Abstract

We present an algorithm for the computation of computer-generated holograms projecting arbitrary patterns through optical reconstruction systems with strong field-dependent aberrations. The algorithm is based on a modification of the iterative Fourier transform algorithm. Aberrations are specified using Zernike polynomials. The trade-off between reconstruction error and diffraction efficiency can be altered using a simple constant within the algorithm. We show first experimental results for the correction of the reconstruction through a strongly aberrated Fourier system.

© 2015 Optical Society of America

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References

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2014 (3)

2013 (1)

2011 (1)

2010 (1)

2007 (1)

2006 (1)

2000 (1)

1997 (1)

T. Haist, M. Schoenleber, and H. Tiziani, “Computer-generated holograms from 3d-objects written on twisted-nematic liquid crystal displays,” Optics Communications 140, 299–308 (1997).
[Crossref]

1996 (2)

R. Piestun, B. Spektor, and J. Shamir, “Wave fields in three dimensions: analysis and synthesis,” J. Opt. Soc. Am. A 13, 1837–1848 (1996).
[Crossref]

H. Aagedal, M. Schmid, T. Beth, S. Teiwes, and F. Wyrowski, “Theory of speckles in diffractive optics and its application to beam shaping,” Journal of Modern Optics 43, 1409–1421 (1996).
[Crossref]

1993 (1)

1989 (2)

Aagedal, H.

H. Aagedal, M. Schmid, T. Beth, S. Teiwes, and F. Wyrowski, “Theory of speckles in diffractive optics and its application to beam shaping,” Journal of Modern Optics 43, 1409–1421 (1996).
[Crossref]

Ameer-Beg, S. M.

Beth, T.

H. Aagedal, M. Schmid, T. Beth, S. Teiwes, and F. Wyrowski, “Theory of speckles in diffractive optics and its application to beam shaping,” Journal of Modern Optics 43, 1409–1421 (1996).
[Crossref]

Booth, M. J.

Boruah, B. R.

A. Das and B. R. Boruah, “Dynamic control of illumination beam phase profile in a scanning optical microscope,” in “Advanced Microscopy Techniques III,” (Optical Society of America, 2013), p. 87970K.
[Crossref]

Bryngdahl, O.

Chipman, R. A.

Cumming, B. P.

Das, A.

A. Das and B. R. Boruah, “Dynamic control of illumination beam phase profile in a scanning optical microscope,” in “Advanced Microscopy Techniques III,” (Optical Society of America, 2013), p. 87970K.
[Crossref]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, San Francisco, Calif, 1996).

Gu, M.

Haist, T.

M. Reicherter, S. Zwick, T. Haist, C. Kohler, H. Tiziani, and W. Osten, “Fast digital hologram generation and adaptive force measurement in lcd-based holographic tweezers,” Appl. Opt. 45, 888–896 (2006).
[Crossref] [PubMed]

T. Haist, M. Schoenleber, and H. Tiziani, “Computer-generated holograms from 3d-objects written on twisted-nematic liquid crystal displays,” Optics Communications 140, 299–308 (1997).
[Crossref]

M. Reicherter, J. Liesener, T. Haist, and H. J. Tiziani, “Advantages of holographic optical tweezers,” in “Novel Optical Instrumentation for Biomedical Applications,” (Optical Society of America, 2003), pp. 5143–5176.

Henderson, R. K.

Ianni, F.

Jesacher, A.

Kelemen, L.

Knight, R. D.

Kohler, C.

Krstajic, N.

Leonardo, R. D.

Li, X.

Liesener, J.

M. Reicherter, J. Liesener, T. Haist, and H. J. Tiziani, “Advantages of holographic optical tweezers,” in “Novel Optical Instrumentation for Biomedical Applications,” (Optical Society of America, 2003), pp. 5143–5176.

Lin, H.

Louarn, M. L.

Ormos, P.

Osten, W.

Pezzaniti, J. L.

Piestun, R.

Poland, S. P.

Reicherter, M.

M. Reicherter, S. Zwick, T. Haist, C. Kohler, H. Tiziani, and W. Osten, “Fast digital hologram generation and adaptive force measurement in lcd-based holographic tweezers,” Appl. Opt. 45, 888–896 (2006).
[Crossref] [PubMed]

M. Reicherter, J. Liesener, T. Haist, and H. J. Tiziani, “Advantages of holographic optical tweezers,” in “Novel Optical Instrumentation for Biomedical Applications,” (Optical Society of America, 2003), pp. 5143–5176.

Ren, H.

Ruocco, G.

Sarazin, M.

Schmid, M.

H. Aagedal, M. Schmid, T. Beth, S. Teiwes, and F. Wyrowski, “Theory of speckles in diffractive optics and its application to beam shaping,” Journal of Modern Optics 43, 1409–1421 (1996).
[Crossref]

Schoenleber, M.

T. Haist, M. Schoenleber, and H. Tiziani, “Computer-generated holograms from 3d-objects written on twisted-nematic liquid crystal displays,” Optics Communications 140, 299–308 (1997).
[Crossref]

Shamir, J.

Spektor, B.

Teiwes, S.

H. Aagedal, M. Schmid, T. Beth, S. Teiwes, and F. Wyrowski, “Theory of speckles in diffractive optics and its application to beam shaping,” Journal of Modern Optics 43, 1409–1421 (1996).
[Crossref]

Tiziani, H.

M. Reicherter, S. Zwick, T. Haist, C. Kohler, H. Tiziani, and W. Osten, “Fast digital hologram generation and adaptive force measurement in lcd-based holographic tweezers,” Appl. Opt. 45, 888–896 (2006).
[Crossref] [PubMed]

T. Haist, M. Schoenleber, and H. Tiziani, “Computer-generated holograms from 3d-objects written on twisted-nematic liquid crystal displays,” Optics Communications 140, 299–308 (1997).
[Crossref]

Tiziani, H. J.

M. Reicherter, J. Liesener, T. Haist, and H. J. Tiziani, “Advantages of holographic optical tweezers,” in “Novel Optical Instrumentation for Biomedical Applications,” (Optical Society of America, 2003), pp. 5143–5176.

Tokovinin, A.

Vizsnyiczai, G.

von Freymann, G.

Waller, E. H.

Wilson, T.

Wyrowski, F.

H. Aagedal, M. Schmid, T. Beth, S. Teiwes, and F. Wyrowski, “Theory of speckles in diffractive optics and its application to beam shaping,” Journal of Modern Optics 43, 1409–1421 (1996).
[Crossref]

F. Wyrowski and O. Bryngdahl, “Speckle-free reconstruction in digital holography,” J. Opt. Soc. Am. A 6, 1171–1174 (1989).
[Crossref]

F. Wyrowski, “Iterative quantization of digital amplitude holograms,” Appl. Opt. 28, 3864–3870 (1989).
[Crossref] [PubMed]

Zwick, S.

Appl. Opt. (2)

J. Opt. Soc. Am. A (3)

Journal of Modern Optics (1)

H. Aagedal, M. Schmid, T. Beth, S. Teiwes, and F. Wyrowski, “Theory of speckles in diffractive optics and its application to beam shaping,” Journal of Modern Optics 43, 1409–1421 (1996).
[Crossref]

Opt. Express (5)

Opt. Lett. (3)

Optics Communications (1)

T. Haist, M. Schoenleber, and H. Tiziani, “Computer-generated holograms from 3d-objects written on twisted-nematic liquid crystal displays,” Optics Communications 140, 299–308 (1997).
[Crossref]

Other (3)

M. Reicherter, J. Liesener, T. Haist, and H. J. Tiziani, “Advantages of holographic optical tweezers,” in “Novel Optical Instrumentation for Biomedical Applications,” (Optical Society of America, 2003), pp. 5143–5176.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, San Francisco, Calif, 1996).

A. Das and B. R. Boruah, “Dynamic control of illumination beam phase profile in a scanning optical microscope,” in “Advanced Microscopy Techniques III,” (Optical Society of America, 2013), p. 87970K.
[Crossref]

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Figures (4)

Fig. 1
Fig. 1 Modification of the iterative Fourier transform algorithm to optimize phase only holograms in the presence of field-dependent aberrations. The reconstructions of the hologram for different isoplanatic patches is shown on the right hand side. During iteration the hologram is given by the phase of the complex sum of the individual holograms due to the isoplanatic patches.
Fig. 2
Fig. 2 Speckle reduction using artifical discretization duing optimization. Optical reconstructions of optimized Fourier holograms using the described algorithm.
Fig. 3
Fig. 3 Experimental setup. The holograms are reconstructed using a strongly aberrated Fourier system (achromatic lens tilted by 30°).
Fig. 4
Fig. 4 Optical reconstruction under strong field dependent aberrations. Corrected with global aberration correction (conventional method) and the proposed method.

Equations (3)

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h ( x , y , z h ) = | r ( x , y , z h ) + j = 1 N exp ( i k S [ P j ( x j , y j , z j ) ] ( x , y , z h ) ) | 2
φ = arg ( j = 1 N exp ( i k S [ P j ( x j , y j , z j ) ] ( x , y , z h ) ) )
I ( u , v ) ~ | h ( x p , y p ) e 2 π i ( u x p + v y p ) e i ϕ k ( x p , y p ) d x p d y p | 2

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