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Sep 20, 2010 - This paper reports a fuzzy logic based feedback control system for beam pointing stabilization of a high- power nanosecond Nd:YAG laser ...
Fuzzy logic based feedback control system for laser beam pointing stabilization Ranjeet Singh, Kiran Patel, J. Govindarajan, and Ajai Kumar* Institute for Plasma Research, Bhat, Gandhinagar 382 428, India *Corresponding author: [email protected] Received 6 July 2010; accepted 12 August 2010; posted 25 August 2010 (Doc. ID 131183); published 16 September 2010

This paper reports a fuzzy logic based feedback control system for beam pointing stabilization of a highpower nanosecond Nd:YAG laser operating at 30 Hz. This is achieved by generating the correcting signal for each consequent pulse from the error in the pointing position of the previous laser pulse. We have successfully achieved a reduction of beam position fluctuation from 60 to 5:0 μrad without the focusing optics and 0:9 μrad with focusing optics. © 2010 Optical Society of America OCIS codes: 140.3425, 140.3295.

1. Introduction

High-power lasers have very diverse scientific, commercial, industrial, and military applications, such as medical treatment, atmospheric or orbital targeting in aeronautics and aerospace, micromachining, microetching, and inspection of microlithography fabrication. In many of these scientific applications, a highly spatially stable laser source is one of the important issues for successful operation of many modern techniques, such as pulse shortening and gas-phase spectroscopy in gas-filled hollow waveguides, femtosecond pulse shaping, and nonlinear spectroscopy with femtosecond-shaped pulses. In addition to these applications, lasers have been widely used as diagnostics tools in tokamak plasma experiments, such as laser blow-off, laser-induced fluorescence, Thomson scattering, etc. In many of the above cases, the laser beam must travel a long path to reach the experimental area, hence, even small deviations of the adjusted beam direction may cause unpredictable distortion in the experimental data. Fluctuation in the laser beam pointing direction is an important issue related to the laser. There are three major factors that contribute to pointing stability— air convection in the beam path, mechanical vibra0003-6935/10/275143-05$15.00/0 © 2010 Optical Society of America

tions of optical devices, and instabilities in the laser cavity. The first two can be reduced by modification in the experimental setup. The deviation in the spatial beam position of pulsed system is recorded only when a pulse is emitted. Therefore, using optoelectronic feedback for correcting the path of the laser will not be of much use. Instead, the deviation in positions must be estimated based on the preceding pulses. An extrapolating process known as time series prediction is applied on the measured beam position, which can often be realized by filters or, often better, by some sort of logic. The possibility of controlling the pointing stability of the pulsed Ti:sapphire laser system by performing time series analysis and computer simulations on experimentally measured data sets using low-pass filters and artificial neural networks (NNs) has been reported in the literature [1]. It was shown that at optimal cutoff frequency (0:09 Hz), the simulated prediction reduces the standard deviation of the time series by more than 50% in the x direction (σ x ) from 0.577 to 0:247 μrad and in the y direction (σ y ) from 0.880 to 0:467 μrad. In another report [2] for Ti:sapphire femtosecond lasers using focusing optics in path and without feedback control, the beam fluctuations were 87 μm (30 μm rms) in the horizontal direction and 110 μm (42 μm rms) in the vertical direction. These fluctuations were stabilized by feedback control using proportional-integral-derivative 20 September 2010 / Vol. 49, No. 27 / APPLIED OPTICS

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(PID) to within 4:2 μm (1:0 μm rms) and 4:7 μm (1:1 μm rms) in the horizontal and vertical directions, respectively. These methods suffer from problems such as the need for the linearity of the control parameters, the accurate modeling of the phenomenon, a long learning process, retuning parameters for change in the system, etc. This work tries to eliminate such problems by using fuzzy logic based feedback control design, which can inherently reduce nonlinear parameter behavior besides being fault tolerant, robust, and smart in controlling the system. The present logic configuration uses working experience for setting the control rules. However, this holds the future promise of being converted to a self-learning system when the NN is also incorporated into them. This paper describes the design and implementation of a fast and multipurpose feedback system based on fuzzy logic for the spatial stabilization [3–5] of a nanosecond laser beam. The present feedback control system uses the fuzzy logic toolkit of LabVIEW, piezo electrically driven mirrors, and a CCD camera. The developed feedback control system was implemented using fuzzy logic, as fuzzy logic is faster and requires fewer stages than the conventional logic. We report the laser position feedback control system for both types of applications, where the laser beam is directly coupled without using focusing optics and with using the focusing optics in the laser beam path. 2. Experimental Setup

Figure 1 shows the schematic diagram of the laser beam feedback control setup. Maintaining the spatial laser beam position in a particular point on a plane is achieved with the help of a position sensor, desired reference position, and a mechanism for moving the beam with respect to the reference position. Usually, the devices used for position sensing are position sensitive detectors (PSDs), charge coupled devices (CCDs), and quadrant diodes (QDs). The precise steering of the laser beam is achieved with the help of a gimbal mirror mount fitted with highresolution piezo actuators. At longer distances, it

Fig. 1. (Color online) Schematic arrangement of the laser beam feedback control system. 5144

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is difficult to monitor the laser beam having a large diameter using PSDs or QDs due to the limited size of the detector area. As the requirement of the complete beam size is needed for the beam position calculation, it limits the use of the PSD as an optical sensor. Moreover, these are small size detectors and most often require the beam diameter of ≤1 mm to calculate the laser beam position precisely, which is not possible without the use of focusing optics. It is observed (discussed in the latter section) that if beam-focusing optics is used in the path of the beam position measurement where the laser beam is coupled to other systems without any focusing optics, the measured feedback results are not precise. Usage of a high-resolution CCD camera for monitoring the beam position can solve the limitations of the PSD for large diameter beams. Hence, in the present setup, a high-resolution monochrome CCD camera is used for monitoring the beam position and a Picomotor™ for precise steering of the gimbal mirror mount to the reference points. The CCD-based feedback control system can be used for laser beam lines having focusing optics, too. A. Measurement Technique

The laser beam pointing stability is described as the angular movement of the beam and is given as the center-of-gravity distribution of the far field beam profiles measured in μrad. The beam pointing is normally measured by tracking the centroid of the beam on a CCD camera. A typical beam position measurement involves tracking the centroid of the beam over several minutes, and the rms deviation of the drift in centroid data gives a clear picture of the laser beam pointing stability. The drift of the laser beam is an entirely random phenomenon, which adds difficulty in reducing the position movement at a desired location. In the present setup, a laser beam (laser pulse energy, 1:6 J; pulse width, 10 ns; pulse repetition rate, 30 Hz) is steered to the target location with the help of the gimbal mirror mount (Newport, SL15ABM), in which the manual micrometer screws are replaced with Picomotor (New Focus, 8302). The Picomotor is a piezoelectric screw actuator, driven by an impulse. On receiving an impulse, the Picomotor turns the attached screw in small steps of ∼30 nm. Picomotors are very useful in applications, which a require compact and high-resolution positioner. Among the other advantages of the Picomotor is the direct accessibility of the screw for aligning the mirror manually, as well as its remote operation. Moreover, these motors can also be used in a high magnetic field environment. There are some disadvantages associated with the Picomotor, such as the motion corresponding to each step size not being constant, as it is based on the friction drive mechanism for turning the Picomotor screw. However, this drawback is not reflected in the position measurement, as it is done using an independent detector. On coupling with gimbal mount, the resolution and linear speed of the Picomotor are

30 nm and 20 μm=s, respectively, which correspond to the angular resolution and speed of 0:30 μrad and 0:2 mrad=s, respectively. A special driver unit (New Focus, 8732) is used for controlling the Picomotors. The input information required for the driver is the direction of motion, speed of movement, and number of steps. For measuring the laser beam position, a small fraction of the laser beam is sampled using a wedge plate and is allowed to fall on a fluorescent screen. The fluorescent image is tracked using a highresolution monochrome CCD camera (Basler, A641f). This camera is triggered externally via TTL sync pulses from the laser to capture each laser pulse position. Absorptive type neutral density (ND) filters are used in the imaging path to decrease the laser beam intensity to the required sensitivity of the CCD camera. The CCD camera is positioned in such a manner that the image of the laser beam falls on the required region of interest (ROI) of the image. A temperature stabilized He–Ne laser, which is collinear with the Nd:YAG laser, is used to define the optical axis. It is aligned to a desired position with the help of the feedback control system, and hereafter, this laser beam position is referred as “reference position.” In the present configuration, the CCD camera can detect a 50 and 10 μm drift in the beam position without and with focusing optics in the laser beam path, respectively. B.

Image Processing

The CCD camera uses a FireWire (IEEE 1394) interface along with a fiber optic FireWire extender to transfer the images from the camera to the frame grabber card at 30 Hz. A program is developed using a Vision Development Module in the LabVIEW™ platform to find out the centroid of the laser beam image acquired through the CCD camera. The program finds the centroid of the laser beam image after subtracting the background and thresholding. The centroid of the processed image gives the laser beam position in the X and Y coordinates of the pixel. The origin (0, 0) of the captured image is fixed at the left and topmost corner. The right -hand side indicates the X direction, and the bottom side indicates the Y direction. The calculated centroid location of each laser beam image is then compared with the previously defined reference of the laser beam, which gives the drift in the beam position in the image plane. These data are used for generating the feedback control signal using the fuzzy logic controller. The program has the capability to take care of some common errors, such as the absence of the laser beam on the screen or the misalignment of the camera. C.

that defines how each point in the input or output space is mapped to a membership value (or degree of membership) between 0 and 1. The fuzzy logic algorithm involves three elements: (i) Fuzzification, (ii) inference process, and (iii) defuzzification. Fuzzification is the process of converting crisp, real-world values into the degree of membership of the fuzzy set. The inference process is the evaluation of rule strengths based on rules and inputs. The purpose of the rule base is to supply all the actions to be taken by the fuzzy controller in a particular situation. Defuzzification is a conversion process of the output fuzzy set into numerical value. A LabVIEW-based fuzzy logic toolkit is used for defining input and output space, rule base and inference process, and defuzzification method. The input space of the fuzzy logic controller accepts the beam position data in pixels and determines the degree to which they belong to each of the appropriate fuzzy sets via membership functions. The rule base is defined according to the membership function. In the present case, the Mamdani-style fuzzy inference process is implemented with nine antecedence and consequence membership functions. The degree of support for the entire rule shapes the output fuzzy set. Defuzzification of the output sets provides the data required by the Picomotor driver. D.

Beam Position Controls

Figure 2 shows the snapshot of the laser beam position control program. The captured image of the laser beam, camera acquisition rate, feedback control on/off status, and measured position of the laser beam is displayed on the front panel. The measured deviation in the beam position with respect to the reference position is fed to the fuzzy logic

Fuzzy Logic Controller

Fuzzy logic [6] is a rule-based decision-making method used for problem-solving and process control systems. The basis of fuzzy logic is “fuzzy sets,” which contain elements with only a partial degree of membership. A membership function (MF) is a curve

Fig. 2. (Color online) Snap shot of the developed program using the fuzzy logic controller in LabVIEW. 20 September 2010 / Vol. 49, No. 27 / APPLIED OPTICS

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controller, where its logic program calculates the number of required pulses, the direction of the movement to keep the beam-pointing stability within the limit of tolerance using the fuzzy logic, and transmits the required information to the Picomotor driver through digital input/output (I/O). The Picomotor can take pulses at 2 KHz, and it takes approximately 7 ms to change the direction from clockwise to counterclockwise and vice versa. All the processes, i.e., the capturing of the image, processing of the image, calculation of the centroid, calculation of the number of pulses, frequency, direction, and Picomotor movement are completed in less than 25 ms, which is well before the arrival of the next laser pulse. For higher repetition rate laser systems, a fast frame rate camera and fast response Picomotor driver must be used. 3. Results and Discussion

A feedback control system, based on fuzzy logic, to improve laser beam pointing stability is developed. The developed hardware and software is tested for a 10 m long beam path. The system can work well with and without focusing optics in the beam path, depending on the experimental needs. At the first instance, we consider the case in which the laser beam is not focused. In this case, the complete beam diameter is used for the calculation of the beam centroid, then the corresponding feedback signal to the Picomotor driver is generated from the fuzzy logic controller for improving beam pointing stability. Normally, the camera is aligned in such a manner that the beam falls near the reference point (256 pixels in the present setup; any of the pixels can be used). The centroid of the subsequent Nd:YAG laser beam pulses is computed and processed by the program for estimating the deviation of the laser beam with respect to the reference point for generating the feedback. Figure 3 shows the recorded fluctuations in the beam position with and without the feedback control. The feedback control is applied for a duration of ∼1 min (2000 laser pulses) indicated by “ON” in the figure. The fluctuation in the laser beam position in the feedback off condition is 60 μrad (∼  20 pixel), which reduces to 5:0 μrad (1 pixel) when the feedback control is on. Figure 4 shows the histogram of the beam position along the horizontal (X axis) and vertical (Y axis) directions with and without the feedback control. From the figure, it is apparent that the feedback control suppresses the fluctuation significantly. It is also observed that in the absence of the feedback control, the fluctuations are more in the horizontal direction (X axis) than vertical direction (Y axis), which is due to the laser head design. In the laser head, two flash lamps are oriented at an angle of 180° in the vertical plane. This orientation gives better thermal stability in the vertical direction, resulting in less fluctuation in the Y direction. On analyzing the acquired laser beam images statistically (sample size 65,000), it is found that only 30% of points lie near the reference point (1 pixel) when the feedback con5146

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Fig. 3. Effect of feedback control on the laser beam fluctuation in (a) pixel number and (b) μrad as function of number of laser pulses. The applied condition is represented by “OFF” (feedback control off) and “ON” (feedback control on).

trol is off, which subsequently increase to 96% on the application of the feedback control. As stated above, when the feedback control is applied, 96% of the laser beam pulses are lying within the tolerance of 1 pixel, where one pixel has a 50 μm spatial resolution. The laser beam pulses, which lie outside 1 pixel with respect to reference position, are due to an uneven step size of Picomotor, which varies depending on the direction of the movement and the active load on it. Further improvement in the present setup is not possible because of the large laser beam size and limited camera resolution. In the second case, in which the focusing optics are used in the beam path (e.g., in Thomson scattering, micromachining, material processing, and coupling of a high-power laser to small core diameter fiber optic cable, etc.), it is quite evident from Fig. 5 that the introduction of the focusing optics in the path suppresses the beam fluctuations to some extent.

Fig. 4. (Color online) Spread of laser beam fluctuation in the horizontal (X axis) and vertical (Y axis) directions with and without feedback control condition is represented in histogram.

Fig. 5. (Color online) Scatter plot for the laser beam fluctuation when focusing optics is used in the beam path. The black dark and light dark square portions show the corrected beam position within limit and over shooting fluctuation of the laser beam under feedback condition.

However, even this magnitude of fluctuations can be problematic in the case of high-power laser applications mentioned above. Therefore, the same feedback control system with appropriate modification in the control logic is applied to correct the beam positions in this case, too. Focusing optics in the beam line has the advantage of using a magnifying lens for imaging the beam spots, which thereby improves the accuracy in the position measurement from 50 to 10 μm. It is observed that the extent of the beam position fluctuation reduces from 600 to 70 μm due to focusing optics. When the feedback is applied, 99% of the laser pulses lie near the reference point with a tolerance of 1 pixel, where 1 pixel corresponds to a 10 μm spatial resolution. In terms of angular deviation (μrad), the beam fluctuation is reduced from 60 to 7:0 μrad (due to focusing optics) and 0:9 μrad with the application of feedback control, which is a significant improvement in the beam pointing stability. 4. Conclusion

We have developed a feedback control system based on fuzzy logic for spatial stabilization of a high-power

nanosecond laser operating at a 30 Hz repetition rate. On application of feedback control, laser beam position fluctuations are reduced from 60 μrad to 5:0 μrad without focusing optics and 0:9 μrad with the use of focusing optics. The reproducibility test of the beam stabilization was performed on 20 sets of data (each set having 60,000 data points). The average variation in the results of beam position pointing stabilization was found to be less than 1%. The reported results for stabilization of laser beam position fluctuations are much better than the previously reported one in terms of ratio of stabilized and unstabilized values. The developed feedback control system is reliable, simple in implementation, and cost effective. With slight modification in fuzzy logic controller, the control system can be utilized for various experiments. Further improvement in the speed can be achieved by implementing the fuzzy logic and Picomotor driver in the hardware like FPGA (Field Programmable Gate Array) and the embedded controller. The authors are thankful to Y. C. Saxena, H. C. Joshi, and Jinto Thomas for fruitful discussion and critically evaluating the manuscript. References 1. F. Breitling, R. S. Weigel, M. C. Downer, and T. Tajima, “Laser pointing stabilization and control in the submicroradian regime with neural networks,” Rev. Sci. Instrum. 72, 1339–1342 (2001). 2. T. Kanai, A. Suda, S. Bohman, M. Kaku, S. Yamaguchi, and K. Midorikawa, “Pointing stabilization of a high-repetition-rate high-power femtosecond laser for intense few-cycle pulse generation,” Appl. Phys. Lett. 92, 061106 (2008). 3. I. Yamada, K. Narihara, K. Yamauchi, and H. Hayashi, “Active control of laser beam direction for LHD YAG Thomson scattering,” Rev. Sci. Instrum. 72, 1126–1128 (2001). 4. A. Stalmashonak, N.I Zhavoronkov, I. Volker H., Sergei Vetrov, and K. Schmid, “Spatial control of femtosecond laser system output with submicroradian accuracy,” Appl. Opt. 45, 1271–1274 (2006). 5. L. Kral, “Automatic beam alignment system for a pulsed infrared laser,” Rev. Sci. Instrum. 80, 013102 (2009). 6. E. Cox, The Fuzzy Systems Handbook (Academic, 1994).

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