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Theory

  • Stephan Stuerwald
Chapter
Part of the Springer Series in Optical Sciences book series (SSOS, volume 221)

Abstract

This chapter comprises an introduction into the most significant theoretical backgrounds of digital holography. For a better understanding, also the basics of conventional, classic holography including temporal and spatial phase shifting techniques are summarized at the beginning of this chapter, before proceeding with the numerical propagation of complex object waves and special considerations that are required for application in a microscope system. Further, different types of spatial light modulators for a complex manipulation of electromagnetic waves are introduced and discussed. Several approaches for their utilization in a microscope system are then introduced. These include aberration control, focusing possibilities and the exertion of a momentum for single or multiple holographic optical traps (HOTs). Furthermore, dynamic holography for optical micromanipulation in life science microscopy and different applications of optical tweezers are theoretically discussed. As a significant topic in latest research, so-called diffractive and non-diffractive beam types are introduced comprising Bessel, Mathieu and Airy beams. In a last part of this chapter, the basics of direct laser writing with two-photon polymerization are explained which can be improved by utilization of spatial light modulators.

References

  1. 1.
    Gabor, D.: A new microscopic principle. Nature 161, 777–778 (1948)ADSCrossRefGoogle Scholar
  2. 2.
    Menzel, E., Mirandé, W., Weingärtner, I.: Fourier-Optik und Holographie, vol. 1, pp. 140–142. Springer, Wien (1973)CrossRefGoogle Scholar
  3. 3.
    Kreis, T.: Handbook of Holographic Interferometry: Optical and Digital Methods. Wiley-VCH, Weinheim (2005). ISBN 9783527405466Google Scholar
  4. 4.
    Poon, T.-C.: Digital Holography and Three-Dimensional Display: Principles and Applications, vol. 1. Springer, Wien (2006)Google Scholar
  5. 5.
    Yaroslavsky, L.: Introduction to Digital Holography [Saif Zone and Sharjah and U.A.E.], vol. 1. Bentham eBooks (2009). ISBN 9781608050796Google Scholar
  6. 6.
    Kreis, T.: Holographic Interferometry: Principles and Methods. Akademie Verlag Series in Optical Metrology. Akademie Verlag (1996). http://books.google.de/books?id=qfJRAAAAMAAJ, ISBN 9783055016448
  7. 7.
    Leith, E.N., Upatnieks, J.: Reconstructed wavefronts and communication theory. J. Opt. Soc. Am. 52(10), 1123–1128 (1962).  https://doi.org/10.1364/JOSA.52.001123ADSCrossRefGoogle Scholar
  8. 8.
    Leith, E.N., Upatnieks, J.: Wavefront reconstruction with continuous-tone objects. J. Opt. Soc. Am. 53(12), 1377–1381 (1963).  https://doi.org/10.1364/JOSA.53.001377ADSCrossRefGoogle Scholar
  9. 9.
    Goodman, J.W.: Introduction to Fourier Optics. McGraw-Hill Physical and Quantum Electronics Series. Roberts & Company (2005). http://books.google.de/books?id=ow5xs_Rtt9AC, ISBN 9780974707723
  10. 10.
    Lesem, L.B., Hirsch, P.M.: The kinoform: a new wavefront reconstruction device. IBM J. Res. Dev. 13, 150–155 (1969)CrossRefGoogle Scholar
  11. 11.
    Schnars, U., Jueptner, W.: Direct recording of holograms by a CCD target and numerical reconstruction. Appl. Opt. 33(2), 179–181 (1994).  https://doi.org/10.1364/AO.33.000179ADSCrossRefGoogle Scholar
  12. 12.
    Schnars, Ulf., Jüptner, W.P.O.: Digital recording and numerical reconstruction of holograms. Meas. Sci. Technol. 13(9), R85 (2002). http://stacks.iop.org/0957-0233/13/i=9/a=201ADSCrossRefGoogle Scholar
  13. 13.
    Schnars, Ulf., Jüptner, W.: Digital Holography. Springer, Berlin (2005)Google Scholar
  14. 14.
    Gerchberg, R., Saxton, W.: A practical algorithm for the determination of phase from image and diffraction plane pictures. Optik 35(2), 237–246 (1972)Google Scholar
  15. 15.
    Allebach, J., Seldowitz, M.: Synthesis of digital holograms by direct binary search. Appl. Opt. 26(14), 2788–2798 (1987)ADSCrossRefGoogle Scholar
  16. 16.
    Schmit, J., Creath, K.: Extended averaging technique for derivation of error-compensating algorithms in phase-shifting interferometry. Appl. Opt. 34(19), 3610–3619 (1995).  https://doi.org/10.1364/AO.34.003610ADSCrossRefGoogle Scholar
  17. 17.
    El Jarad, A., Gulker, G., Hinsch, K.D.: Microscopic ESPI: better fringe qualities by the Fourier transform method. Proc. SPIE 4933, 335–341 (2003).  https://doi.org/10.1117/12.516662
  18. 18.
    Mills, G.A., Yamaguchi, I.: Effects of quantization in phase-shifting digital holography. Appl. Opt. 44(7), 1216–1225 (2005).  https://doi.org/10.1364/AO.44.001216ADSCrossRefGoogle Scholar
  19. 19.
    Schwider, J., Burow, R., Elssner, K.-E., Grzanna, J., Spolaczyk, R., Merkel, K.: Digital wave-front measuring interferometry: some systematic error sources. Appl. Opt. 22(21), 3421–3432 (1983).  https://doi.org/10.1364/AO.22.003421ADSCrossRefGoogle Scholar
  20. 20.
    Malacara, D.: Optical Shop Testing, vol. 3. Wiley-VCH, New Jersey (2007)Google Scholar
  21. 21.
    Malacara, D.: Optical Shop Testing. Wiley Series in Pure and Applied Optics. Wiley, New York (2007). http://books.google.de/books?id=qMHKB1mKFr4C, ISBN 9780470135969
  22. 22.
    Burke, J., Helmers, H.: Spatial versus temporal phase shifting in electronic speckle-pattern interferometry: noise comparison in phase maps. Appl. Opt. 39(25), 4598–4606 (2000).  https://doi.org/10.1364/AO.39.004598ADSCrossRefGoogle Scholar
  23. 23.
    Brophy, C.P.: Effect of intensity error correlation on the computed phase of phase-shifting interferometry. J. Opt. Soc. Am. A 7(4), 537–541 (1990).  https://doi.org/10.1364/JOSAA.7.000537ADSCrossRefGoogle Scholar
  24. 24.
    Bothe, T., Burke, J., Helmers, H.: Spatial phase shifting in electronic speckle pattern interferometry: minimization of phase reconstruction errors. Appl. Opt. 36(22), 5310–5316 (1997).  https://doi.org/10.1364/AO.36.005310ADSCrossRefGoogle Scholar
  25. 25.
    Liebling, M., Blu, T., Cuche, E., Marquet, P., Depeursinge, C., Unser, M.: A novel non-diffractive reconstruction method for digital holographic microscopy. In: Proceedings of the 2002 IEEE International Symposium on Biomedical Imaging, pp. 625–628 (2002)Google Scholar
  26. 26.
    Liebling, M., Blu, T., Unser, M.: Complex-wave retrieval from a single off-axis hologram. J. Opt. Soc. Am. A 21(3), 367–377 (2004).  https://doi.org/10.1364/JOSAA.21.000367ADSCrossRefGoogle Scholar
  27. 27.
    Carl, D., Kemper, B., Wernicke, G., von Bally, G.: Parameter-optimized digital holographic microscope for high-resolution living-cell analysis. Appl. Opt. 43(36), 6536–6544 (2004).  https://doi.org/10.1364/AO.43.006536ADSCrossRefGoogle Scholar
  28. 28.
    Stuerwald, S., Schmitt, R.: Readjusting image sharpness by numerical parametric lenses in Forbes-representation and Halton sampling for selective refocusing in digital holographic microscopy - Errata. Version 2010.  https://doi.org/10.1117/12.903693
  29. 29.
    Remmersmann, C., Stürwald, S., Kemper, B., Langehanenberg, P., von Bally, G.: Phase noise optimization in temporal phase-shifting digital holography with partial coherence light sources and its application in quantitative cell imaging. Appl. Opt. 48(8), 1463–1472 (2009).  https://doi.org/10.1364/AO.48.001463ADSCrossRefGoogle Scholar
  30. 30.
    Cuche, E., Depeursinge, C.: Digital holography for quantitative phase-contrast imaging. Opt. Lett. 24(5), 291–293 (1999)ADSCrossRefGoogle Scholar
  31. 31.
    Marquet, P., Rappaz, B., Magistretti, P.J., Cuche, E., Emery, Y., Colomb, T., Depeursinge, C.: Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy. Opt. Lett. 30(5), 468–470 (2005).  https://doi.org/10.1364/OL.30.000468ADSCrossRefGoogle Scholar
  32. 32.
    Dubois, F., Requena, M.-L.N., Minetti, C., Monnom, O., Istasse, E.: Partial spatial coherence effects in digital holographic microscopy with a laser source. Appl. Opt. 43(5), 1131–1139 (2004).  https://doi.org/10.1364/AO.43.001131ADSCrossRefGoogle Scholar
  33. 33.
    Shamir, J.: Press Monographs. Optical Systems and Processes, vol. 3. OSA (1986).  https://doi.org/10.1364/JOSAA.3.000847, ISBN 9780819432261ADSCrossRefGoogle Scholar
  34. 34.
    Lankenau, E., Klinger, D., Winter, C., Malik, A., Müller, H., Oelckers, S., Pau, H.-W., Just, T., Hüttmann, G.: Combining optical coherence tomography (OCT) with an operating microscope. In: Buzug, T.M., Holz, D., Bongartz, J., Kohl-Bareis, M., Hartmann, U., Weber, S. (eds.) Advances in Medical Engineering, vol. 114, pp. 343–348. Springer, Berlin (2007). ISBN 978–3–540–68763–4Google Scholar
  35. 35.
    Haferkorn, H.: Optik: Physikalisch-technische Grundlagen und Anwendungen, vol. 4. Wiley-VCH Verlag (2002)Google Scholar
  36. 36.
    Jahns, J.: Photonik: Grundlagen, Komponenten und Systeme. Oldenbourg Wissenschaftsverlag (2000)Google Scholar
  37. 37.
    vision.at/images01/DMD2.JPG, 14.08.2012. InVision. http://www.science-vision.at/images01/DMD2.JPG
  38. 38.
    Liesener, J.: Zum Einsatz räumlicher Lichtmodulatoren in der interferometrischen Wellenfrontmesstechnik. Dissertation, Universität Stuttgart, Stuttgart, 24.03.2007Google Scholar
  39. 39.
    Texas Instruments: Introduction to digital micromirror device (DMD) technology (2008). http://www.ti.com/lit/an/dlpa008/dlpa008.pdf
  40. 40.
  41. 41.
    Dai, H., Liu, K.X.Y., Wang, X., Liu, J.: Characteristics of LCoS phase-only spatial light modulator and its applications. Opt. Commun. 238(4–6), 269–276 (2004). ISSN 00304018ADSCrossRefGoogle Scholar
  42. 42.
    Hecht, E.: Optik, vol. 5. Oldenbourg, München (2009). ISBN 9783486588613Google Scholar
  43. 43.
    Wilkinson, T.D., Henderson, C.D., Leyva, D.G., Crossland, W.A.: Phase modulation with the next generation of liquid crystal over silicon technology. J. Mater. Chem. 16(33), 3359 (2006). ISSN 0959–9428CrossRefGoogle Scholar
  44. 44.
    Serati, S., Xia, X.: High-resolution phase-only spatial light modulators with submillisecond response. In: SPIE Proceedings, vol. 5106 (2003)Google Scholar
  45. 45.
    Serati, S., Harriman, J.: Spatial light modulator considerations for beam control in optical manipulation applications. Version 2006.  https://doi.org/10.1117/12.681156
  46. 46.
    Lizana, A., Márquez, A., Lobato, L., Rodange, Y., Moreno, I., Iemmi, C., Campos, J.: The minimum Euclidean distance principle applied to improve the modulation diffraction efficiency in digitally controlled spatial light modulators. Opt. Express 18(10), 10581–10593 (2010).  https://doi.org/10.1364/OE.18.010581ADSCrossRefGoogle Scholar
  47. 47.
    Kohler, C.: Optimierung von Flüssigkristall-Lichtmodulatoren in aktiven optischen Systemen. Dissertation, Universität Stuttgart, Stuttgart, 23.07.2009Google Scholar
  48. 48.
    Zwick, S.: Flexible Mikromanipulation durch räumliche Lichtmodulation in der Mikroskopie. Dissertation, Universität Stuttgart, Stuttgart, 19.05.2010Google Scholar
  49. 49.
    Ashkin, A.: Acceleration and trapping of particles by radiation pressure. Phys. Rev. Lett. 24(4), 156–159 (1970)ADSCrossRefGoogle Scholar
  50. 50.
    Maurer, C., Jesacher, A., Bernet, S., Ritsch-Marte, M.: What spatial light modulators can do for optical microscopy. Laser Photonics Rev. 5(1), 81–101 (2011).  https://doi.org/10.1002/lpor.200900047, ISSN 18638880ADSCrossRefGoogle Scholar
  51. 51.
    Ashkin, A.: History of optical trapping and manipulation of small neutral particles, atoms, and molecules. Springer Series in Chemical Physics, vol. 67, pp. 1–31. Springer, Berlin (2001).  https://doi.org/10.1007/978-3-642-56544-1_1, ISBN 978–3–642–62702–6Google Scholar
  52. 52.
    Svoboda, K., Block, S.M.: Biological applications of optical forces. Annu. Rev. Biophys. Biomol. Struct. 23(1), 247–285 (1994).  https://doi.org/10.1146/annurev.bb.23.060194.001335, PMID: 7919782CrossRefGoogle Scholar
  53. 53.
    Fällman, E., Axner, O.: Design for fully steerable dual-trap optical tweezers. Appl. Opt. 36(10), 2107–2113 (1997).  https://doi.org/10.1364/AO.36.002107ADSCrossRefGoogle Scholar
  54. 54.
    Sasaki, K., Koshioka, M., Misawa, H., Kitamura, N., Masuhara, H.: Pattern formation and flow control of fine particles by laser-scanning micromanipulation. Opt. Lett. 16(19), 1463–1465 (1991).  https://doi.org/10.1364/OL.16.001463ADSCrossRefGoogle Scholar
  55. 55.
    Brouhard, G.J., Schek, H.J., Hunt, A.J.: Advanced optical tweezers for the study of cellular and molecular biomechanics. IEEE Trans. Biomed. Eng. 50(1), 121–125 (2003).  https://doi.org/10.1109/TBME.2002.805463CrossRefGoogle Scholar
  56. 56.
    Dufresne, E.R., Spalding, G.C., Dearing, M.T., Sheets, S.A., Grier, D.G.: Computer-generated holographic optical tweezer arrays. Rev. Sci. Instrum. 72(3), 1810–1816 (2001).  https://doi.org/10.1063/1.1344176ADSCrossRefGoogle Scholar
  57. 57.
    Dufresne, E.R., Grier, D.G.: Optical tweezer arrays and optical substrates created with diffractive optics. Rev. Sci. Instrum. 69(5), 1974–1977 (1998).  https://doi.org/10.1063/1.1148883ADSCrossRefGoogle Scholar
  58. 58.
    Reicherter, M., Haist, T., Wagemann, E.U., Tiziani, H.J.: Optical particle trapping with computer-generated holograms written on a liquid-crystal display. Opt. Lett. 24(9), 608–610 (1999).  https://doi.org/10.1364/OL.24.000608ADSCrossRefGoogle Scholar
  59. 59.
    Curtis, J.E., Koss, B.A., Grier, D.G.: Dynamic holographic optical tweezers. Opt. Commun. 207(1–6), 169–175 (2002).  https://doi.org/10.1016/S0030-4018(02)01524-9, ISSN 0030–4018ADSCrossRefGoogle Scholar
  60. 60.
    Kawata, Y., Fujita, K.: 4Pi confocal optical system with phase conjugation. Opt. Lett. 21(18), 1415–1417 (1996)ADSCrossRefGoogle Scholar
  61. 61.
    Knox, K., Burnham, D.: Observation of bistability of trapping position in aerosol optical tweezers. J. Opt. Soc. Am. B 27(3), 582–591 (2010)CrossRefGoogle Scholar
  62. 62.
    Ashkin, A.: Optical trapping and manipulation of neutral particles using lasers. Proc. Natl. Acad. Sci. USA 94, 4853–4860 (1997)ADSCrossRefGoogle Scholar
  63. 63.
    Ashkin, A., Dziedzic, J.M., Bjorkholm, J.E., Chu, S.: Observation of a single-beam gradient force optical trap for dielectric particles. Opt. Lett. 11(5), 288–290 (1986).  https://doi.org/10.1364/OL.11.000288ADSCrossRefGoogle Scholar
  64. 64.
    Ashkin, A.: Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime. Biophys. J. 61, 569–582 (1992)ADSCrossRefGoogle Scholar
  65. 65.
    Svoboda, K., Block, S.M.: Biological applications of optical forces. Dissertation, Harvard University, Cambridge and Massachusetts (1994)CrossRefGoogle Scholar
  66. 66.
    Reicherter, M.: Optical particle trapping with computer-generated holograms written on a liquid-crystal display. Opt. Lett. 24(9), 608–610 (1999)ADSCrossRefGoogle Scholar
  67. 67.
    Wright, W.H., Sonek, G.J., Berns, M.W.: Parametric study of the forces on microspheres held by optical tweezers. Appl. Opt. 33(9), 1735–1748 (1994)ADSCrossRefGoogle Scholar
  68. 68.
    Wright, W.H.: Radiation trapping forces on microspheres with optical tweezers. Appl. Phys. Lett. 63(6), 715–717 (1993)ADSCrossRefGoogle Scholar
  69. 69.
    Hwang, S.-Uk., Park, Y.-H., Lee, Y.-G.: Interactive Control of holographic optical traps with fast hologram generation. IEEE 1, 183–188 (2009)Google Scholar
  70. 70.
    Saleh, B.E.A., Teich, M.C.: Grundlagen der Photonik. Lehrbuch Physik, vol. 2, vollst. überarb. und erw. Aufl. [=1. dt. Aufl.]. Wiley-VCH, Weinheim (2008). ISBN 9783527406777Google Scholar
  71. 71.
    Reicherter, M.: Einsatz von Lichtmodulatoren zum Teilcheneinfang und zur Aberrationskontrolle in holografischen Pinzetten. Dissertation, Universität Stuttgart, Stuttgart, 29.09.2006Google Scholar
  72. 72.
    Kegler, K., Salomo, M., Kremer, F.: Forces of interaction between DNA-grafted colloids: an optical tweezer measurement. Phys. Rev. Lett. 98, 058304 (2007).  https://doi.org/10.1103/PhysRevLett.98.058304
  73. 73.
    Perkins, T.T.: Optical traps for single molecule biophysics: a primer. Laser Photonics Rev. 3(1–2), 203–220 (2009). ISSN 18638880ADSCrossRefGoogle Scholar
  74. 74.
    Enger, J.: Optical tweezers applied to a microfluidic system. Lab Chip 4(3), 196–200 (2004). ISSN 1473–0197CrossRefGoogle Scholar
  75. 75.
    Seeger, S.: Application of laser optical tweezers in immunology and molecular genetics. Cytometry 12, 497–504 (1991)CrossRefGoogle Scholar
  76. 76.
    Ladavac, K., Grier, D.: Microoptomechanical pumps assembled and driven by holographic optical vortex arrays. Opt. Express 12(6), 1144–1149 (2004)ADSCrossRefGoogle Scholar
  77. 77.
    Jackson, J.D.: Klassische Elektrodynamik. de Gruyter (1981). http://books.google.de/books?id=JFdwygAACAAJ, ISBN 9783110074154
  78. 78.
    Durnin, J.: Exact solutions for nondiffracting beams. I. The scalar theory. J. Opt. Soc. Am. A 4(4), 651–654 (1987).  https://doi.org/10.1364/JOSAA.4.000651ADSCrossRefGoogle Scholar
  79. 79.
    Arlt, J., Garces-Chavez, V., Sibbett, W., Dholakia, K.: Optical micromanipulation using a Bessel light beam. Opt. Commun. 197(4–6), 239–245 (2001).  https://doi.org/10.1016/S0030-4018(01)01479-1, ISSN 0030–4018ADSCrossRefGoogle Scholar
  80. 80.
    Born, M., Wolf, E., Bhatia, A.B.: Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light. Cambridge University Press, Cambridge (1999). http://books.google.de/books?id=aoX0gYLuENoC, ISBN 9780521642224
  81. 81.
    Wright, E.M.: The generalized Bessel function of order greater than one. Q. J. Math. os-11(1), 36–48 (1940).  https://doi.org/10.1093/qmath/os-11.1.36ADSMathSciNetCrossRefGoogle Scholar
  82. 82.
    Gori, F., Guattari, G., Padovani, C.: Bessel–Gauss beams. Opt. Commun. 64(6), 491–495 (1987).  https://doi.org/10.1016/0030-4018(87)90276-8, ISSN 0030–4018ADSCrossRefGoogle Scholar
  83. 83.
    Arlt, J., Dholakia, K.: Generation of high-order Bessel beams by use of an axicon. Opt. Commun. 177(1–6), 297–301 (2000).  https://doi.org/10.1016/S0030-4018(00)00572-1, ISSN 0030–4018ADSCrossRefGoogle Scholar
  84. 84.
    Vasara, A., Turunen, J., Friberg, A.T.: Realization of general nondiffracting beams with computer-generated holograms. J. Opt. Soc. Am. A 6(11), 1748–1754 (1989).  https://doi.org/10.1364/JOSAA.6.001748ADSCrossRefGoogle Scholar
  85. 85.
    Chattrapiban, N., Rogers, E.A., Cofield, D., Hill III, W.T., Roy, R.: Generation of nondiffracting Bessel beams by use of a spatial light modulator. Opt. Lett. 28(22), 2183–2185 (2003).  https://doi.org/10.1364/OL.28.002183
  86. 86.
    Allen, L., Beijersbergen, M.W., Spreeuw, R.J.C., Woerdman, J.P.: Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes. Phys. Rev. A 45, 8185–8189 (1992).  https://doi.org/10.1103/PhysRevA.45.8185ADSCrossRefGoogle Scholar
  87. 87.
    Matsumoto, N., Ando, T., Inoue, T., Ohtake, Y., Fukuchi, N., Hara, T.: Generation of high-quality higher-order Laguerre–Gaussian beams using liquid-crystal-on-silicon spatial light modulators. J. Opt. Soc. Am. A 25(7), 1642–1651 (2008).  https://doi.org/10.1364/JOSAA.25.001642ADSCrossRefGoogle Scholar
  88. 88.
    Debailleul, M., Simon, B., Georges, V., Haeberl, O., Lauer, V.: Holographic microscopy and diffractive microtomography of transparent samples. Meas. Sci. Technol. 19(7), 074009 (2008). http://stacks.iop.org/0957-0233/19/i=7/a=074009ADSCrossRefGoogle Scholar
  89. 89.
    Kimel, I., Elias, L.R.: Relations between Hermite and Laguerre Gaussian modes. IEEE J. Quantum Electron. 29(9), 2562–2567 (1993).  https://doi.org/10.1109/3.247715, ISSN 0018–9197ADSCrossRefGoogle Scholar
  90. 90.
    Stamnes, J.J., Spjelkavik, B.: New method for computing eigenfunctions (Mathieu functions) for scattering by elliptical cylinders. Pure Appl. Opt. J. Eur. Opt. Soc. Part A 4(3), 251 (1995). http://stacks.iop.org/0963-9659/4/i=3/a=011CrossRefGoogle Scholar
  91. 91.
    Cojocaru, E.: Mathieu functions computational toolbox implemented in Matlab (2008). arXiv:0811.1970, Forschungsbericht, Comments: 20 pages, 0 figures, 6 tables
  92. 92.
    Morris, J.E., Mazilu, M., Baumgartl, J., Cizmar, T., Dholakia, K.: Supercontinuum Airy beams. Version: 2009.  https://doi.org/10.1117/12.826098
  93. 93.
    Goeppert-Mayer, M.: Ueber Elementarakte mit zwei Quantenspruengen. Dissertation, Universitaet Goettingen (1931)Google Scholar
  94. 94.
    Goeppert-Mayer, M.: Ueber Elementarakte mit zwei Quantenspruengen. Annalen der Physik 401(3), 273–294 (1931).  https://doi.org/10.1002/andp.19314010303, ISSN 1521–3889ADSCrossRefGoogle Scholar
  95. 95.
    Bayer, E., Schaack, G.: Two-photon absorption of CaF2:Eu2+. Phys. Status Solidi (b) 41(2), 827–835 (1970).  https://doi.org/10.1002/pssb.19700410239, ISSN 1521–3951ADSCrossRefGoogle Scholar
  96. 96.
    McClain, M.: Two-photon molecular spectroscopy. Phys. Rev. Lett. (1974)Google Scholar
  97. 97.
    Kafri, O., Kimel, S.: Theory of two-photon absorption and emission second-order saturation effect. Chem. Phys. 5(3), 488–493 (1974).  https://doi.org/10.1016/0301-0104(74)85052-4, ISSN 0301–0104ADSCrossRefGoogle Scholar
  98. 98.
    Nanoscribe GmbH. http://www.nanoscribe.de/
  99. 99.
    Schaeffer, S.: Characterization of two-photon induced cross-linking of proteins. Master thesis, RWTH Aachen (2013)Google Scholar

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Authors and Affiliations

  1. 1.University of California, BerkeleyBerkeleyUSA

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