 )
(2)
where cx,y ( aberrated , 0,0 ) is the two-dimensional electric field coupling coefficient to TEM00 two-dimensional ∗ ( Hermite–Gaussian modes and cx,y aberrated , 0,0 ) is complex conjugate of cx,y ( aberrated , 0,0 ). Because there is no analytical expression giving the coupling between an ideal TEM00 laser beam
0030-4026/$ – see front matter © 2011 Elsevier GmbH. All rights reserved. doi:10.1016/j.ijleo.2011.11.071
Please cite this article in press as: J. Li, X. Chen, Aberration compensation of laser mode unging a novel intra-cavity adaptive optical system, Optik - Int. J. Light Electron Opt. (2012), doi:10.1016/j.ijleo.2011.11.071
G Model IJLEO-52001; No. of Pages 4
ARTICLE IN PRESS J. Li, X. Chen / Optik xxx (2012) xxx–xxx
2
and a laser beam aberrated with a Zernike polynomial, the effect of Zernike polynomial aberration has to be determined numerically. The electric field of a aberrated laser beam can be described in a transverse plane as the product of the modulus term, | 0,0 |, and a phase term exp(i): aberrated
=|
0,0 |
exp(i)
(3)
where (x, y) = (2/)ϕ(x, y). The function (x, y) represents the optical path difference between the aberrated wave-front and nonaberrated wave-front. This aberration function can be expanded as a linear combination of N Zernike polynomials, Zk (x,y), as follows: ϕ(x, y) =
N
ak Zk (x, y)
(4)
k=0
where Zk (x,y) are dimensionless polynomial functions and the length dimension is embedded in the coefficients of the expansion, ak . From (1)–(4), we can calculate the effect of the Zernike aberrations on the lowest-order Hermite–Gauss mode. Fig. 1 shows the result of a numerical two-dimensional overlap integral calculation, which gives the two-dimensional electric field coupling between the ideal TEM00 mode and the aberrated TEM00 mode, with respect to the amplitude of the Zernike aberration. From Fig. 1, we can find that some Zernike aberrations cause rapid deterioration of the coupling coefficient, while others show much more gradual deterioration. In practice, the shape of many common aberrations is not easily predicted, so the aberration shape has to be measured with a wave-front sensor. A Hartman-type wave-front sensor was used in our experiments.
Fig. 2. Schematic of intra-cavity adaptive optical system.
1.2. Experimental configuration The intra-cavity adaptive optical system is shown in Fig. 2. This system consists of Nd:YAG resonator (including an intracavity MEMS deformable mirror, Nd:YAG rod, beam expander and output mirror), computer, Hartman-shack wavefront sensor, beam splitter, two reflective mirror and high voltage driver for MEMS deformable mirror. A beaconing light (He–Ne laser beam) is directed into Nd:YAG resonator and reflected from the intracavity MEMS-DMs and then is redirected by the beam splitter to Hartman-shack wavefront sensor. The thermally induced wavefront aberration of beaconing light could be measured by the wavefront sensor. The deformable mirror is operated in a computer controlled feedback scheme to enable self-optimization of the beam quality of the laser. 2. MEMS deformable mirrors Although several micromachining methods are used to fabricate deformable mirrors, one of the most promising is bulk micromachining because of the low fabrication cost, the ability to create continuous membranes, and the ability to keep the mirror surface in tension to keep the mirror flat. Fig. 3a shows the cross section of a typical membrane DM. This membrane DM consists of a silicon chip mounted over an array of electrostatic pads for actuation. The chip contains a thin section with a reflective coating that forms the mirror. When a potential difference is applied between the mirror
Fig. 1. (a) Electric field amplitude in the lowest-order Hermite–Gaussian laser mode versus the magnitude of Zernike polynomials Z10 and Z11 . (b) Electric field amplitude in the lowest-order Hermite–Gaussian laser mode versus the magnitude of Zernike polynomials Z21 and Z20 .
Fig. 3. MEMS-DMs used in the experiments. (a) Cross section and (b) actuator layout.
Please cite this article in press as: J. Li, X. Chen, Aberration compensation of laser mode unging a novel intra-cavity adaptive optical system, Optik - Int. J. Light Electron Opt. (2012), doi:10.1016/j.ijleo.2011.11.071
G Model IJLEO-52001; No. of Pages 4
ARTICLE IN PRESS J. Li, X. Chen / Optik xxx (2012) xxx–xxx
3
Fig. 7. Genes of actuators on a deformable mirror.
Start STEP1 :
Generation of Initial Group
Fig. 4. Mirror surface with no applied voltage.
STEP2 : Calculate fitness function and a pad, an electrostatic force is produced on the portion of the membrane above the electrode inducing mirror deformation. The MEMS-DMs has 37 channels, which are located in a beehive shape (Fig. 3b). The diameter is 25 mm and the actuator spacing is 2 mm. The membrane with a coating for = 632.8 nm has a surface roughness (rms) of 5 nm (Fig. 4). The analog output from highvoltage digital driver ranges from 0 to 195 V with a 3 dB bandwidth of 30 kHz. The influence functions for a conventional membrane mirror can be calculated by solving the second order equation for the surface of a stretched membrane with fixed circular boundary conditions εV (, ) ∇ S(, ) = − Td2
2
(5)
where S is the surface displacement, V is the electrode voltage, T is the membrane tension, and d is the separation between the membrane and the electrodes. Fig. 5 shows the surface deformation produced when single actuator are energized. Fig. 6 shows the surface deformation produced when two actuators are energized.
Fig. 5. Measured influence functions from single actuator.
Fig. 6. Measured influence functions from two actuators.
STEP3 : Select and Conserve Elite
I=I+1
STEP4 : Selection and Reproduction STEP5 : Crossover STEP6 : Mutation
I> NLOOP
no
yes Stop Fig. 8. Flowchart of the genetic algorithm.
3. Genetic algorithm The genetic algorithm is one of a group of stochastic optimization algorithms which is well-suited to finding a global minimum (or maximum) of some objective error function. In the context of adaptive-optical control, the genetic algorithm is well-suited to the task because of its ability to independently optimize many variables at once. In the case of a deformable mirror, each actuator voltage represents one independently adjustable variable. All stochastic algorithms work by assessing the quality of any proposed solution by defining an error function – normally a single number – whose value indicates how close any solution is to the target. In this way, deformable mirrors can be used together with evolutionary algorithms to optimize the laser beam shape. The genetic algorithm uses the concept of ‘survival of the fittest’ in evolution to locate the best solution to multidimensional problems. In the GA, first the control variables that are converted to binary codes are treated as genes. Second, selection from among the individuals and reproduction are performed in groups consisting of several individuals with different genes. Third, the individuals evolve because of mutations and crossovers. Mutation avoids converging to the local optima, and convergence to the global optimum is performed by crossover and selection. The basic GA’s are referred to as simple GA’s, and they repeat the following process from (2) to (6), so that a group becomes an optimum group as the number of generations increases: (1) Random generation of the initial group consisting of several individuals. (2) Calculation of the fitness value for each individual. (3) Selection and reproduction. (4) Crossover. (5) Mutation. (6) Evaluation of the group.
Please cite this article in press as: J. Li, X. Chen, Aberration compensation of laser mode unging a novel intra-cavity adaptive optical system, Optik - Int. J. Light Electron Opt. (2012), doi:10.1016/j.ijleo.2011.11.071
G Model IJLEO-52001; No. of Pages 4
ARTICLE IN PRESS J. Li, X. Chen / Optik xxx (2012) xxx–xxx
4
We have tried to obtain an optimum mirror surface profile by using a GA to control the laser beam quality control system. Use of a GA to control a complex system such as this has the distinct advantage of dispensing with the need to analyze the transfer function of the system. In this system, the voltages supplied to the 37 actuators are coded to binary digits, as shown in Fig. 7, and a series of these binary digits is treated as a gene. Thus, the mirror surface profile or the laser beam intensity profile is regarded as virtual creatures. The algorithm that we used in this study is shown in Fig. 8. This algorithm differs from the simple GA in the following ways: (1) The first generation is assumed to consist of identical individuals. (2) The mutation rate is selected as 0.2, which is high compared with those used in GA’s for optimization. (3) The individual with a maximum fitness value in each generation is considered elite and does not undergo crossover and mutation. Thus, this algorithm avoids convergence to a local maximum. It was found that 40 generations of 40 individuals with a crossover rate of 0.85 and a mutation rate of 0.2 would ensure a final solution close to the global maximum. The whole process would take about 15 min. 4. Experimental results
Fig. 9. Aberrated and compensated wavefront.
The dynamic wavefront aberration of laser beam leads to a turbulence of 1.55 m in wavefront PV (Fig. 9a). After correction using intra-cavity adaptive optical system, the wavefront aberration gets corrected to 0.01 m (Fig. 9b). Measured laser beam profile before correction is shown in Fig. 10a. After correction using intra-cavity adaptive optical system, the result is shown in Fig. 10b. Accompanying this modal improvement the output power increased from 230 mW to 546 mW. From the experimental result, it is explicit that the intracavity adaptive optical system can effectively correct the thermally induced aberration of high power lasers. 5. Conclusion In summary, we have demonstrated a novel intra-cavity adaptive optical system based on the combination of a MEMS deformable mirror and a genetic algorithm. The experimental result showed that the output power was increased nearly 3 times and the beam quality was improved obviously by closed loop automatic control of the adaptive optical system. Acknowledgment This work was supported by the National Natural Science Foundation of China (No. 10476010). References
Fig. 10. Measured laser beam profile.
[1] J.M. Eggleston, T.J. Kane, K. Kuhn, J. Unternahrer, R.L. Byer, The slab geometry laser. I. Theory, IEEE J. Quantum Electron. 20 (1984) 289–301. [2] W. Koechner, Solid-State Laser Engineering, 5th ed., Springer Series in Optical Sciences, 1999, pp. 200–240. [3] R. Tyson, Principles of Adaptive Optics, 2nd ed., Academic Press, 1998, pp. 60–80. [4] J.D. Mansell, S. Sinha, R.L. Byer, Deformable mirror development at standford university, Proc. SPIE 4493 (2002) 1–12.
Please cite this article in press as: J. Li, X. Chen, Aberration compensation of laser mode unging a novel intra-cavity adaptive optical system, Optik - Int. J. Light Electron Opt. (2012), doi:10.1016/j.ijleo.2011.11.071
ARTICLE IN PRESS Optik xxx (2012) xxx–xxx
Contents lists available at SciVerse ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Aberration compensation of laser mode unging a novel intra-cavity adaptive optical system Jie Li a,∗ , Xiqu Chen b a b
Department of Electrical and Information Engineering, Wuhan Polytechnic University, Wuhan, China Department of Mathematics and Physics, Wuhan Polytechnic University, Wuhan, China
a r t i c l e
i n f o
Article history: Received 12 July 2011 Accepted 19 November 2011 Available online xxx Keywords: Adaptive optics Deformable micro-mirror Laser aberration compensation
a b s t r a c t Thermally induced optically distortion effects are one of the main impediments to be overcome in developing high power solid-state lasers. To compensate the dynamic aberration of laser beam, an intra-cavity adaptive optical system was developed. A beaconing light was introduced to measure the wavefront aberration of intracavity laser beam and a MEMS deformable mirror was used to improve the wavefront aberration and output power of the laser. A genetic algorithm was used to adjust the control voltages of 37 independent electrodes to vary the shape of the deformable mirror surface such that the aberration of laser beam can be compensated. The experimental result showed that the output power was increased nearly 3 times and the beam quality was improved obviously by closed loop automatic control of the adaptive optical system. © 2011 Elsevier GmbH. All rights reserved.
1. Introduction
1.1. The effect of Zernike aberrations on Gaussian beams
High-power lasers with excellent spectral- and spatial-mode properties are required for applications such as laser machining, medicine, quantum optics, nonlinear optics, and fusion [1]. But high power laser often suffers from reduced beam quality due to thermally induced aberrations [2]. These problems of obtaining a good transverse mode oscillation from high average power lasers are related to the heat load induced by the high pump powers deposited into the gain medium. Performance is degraded due to thermally induced birefringence and lensing in the gain material. There are a variety of ways of removing aberrations from a beam of light. Some pieces of glass can be shaped to provide a phase shift that cancels out the aberrations. But these pieces of glass only work well for static aberration. Adaptive optics has been developed over the last several decades to compensate the dynamical aberrations [3]. The concept of adaptive optics was invented by the astronomy community to provide engineering control over the spatial phase of a beam of light for obtaining high quality images through the rapidly fluctuating atmospheric aberrations. With an adaptive optics system, an aberrated laser beam can be compensated and returned to the TEM00 spatial mode [4]. In this paper, we describe a novel intra-cavity adaptive optical system based on the combination of a MEMS deformable mirror and a genetic algorithm.
The Hermite–Gauss laser modes are introduced here to help determine the effect of aberrations on laser beam. The effect of an aberration on TEM00 laser is to convert light from the TEM00 mode into higher order Hermite–Gauss modes. The fraction of light coupled to the higher-order Hermite–Gauss modes provides one way to evaluate laser beam quality. From the theory of modal coupling coefficients, we can get that:
∗ Corresponding author. E-mail addresses: [email protected] (J. Li), [email protected] (X. Chen).
cx,y (
aberrated ,
m,n )
+∞
=
+∞ m,n (x, y) ·
dy −∞
−∞
∗ (x, y)dx aberrated
(1)
where aberrated (x, y) is the electric field distribution of aberrated beam, m,n (x, y) is the electric field distribution of a two-dimensional Hermite–Gaussian modes, cx,y ( aberrated , m,n ) is the amplitude coupling of an aberrated beam with an electric field aberrated (x, y) to two-dimensional Hermite–Gaussian modes m,n (x, y). The power coupled from an incoming beam to an outgoing TEM00 mode beam, k, is the product of the two-dimensional electric field coupling coefficient to TEM00 two-dimensional Hermite–Gaussian modes and its complex conjugate:
k = cx,y (
aberrated ,
∗ 0,0 ) · cx,y (
aberrated ,
0,0 )
(2)
where cx,y ( aberrated , 0,0 ) is the two-dimensional electric field coupling coefficient to TEM00 two-dimensional ∗ ( Hermite–Gaussian modes and cx,y aberrated , 0,0 ) is complex conjugate of cx,y ( aberrated , 0,0 ). Because there is no analytical expression giving the coupling between an ideal TEM00 laser beam
0030-4026/$ – see front matter © 2011 Elsevier GmbH. All rights reserved. doi:10.1016/j.ijleo.2011.11.071
Please cite this article in press as: J. Li, X. Chen, Aberration compensation of laser mode unging a novel intra-cavity adaptive optical system, Optik - Int. J. Light Electron Opt. (2012), doi:10.1016/j.ijleo.2011.11.071
G Model IJLEO-52001; No. of Pages 4
ARTICLE IN PRESS J. Li, X. Chen / Optik xxx (2012) xxx–xxx
2
and a laser beam aberrated with a Zernike polynomial, the effect of Zernike polynomial aberration has to be determined numerically. The electric field of a aberrated laser beam can be described in a transverse plane as the product of the modulus term, | 0,0 |, and a phase term exp(i): aberrated
=|
0,0 |
exp(i)
(3)
where (x, y) = (2/)ϕ(x, y). The function (x, y) represents the optical path difference between the aberrated wave-front and nonaberrated wave-front. This aberration function can be expanded as a linear combination of N Zernike polynomials, Zk (x,y), as follows: ϕ(x, y) =
N
ak Zk (x, y)
(4)
k=0
where Zk (x,y) are dimensionless polynomial functions and the length dimension is embedded in the coefficients of the expansion, ak . From (1)–(4), we can calculate the effect of the Zernike aberrations on the lowest-order Hermite–Gauss mode. Fig. 1 shows the result of a numerical two-dimensional overlap integral calculation, which gives the two-dimensional electric field coupling between the ideal TEM00 mode and the aberrated TEM00 mode, with respect to the amplitude of the Zernike aberration. From Fig. 1, we can find that some Zernike aberrations cause rapid deterioration of the coupling coefficient, while others show much more gradual deterioration. In practice, the shape of many common aberrations is not easily predicted, so the aberration shape has to be measured with a wave-front sensor. A Hartman-type wave-front sensor was used in our experiments.
Fig. 2. Schematic of intra-cavity adaptive optical system.
1.2. Experimental configuration The intra-cavity adaptive optical system is shown in Fig. 2. This system consists of Nd:YAG resonator (including an intracavity MEMS deformable mirror, Nd:YAG rod, beam expander and output mirror), computer, Hartman-shack wavefront sensor, beam splitter, two reflective mirror and high voltage driver for MEMS deformable mirror. A beaconing light (He–Ne laser beam) is directed into Nd:YAG resonator and reflected from the intracavity MEMS-DMs and then is redirected by the beam splitter to Hartman-shack wavefront sensor. The thermally induced wavefront aberration of beaconing light could be measured by the wavefront sensor. The deformable mirror is operated in a computer controlled feedback scheme to enable self-optimization of the beam quality of the laser. 2. MEMS deformable mirrors Although several micromachining methods are used to fabricate deformable mirrors, one of the most promising is bulk micromachining because of the low fabrication cost, the ability to create continuous membranes, and the ability to keep the mirror surface in tension to keep the mirror flat. Fig. 3a shows the cross section of a typical membrane DM. This membrane DM consists of a silicon chip mounted over an array of electrostatic pads for actuation. The chip contains a thin section with a reflective coating that forms the mirror. When a potential difference is applied between the mirror
Fig. 1. (a) Electric field amplitude in the lowest-order Hermite–Gaussian laser mode versus the magnitude of Zernike polynomials Z10 and Z11 . (b) Electric field amplitude in the lowest-order Hermite–Gaussian laser mode versus the magnitude of Zernike polynomials Z21 and Z20 .
Fig. 3. MEMS-DMs used in the experiments. (a) Cross section and (b) actuator layout.
Please cite this article in press as: J. Li, X. Chen, Aberration compensation of laser mode unging a novel intra-cavity adaptive optical system, Optik - Int. J. Light Electron Opt. (2012), doi:10.1016/j.ijleo.2011.11.071
G Model IJLEO-52001; No. of Pages 4
ARTICLE IN PRESS J. Li, X. Chen / Optik xxx (2012) xxx–xxx
3
Fig. 7. Genes of actuators on a deformable mirror.
Start STEP1 :
Generation of Initial Group
Fig. 4. Mirror surface with no applied voltage.
STEP2 : Calculate fitness function and a pad, an electrostatic force is produced on the portion of the membrane above the electrode inducing mirror deformation. The MEMS-DMs has 37 channels, which are located in a beehive shape (Fig. 3b). The diameter is 25 mm and the actuator spacing is 2 mm. The membrane with a coating for = 632.8 nm has a surface roughness (rms) of 5 nm (Fig. 4). The analog output from highvoltage digital driver ranges from 0 to 195 V with a 3 dB bandwidth of 30 kHz. The influence functions for a conventional membrane mirror can be calculated by solving the second order equation for the surface of a stretched membrane with fixed circular boundary conditions εV (, ) ∇ S(, ) = − Td2
2
(5)
where S is the surface displacement, V is the electrode voltage, T is the membrane tension, and d is the separation between the membrane and the electrodes. Fig. 5 shows the surface deformation produced when single actuator are energized. Fig. 6 shows the surface deformation produced when two actuators are energized.
Fig. 5. Measured influence functions from single actuator.
Fig. 6. Measured influence functions from two actuators.
STEP3 : Select and Conserve Elite
I=I+1
STEP4 : Selection and Reproduction STEP5 : Crossover STEP6 : Mutation
I> NLOOP
no
yes Stop Fig. 8. Flowchart of the genetic algorithm.
3. Genetic algorithm The genetic algorithm is one of a group of stochastic optimization algorithms which is well-suited to finding a global minimum (or maximum) of some objective error function. In the context of adaptive-optical control, the genetic algorithm is well-suited to the task because of its ability to independently optimize many variables at once. In the case of a deformable mirror, each actuator voltage represents one independently adjustable variable. All stochastic algorithms work by assessing the quality of any proposed solution by defining an error function – normally a single number – whose value indicates how close any solution is to the target. In this way, deformable mirrors can be used together with evolutionary algorithms to optimize the laser beam shape. The genetic algorithm uses the concept of ‘survival of the fittest’ in evolution to locate the best solution to multidimensional problems. In the GA, first the control variables that are converted to binary codes are treated as genes. Second, selection from among the individuals and reproduction are performed in groups consisting of several individuals with different genes. Third, the individuals evolve because of mutations and crossovers. Mutation avoids converging to the local optima, and convergence to the global optimum is performed by crossover and selection. The basic GA’s are referred to as simple GA’s, and they repeat the following process from (2) to (6), so that a group becomes an optimum group as the number of generations increases: (1) Random generation of the initial group consisting of several individuals. (2) Calculation of the fitness value for each individual. (3) Selection and reproduction. (4) Crossover. (5) Mutation. (6) Evaluation of the group.
Please cite this article in press as: J. Li, X. Chen, Aberration compensation of laser mode unging a novel intra-cavity adaptive optical system, Optik - Int. J. Light Electron Opt. (2012), doi:10.1016/j.ijleo.2011.11.071
G Model IJLEO-52001; No. of Pages 4
ARTICLE IN PRESS J. Li, X. Chen / Optik xxx (2012) xxx–xxx
4
We have tried to obtain an optimum mirror surface profile by using a GA to control the laser beam quality control system. Use of a GA to control a complex system such as this has the distinct advantage of dispensing with the need to analyze the transfer function of the system. In this system, the voltages supplied to the 37 actuators are coded to binary digits, as shown in Fig. 7, and a series of these binary digits is treated as a gene. Thus, the mirror surface profile or the laser beam intensity profile is regarded as virtual creatures. The algorithm that we used in this study is shown in Fig. 8. This algorithm differs from the simple GA in the following ways: (1) The first generation is assumed to consist of identical individuals. (2) The mutation rate is selected as 0.2, which is high compared with those used in GA’s for optimization. (3) The individual with a maximum fitness value in each generation is considered elite and does not undergo crossover and mutation. Thus, this algorithm avoids convergence to a local maximum. It was found that 40 generations of 40 individuals with a crossover rate of 0.85 and a mutation rate of 0.2 would ensure a final solution close to the global maximum. The whole process would take about 15 min. 4. Experimental results
Fig. 9. Aberrated and compensated wavefront.
The dynamic wavefront aberration of laser beam leads to a turbulence of 1.55 m in wavefront PV (Fig. 9a). After correction using intra-cavity adaptive optical system, the wavefront aberration gets corrected to 0.01 m (Fig. 9b). Measured laser beam profile before correction is shown in Fig. 10a. After correction using intra-cavity adaptive optical system, the result is shown in Fig. 10b. Accompanying this modal improvement the output power increased from 230 mW to 546 mW. From the experimental result, it is explicit that the intracavity adaptive optical system can effectively correct the thermally induced aberration of high power lasers. 5. Conclusion In summary, we have demonstrated a novel intra-cavity adaptive optical system based on the combination of a MEMS deformable mirror and a genetic algorithm. The experimental result showed that the output power was increased nearly 3 times and the beam quality was improved obviously by closed loop automatic control of the adaptive optical system. Acknowledgment This work was supported by the National Natural Science Foundation of China (No. 10476010). References
Fig. 10. Measured laser beam profile.
[1] J.M. Eggleston, T.J. Kane, K. Kuhn, J. Unternahrer, R.L. Byer, The slab geometry laser. I. Theory, IEEE J. Quantum Electron. 20 (1984) 289–301. [2] W. Koechner, Solid-State Laser Engineering, 5th ed., Springer Series in Optical Sciences, 1999, pp. 200–240. [3] R. Tyson, Principles of Adaptive Optics, 2nd ed., Academic Press, 1998, pp. 60–80. [4] J.D. Mansell, S. Sinha, R.L. Byer, Deformable mirror development at standford university, Proc. SPIE 4493 (2002) 1–12.
Please cite this article in press as: J. Li, X. Chen, Aberration compensation of laser mode unging a novel intra-cavity adaptive optical system, Optik - Int. J. Light Electron Opt. (2012), doi:10.1016/j.ijleo.2011.11.071