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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 5 — Feb. 27, 2012
  • pp: 5601–5606
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Improving high-order harmonic yield using wavefront-controlled ultrashort laser pulses

Stefan Eyring, Christian Kern, Michael Zürch, and Christian Spielmann  »View Author Affiliations


Optics Express, Vol. 20, Issue 5, pp. 5601-5606 (2012)
http://dx.doi.org/10.1364/OE.20.005601


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Abstract

In this work we show that it is possible to increase the high-order harmonic yield when using wavefront-shaped laser beams. The investigation of the beam profile near the interaction region shows that the optimized beam is asymmetric and has a larger diameter. Thus, the optimized beam leads to a higher yield even if the peak intensity is lower compared to an unoptimized beam. This indicates that the wavefront of the fundamental laser beam and, accordingly, the focal profile play an important role in the efficient generation of high-order harmonic radiation.

© 2012 OSA

1. Introduction

The availability of brilliant XUV radiation sources with high beam quality is crucial for many experiments [1

1. M. Fajardo, P. Zeitoun, G. Faivre, S. Sebban, T. Mocek, A. Hallou, D. Aubert, P. Balcou, F. Burgy, D. Douillet, P. Mercère, A. S. Morlens, J. P. Rousseau, C. Valentin, S. Kazamias, G. Lachèze-Murel, T. Lefrou, H. Merdji, S. Le Pape, M. F. Ravet, F. Delmotte, and J. Gautier, “Second generation x-ray lasers,” J. Quant. Spectrosc. Radiat. Transf. 99, 142–152 (2006). [CrossRef]

3

3. H. M. Quiney, “Coherent diffractive imaging using short wavelength light sources,” J. Mod. Opt. 57, 1109–1149 (2010). [CrossRef]

]. With its unprecedented temporal and spatial characteristics [4

4. P. Antoine, A. L’Huillier, and M. Lewenstein, “Attosecond pulse trains using high-order harmonics,” Phys. Rev. Lett. 77, 1234–1237 (1996). [CrossRef] [PubMed]

,5

5. M. C. Chen, M. R. Gerrity, S. Backus, T. Popmintchev, X. Zhou, P. Arpin, X. Zhang, H. C. Kapteyn, and M. M. Murnane, “Spatially coherent, phase matched, high-order harmonic euv beams at 50 khz,” Opt. Express 17, 17376–17383 (2009). [CrossRef] [PubMed]

], high-order harmonic generation (HHG) can act as suitable XUV source [6

6. M. Wieland, Ch. Spielmann, U. Kleineberg, Th. Westerwalbesloh, U. Heinzmann, and T. Wilhein, “Toward time-resolved soft x-ray microscopy using pulsed fs-high-harmonic radiation,” Ultramicroscopy 102, 93–100 (2005). [CrossRef]

,7

7. P. Tzallas, E. Skantzakis, L. A. A. Nikolopoulos, G. D. Tsakiris, and D. Charalambidis, “Extreme-ultraviolet pump-probe studies of one-femtosecond-scale electron dynamics,” Nat. Phys. 7, 781– 784 (2011). [CrossRef]

]. Using high-order harmonics it is possible to create the shortest pulses available today [8

8. D. H. Ko, K. T. Kim, J. Park, J.-H. Lee, and C. H. Nam, “Attosecond chirp compensation over broadband high-order harmonics to generate near transform-limited 63 as pulses,” New. J. Phys. 12, 063008 (2010). [CrossRef]

].

Using a high-resolution spatial light modulator (SLM) it is possible to manipulate the wavefront in many different ways. This method of wavefront-control offers a high number of degrees of freedom. As mentioned above, it is highly non-trivial to determine the optimal wavefront for the efficient generation of high-order harmonics ab-initio. To counter this, closed-loop optimization algorithms are typically employed [14

14. R. Bartels, S. Backus, I. Christov, H. Kapteyn, and M. Murnane, “Attosecond time-scale feedback control of coherent x-ray generation,” Chem. Phys. 267, 277–289 (2001). [CrossRef]

]. In this work a genetic algorithm similar to the one in Ref. [15

15. D. Walter, S. Eyring, J. Lohbreier, R. Spitzenpfeil, and C. Spielmann, “Spatial optimization of filaments,” Appl. Phys. B 88, 175–178 (2007). [CrossRef]

] was used.

2. Experimental setup

The experimental setup is shown in Fig. 1. A Ti:sapphire amplifier system with a repetition rate of 1 kHz delivered laser pulses with a central wavelength of 800 nm. The laser pulses had a duration of about 30 fs and a pulse energy of about 800 μJ.

Fig. 1 Setup for high-order harmonic generation with wavefront controlled laser pulses. The laser beam is spatially shaped before it is focused into the generation chamber. The generated high-order harmonics are refocused onto a spectrometer where they are analyzed. A long-working-distance microscope is available to measure the beam profile of the fundamental laser beam near the focus.

The wavefront of the laser pulses was manipulated using a reflective spatial light modulator (Hamamatsu LCOS-SLM X10468) with a spatial resolution of 800×600 pixels. The LCOS-SLM is based on a liquid-crystal design. A direct phase-only modulation with a modulation depth of 2π of the laser beam is realized via a pixel by pixel control of the alignment of the liquid crystals. This way, the wavefront of the reflected laser beam can be controlled freely. To allow for interpretation of the applied wavefronts, the phase-masks were generated using Zernike polynomials [16

16. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University Press, 1999). [PubMed]

]. They can thus be calculated as
W(x,y)=ncnZn(x,y)
(1)
with Zernike polynomials Zn(x,y) and Zernike coefficients cn. In order to increase the modulation depth beyond 2π a phase wrapping technique with sharp phase jumps of 2π was used before the phase-masks were applied to the SLM.

The wavefront-controlled laser beam was focused with a fused silica glass lens (f = 300 mm, f/# = 15) into a sealed nickel tube with a diameter of about 2 mm, placed inside a vacuum chamber. The laser drilled holes into the front and the back of the nickel tube approximately 70 μm in diameter. Therefore, the interaction of the laser pulses, having a peak intensity of 3 × 1015 W/cm2, was limited longitudinally to approximately the tube diameter of 2 mm. As interaction medium, argon gas at a backing pressure of approximately 120 mbar was used.

In order to characterize the beam profile of the driving laser pulse at the interaction region, a focus diagnostic setup was implemented. It employs a standard SLR camera objective. The SLR objective was chosen because of its wide aperture and its very good imaging properties. The objective creates a real intermediate image of the interaction region at its back focal plane. In order to examine the beam profile at the beam waist, a standard 20× microscope objective is used as ocular lens, and a near-infrared sensitive CCD camera serves as detector. The overall magnification of this setup is 2.3× with a spatial resolution of about 5 μm. The generated high-order harmonic radiation is spectrally analyzed using a McPherson 248/310G XUV spectrometer with a 300 lines/mm grating. The spectrometer uses an imaging detection option consisting of a gated MCP and fiber-optically coupled CCD. Each spectrum is recorded by averaging over about 200 laser shots. The yield optimization is carried out using a genetic algorithm similar to the one in Ref. [15

15. D. Walter, S. Eyring, J. Lohbreier, R. Spitzenpfeil, and C. Spielmann, “Spatial optimization of filaments,” Appl. Phys. B 88, 175–178 (2007). [CrossRef]

]. The genetic algorithm searches for an optimum in the yield, applying Zernike polynomials up to the 6th radial order. The fitness function is calculated from the overall signal of the high-order harmonic spectra. In order to monitor the stability of the experimental conditions, a spectrum generated by an unshaped reference beam was recorded for every generation. This reference beam was created by applying a flat phase-mask to the SLM.

3. Optimization

In Fig. 2 the resulting spectra of the reference (black curve) and the fittest individual (red curve) at the end of the optimization are shown. These spectra were also used to calculate the fitness. Three spectral regions, called A, B and C were defined. These three regions, marked by the blue cursors, are also shown. From these, the fitness was calculated using the fitness function
FB+C.
(2)
The spectra clearly show a significant increase of the high-order harmonic yield. The signal count of the 25th harmonic, for example, increased by a factor of about 6. In the cut-off region three additional harmonics (31st – 35th) can be seen above the noise level in the optimized spectrum. Additional harmonics are usually attributed to an intensity increase inside the interaction region, whereas the non-uniformly increased yield in the plateau indicates phase-matching effects [10

10. D. Yoshitomi, J. Nees, N. Miyamoto, T. Sekikawa, T. Kanai, G. Mourou, and S. Watanabe, “Phase-matched enhancements of high-harmonic soft x-rays by adaptive wave-front control with a genetic algorithm,” Appl. Phys. B 78, 275–280 (2004). [CrossRef]

, 11

11. P. Villoresi, S. Bonora, M. Pascolini, L. Poletto, G. Tondello, C. Vozzi, M. Nisoli, G. Sansone, S. Stagira, and S. Silvestri, “Optimization of high-order harmonic generation by adaptive control of a sub-10-fs pulse wave front,” Opt. Lett. 29, 207–209 (2004). [CrossRef] [PubMed]

]. Further studies were conducted in order to examine more closely the improvement of high-order harmonic generation by ways of wavefront-shaping the fundamental.

Fig. 2 The high-order harmonic spectrum before (black curve) and after (red curve) optimization. The optimization goal was set to increase the overall high-order harmonic yield in the regions B and C. The order of each harmonic is shown on top of the harmonic line. The spectra are rescaled for a better readability while preserving the relative intensities.

4. Examination of the beam profile

In order to evaluate how the optimized wavefront modifies the intensity distribution of the fundamental laser beam, the beam profile near the interaction region was recorded directly. For this, the focus diagnostic setup described above was used. The beam profile of the reference beam is shown in Fig. 3. As can be seen, it is nearly Gaussian and has a diameter of about 43 μm. Below the actual beam profile small disturbances are visible. These disturbances are caused by multiple reflections at two neutral density filters. The filters were placed directly in front of the microscope and were used to attenuate the beam. The same measurement was also done for an optimized beam. From the phase-mask applied to the SLM the intensity distribution near the focus was simulated. For this, the phase-mask, shown in Fig. 4, was assumed for the spatial phase of the incident beam. The simulation was then done by numerically calculating the Fresnel propagation integral. This way, the beam profiles of the optimized beam at different experimental conditions can be compared. In Fig. 5 the calculated and the measured beam profiles are compared. As can be seen, the calculated profile in the interaction region, shown in Fig. 5(a), is slightly distorted. The beam diameter along the longer main axis is about 46 μm. The resolution achieved by the calculation is about 10 μm and is limited by the available computational power and the limited resolution of the SLM.

Fig. 3 Beam profile of the reference beam at full intensity with argon gas (120 mbar backing pressure) as interaction medium. The spatial resolution of the beam profile measurement is about 5 μm.
Fig. 4 Phase-mask applied to the SLM to create the optimized laser beam. The phase-mask is dominated by large Zernike coefficients for trefoil, coma and astigmatism.
Fig. 5 (a) Beam profile of the optimized beam calculated from the SLM phase-mask assuming a Gaussian beam profile. The spatial resolution of the calculation is 10 μm. (b) Beam profile of the optimized beam at low intensity (attenuation: 10−9 in front of focusing lens) with no interaction medium present. (c) Beam profile of the optimized beam at full intensity with argon gas (120 mbar backing pressure) as interaction medium. The spatial resolution of the beam profile measurement is about 5 μm.

The measured beam profile, shown in Fig. 5(b), was recorded using an attenuated beam with an optimized wavefront. Also no gas was present in the interaction region. This allows for comparison of the measured data with the simulation, as the calculation assumes medium-free space during propagation. The calculated beam diameter of about 46 μm is in good agreement with the measured beam diameter of about 48 μm. Similar to Fig. 3, small disturbances appear below and on the left of the actual beam profile. Again, these disturbances are caused by multiple reflections at two neutral density filters. This time, the filters were placed in front of the focusing lens. Thus, the intensity at the interaction region was very low, so no nonlinear effects occurred.

Figure 5(c) shows the beam profile measured under the same experimental conditions as were used for the optimization, i.e., with full intensity and interaction medium present. Under these conditions the beam diameter of about 53 μm is slightly larger than the beam diameter at low intensities and absence of the interaction medium. Similar to Fig. 3, attenuation of the beam occurred directly in front of the microscope, using the same two neutral density filters. This way, all nonlinear effects in the interaction medium which might affect the beam profile were present.

When comparing the different beam profiles, several interesting characteristics can be noticed. The comparison of Fig. 5(a) and Fig. 5(b) shows that the beam profile at the interaction region is influenced only by the phase-mask applied to the SLM. The calculated and the measured beam diameter agree very well. By comparing Fig. 5(b) and Fig. 5(c) the influence of nonlinear effects in the interaction medium on the beam profile can be detected. As can be seen, these effects slightly reduce the asymmetry of the laser beam, but increase the beam diameter significantly. A comparison of Fig. 5(c) and Fig. 3 clearly shows that the beam diameter of the beam optimized for an increased high-order harmonic signal is larger than the beam diameter of the reference beam, additionally showing a pronounced asymmetry. Even though this optimized beam has a reduced peak intensity compared to the reference beam, the high-order harmonic yield in the plateau from this beam is higher. These findings add complementary knowledge to results from [10

10. D. Yoshitomi, J. Nees, N. Miyamoto, T. Sekikawa, T. Kanai, G. Mourou, and S. Watanabe, “Phase-matched enhancements of high-harmonic soft x-rays by adaptive wave-front control with a genetic algorithm,” Appl. Phys. B 78, 275–280 (2004). [CrossRef]

, 11

11. P. Villoresi, S. Bonora, M. Pascolini, L. Poletto, G. Tondello, C. Vozzi, M. Nisoli, G. Sansone, S. Stagira, and S. Silvestri, “Optimization of high-order harmonic generation by adaptive control of a sub-10-fs pulse wave front,” Opt. Lett. 29, 207–209 (2004). [CrossRef] [PubMed]

] where an extension of the cut-off was observed.

5. Conclusion

It has been shown that it is possible to increase the high-order harmonic yield by using wavefront-shaped laser beams. The investigation of the beam profile near the interaction region showed that the optimized beam has an asymmetric beam profile with a larger beam diameter. Thus, the optimized beam leads to a higher yield even when the peak intensity is lower compared to an unoptimized beam. This shows that the wavefront and the focal profile of the fundamental laser beam play an important role in the efficient generation of high-order harmonic radiation.

Acknowledgments

This study has been supported by TMKWB grants B154-09030 and B 715-08008. C. Kern acknowledges support from a fellowship of the Abbe School of Photonics Jena. M. Zürch acknowledges support from the FSU grant “ProChance 2009 A1”.

References and links

1.

M. Fajardo, P. Zeitoun, G. Faivre, S. Sebban, T. Mocek, A. Hallou, D. Aubert, P. Balcou, F. Burgy, D. Douillet, P. Mercère, A. S. Morlens, J. P. Rousseau, C. Valentin, S. Kazamias, G. Lachèze-Murel, T. Lefrou, H. Merdji, S. Le Pape, M. F. Ravet, F. Delmotte, and J. Gautier, “Second generation x-ray lasers,” J. Quant. Spectrosc. Radiat. Transf. 99, 142–152 (2006). [CrossRef]

2.

A. Sakdinawat and D. Attwood, “Nanoscale x-ray imaging,” Nat. Photonics 4, 840–848 (2010). [CrossRef]

3.

H. M. Quiney, “Coherent diffractive imaging using short wavelength light sources,” J. Mod. Opt. 57, 1109–1149 (2010). [CrossRef]

4.

P. Antoine, A. L’Huillier, and M. Lewenstein, “Attosecond pulse trains using high-order harmonics,” Phys. Rev. Lett. 77, 1234–1237 (1996). [CrossRef] [PubMed]

5.

M. C. Chen, M. R. Gerrity, S. Backus, T. Popmintchev, X. Zhou, P. Arpin, X. Zhang, H. C. Kapteyn, and M. M. Murnane, “Spatially coherent, phase matched, high-order harmonic euv beams at 50 khz,” Opt. Express 17, 17376–17383 (2009). [CrossRef] [PubMed]

6.

M. Wieland, Ch. Spielmann, U. Kleineberg, Th. Westerwalbesloh, U. Heinzmann, and T. Wilhein, “Toward time-resolved soft x-ray microscopy using pulsed fs-high-harmonic radiation,” Ultramicroscopy 102, 93–100 (2005). [CrossRef]

7.

P. Tzallas, E. Skantzakis, L. A. A. Nikolopoulos, G. D. Tsakiris, and D. Charalambidis, “Extreme-ultraviolet pump-probe studies of one-femtosecond-scale electron dynamics,” Nat. Phys. 7, 781– 784 (2011). [CrossRef]

8.

D. H. Ko, K. T. Kim, J. Park, J.-H. Lee, and C. H. Nam, “Attosecond chirp compensation over broadband high-order harmonics to generate near transform-limited 63 as pulses,” New. J. Phys. 12, 063008 (2010). [CrossRef]

9.

P. Balcou, P. Salières, A. L’Huillier, and M. Lewenstein, “Generalized phase-matching conditions for high harmonics: the role of field-gradient forces,” Phys. Rev. A 55, 3204–3210 (1997). [CrossRef]

10.

D. Yoshitomi, J. Nees, N. Miyamoto, T. Sekikawa, T. Kanai, G. Mourou, and S. Watanabe, “Phase-matched enhancements of high-harmonic soft x-rays by adaptive wave-front control with a genetic algorithm,” Appl. Phys. B 78, 275–280 (2004). [CrossRef]

11.

P. Villoresi, S. Bonora, M. Pascolini, L. Poletto, G. Tondello, C. Vozzi, M. Nisoli, G. Sansone, S. Stagira, and S. Silvestri, “Optimization of high-order harmonic generation by adaptive control of a sub-10-fs pulse wave front,” Opt. Lett. 29, 207–209 (2004). [CrossRef] [PubMed]

12.

J. Lohbreier, S. Eyring, R. Spitzenpfeil, C. Kern, M. Weger, and C. Spielmann, “Maximizing the brilliance of high-order harmonics in a gas jet,” New. J. Phys. 11, 023016 (2009). [CrossRef]

13.

R. Spitzenpfeil, S. Eyring, C. Kern, C. Ott, J. Lohbreier, J. Henneberger, N. Franke, S. Jung, D. Walter, M. Weger, C. Winterfeldt, T. Pfeifer, and C. Spielmann, “Enhancing the brilliance of high-harmonic generation,” Appl. Phys A 96, 69–81 (2009). [CrossRef]

14.

R. Bartels, S. Backus, I. Christov, H. Kapteyn, and M. Murnane, “Attosecond time-scale feedback control of coherent x-ray generation,” Chem. Phys. 267, 277–289 (2001). [CrossRef]

15.

D. Walter, S. Eyring, J. Lohbreier, R. Spitzenpfeil, and C. Spielmann, “Spatial optimization of filaments,” Appl. Phys. B 88, 175–178 (2007). [CrossRef]

16.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University Press, 1999). [PubMed]

OCIS Codes
(320.7110) Ultrafast optics : Ultrafast nonlinear optics
(340.7480) X-ray optics : X-rays, soft x-rays, extreme ultraviolet (EUV)
(020.2649) Atomic and molecular physics : Strong field laser physics

ToC Category:
Ultrafast Optics

History
Original Manuscript: December 14, 2011
Revised Manuscript: January 26, 2012
Manuscript Accepted: January 27, 2012
Published: February 22, 2012

Citation
Stefan Eyring, Christian Kern, Michael Zürch, and Christian Spielmann, "Improving high-order harmonic yield using wavefront-controlled ultrashort laser pulses," Opt. Express 20, 5601-5606 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-5-5601


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References

  1. M. Fajardo, P. Zeitoun, G. Faivre, S. Sebban, T. Mocek, A. Hallou, D. Aubert, P. Balcou, F. Burgy, D. Douillet, P. Mercère, A. S. Morlens, J. P. Rousseau, C. Valentin, S. Kazamias, G. Lachèze-Murel, T. Lefrou, H. Merdji, S. Le Pape, M. F. Ravet, F. Delmotte, and J. Gautier, “Second generation x-ray lasers,” J. Quant. Spectrosc. Radiat. Transf.99, 142–152 (2006). [CrossRef]
  2. A. Sakdinawat and D. Attwood, “Nanoscale x-ray imaging,” Nat. Photonics4, 840–848 (2010). [CrossRef]
  3. H. M. Quiney, “Coherent diffractive imaging using short wavelength light sources,” J. Mod. Opt.57, 1109–1149 (2010). [CrossRef]
  4. P. Antoine, A. L’Huillier, and M. Lewenstein, “Attosecond pulse trains using high-order harmonics,” Phys. Rev. Lett.77, 1234–1237 (1996). [CrossRef] [PubMed]
  5. M. C. Chen, M. R. Gerrity, S. Backus, T. Popmintchev, X. Zhou, P. Arpin, X. Zhang, H. C. Kapteyn, and M. M. Murnane, “Spatially coherent, phase matched, high-order harmonic euv beams at 50 khz,” Opt. Express17, 17376–17383 (2009). [CrossRef] [PubMed]
  6. M. Wieland, Ch. Spielmann, U. Kleineberg, Th. Westerwalbesloh, U. Heinzmann, and T. Wilhein, “Toward time-resolved soft x-ray microscopy using pulsed fs-high-harmonic radiation,” Ultramicroscopy102, 93–100 (2005). [CrossRef]
  7. P. Tzallas, E. Skantzakis, L. A. A. Nikolopoulos, G. D. Tsakiris, and D. Charalambidis, “Extreme-ultraviolet pump-probe studies of one-femtosecond-scale electron dynamics,” Nat. Phys.7, 781– 784 (2011). [CrossRef]
  8. D. H. Ko, K. T. Kim, J. Park, J.-H. Lee, and C. H. Nam, “Attosecond chirp compensation over broadband high-order harmonics to generate near transform-limited 63 as pulses,” New. J. Phys.12, 063008 (2010). [CrossRef]
  9. P. Balcou, P. Salières, A. L’Huillier, and M. Lewenstein, “Generalized phase-matching conditions for high harmonics: the role of field-gradient forces,” Phys. Rev. A55, 3204–3210 (1997). [CrossRef]
  10. D. Yoshitomi, J. Nees, N. Miyamoto, T. Sekikawa, T. Kanai, G. Mourou, and S. Watanabe, “Phase-matched enhancements of high-harmonic soft x-rays by adaptive wave-front control with a genetic algorithm,” Appl. Phys. B78, 275–280 (2004). [CrossRef]
  11. P. Villoresi, S. Bonora, M. Pascolini, L. Poletto, G. Tondello, C. Vozzi, M. Nisoli, G. Sansone, S. Stagira, and S. Silvestri, “Optimization of high-order harmonic generation by adaptive control of a sub-10-fs pulse wave front,” Opt. Lett.29, 207–209 (2004). [CrossRef] [PubMed]
  12. J. Lohbreier, S. Eyring, R. Spitzenpfeil, C. Kern, M. Weger, and C. Spielmann, “Maximizing the brilliance of high-order harmonics in a gas jet,” New. J. Phys.11, 023016 (2009). [CrossRef]
  13. R. Spitzenpfeil, S. Eyring, C. Kern, C. Ott, J. Lohbreier, J. Henneberger, N. Franke, S. Jung, D. Walter, M. Weger, C. Winterfeldt, T. Pfeifer, and C. Spielmann, “Enhancing the brilliance of high-harmonic generation,” Appl. Phys A96, 69–81 (2009). [CrossRef]
  14. R. Bartels, S. Backus, I. Christov, H. Kapteyn, and M. Murnane, “Attosecond time-scale feedback control of coherent x-ray generation,” Chem. Phys.267, 277–289 (2001). [CrossRef]
  15. D. Walter, S. Eyring, J. Lohbreier, R. Spitzenpfeil, and C. Spielmann, “Spatial optimization of filaments,” Appl. Phys. B88, 175–178 (2007). [CrossRef]
  16. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University Press, 1999). [PubMed]

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