## Active beam position stabilization of pulsed lasers for long-distance ion profile diagnostics at the Spallation Neutron Source (SNS) |

Optics Express, Vol. 19, Issue 4, pp. 2874-2885 (2011)

http://dx.doi.org/10.1364/OE.19.002874

Acrobat PDF (1348 KB)

### Abstract

A high peak-power Q-switched laser has been used to monitor the ion beam profiles in the superconducting linac at the Spallation Neutron Source (SNS). The laser beam suffers from position drift due to movement, vibration, or thermal effects on the optical components in the 250-meter long laser beam transport line. We have designed, bench-tested, and implemented a beam position stabilization system by using an Ethernet CMOS camera, computer image processing and analysis, and a piezo-driven mirror platform. The system can respond at frequencies up to 30 Hz with a high position detection accuracy. With the beam stabilization system, we have achieved a laser beam pointing stability within a range of 2 μrad (horizontal) to 4 μrad (vertical), corresponding to beam drifts of only 0.5 mm × 1 mm at the furthest measurement station located 250 meters away from the light source.

© 2011 OSA

## 1. Introduction

1. A. Stalmashonak, N. Zhavoronkov, I. V. Hertel, S. Vetrov, and K. Schmid, “Spatial control of femtosecond laser system output with submicroradian accuracy,” Appl. Opt. **45**(6), 1271–1274 (2006). [CrossRef] [PubMed]

4. J. Liu, Y. Kida, T. Teramoto, and T. Kobayashi, “Generation of stable sub-10 fs pulses at 400 nm in a hollow fiber for UV pump-probe experiment,” Opt. Express **18**(5), 4664–4672 (2010). [CrossRef] [PubMed]

5. Y. Liu, A. Aleksandrov, S. Assadi, W. Blokland, C. Deibele, W. Grice, C. Long, T. Pelaia, and A. Webster, “Laser wire beam profile monitor in the spallation neutron source (SNS) superconducting linac,” Nucl. Instr. Meth. A **612**(2), 241–253 (2010). [CrossRef]

5. Y. Liu, A. Aleksandrov, S. Assadi, W. Blokland, C. Deibele, W. Grice, C. Long, T. Pelaia, and A. Webster, “Laser wire beam profile monitor in the spallation neutron source (SNS) superconducting linac,” Nucl. Instr. Meth. A **612**(2), 241–253 (2010). [CrossRef]

1. A. Stalmashonak, N. Zhavoronkov, I. V. Hertel, S. Vetrov, and K. Schmid, “Spatial control of femtosecond laser system output with submicroradian accuracy,” Appl. Opt. **45**(6), 1271–1274 (2006). [CrossRef] [PubMed]

4. J. Liu, Y. Kida, T. Teramoto, and T. Kobayashi, “Generation of stable sub-10 fs pulses at 400 nm in a hollow fiber for UV pump-probe experiment,” Opt. Express **18**(5), 4664–4672 (2010). [CrossRef] [PubMed]

7. P. M. Sinclair, J. R. Drummond, and A. D. May, “Digital divider circuit for a laser-beam-pointing stabilization system,” Appl. Opt. **34**(3), 408–409 (1995). [CrossRef] [PubMed]

8. 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**(2), 1339–1342 (2001). [CrossRef]

9. Y. Wu, D. French, and I. Jovanovic, “Passive beam pointing stabilization,” Opt. Lett. **35**(2), 250–252 (2010). [CrossRef] [PubMed]

10. P. Fritschel, N. Mavalvala, D. Shoemaker, D. Sigg, M. Zucker, and G. González, “Alignment of an interferometric gravitational wave detector,” Appl. Opt. **37**(28), 6734–6747 (1998). [CrossRef]

5. Y. Liu, A. Aleksandrov, S. Assadi, W. Blokland, C. Deibele, W. Grice, C. Long, T. Pelaia, and A. Webster, “Laser wire beam profile monitor in the spallation neutron source (SNS) superconducting linac,” Nucl. Instr. Meth. A **612**(2), 241–253 (2010). [CrossRef]

## 2. Modeling and bench test experiment of feedback scheme

*y*(

*t*) is the observed position of the laser beam,

*x*(

*t*) is the external perturbation input which represents a modulation signal in the simulation/bench test experiment or an external noise in the actual system,

*V*(

*t*) is the output voltage from the piezomotor controller,

*δ*(

*t*) is the difference between the position set point

*SP*and the observed position in pixels

*y*(

*t*),

*γ*is the feedback gain, and

*V*(Volt per pixel) is the coefficient between the controller voltage and the beam position.

_{pp}*V*is measured by manually adjusting the output voltages and observing the number of pixels the beam moves for each axis (horizontal and vertical). Obviously,

_{pp}*V*is both an axis and a (image sensor) location dependent parameter.

_{pp}*t*is the time difference between two consecutive measurements and in our experiments using pulsed laser,

_{d}*t*= 1/

_{d}*f*where

_{d}*f*is the repetition rate of the laser pulse.

_{d}*f*=20 Hz to match the bench test parameter.

_{d}*γ*=2 where the system shows a resonant response, the better reduction ratio the feedback system will achieve. However, this does not take into consideration the stability.

*γ*-1)exp(-

*iωt*) factor in the denominator, which we define as

_{d}*D*(

*iω*). The Nyquist stability diagram is a graphical method of applying the stability criterion by plotting the real and imaginary parts of

*D*(

*iω*) in the complex plane, and determining if the point (−1,0) is enclosed by the plot

*D*(

*iω*) [11,12]. If the Nyquist plot loop encircles or passes through the point (−1,0) the system is unstable, otherwise it is stable.

*γ*of 0.1 is close to being unstable, as the gain is increased to 2, the Nyquist plots first shrink in to the origin at a gain factor of 1 (square), and then expands again until at encircling the point (−1,0) at a gain factor of 2 and becoming unstable. Note that the plot of

*γ*= 0.5 overlaps with that of

*γ*= 1.5. Thus the Nyquist stability diagrams indicate the range of stability for the gain factors to be 0<

*γ*<2. Furthermore, for the gain factors within the range of stability, the overall stability does not depend on frequency.

*γ*. A comparison of the analytical (Eq. (3)) and experimental reduction ratios (feedback ON/feedback OFF magnitudes) for several gain factors, as a function of driving frequency, is shown in Fig. 6 . The reduction ratios are determined by calculating the standard deviation on the position differences from the set point over 10 oscillation periods in both feedback off and on phases. A set of vertical experimental reduction ratios as a function of frequency are indicated by the data points (circle, square, etc.) while the analytical reduction ratios are shown as lines. As the driving frequency is reduced from 3 Hz, the reduction ratios for all gain factors approach the limit of a perfect feedback system of zero. Assuming a single pixel to be the minimum amplitude, including any errors, the reduction ratio minimum would be approximately 0.043 in the horizontal and 0.037 in the vertical. Additionally, for all gain factors tested, reduction ratios at or below 2 Hz are below 1. At 3 Hz and the gain factors of 0.5 and 0.8, the beam movement is no longer being reduced, but rather being enhanced. This demonstrates that the piezoelectric driven mirror and feedback routine examined here should easily compensate beam motion (reduction ratio < 1) up to frequencies of 3 Hz, or roughly 15% of the laser pulse rate (20 Hz), for an appropriate gain factor.

## 3. Application to SNS laser wire system

**612**(2), 241–253 (2010). [CrossRef]

*x*and

*y*coordinate over a particular amount of time. The standard deviation for each measurement is calculated to determine a consistent range of spatial variation. This provides the means for determining the radial stability calculations for each camera and camera axis, based on the values given in Table 1.

*γ*). Negative (real part of) Lyapunov exponents (corresponding to 0<

*γ*<2) are necessary to achieve a stable feedback control. At

*γ*=1, the Lyapunov exponent has a value of negative infinity, which indicates the feedback system is most stable at the gain factor of unity [13]. Fig. 8 also illustrates that the location of the set point can play a role in how well the feedback system stabilizes the beam. For example, the data for camera B with a gain factor of 0.5 shows a standard deviation of ~2.2 mm (red open circle) for one set point and a deviation of ~0.6 mm (black closed circle). While not investigated in this work, a more thorough examination of the set point effect on the beam stabilization would be beneficial.

## 4. Conclusions

*γ*< 2, and produces successful noise reduction effect for a bandwidth of up to 3 Hz. Bench test data agree with the analytical prediction quite well. After the installation of the feedback system in the SNS laser wire diagnostic system, the standard deviation of the laser beam position was reduced to less than one pixel, corresponding to angular stabilities within a range of 2.1 to 4.2 μrad over a distance of 225 meters. The laser beam pointing stabilization has significantly improved the laser wire measurement performance.

## Acknowledgements

## References and links

1. | A. Stalmashonak, N. Zhavoronkov, I. V. Hertel, S. Vetrov, and K. Schmid, “Spatial control of femtosecond laser system output with submicroradian accuracy,” Appl. Opt. |

2. | F. Lindau, O. Lundh, A. Persson, K. Cassou, S. Kazamias, D. Ros, F. Plé, G. Jamelot, A. Klisnick, S. de Rossi, D. Joyeux, B. Zielbauer, D. Ursescu, T. Kühl, and C. G. Wahlström, “Quantitative study of 10 Hz operation of a soft x-ray laser-energy stability and target considerations,” Opt. Express |

3. | 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. |

4. | J. Liu, Y. Kida, T. Teramoto, and T. Kobayashi, “Generation of stable sub-10 fs pulses at 400 nm in a hollow fiber for UV pump-probe experiment,” Opt. Express |

5. | Y. Liu, A. Aleksandrov, S. Assadi, W. Blokland, C. Deibele, W. Grice, C. Long, T. Pelaia, and A. Webster, “Laser wire beam profile monitor in the spallation neutron source (SNS) superconducting linac,” Nucl. Instr. Meth. A |

6. | W. Blokland, A. Barker, and W. Grice, “Drift Compensation for the SNS Laserwire,” Proceedings of ICALEPCS 2007, Knoxville, Tennessee, USA (2007). |

7. | P. M. Sinclair, J. R. Drummond, and A. D. May, “Digital divider circuit for a laser-beam-pointing stabilization system,” Appl. Opt. |

8. | 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. |

9. | Y. Wu, D. French, and I. Jovanovic, “Passive beam pointing stabilization,” Opt. Lett. |

10. | P. Fritschel, N. Mavalvala, D. Shoemaker, D. Sigg, M. Zucker, and G. González, “Alignment of an interferometric gravitational wave detector,” Appl. Opt. |

11. | D. A. Neamen, |

12. | J. DiStefano, A. Stubberud, and I. Williams, |

13. | E. Ott, |

**OCIS Codes**

(000.2170) General : Equipment and techniques

(000.3110) General : Instruments, apparatus, and components common to the sciences

(120.4820) Instrumentation, measurement, and metrology : Optical systems

(260.5210) Physical optics : Photoionization

(140.3425) Lasers and laser optics : Laser stabilization

**ToC Category:**

Instrumentation, Measurement, and Metrology

**History**

Original Manuscript: December 20, 2010

Revised Manuscript: January 14, 2011

Manuscript Accepted: January 17, 2011

Published: January 31, 2011

**Citation**

Robert A. Hardin, Yun Liu, Cary Long, Alexander Aleksandrov, and Willem Blokland, "Active beam position stabilization of pulsed lasers for long-distance ion profile diagnostics at the Spallation Neutron Source (SNS)," Opt. Express **19**, 2874-2885 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-4-2874

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### References

- A. Stalmashonak, N. Zhavoronkov, I. V. Hertel, S. Vetrov, and K. Schmid, “Spatial control of femtosecond laser system output with submicroradian accuracy,” Appl. Opt. 45(6), 1271–1274 (2006). [CrossRef] [PubMed]
- F. Lindau, O. Lundh, A. Persson, K. Cassou, S. Kazamias, D. Ros, F. Plé, G. Jamelot, A. Klisnick, S. de Rossi, D. Joyeux, B. Zielbauer, D. Ursescu, T. Kühl, and C. G. Wahlström, “Quantitative study of 10 Hz operation of a soft x-ray laser-energy stability and target considerations,” Opt. Express 15(15), 9486–9493 (2007). [CrossRef] [PubMed]
- 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(6), 061106 (2008). [CrossRef]
- J. Liu, Y. Kida, T. Teramoto, and T. Kobayashi, “Generation of stable sub-10 fs pulses at 400 nm in a hollow fiber for UV pump-probe experiment,” Opt. Express 18(5), 4664–4672 (2010). [CrossRef] [PubMed]
- Y. Liu, A. Aleksandrov, S. Assadi, W. Blokland, C. Deibele, W. Grice, C. Long, T. Pelaia, and A. Webster, “Laser wire beam profile monitor in the spallation neutron source (SNS) superconducting linac,” Nucl. Instr. Meth. A 612(2), 241–253 (2010). [CrossRef]
- W. Blokland, A. Barker, and W. Grice, “Drift Compensation for the SNS Laserwire,” Proceedings of ICALEPCS 2007, Knoxville, Tennessee, USA (2007).
- P. M. Sinclair, J. R. Drummond, and A. D. May, “Digital divider circuit for a laser-beam-pointing stabilization system,” Appl. Opt. 34(3), 408–409 (1995). [CrossRef] [PubMed]
- 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(2), 1339–1342 (2001). [CrossRef]
- Y. Wu, D. French, and I. Jovanovic, “Passive beam pointing stabilization,” Opt. Lett. 35(2), 250–252 (2010). [CrossRef] [PubMed]
- P. Fritschel, N. Mavalvala, D. Shoemaker, D. Sigg, M. Zucker, and G. González, “Alignment of an interferometric gravitational wave detector,” Appl. Opt. 37(28), 6734–6747 (1998). [CrossRef]
- D. A. Neamen, Electronic Circuit Analysis and Design (McGraw-Hill, 2001).
- J. DiStefano, A. Stubberud, and I. Williams, Schaum’s Outlines: Feedback and Control Systems, 2nd Edition. (McGraw-Hill, 1990).
- E. Ott, Chaos in Dynamical System (Cambridge University Press, 2002).

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