Abstract

We present a novel approach for the design and fabrication of multiplexed computer generated volume holograms (CGVH) which allow for a dynamic synthesis of arbitrary wave field distributions. To achieve this goal, we developed a hybrid system that consists of a CGVH as a static element and an electronically addressed spatial light modulator as the dynamic element. We thereby derived a new model for describing the scattering process within the inhomogeneous dielectric material of the hologram. This model is based on the linearization of the scattering process within the Rytov approximation and incorporates physical constraints that account for voxel based laser-lithography using micro-fabrication of the holograms in a nonlinear optical material. In this article we demonstrate that this system basically facilitates a high angular Bragg selectivity on the order of 1°. Additionally, it allows for a qualitatively low cross-talk dynamic synthesis of predefined wave fields with a much larger space-bandwidth product (SBWP ≥ 8.7 × 106) as compared to the current state of the art in computer generated holography.

© 2015 Optical Society of America

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References

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  1. D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948).
    [Crossref] [PubMed]
  2. E. Leith, A. Kozma, J. Upatnieks, J. Marks, and N. Massey, “Holographic data storage in three-dimensional media,” Appl. Opt. 5(8), 1303–1311 (1966).
    [Crossref] [PubMed]
  3. K. Curtis, L. Dhar, A. Hill, W. Wilson, and M. Ayres, Holographic Data Storage (Wiley, New York, 2010).
    [Crossref]
  4. S. Huferath-vonLuepke, E. Kamau, T. Kreis, and C. von Kopylow, “Single-shot multiwavelength shape measurements with restricted aperture,” in Optical Engineering and Applications, J. Schmit, K. Creath, C. E. Towers, and J. Burke, eds., Proc. SPIE8493, 84930V (2012).
  5. C. von Kopylow and R. B. Bergmann, “Optical Metrology,” in Micro Metal FormingF. Vollertsen, ed., (Springer, Berlin, 2013).
  6. U. Schnars, C. Falldorf, J. Watson, and W. Jüptner, Digital Holography and Wavefront Sensing (Springer, Berlin Heidelberg, 2015).
  7. E. N. Kamau, N. M. Burns, C. Falldorf, C. von Kopylow, J. Watson, and R. B. Bergmann, “Least-squares based inverse reconstruction of in-line digital holograms,” J. Opt. 15(7), 075716 (2013).
    [Crossref]
  8. W. Osten, A. Faridian, P. Gao, K. Körner, D. Naik, G. Pedrini, A. K. Singh, M. Takeda, and M. Wilke, “Recent advances in digital holography [Invited],” Appl. Opt. 53(27), G44–G63 (2014).
    [Crossref] [PubMed]
  9. C. Falldorf, M. Agour, and R. B. Bergmann, “Digital holography and quantitative phase contrast imaging using computational shear interferometry,” Opt. Eng. 54(2), 024110 (2015).
    [Crossref]
  10. A. W. Lohmann and D. Paris, “Binary Fraunhofer holograms, generated by computer,” Appl. Opt. 6(10), 1739–1748 (1967).
    [Crossref] [PubMed]
  11. J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Comm. 207(1), 169–175 (2002).
    [Crossref]
  12. J. Kacperski and M. Kujawinska, “LCoS Active based laser interferometer for microelements studies,” Opt. Express 14(21), 9664–9678 (2006).
    [Crossref] [PubMed]
  13. C. Falldorf, C. von Kopylow, and R. B. Bergmann, “Wave field sensing by means of computational shear interferometry,” J. Opt. Soc. Am. A 30(10), 1905–1912 (2013).
    [Crossref]
  14. D. Wang, Q.-H. Wang, C. Shen, X. Zhou, and C.-M. Liu, “Active optical zoom system,” Appl. Opt. 53(31), 7402–7406 (2014).
    [Crossref] [PubMed]
  15. S. Borgsmüller, S. Noehte, C. Dietrich, T. Kresse, and R. Männer, “Computer-generated stratified diffractive optical elements,” Appl. Opt. 42(26), 5274–5283 (2003).
    [Crossref] [PubMed]
  16. A. A. Gülses and B. K. Jenkins, “Cascaded diffractive optical elements for improved multiplane image reconstruction,” Appl. Opt. 52(15), 3608–3616 (2013).
    [Crossref] [PubMed]
  17. T. D. Gerke and R. Piestun, “Aperiodic computer-generated volume holograms improve the performance of amplitude volume gratings,” Opt. Express 15(23), 14954–14960 (2007).
    [Crossref] [PubMed]
  18. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48(9), 2909–2947 (1969).
    [Crossref]
  19. D. Brady and D. Psaltis, “Control of volume holograms,” J. Opt. Soc. Am. A 9(7), 1167–1182 (1992).
    [Crossref]
  20. W. Cai, T. J. Reber, and R. Piestun, “Computer-generated volume holograms fabricated by femtosecond laser micromachining,” Opt. Lett. 31(12), 1836–1838 (2006).
    [Crossref] [PubMed]
  21. T. D. Gerke and R. Piestun, “Aperiodic volume optics,” Nature Photonics 4, 188–193 (2010).
    [Crossref]
  22. E. N. Kamau, C. Falldorf, and R. B. Bergmann, “A new approach to dynamic wave field synthesis using computer generated volume holograms,” in 12th Workshop on information Optics, (IEEE, 2013), pp. 1–3.
  23. E. N. Kamau, V. V. P. Sreenivas, M. Bülters, C. Falldorf, and R. B. Bergmann, “Fabrication of Multiplexed Computer Generated Volume Holograms in Photosensitive Glass,” in Frontiers in Optics, (Optical Society of America, 2014), pp. FTh4G–1.
  24. E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Comm. 1(4), 153–156 (1969).
    [Crossref]
  25. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).
    [Crossref]
  26. A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (Society for Industrial and Applied Mathematics, 2001).
    [Crossref]
  27. T. D. Gerke, Aperiodic Volume Optics, Ph.D. thesis, University of Colorado at Boulder (2010).
  28. Y. Cheng, Digital Holographic Microscopy, Ph.D. thesis, Northeastern University Boston, (2009).
  29. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21(15), 2758–2769 (1982).
    [Crossref] [PubMed]
  30. H. Misawa and S. Juodkazis, 3D Laser Microfabrication: Principles and Applications (John Wiley & Sons, 2006).
    [Crossref]
  31. Y. Cheng, K. Sugioka, and M. Masuda, “Optical gratings embedded in photosensitive glass by photochemical reaction using a femtosecond laser,” Opt. Express 11(15), 1809–1816 (2003).
    [Crossref] [PubMed]
  32. J. W. Goodman, Introduction to Fourier Optics (Roberts & Company Publishers, 2005).
  33. C. Falldorf, S. Osten, C. v. Kopylow, and W. Jüptner, “Shearing interferometer based on the birefringent properties of a spatial light modulator,” Opt. Lett. 34(18), 2727–2729 (2009).
    [Crossref] [PubMed]

2015 (1)

C. Falldorf, M. Agour, and R. B. Bergmann, “Digital holography and quantitative phase contrast imaging using computational shear interferometry,” Opt. Eng. 54(2), 024110 (2015).
[Crossref]

2014 (2)

2013 (3)

2010 (1)

T. D. Gerke and R. Piestun, “Aperiodic volume optics,” Nature Photonics 4, 188–193 (2010).
[Crossref]

2009 (1)

2007 (1)

2006 (2)

2003 (2)

2002 (1)

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Comm. 207(1), 169–175 (2002).
[Crossref]

1992 (1)

1982 (1)

1969 (2)

E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Comm. 1(4), 153–156 (1969).
[Crossref]

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48(9), 2909–2947 (1969).
[Crossref]

1967 (1)

1966 (1)

1948 (1)

D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948).
[Crossref] [PubMed]

Agour, M.

C. Falldorf, M. Agour, and R. B. Bergmann, “Digital holography and quantitative phase contrast imaging using computational shear interferometry,” Opt. Eng. 54(2), 024110 (2015).
[Crossref]

Ayres, M.

K. Curtis, L. Dhar, A. Hill, W. Wilson, and M. Ayres, Holographic Data Storage (Wiley, New York, 2010).
[Crossref]

Bergmann, R. B.

C. Falldorf, M. Agour, and R. B. Bergmann, “Digital holography and quantitative phase contrast imaging using computational shear interferometry,” Opt. Eng. 54(2), 024110 (2015).
[Crossref]

E. N. Kamau, N. M. Burns, C. Falldorf, C. von Kopylow, J. Watson, and R. B. Bergmann, “Least-squares based inverse reconstruction of in-line digital holograms,” J. Opt. 15(7), 075716 (2013).
[Crossref]

C. Falldorf, C. von Kopylow, and R. B. Bergmann, “Wave field sensing by means of computational shear interferometry,” J. Opt. Soc. Am. A 30(10), 1905–1912 (2013).
[Crossref]

E. N. Kamau, C. Falldorf, and R. B. Bergmann, “A new approach to dynamic wave field synthesis using computer generated volume holograms,” in 12th Workshop on information Optics, (IEEE, 2013), pp. 1–3.

C. von Kopylow and R. B. Bergmann, “Optical Metrology,” in Micro Metal FormingF. Vollertsen, ed., (Springer, Berlin, 2013).

E. N. Kamau, V. V. P. Sreenivas, M. Bülters, C. Falldorf, and R. B. Bergmann, “Fabrication of Multiplexed Computer Generated Volume Holograms in Photosensitive Glass,” in Frontiers in Optics, (Optical Society of America, 2014), pp. FTh4G–1.

Borgsmüller, S.

Born, M.

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

Brady, D.

Bülters, M.

E. N. Kamau, V. V. P. Sreenivas, M. Bülters, C. Falldorf, and R. B. Bergmann, “Fabrication of Multiplexed Computer Generated Volume Holograms in Photosensitive Glass,” in Frontiers in Optics, (Optical Society of America, 2014), pp. FTh4G–1.

Burns, N. M.

E. N. Kamau, N. M. Burns, C. Falldorf, C. von Kopylow, J. Watson, and R. B. Bergmann, “Least-squares based inverse reconstruction of in-line digital holograms,” J. Opt. 15(7), 075716 (2013).
[Crossref]

Cai, W.

Cheng, Y.

Curtis, J. E.

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Comm. 207(1), 169–175 (2002).
[Crossref]

Curtis, K.

K. Curtis, L. Dhar, A. Hill, W. Wilson, and M. Ayres, Holographic Data Storage (Wiley, New York, 2010).
[Crossref]

Dhar, L.

K. Curtis, L. Dhar, A. Hill, W. Wilson, and M. Ayres, Holographic Data Storage (Wiley, New York, 2010).
[Crossref]

Dietrich, C.

Falldorf, C.

C. Falldorf, M. Agour, and R. B. Bergmann, “Digital holography and quantitative phase contrast imaging using computational shear interferometry,” Opt. Eng. 54(2), 024110 (2015).
[Crossref]

E. N. Kamau, N. M. Burns, C. Falldorf, C. von Kopylow, J. Watson, and R. B. Bergmann, “Least-squares based inverse reconstruction of in-line digital holograms,” J. Opt. 15(7), 075716 (2013).
[Crossref]

C. Falldorf, C. von Kopylow, and R. B. Bergmann, “Wave field sensing by means of computational shear interferometry,” J. Opt. Soc. Am. A 30(10), 1905–1912 (2013).
[Crossref]

C. Falldorf, S. Osten, C. v. Kopylow, and W. Jüptner, “Shearing interferometer based on the birefringent properties of a spatial light modulator,” Opt. Lett. 34(18), 2727–2729 (2009).
[Crossref] [PubMed]

U. Schnars, C. Falldorf, J. Watson, and W. Jüptner, Digital Holography and Wavefront Sensing (Springer, Berlin Heidelberg, 2015).

E. N. Kamau, C. Falldorf, and R. B. Bergmann, “A new approach to dynamic wave field synthesis using computer generated volume holograms,” in 12th Workshop on information Optics, (IEEE, 2013), pp. 1–3.

E. N. Kamau, V. V. P. Sreenivas, M. Bülters, C. Falldorf, and R. B. Bergmann, “Fabrication of Multiplexed Computer Generated Volume Holograms in Photosensitive Glass,” in Frontiers in Optics, (Optical Society of America, 2014), pp. FTh4G–1.

Faridian, A.

Fienup, J. R.

Gabor, D.

D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948).
[Crossref] [PubMed]

Gao, P.

Gerke, T. D.

T. D. Gerke and R. Piestun, “Aperiodic volume optics,” Nature Photonics 4, 188–193 (2010).
[Crossref]

T. D. Gerke and R. Piestun, “Aperiodic computer-generated volume holograms improve the performance of amplitude volume gratings,” Opt. Express 15(23), 14954–14960 (2007).
[Crossref] [PubMed]

T. D. Gerke, Aperiodic Volume Optics, Ph.D. thesis, University of Colorado at Boulder (2010).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (Roberts & Company Publishers, 2005).

Grier, D. G.

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Comm. 207(1), 169–175 (2002).
[Crossref]

Gülses, A. A.

Hill, A.

K. Curtis, L. Dhar, A. Hill, W. Wilson, and M. Ayres, Holographic Data Storage (Wiley, New York, 2010).
[Crossref]

Huferath-vonLuepke, S.

S. Huferath-vonLuepke, E. Kamau, T. Kreis, and C. von Kopylow, “Single-shot multiwavelength shape measurements with restricted aperture,” in Optical Engineering and Applications, J. Schmit, K. Creath, C. E. Towers, and J. Burke, eds., Proc. SPIE8493, 84930V (2012).

Jenkins, B. K.

Juodkazis, S.

H. Misawa and S. Juodkazis, 3D Laser Microfabrication: Principles and Applications (John Wiley & Sons, 2006).
[Crossref]

Jüptner, W.

Kacperski, J.

Kak, A. C.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (Society for Industrial and Applied Mathematics, 2001).
[Crossref]

Kamau, E.

S. Huferath-vonLuepke, E. Kamau, T. Kreis, and C. von Kopylow, “Single-shot multiwavelength shape measurements with restricted aperture,” in Optical Engineering and Applications, J. Schmit, K. Creath, C. E. Towers, and J. Burke, eds., Proc. SPIE8493, 84930V (2012).

Kamau, E. N.

E. N. Kamau, N. M. Burns, C. Falldorf, C. von Kopylow, J. Watson, and R. B. Bergmann, “Least-squares based inverse reconstruction of in-line digital holograms,” J. Opt. 15(7), 075716 (2013).
[Crossref]

E. N. Kamau, C. Falldorf, and R. B. Bergmann, “A new approach to dynamic wave field synthesis using computer generated volume holograms,” in 12th Workshop on information Optics, (IEEE, 2013), pp. 1–3.

E. N. Kamau, V. V. P. Sreenivas, M. Bülters, C. Falldorf, and R. B. Bergmann, “Fabrication of Multiplexed Computer Generated Volume Holograms in Photosensitive Glass,” in Frontiers in Optics, (Optical Society of America, 2014), pp. FTh4G–1.

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48(9), 2909–2947 (1969).
[Crossref]

Kopylow, C. v.

Körner, K.

Koss, B. A.

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Comm. 207(1), 169–175 (2002).
[Crossref]

Kozma, A.

Kreis, T.

S. Huferath-vonLuepke, E. Kamau, T. Kreis, and C. von Kopylow, “Single-shot multiwavelength shape measurements with restricted aperture,” in Optical Engineering and Applications, J. Schmit, K. Creath, C. E. Towers, and J. Burke, eds., Proc. SPIE8493, 84930V (2012).

Kresse, T.

Kujawinska, M.

Leith, E.

Liu, C.-M.

Lohmann, A. W.

Männer, R.

Marks, J.

Massey, N.

Masuda, M.

Misawa, H.

H. Misawa and S. Juodkazis, 3D Laser Microfabrication: Principles and Applications (John Wiley & Sons, 2006).
[Crossref]

Naik, D.

Noehte, S.

Osten, S.

Osten, W.

Paris, D.

Pedrini, G.

Piestun, R.

Psaltis, D.

Reber, T. J.

Schnars, U.

U. Schnars, C. Falldorf, J. Watson, and W. Jüptner, Digital Holography and Wavefront Sensing (Springer, Berlin Heidelberg, 2015).

Shen, C.

Singh, A. K.

Slaney, M.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (Society for Industrial and Applied Mathematics, 2001).
[Crossref]

Sreenivas, V. V. P.

E. N. Kamau, V. V. P. Sreenivas, M. Bülters, C. Falldorf, and R. B. Bergmann, “Fabrication of Multiplexed Computer Generated Volume Holograms in Photosensitive Glass,” in Frontiers in Optics, (Optical Society of America, 2014), pp. FTh4G–1.

Sugioka, K.

Takeda, M.

Upatnieks, J.

von Kopylow, C.

E. N. Kamau, N. M. Burns, C. Falldorf, C. von Kopylow, J. Watson, and R. B. Bergmann, “Least-squares based inverse reconstruction of in-line digital holograms,” J. Opt. 15(7), 075716 (2013).
[Crossref]

C. Falldorf, C. von Kopylow, and R. B. Bergmann, “Wave field sensing by means of computational shear interferometry,” J. Opt. Soc. Am. A 30(10), 1905–1912 (2013).
[Crossref]

S. Huferath-vonLuepke, E. Kamau, T. Kreis, and C. von Kopylow, “Single-shot multiwavelength shape measurements with restricted aperture,” in Optical Engineering and Applications, J. Schmit, K. Creath, C. E. Towers, and J. Burke, eds., Proc. SPIE8493, 84930V (2012).

C. von Kopylow and R. B. Bergmann, “Optical Metrology,” in Micro Metal FormingF. Vollertsen, ed., (Springer, Berlin, 2013).

Wang, D.

Wang, Q.-H.

Watson, J.

E. N. Kamau, N. M. Burns, C. Falldorf, C. von Kopylow, J. Watson, and R. B. Bergmann, “Least-squares based inverse reconstruction of in-line digital holograms,” J. Opt. 15(7), 075716 (2013).
[Crossref]

U. Schnars, C. Falldorf, J. Watson, and W. Jüptner, Digital Holography and Wavefront Sensing (Springer, Berlin Heidelberg, 2015).

Wilke, M.

Wilson, W.

K. Curtis, L. Dhar, A. Hill, W. Wilson, and M. Ayres, Holographic Data Storage (Wiley, New York, 2010).
[Crossref]

Wolf, E.

E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Comm. 1(4), 153–156 (1969).
[Crossref]

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

Zhou, X.

Appl. Opt. (7)

Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48(9), 2909–2947 (1969).
[Crossref]

J. Opt. (1)

E. N. Kamau, N. M. Burns, C. Falldorf, C. von Kopylow, J. Watson, and R. B. Bergmann, “Least-squares based inverse reconstruction of in-line digital holograms,” J. Opt. 15(7), 075716 (2013).
[Crossref]

J. Opt. Soc. Am. A (2)

Nature (1)

D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948).
[Crossref] [PubMed]

Nature Photonics (1)

T. D. Gerke and R. Piestun, “Aperiodic volume optics,” Nature Photonics 4, 188–193 (2010).
[Crossref]

Opt. Comm. (2)

E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Comm. 1(4), 153–156 (1969).
[Crossref]

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Comm. 207(1), 169–175 (2002).
[Crossref]

Opt. Eng. (1)

C. Falldorf, M. Agour, and R. B. Bergmann, “Digital holography and quantitative phase contrast imaging using computational shear interferometry,” Opt. Eng. 54(2), 024110 (2015).
[Crossref]

Opt. Express (3)

Opt. Lett. (2)

Other (12)

K. Curtis, L. Dhar, A. Hill, W. Wilson, and M. Ayres, Holographic Data Storage (Wiley, New York, 2010).
[Crossref]

S. Huferath-vonLuepke, E. Kamau, T. Kreis, and C. von Kopylow, “Single-shot multiwavelength shape measurements with restricted aperture,” in Optical Engineering and Applications, J. Schmit, K. Creath, C. E. Towers, and J. Burke, eds., Proc. SPIE8493, 84930V (2012).

C. von Kopylow and R. B. Bergmann, “Optical Metrology,” in Micro Metal FormingF. Vollertsen, ed., (Springer, Berlin, 2013).

U. Schnars, C. Falldorf, J. Watson, and W. Jüptner, Digital Holography and Wavefront Sensing (Springer, Berlin Heidelberg, 2015).

J. W. Goodman, Introduction to Fourier Optics (Roberts & Company Publishers, 2005).

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

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (Society for Industrial and Applied Mathematics, 2001).
[Crossref]

T. D. Gerke, Aperiodic Volume Optics, Ph.D. thesis, University of Colorado at Boulder (2010).

Y. Cheng, Digital Holographic Microscopy, Ph.D. thesis, Northeastern University Boston, (2009).

E. N. Kamau, C. Falldorf, and R. B. Bergmann, “A new approach to dynamic wave field synthesis using computer generated volume holograms,” in 12th Workshop on information Optics, (IEEE, 2013), pp. 1–3.

E. N. Kamau, V. V. P. Sreenivas, M. Bülters, C. Falldorf, and R. B. Bergmann, “Fabrication of Multiplexed Computer Generated Volume Holograms in Photosensitive Glass,” in Frontiers in Optics, (Optical Society of America, 2014), pp. FTh4G–1.

H. Misawa and S. Juodkazis, 3D Laser Microfabrication: Principles and Applications (John Wiley & Sons, 2006).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1 (a) Schematic of the geometry considered for a general scattering problem. The gray area corresponds to the volume V of the volume hologram, which is defined by the scattering potential F ( r , ν ) while the intermediate region corresponds to the volume of the base dielectric material with a refractive index no. A wave field incident (wave vector, k o = k q o) upon this volume will be scattered such that a predefined scattered field (wave vector, k s = k q s) is projected into the signal window W across the plane { ξ }, in the far-field domain of the hologram. (b) Frequency space representation of the scattering problem where values of the scattered field are seen to lie on a portion (solid line) of the Ewald’s sphere (broken line). These values are projected onto a planar detector, whereby each pixel on this plane integrates the light scattered within a solid angle Δ Ω ( k s ).
Fig. 2
Fig. 2 Comparison of the convergence behavior of the design algorithm for both the model based on the Rytov approximation (broken line) and the conventional method which is based on the Born approximation. It is apparent from these results that in the former, the algorithm converges to higher Δn values as it was discussed in Sect. 3.1.
Fig. 3
Fig. 3 (a) A conceptual sketch of a 4 f-setup that allows for the decoupling of individual far-field projections Ψi from a CGVH, which is defined by the scattering potential S ( r ), by inscribing the transfer function H ( ν ) on an SLM. (b) A schematic representation of angular multiplexing, whereby for each angle αi a far field projection ψi is decoupled. (c) Bragg effect is shown in terms of the relative diffraction efficiency η/ηo of a test CGVH. This shows how the efficiency of a single projection from a CGVH decreases as the angle of the reference wave deviates from the Bragg angle θB.
Fig. 4
Fig. 4 (a) An experimental setup which comprises in a 4f-setup consisting of a fiber coupled diode laser, 2 lenses with a focal length of f1 = 105 mm, a λ/2 wave plate and a polarizer (not drawn to scale). This part is used to implement a non-mechanical beam modulation unit with the help of an SLM. The other part, high precision positioning stages are used to position the CGVH and a lens is used to collimate and couple in single or a set of reference waves at different angles θ into the CGVH. For instance light that is polarized along its slow (dashed line) axis can be modulated to generate a given reference wave, while light polarized along the fast axis (solid line) represents a second reference wave. With this setup the target intensities in (b) were decoded experimentally from a single CGVH with dimensions of 683×683×100 μm3 for four different angles. The resulting far-field projections ψi (false color coded) are shown in (c). Each projection was offset by an angle step of 2° from each other.
Fig. 5
Fig. 5 Dynamically synthesized fields. (a) a single projection ψ2 corresponding to a single reference wave is decoupled by light polarized in the fast axis. (b) a second projection ψ3 corresponding to a single reference wave is decoupled by light polarized in the slow axis and modulated using the SLM in order to generate a deflected reference wave k θ. (c) projections ψ2 and ψ3 are decoupled simultaneously and are superposed within the same signal window W leading to the synthesis of a new field ψ2 +ψ3. (d) Vectorial representation of the reconstruction process, whereby the same signal window W is chosen and hence both reference waves k 2 and K 2 have the same scattering vector k s. This leads to the superposition of ψ2 and ψ3 even though the corresponding reference waves are offset by an angle θ.

Tables (1)

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Table 1 Overview of typical constituents and concentrations (in mass percentage - wt%) found in a commercially available Foturan photostructurable glass ceramic [30].

Equations (28)

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U ( r , ν ) = U o ( r , ν ) + U s ( r , ν ) .
U ( r , ν ) = U o ( r , ν ) + V F ( r , ν ) U ( r , ν ) G ( | r r | , ν ) d 3 r .
G ( | r r | , ν ) = e i k | r r | | r r |
G ( | r r | , ν ) e i k r r e i k q s r .
U ( r q s , ν ) U o ( r , ν ) + e i k r r V F ( r , ν ) e i k ( q s q o ) r d 3 r ,
F ( r , ν ) = 1 4 π k 2 [ n 2 ( r , ν ) n o 2 ] .
U B ( r q s , ν ) = e i k r r V F ( r , ν ) e i k ( q s q o ) r d 3 r ,
n ( r , v ) = n o + Δ n ( ( r ) ) ,
F ˜ ( K , ν ) = V F ( r , ν ) e i K r d 3 r .
K = k ( q s q o ) .
L ( n ˜ j ) = U t U ( n ˜ j ) 2
Φ ( r q s , ν ) Φ o ( r , ν ) + 1 U o ( r , ν ) e i k r r V F ( r , ν ) e i k ( q s q o ) r d 3 r ,
Φ R ( r , ν ) = U B ( r , ν ) U o ( r , ν )
Δ n < [ Φ R λ 2 π ] 2 .
U ˜ j ( K ) = exp [ e i k r r F ˜ ( K ) / U o ( r , ν ) ] .
U ˜ j ( K , ν ) = { c k I t ( K , ν ) e [ i ϕ j ( K , ν ) ] ( K , ν ) W U ˜ j ( K , ν ) otherwise ,
F j + 1 ( r , ν ) = { 1 4 π k 2 [ n j 2 ( r , ν ) n o 2 ] F ´ j ( r , ν ) 1 8 π k 2 [ n j 2 ( r , ν ) n o 2 ] 0 otherwise .
H s ( ν ) = e i 2 π ν s .
U f ( r ) = 1 i λ f { U i ( r ) } ( r λ f ) ,
t s ( r ) = H d ( r λ f ) = e i 2 π r λ f s
U f ( r ) = { { U i ( r ) } t s } = U i ( ( r s ) ) ,
U ( r ) = i = 1 I A i e i ϕ i ψ i ( r ) ,
rect ( z L ) F ( r , ν ) z π sin c ( z 2 k z ) * F ˜ ( K ˜ , ν ) .
S ( r ) = F ( r ) rect [ x L x , y L y , z L z ] ,
S ˜ ( K , ν ) = F ˜ ( K , ν ) L x L y L z sin c [ L x k x 2 π , L y k y 2 π , L z k z 2 π ] .
η = | U ˜ ( k x , k y ) | 2 I t ( k x , k y ) d k x d k y | U ˜ ( k x , k y ) | 2 d k x d k y
U s ( x , y , z , ν ) U s ( m Δ x , n Δ y , p Δ z , ν )
S B W P = C 8 [ L x L y L z B x B y B z ] .

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