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4 - Coherence at Short Wavelengths

Published online by Cambridge University Press:  24 November 2016

David Attwood
Affiliation:
University of California, Berkeley
Anne Sakdinawat
Affiliation:
SLAC National Accelerator Laboratory
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X-Rays and Extreme Ultraviolet Radiation
Principles and Applications
, pp. 110 - 147
Publisher: Cambridge University Press
Print publication year: 2017

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References

1. Born, M. and Wolf, E., Principles of Optics (Cambridge University Press, 1999); Section 7.3.1 for a discussion of Young's double-pinhole technique, Section 7.58 for a discussion of bandwidths and coherence length; Section 8.5.2 for a discussion of the Airy pattern; and Chapter 10 for a broad discussion of coherence and partial coherence, correlation functions, and the van Cittert–Zernike theorem. Also see L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).
2. Goodman, J.W., Statistical Optics (Wiley, New York, 1985); Chapter 3 for a clear and concise exposition of diffraction theory, pp. 207–210 regarding the van Cittert–Zernike theorem, and pp. 215–218 regarding Young's double-pinhole technique.
3. Knox, W.H., Alonso, M. and Wolf, E., “Spatial Coherence from Ducks,” Physics Today (March 2010).
4. Collier, R.J., Burkhardt, C. and Lin, L.H., Optical Holography (Academic Press, New York, 1985).
5. Tipler, P.A. and Llewellyn, R.A., Modern Physics (Freeman, New York, 2012), Section 5.5.; also see R.N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1986), Sixth Edition, p. 160.
6. Sifvast, W.T., Laser Fundamentals (Cambridge University Press, 2004); Second Edition.
7. Siegman, A.E., Lasers (University Science, Mill Valley, CA, 1986), Chapters 1, 14, and 17, and Eq. 17–5, recast here for Eq.(4.8) in terms of rms quantities. For Rayleigh range and depth of focus considerations, Eq.(4.9), standard 1∕e2 description used.
8. Fowles, G.R., Introduction to Modern Optics (Dover, New York, 1989), Chapters 3 and 9.
9. Schawlow, A., “Laser Light,Scientific American 219, 120 (September1968).Google Scholar
10. Attwood, D., Halbach, K. and Kim, K.-J., “Tunable Coherent X-Rays,” Science 228, 1265 (June 14, 1985).Google Scholar
11. Hecht, E., Optics (Addison-Wesley, San Francisco, 2002), Fourth Edition, Chapters 10–12; see Sec. 10.2.5 and 10.2.5 regarding diffraction by a circular aperture and the resultant Airy pattern.
12. Kikuta, S., Aoki, S., Kosaki, S. and Kohra, K., “X-ray Holography of Lenseless Fourier-Transform Type,Opt. Commun. 5, 86 (1972).Google Scholar
13. Aoki, S., Ichihara, Y., and Kikuta, S., “X-ray Hologram Obtained by Using Synchrotron Radiation,Jpn. J. Appl. Phys. 11, 1857 (1972).Google Scholar
14. Reuter, B. and Mahr, H., “Experiments with Fourier Transform Holograms Using 4.48 nm X-rays,J. Physics E: Scientific Instrum. 9, 746 (1976).Google Scholar
15. Kondratenko, A.M. and Skrinsky, A.N., “Use of Radiation of Electron Storage Rings in X-ray Holography of Objects,Opt. Spectrosc. 42, 189 (February 1077); “X-Ray Holography of Microobjects”, Institute for Nuclear Physics, Novosibirsk, preprint 76–405 (1976).Google Scholar
16. Kondratenko, A.M. and Skrinsky, A.N., “X-Ray Holographic Microscopy,Avtometriya 2, 3 (Novosibirsk, March–April 1977).Google Scholar
17. McNulty, I., Kirz, J., Jaconsen, C., Howells, M.R. and Kern, D.P., “High-Resolution Imaging by Fourier Transform X-ray Holography,Science 256, 1009 (May 15, 1992).Google Scholar
18. Eisebitt, S., Lüning, J., Schlotter, W.F. et al., “Lenseless Imaging of Magnetic nanostructures by X-ray Spectro-Holography,Nature 432, 885 (December 16, 2004); J. Geilhufe et al., “Monolithic Focused Reference Beam X-ray Holography,” Nature Commun. 5, 3008 (January 7, 2014); E. Guehrs, M. Fohler, S. Frömmel et al., “Mask-Based Dual-Axis Tomoholography Using Soft X-Rays,” New J. Physics 17 (October 2015).Google Scholar
19. Schlotter, W.F. et al., “Multiple Reference Fourier Transform Holography with Soft X-rays,Appl. Phys. Lett. 89, 163112 (2006).Google Scholar
20. Marchesini, S., Boutet, S., Sakdinawat, A.E. et al., “Massively Parallel X-ray Holography,Nature Photonics 2, 560 (September 2008); S. Eisebitt, “X-Ray Holography: The Hole Story,” Nature Photonics 2, 529 (September 2008).Google Scholar
21. Chapman, H. N., Hau-Riege, S. P., Bogan, M. J. et al., “Femtosecond Time-Delay X-Ray Holography,” Nature 448, 676 (2007).Google Scholar
22. Vartanyants, I.A. and Singer, A., “Coherence Properties of 3-rd Generation Synchrotron Sources and Free Electron Lasers”, Chapter 1 in Handbook on Synchrotron Radiation and Free-Electron Lasers (Springer, Heidelberg, 2015), E. Jaeschke, S. Khan, J.R. Schneider and J.B. Hastings, Editors.
23. Nugent, K., “Coherent Methods in the X-Ray Sciences,Advances in Physics 59, 1–99 (2010).Google Scholar
24. Bedzyk, M.J., Bommarito, G.M. and Schildkraut, J.S., “X-ray Standing Waves at a Reflecting Mirror Surface,Phys. Rev. Lett. 62, 1376 (March 20, 1989).Google Scholar
25. Tiwari, M.K., Das, G. and Bedzyk, M.J., “X-ray Standing Wave Analysis of Nanostructures using Partially Coherent Radiation,Appl. Phys. Lett. 107, 103104 (September 7, 2015).Google Scholar
26. Beckhoff, B., “Reference-Free X-ray Spectrometry Based on Metrology Using Synchrotron Radiation,J. Analyt. Atomic Spectrom. 23, 845 (2008).Google Scholar
27. Pollakowski, B., Hoffmann, P., Kosinova, M. et al., “Nondestructive and Nonpreparative Chemical Nanometrometry of Internal Material Interfaces at Tunable High Information Depths,Analyt. Chem. 85, 193 (2013).Google Scholar
28. Becker, C., Pagels, M., Zachäus, C. et al., “Chemical Speciation at Buried Interfaces in High-Tempature Processed Polycrystalline Silicon Thin-Film Solar Cells on ZnO:Al,J. Appl. Phys. 113, 044519 (2013).Google Scholar
29. Cittert, P.H. van, “Die Wahrscheinliche Schwingungsverteilung in Einer von Einer Lichtquelle Direkt oder Mittels Einer Linse Beleuchteten Ebene” [The Probable Distribution of Vibrations in a Plane Illuminated by a Light Source Either Directly or Through a Lens], Physica 1, 210 (1934); see Coherence and Fluctuations of Light (1850–1966) (SPIE, Bellingham, WA, 1990), L. Mandel and E. Wolf, Editors, p. 1.Google Scholar
30. Zernike, F., “The Concept of Degree of Coherence and its Application to Optical Problems,” Physica 5, 785 (1938); see Coherence and Fluctuations of Light 1850–1966) (SPIE, Bellingham, WA, 1990), L. Mandel and E. Wolf, Editors, p. 100.Google Scholar
31. Watson, G.N., A Treatise on the Theory of Bessel Functions (Cambridge University Press, 1944), p. 20.
32. Gradshteyn, I.S. and Ryzhik, I.M., Table of Integrals, Series and Products (Academic Press, New York, 1994), Fifth Edition, Section 8.411, No. 1, p. 961.
33. Oliver, F.W., “Bessel Functions of Integer Order,” p. 360, No. 9.1.21, in Handbook of Mathematical Functions (Dover, New York, 1972), M. Abramowitz and I. Stegun, Editors.
34. Kreyszig, E., Advanced Engineering Mathematics (Wiley, New York, 1993), Seventh Edition, pp. 225 and A97; p. 834 shows the function.
35. Bracewell, R.N., The Fourier Transform and Its Applications (McGraw-Hill, New York, 1978), Second Edition, Chapter 12.
36. Sneddon, I.N., Fourier Transforms (Dover, New York, 1995).
37. Reference 32, p. 382, Section 3.460, No. 3, and p. 738, Section 6.632, No. 4.
38. Reference 32, p. 707, Section 6.561, No. 5.
39. Young, T., A Course of Lectures on Natural Philosophy and the Mechanical Arts, Volume 1, Lecture XXXIX, “On the Nature of Light and Colours” (J. Johnson, London, 2007), pp. 464–465 and 776–777; A. Robinson, The Last Man Who Knew Everything (Pearson Education, Penquin Books, Pi Press, 2006).
40. Thompson, B.J. and Wolf, E., “Two-Beam Interference with Partially Coherent Light,J. Opt. Soc. Amer. 47, 898 (October 1957).Google Scholar
41. C. Chang, “Coherence Techniques at Extreme Ultraviolet Wavelengths”, PhD thesis, EECS, University of California, Berkeley, 2002; Chang, C., Naulleau, P., Anderson, E. and Attwood, D., “Spatial Coherence Characterization of Undulator Radiation,Optics Commun. 182, 25 (August 1, 2000).Google Scholar
42. Skopintsev, P., Singer, A., Bach, J. et al., “Characterization of Spatial Coherence of Synchrotron radiation with Non-Redundant Arrays of Apertures,J. Synchr. Rad. 21 (4), 722 (July 2014).Google Scholar
43. Shore, R.A., Thompson, B.J., and Whitney, R.E., “Diffraction by Apertures Illuminated with Partially Coherent Light,” J. Opt. Soc. Amer. 56, 733 (June 1966).Google Scholar

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