Abstract

Synthetic optical holography (SOH) provides efficient encoding of the complex optical signal, both amplitude and phase, for scanning imaging methods. Prior demonstrations have synthesized reference fields with a plane-wave-like linear variation of the phase with position. To record large images without probe-mirror synchronization, a long-travel, closed-loop reference mirror stage has been required. Here we present SOH with a synthetic reference wave with sinusoidal spatial variation of the phase. This allows the use of open loop, limited mirror travel range in SOH, and leads to a novel holographic inversion algorithm. We validate the theory with scans of graphene grain boundaries from a scanning near-field optical microscope, for which SOH has been shown to drastically increase scan speeds [Nat. Commun. 5, 3499 (2014)]

© 2014 Optical Society of America

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References

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2014 (2)

2013 (1)

Z. Fei, A. S. Rodin, W. Gannett, S. Dai, W. Regan, M. Wagner, M. K. Liu, A. S. McLeod, G. Dominguez, M. Thiemens, A. H. C. Neto, F. Keilmann, A. Zettl, R. Hillenbrand, M. M. Fogler, and D. N. Basov, “Electronic and plasmonic phenomena at graphene grain boundaries,” Nat. Nano. 8, 821–825 (2013).
[Crossref]

2012 (2)

2011 (1)

2010 (1)

2009 (1)

E. Cuche, Y. Emery, and F. Montfort, “Microscopy: One-shot analysis,” Nat Photon 3, 633–635 (2009).
[Crossref]

2008 (2)

J. Rosen and G. Brooker, “Non-scanning motionless fluorescence three-dimensional holographic microscopy,” Nat. Photon. 2, 190–195 (2008).
[Crossref]

R. Esteban, R. Vogelgesang, J. Dorfmüller, A. Dmitriev, C. Rockstuhl, C. Etrich, and K. Kern, “Direct near-field optical imaging of higher order plasmonic resonances,” Nano Lett. 8, 3155–3159 (2008).
[Crossref] [PubMed]

2006 (1)

N. Ocelic, A. Huber, and R. Hillenbrand, “Pseudoheterodyne detection for background-free near-field spectroscopy,” Appl. Phys. Lett. 89, 101124 (2006).
[Crossref]

2005 (4)

C. Mann, L. Yu, C.-M. Lo, and M. Kim, “High-resolution quantitative phase-contrast microscopy by digital holography,” Opt. Express 13, 8693–8698 (2005).
[Crossref] [PubMed]

B. Rappaz, P. Marquet, E. Cuche, Y. Emery, C. Depeursinge, and P. Magistretti, “Measurement of the integral refractive index and dynamic cell morphometry of living cells with digital holographic microscopy,” Opt. Express 13, 9361–9373 (2005).
[Crossref] [PubMed]

D. Roy, S. H. Leong, and M. E. Welland, “Dielectric contrast imaging using apertureless scanning near-field optical microscopy in the reflection mode,” J. Kor. Phys. Soc. 47, 140 (2005).

I. Stefanon, S. Blaize, A. Bruyant, S. Aubert, G. Lerondel, R. Bachelot, and P. Royer, “Heterodyne detection of guided waves using a scattering-type scanning near-field optical microscope,” Opt. Expr. 13, 5553–5564 (2005).
[Crossref]

2004 (1)

F. Keilmann and R. Hillenbrand, “Near-field microscopy by elastic light scattering from a tip,” Phil. Trans. R. Soc. Lond. A 362, 787 (2004).
[Crossref]

2003 (1)

T. Taubner, R. Hillenbrand, and F. Keilmann, “Performance of visible and mid-infrared scattering-type near-field optical microscopes,” J. Microsc. 210, 311–314 (2003).
[Crossref] [PubMed]

2001 (2)

N. Maghelli, M. Labardi, S. Patan, F. Irrera, and M. Allegrini, “Optical near-field harmonic demodulation in apertureless microscopy,” J. Microsc. 202, 84–93 (2001).
[Crossref] [PubMed]

A. Nesci, R. Dändliker, and H. P. Herzig, “Quantitative amplitude and phase measurement by use of a heterodyne scanning near-field optical microscope,” Opt. Lett. 26, 208–210 (2001).
[Crossref]

2000 (2)

R. Hillenbrand and F. Keilmann, “Complex optical constants on a subwavelength scale,” Phys. Rev. Lett. 85, 3029–3032 (2000).
[Crossref] [PubMed]

Y. Sasaki and H. Sasaki, “Heterodyne detection for the extraction of the probe-scattering signal in scattering-type scanning near-field optical microscope,” Japanese J. of Appl. Phys. 39, 321 (2000).
[Crossref]

1999 (2)

1998 (1)

1997 (1)

1995 (1)

S. Kawata and Y. Inouye, “Scanning probe optical microscopy using a metallic probe tip,” Ultramicrosc. 57(2–3), 313–317 (1995).
[Crossref]

1994 (3)

R. Bachelot, P. Gleyzes, and A. C. Boccara, “Near-field optical microscopy by local perturbation of a diffraction spot,” Microscopy Microanalysis Microstructures 5(4–6), 389–397 (1994).
[Crossref]

F. Zenhausern, M. P. O’Boyle, and H. K. Wickramasinghe, “Apertureless near-field optical microscope,” Appl. Phys. Lett. 65, 1623–1625 (1994).
[Crossref]

U. Schnars and W. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Applied Optics 33, 179 (1994).
[Crossref] [PubMed]

1992 (1)

1986 (1)

B. Moslehi, “Noise power spectra of optical two-beam interferometers induced by the laser phase noise,” J. Lightwave Tech. 4, 1704–1710 (1986).
[Crossref]

1982 (2)

R. P. Porter and A. J. Devaney, “Generalized holography and computational solutions to inverse source problems,” J. Opt. Soc. of Am. 72, 1707 (1982).
[Crossref]

D. A. Jackson., “Pseudoheterodyne detection scheme for optical interferometers,” Elect. Lett. 18(25), 1081–1083 (1982).
[Crossref]

1962 (1)

E. N. Leith and J. Upatnieks, “Reconstructed wavefronts and communication theory,” J. Opt. Soc. Am. 52, 11231130 (1962).
[Crossref]

1948 (1)

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

Allegrini, M.

N. Maghelli, M. Labardi, S. Patan, F. Irrera, and M. Allegrini, “Optical near-field harmonic demodulation in apertureless microscopy,” J. Microsc. 202, 84–93 (2001).
[Crossref] [PubMed]

Amidror, I.

I. Amidror, Mastering the Discrete Fourier Transform in One, Two or Several Dimensions: Pitfalls and Artifacts (Springer, 2013).
[Crossref]

Aubert, S.

I. Stefanon, S. Blaize, A. Bruyant, S. Aubert, G. Lerondel, R. Bachelot, and P. Royer, “Heterodyne detection of guided waves using a scattering-type scanning near-field optical microscope,” Opt. Expr. 13, 5553–5564 (2005).
[Crossref]

Bachelot, R.

I. Stefanon, S. Blaize, A. Bruyant, S. Aubert, G. Lerondel, R. Bachelot, and P. Royer, “Heterodyne detection of guided waves using a scattering-type scanning near-field optical microscope,” Opt. Expr. 13, 5553–5564 (2005).
[Crossref]

R. Bachelot, P. Gleyzes, and A. C. Boccara, “Near-field optical microscopy by local perturbation of a diffraction spot,” Microscopy Microanalysis Microstructures 5(4–6), 389–397 (1994).
[Crossref]

Banerjee, P. P.

Barada, D.

Basov, D. N.

Z. Fei, A. S. Rodin, W. Gannett, S. Dai, W. Regan, M. Wagner, M. K. Liu, A. S. McLeod, G. Dominguez, M. Thiemens, A. H. C. Neto, F. Keilmann, A. Zettl, R. Hillenbrand, M. M. Fogler, and D. N. Basov, “Electronic and plasmonic phenomena at graphene grain boundaries,” Nat. Nano. 8, 821–825 (2013).
[Crossref]

Bhaduri, B.

Blaize, S.

I. Stefanon, S. Blaize, A. Bruyant, S. Aubert, G. Lerondel, R. Bachelot, and P. Royer, “Heterodyne detection of guided waves using a scattering-type scanning near-field optical microscope,” Opt. Expr. 13, 5553–5564 (2005).
[Crossref]

Boccara, A. C.

R. Bachelot, P. Gleyzes, and A. C. Boccara, “Near-field optical microscopy by local perturbation of a diffraction spot,” Microscopy Microanalysis Microstructures 5(4–6), 389–397 (1994).
[Crossref]

Boyer, K.

Brooker, G.

J. Rosen and G. Brooker, “Non-scanning motionless fluorescence three-dimensional holographic microscopy,” Nat. Photon. 2, 190–195 (2008).
[Crossref]

Bruyant, A.

I. Stefanon, S. Blaize, A. Bruyant, S. Aubert, G. Lerondel, R. Bachelot, and P. Royer, “Heterodyne detection of guided waves using a scattering-type scanning near-field optical microscope,” Opt. Expr. 13, 5553–5564 (2005).
[Crossref]

Carney, P. S.

Cuche, E.

Cullen, D.

Dai, S.

Z. Fei, A. S. Rodin, W. Gannett, S. Dai, W. Regan, M. Wagner, M. K. Liu, A. S. McLeod, G. Dominguez, M. Thiemens, A. H. C. Neto, F. Keilmann, A. Zettl, R. Hillenbrand, M. M. Fogler, and D. N. Basov, “Electronic and plasmonic phenomena at graphene grain boundaries,” Nat. Nano. 8, 821–825 (2013).
[Crossref]

Dändliker, R.

Depeursinge, C.

Devaney, A. J.

R. P. Porter and A. J. Devaney, “Generalized holography and computational solutions to inverse source problems,” J. Opt. Soc. of Am. 72, 1707 (1982).
[Crossref]

Dmitriev, A.

R. Esteban, R. Vogelgesang, J. Dorfmüller, A. Dmitriev, C. Rockstuhl, C. Etrich, and K. Kern, “Direct near-field optical imaging of higher order plasmonic resonances,” Nano Lett. 8, 3155–3159 (2008).
[Crossref] [PubMed]

Dominguez, G.

Z. Fei, A. S. Rodin, W. Gannett, S. Dai, W. Regan, M. Wagner, M. K. Liu, A. S. McLeod, G. Dominguez, M. Thiemens, A. H. C. Neto, F. Keilmann, A. Zettl, R. Hillenbrand, M. M. Fogler, and D. N. Basov, “Electronic and plasmonic phenomena at graphene grain boundaries,” Nat. Nano. 8, 821–825 (2013).
[Crossref]

Dorfmüller, J.

R. Esteban, R. Vogelgesang, J. Dorfmüller, A. Dmitriev, C. Rockstuhl, C. Etrich, and K. Kern, “Direct near-field optical imaging of higher order plasmonic resonances,” Nano Lett. 8, 3155–3159 (2008).
[Crossref] [PubMed]

Dubois, F.

Edwards, C.

Emery, Y.

Esteban, R.

R. Esteban, R. Vogelgesang, J. Dorfmüller, A. Dmitriev, C. Rockstuhl, C. Etrich, and K. Kern, “Direct near-field optical imaging of higher order plasmonic resonances,” Nano Lett. 8, 3155–3159 (2008).
[Crossref] [PubMed]

Etrich, C.

R. Esteban, R. Vogelgesang, J. Dorfmüller, A. Dmitriev, C. Rockstuhl, C. Etrich, and K. Kern, “Direct near-field optical imaging of higher order plasmonic resonances,” Nano Lett. 8, 3155–3159 (2008).
[Crossref] [PubMed]

Fei, Z.

Z. Fei, A. S. Rodin, W. Gannett, S. Dai, W. Regan, M. Wagner, M. K. Liu, A. S. McLeod, G. Dominguez, M. Thiemens, A. H. C. Neto, F. Keilmann, A. Zettl, R. Hillenbrand, M. M. Fogler, and D. N. Basov, “Electronic and plasmonic phenomena at graphene grain boundaries,” Nat. Nano. 8, 821–825 (2013).
[Crossref]

Fogler, M. M.

Z. Fei, A. S. Rodin, W. Gannett, S. Dai, W. Regan, M. Wagner, M. K. Liu, A. S. McLeod, G. Dominguez, M. Thiemens, A. H. C. Neto, F. Keilmann, A. Zettl, R. Hillenbrand, M. M. Fogler, and D. N. Basov, “Electronic and plasmonic phenomena at graphene grain boundaries,” Nat. Nano. 8, 821–825 (2013).
[Crossref]

Gabor, D.

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

Gannett, W.

Z. Fei, A. S. Rodin, W. Gannett, S. Dai, W. Regan, M. Wagner, M. K. Liu, A. S. McLeod, G. Dominguez, M. Thiemens, A. H. C. Neto, F. Keilmann, A. Zettl, R. Hillenbrand, M. M. Fogler, and D. N. Basov, “Electronic and plasmonic phenomena at graphene grain boundaries,” Nat. Nano. 8, 821–825 (2013).
[Crossref]

Gleyzes, P.

R. Bachelot, P. Gleyzes, and A. C. Boccara, “Near-field optical microscopy by local perturbation of a diffraction spot,” Microscopy Microanalysis Microstructures 5(4–6), 389–397 (1994).
[Crossref]

Goddard, L. L.

Haddad, W. S.

Hariharan, P.

P. Hariharan, Basics of Holography (Cambridge University, 2002).
[Crossref]

Hayasaki, Y.

Herzig, H. P.

Hillenbrand, R.

M. Schnell, M. J. Perez-Roldan, P. S. Carney, and R. Hillenbrand, “Quantitative confocal phase imaging by synthetic optical holography,” Opt. Express 22, 15267–15276 (2014).
[Crossref] [PubMed]

Z. Fei, A. S. Rodin, W. Gannett, S. Dai, W. Regan, M. Wagner, M. K. Liu, A. S. McLeod, G. Dominguez, M. Thiemens, A. H. C. Neto, F. Keilmann, A. Zettl, R. Hillenbrand, M. M. Fogler, and D. N. Basov, “Electronic and plasmonic phenomena at graphene grain boundaries,” Nat. Nano. 8, 821–825 (2013).
[Crossref]

N. Ocelic, A. Huber, and R. Hillenbrand, “Pseudoheterodyne detection for background-free near-field spectroscopy,” Appl. Phys. Lett. 89, 101124 (2006).
[Crossref]

F. Keilmann and R. Hillenbrand, “Near-field microscopy by elastic light scattering from a tip,” Phil. Trans. R. Soc. Lond. A 362, 787 (2004).
[Crossref]

T. Taubner, R. Hillenbrand, and F. Keilmann, “Performance of visible and mid-infrared scattering-type near-field optical microscopes,” J. Microsc. 210, 311–314 (2003).
[Crossref] [PubMed]

R. Hillenbrand and F. Keilmann, “Complex optical constants on a subwavelength scale,” Phys. Rev. Lett. 85, 3029–3032 (2000).
[Crossref] [PubMed]

M. Schnell, P. S. Carney, and R. Hillenbrand, “Synthetic optical holography for rapid nanoimaging,” Nat. Commun.5 (2014).
[Crossref] [PubMed]

Huber, A.

N. Ocelic, A. Huber, and R. Hillenbrand, “Pseudoheterodyne detection for background-free near-field spectroscopy,” Appl. Phys. Lett. 89, 101124 (2006).
[Crossref]

Indebetouw, G.

Inouye, Y.

S. Kawata and Y. Inouye, “Scanning probe optical microscopy using a metallic probe tip,” Ultramicrosc. 57(2–3), 313–317 (1995).
[Crossref]

Irrera, F.

N. Maghelli, M. Labardi, S. Patan, F. Irrera, and M. Allegrini, “Optical near-field harmonic demodulation in apertureless microscopy,” J. Microsc. 202, 84–93 (2001).
[Crossref] [PubMed]

Jackson., D. A.

D. A. Jackson., “Pseudoheterodyne detection scheme for optical interferometers,” Elect. Lett. 18(25), 1081–1083 (1982).
[Crossref]

Joannes, L.

Jüptner, W.

U. Schnars and W. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Applied Optics 33, 179 (1994).
[Crossref] [PubMed]

U. Schnars and W. Jüptner, Digital Holography: Digital Hologram Recording, Numerical Reconstruction, and Related Techniques (Springer, 2004), 2005 ed.

Kawata, S.

Keilmann, F.

Z. Fei, A. S. Rodin, W. Gannett, S. Dai, W. Regan, M. Wagner, M. K. Liu, A. S. McLeod, G. Dominguez, M. Thiemens, A. H. C. Neto, F. Keilmann, A. Zettl, R. Hillenbrand, M. M. Fogler, and D. N. Basov, “Electronic and plasmonic phenomena at graphene grain boundaries,” Nat. Nano. 8, 821–825 (2013).
[Crossref]

F. Keilmann and R. Hillenbrand, “Near-field microscopy by elastic light scattering from a tip,” Phil. Trans. R. Soc. Lond. A 362, 787 (2004).
[Crossref]

T. Taubner, R. Hillenbrand, and F. Keilmann, “Performance of visible and mid-infrared scattering-type near-field optical microscopes,” J. Microsc. 210, 311–314 (2003).
[Crossref] [PubMed]

R. Hillenbrand and F. Keilmann, “Complex optical constants on a subwavelength scale,” Phys. Rev. Lett. 85, 3029–3032 (2000).
[Crossref] [PubMed]

Kern, K.

R. Esteban, R. Vogelgesang, J. Dorfmüller, A. Dmitriev, C. Rockstuhl, C. Etrich, and K. Kern, “Direct near-field optical imaging of higher order plasmonic resonances,” Nano Lett. 8, 3155–3159 (2008).
[Crossref] [PubMed]

Kiire, T.

Kikuchi, Y.

Kim, M.

Kim, T.

Labardi, M.

N. Maghelli, M. Labardi, S. Patan, F. Irrera, and M. Allegrini, “Optical near-field harmonic demodulation in apertureless microscopy,” J. Microsc. 202, 84–93 (2001).
[Crossref] [PubMed]

Legros, J.-C.

Leith, E. N.

E. N. Leith and J. Upatnieks, “Reconstructed wavefronts and communication theory,” J. Opt. Soc. Am. 52, 11231130 (1962).
[Crossref]

Leong, S. H.

D. Roy, S. H. Leong, and M. E. Welland, “Dielectric contrast imaging using apertureless scanning near-field optical microscopy in the reflection mode,” J. Kor. Phys. Soc. 47, 140 (2005).

Lerondel, G.

I. Stefanon, S. Blaize, A. Bruyant, S. Aubert, G. Lerondel, R. Bachelot, and P. Royer, “Heterodyne detection of guided waves using a scattering-type scanning near-field optical microscope,” Opt. Expr. 13, 5553–5564 (2005).
[Crossref]

Liu, M. K.

Z. Fei, A. S. Rodin, W. Gannett, S. Dai, W. Regan, M. Wagner, M. K. Liu, A. S. McLeod, G. Dominguez, M. Thiemens, A. H. C. Neto, F. Keilmann, A. Zettl, R. Hillenbrand, M. M. Fogler, and D. N. Basov, “Electronic and plasmonic phenomena at graphene grain boundaries,” Nat. Nano. 8, 821–825 (2013).
[Crossref]

Lo, C.-M.

Longworth, J. W.

Maghelli, N.

N. Maghelli, M. Labardi, S. Patan, F. Irrera, and M. Allegrini, “Optical near-field harmonic demodulation in apertureless microscopy,” J. Microsc. 202, 84–93 (2001).
[Crossref] [PubMed]

Magistretti, P.

Mann, C.

Marquet, P.

McLeod, A. S.

Z. Fei, A. S. Rodin, W. Gannett, S. Dai, W. Regan, M. Wagner, M. K. Liu, A. S. McLeod, G. Dominguez, M. Thiemens, A. H. C. Neto, F. Keilmann, A. Zettl, R. Hillenbrand, M. M. Fogler, and D. N. Basov, “Electronic and plasmonic phenomena at graphene grain boundaries,” Nat. Nano. 8, 821–825 (2013).
[Crossref]

McPherson, A.

Montfort, F.

E. Cuche, Y. Emery, and F. Montfort, “Microscopy: One-shot analysis,” Nat Photon 3, 633–635 (2009).
[Crossref]

Moslehi, B.

B. Moslehi, “Noise power spectra of optical two-beam interferometers induced by the laser phase noise,” J. Lightwave Tech. 4, 1704–1710 (1986).
[Crossref]

Nehmetallah, G.

Nesci, A.

Neto, A. H. C.

Z. Fei, A. S. Rodin, W. Gannett, S. Dai, W. Regan, M. Wagner, M. K. Liu, A. S. McLeod, G. Dominguez, M. Thiemens, A. H. C. Neto, F. Keilmann, A. Zettl, R. Hillenbrand, M. M. Fogler, and D. N. Basov, “Electronic and plasmonic phenomena at graphene grain boundaries,” Nat. Nano. 8, 821–825 (2013).
[Crossref]

Nguyen, T. H.

O’Boyle, M. P.

F. Zenhausern, M. P. O’Boyle, and H. K. Wickramasinghe, “Apertureless near-field optical microscope,” Appl. Phys. Lett. 65, 1623–1625 (1994).
[Crossref]

Ocelic, N.

N. Ocelic, A. Huber, and R. Hillenbrand, “Pseudoheterodyne detection for background-free near-field spectroscopy,” Appl. Phys. Lett. 89, 101124 (2006).
[Crossref]

Oppenheim, A. V.

A. V. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing (Prentice Hall, 2009), 3rd ed.

Patan, S.

N. Maghelli, M. Labardi, S. Patan, F. Irrera, and M. Allegrini, “Optical near-field harmonic demodulation in apertureless microscopy,” J. Microsc. 202, 84–93 (2001).
[Crossref] [PubMed]

Perez-Roldan, M. J.

Pham, H.

Poon, T.-C.

Popescu, G.

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R. P. Porter and A. J. Devaney, “Generalized holography and computational solutions to inverse source problems,” J. Opt. Soc. of Am. 72, 1707 (1982).
[Crossref]

Rappaz, B.

Regan, W.

Z. Fei, A. S. Rodin, W. Gannett, S. Dai, W. Regan, M. Wagner, M. K. Liu, A. S. McLeod, G. Dominguez, M. Thiemens, A. H. C. Neto, F. Keilmann, A. Zettl, R. Hillenbrand, M. M. Fogler, and D. N. Basov, “Electronic and plasmonic phenomena at graphene grain boundaries,” Nat. Nano. 8, 821–825 (2013).
[Crossref]

Rhodes, C. K.

Rockstuhl, C.

R. Esteban, R. Vogelgesang, J. Dorfmüller, A. Dmitriev, C. Rockstuhl, C. Etrich, and K. Kern, “Direct near-field optical imaging of higher order plasmonic resonances,” Nano Lett. 8, 3155–3159 (2008).
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Z. Fei, A. S. Rodin, W. Gannett, S. Dai, W. Regan, M. Wagner, M. K. Liu, A. S. McLeod, G. Dominguez, M. Thiemens, A. H. C. Neto, F. Keilmann, A. Zettl, R. Hillenbrand, M. M. Fogler, and D. N. Basov, “Electronic and plasmonic phenomena at graphene grain boundaries,” Nat. Nano. 8, 821–825 (2013).
[Crossref]

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J. Rosen and G. Brooker, “Non-scanning motionless fluorescence three-dimensional holographic microscopy,” Nat. Photon. 2, 190–195 (2008).
[Crossref]

Roy, D.

D. Roy, S. H. Leong, and M. E. Welland, “Dielectric contrast imaging using apertureless scanning near-field optical microscopy in the reflection mode,” J. Kor. Phys. Soc. 47, 140 (2005).

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I. Stefanon, S. Blaize, A. Bruyant, S. Aubert, G. Lerondel, R. Bachelot, and P. Royer, “Heterodyne detection of guided waves using a scattering-type scanning near-field optical microscope,” Opt. Expr. 13, 5553–5564 (2005).
[Crossref]

Sasaki, H.

Y. Sasaki and H. Sasaki, “Heterodyne detection for the extraction of the probe-scattering signal in scattering-type scanning near-field optical microscope,” Japanese J. of Appl. Phys. 39, 321 (2000).
[Crossref]

Sasaki, Y.

Y. Sasaki and H. Sasaki, “Heterodyne detection for the extraction of the probe-scattering signal in scattering-type scanning near-field optical microscope,” Japanese J. of Appl. Phys. 39, 321 (2000).
[Crossref]

Schafer, R. W.

A. V. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing (Prentice Hall, 2009), 3rd ed.

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U. Schnars and W. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Applied Optics 33, 179 (1994).
[Crossref] [PubMed]

U. Schnars and W. Jüptner, Digital Holography: Digital Hologram Recording, Numerical Reconstruction, and Related Techniques (Springer, 2004), 2005 ed.

Schnell, M.

Shinoda, K.

Solem, J. C.

Stefanon, I.

I. Stefanon, S. Blaize, A. Bruyant, S. Aubert, G. Lerondel, R. Bachelot, and P. Royer, “Heterodyne detection of guided waves using a scattering-type scanning near-field optical microscope,” Opt. Expr. 13, 5553–5564 (2005).
[Crossref]

Storrie, B.

Sugisaka, J.

Suzuki, Y.

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T. Taubner, R. Hillenbrand, and F. Keilmann, “Performance of visible and mid-infrared scattering-type near-field optical microscopes,” J. Microsc. 210, 311–314 (2003).
[Crossref] [PubMed]

Thiemens, M.

Z. Fei, A. S. Rodin, W. Gannett, S. Dai, W. Regan, M. Wagner, M. K. Liu, A. S. McLeod, G. Dominguez, M. Thiemens, A. H. C. Neto, F. Keilmann, A. Zettl, R. Hillenbrand, M. M. Fogler, and D. N. Basov, “Electronic and plasmonic phenomena at graphene grain boundaries,” Nat. Nano. 8, 821–825 (2013).
[Crossref]

Upatnieks, J.

E. N. Leith and J. Upatnieks, “Reconstructed wavefronts and communication theory,” J. Opt. Soc. Am. 52, 11231130 (1962).
[Crossref]

Vogelgesang, R.

R. Esteban, R. Vogelgesang, J. Dorfmüller, A. Dmitriev, C. Rockstuhl, C. Etrich, and K. Kern, “Direct near-field optical imaging of higher order plasmonic resonances,” Nano Lett. 8, 3155–3159 (2008).
[Crossref] [PubMed]

Wagner, M.

Z. Fei, A. S. Rodin, W. Gannett, S. Dai, W. Regan, M. Wagner, M. K. Liu, A. S. McLeod, G. Dominguez, M. Thiemens, A. H. C. Neto, F. Keilmann, A. Zettl, R. Hillenbrand, M. M. Fogler, and D. N. Basov, “Electronic and plasmonic phenomena at graphene grain boundaries,” Nat. Nano. 8, 821–825 (2013).
[Crossref]

Wang, Y.

Y. Wang, Optimization and Regularization for Computational Inverse Problems and Applications (Higher Education, 2011).
[Crossref]

Welland, M. E.

D. Roy, S. H. Leong, and M. E. Welland, “Dielectric contrast imaging using apertureless scanning near-field optical microscopy in the reflection mode,” J. Kor. Phys. Soc. 47, 140 (2005).

Wickramasinghe, H. K.

F. Zenhausern, M. P. O’Boyle, and H. K. Wickramasinghe, “Apertureless near-field optical microscope,” Appl. Phys. Lett. 65, 1623–1625 (1994).
[Crossref]

Wu, M. H.

Yamaguchi, I.

Yariv, A.

A. Yariv, Optical Electronics (Oxford University, 1990).

Yatagai., T.

Yu, L.

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F. Zenhausern, M. P. O’Boyle, and H. K. Wickramasinghe, “Apertureless near-field optical microscope,” Appl. Phys. Lett. 65, 1623–1625 (1994).
[Crossref]

Zettl, A.

Z. Fei, A. S. Rodin, W. Gannett, S. Dai, W. Regan, M. Wagner, M. K. Liu, A. S. McLeod, G. Dominguez, M. Thiemens, A. H. C. Neto, F. Keilmann, A. Zettl, R. Hillenbrand, M. M. Fogler, and D. N. Basov, “Electronic and plasmonic phenomena at graphene grain boundaries,” Nat. Nano. 8, 821–825 (2013).
[Crossref]

Zhang, T.

Zhou, R.

Adv. Opt. Photon. (2)

Appl. Opt. (4)

Appl. Phys. Lett. (2)

F. Zenhausern, M. P. O’Boyle, and H. K. Wickramasinghe, “Apertureless near-field optical microscope,” Appl. Phys. Lett. 65, 1623–1625 (1994).
[Crossref]

N. Ocelic, A. Huber, and R. Hillenbrand, “Pseudoheterodyne detection for background-free near-field spectroscopy,” Appl. Phys. Lett. 89, 101124 (2006).
[Crossref]

Applied Optics (1)

U. Schnars and W. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Applied Optics 33, 179 (1994).
[Crossref] [PubMed]

Elect. Lett. (1)

D. A. Jackson., “Pseudoheterodyne detection scheme for optical interferometers,” Elect. Lett. 18(25), 1081–1083 (1982).
[Crossref]

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D. Roy, S. H. Leong, and M. E. Welland, “Dielectric contrast imaging using apertureless scanning near-field optical microscopy in the reflection mode,” J. Kor. Phys. Soc. 47, 140 (2005).

J. Lightwave Tech. (1)

B. Moslehi, “Noise power spectra of optical two-beam interferometers induced by the laser phase noise,” J. Lightwave Tech. 4, 1704–1710 (1986).
[Crossref]

J. Microsc. (2)

N. Maghelli, M. Labardi, S. Patan, F. Irrera, and M. Allegrini, “Optical near-field harmonic demodulation in apertureless microscopy,” J. Microsc. 202, 84–93 (2001).
[Crossref] [PubMed]

T. Taubner, R. Hillenbrand, and F. Keilmann, “Performance of visible and mid-infrared scattering-type near-field optical microscopes,” J. Microsc. 210, 311–314 (2003).
[Crossref] [PubMed]

J. Opt. Soc. Am. (1)

E. N. Leith and J. Upatnieks, “Reconstructed wavefronts and communication theory,” J. Opt. Soc. Am. 52, 11231130 (1962).
[Crossref]

J. Opt. Soc. of Am. (1)

R. P. Porter and A. J. Devaney, “Generalized holography and computational solutions to inverse source problems,” J. Opt. Soc. of Am. 72, 1707 (1982).
[Crossref]

Japanese J. of Appl. Phys. (1)

Y. Sasaki and H. Sasaki, “Heterodyne detection for the extraction of the probe-scattering signal in scattering-type scanning near-field optical microscope,” Japanese J. of Appl. Phys. 39, 321 (2000).
[Crossref]

Microscopy Microanalysis Microstructures (1)

R. Bachelot, P. Gleyzes, and A. C. Boccara, “Near-field optical microscopy by local perturbation of a diffraction spot,” Microscopy Microanalysis Microstructures 5(4–6), 389–397 (1994).
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Nano Lett. (1)

R. Esteban, R. Vogelgesang, J. Dorfmüller, A. Dmitriev, C. Rockstuhl, C. Etrich, and K. Kern, “Direct near-field optical imaging of higher order plasmonic resonances,” Nano Lett. 8, 3155–3159 (2008).
[Crossref] [PubMed]

Nat Photon (1)

E. Cuche, Y. Emery, and F. Montfort, “Microscopy: One-shot analysis,” Nat Photon 3, 633–635 (2009).
[Crossref]

Nat. Nano. (1)

Z. Fei, A. S. Rodin, W. Gannett, S. Dai, W. Regan, M. Wagner, M. K. Liu, A. S. McLeod, G. Dominguez, M. Thiemens, A. H. C. Neto, F. Keilmann, A. Zettl, R. Hillenbrand, M. M. Fogler, and D. N. Basov, “Electronic and plasmonic phenomena at graphene grain boundaries,” Nat. Nano. 8, 821–825 (2013).
[Crossref]

Nat. Photon. (1)

J. Rosen and G. Brooker, “Non-scanning motionless fluorescence three-dimensional holographic microscopy,” Nat. Photon. 2, 190–195 (2008).
[Crossref]

Nature (1)

D. Gabor, “A new microscopic principle,” Nature 161, 777–778 (1948).
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Opt. Expr. (1)

I. Stefanon, S. Blaize, A. Bruyant, S. Aubert, G. Lerondel, R. Bachelot, and P. Royer, “Heterodyne detection of guided waves using a scattering-type scanning near-field optical microscope,” Opt. Expr. 13, 5553–5564 (2005).
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Opt. Express (3)

Opt. Lett. (5)

Phil. Trans. R. Soc. Lond. A (1)

F. Keilmann and R. Hillenbrand, “Near-field microscopy by elastic light scattering from a tip,” Phil. Trans. R. Soc. Lond. A 362, 787 (2004).
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Phys. Rev. Lett. (1)

R. Hillenbrand and F. Keilmann, “Complex optical constants on a subwavelength scale,” Phys. Rev. Lett. 85, 3029–3032 (2000).
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S. Kawata and Y. Inouye, “Scanning probe optical microscopy using a metallic probe tip,” Ultramicrosc. 57(2–3), 313–317 (1995).
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I. Amidror, Mastering the Discrete Fourier Transform in One, Two or Several Dimensions: Pitfalls and Artifacts (Springer, 2013).
[Crossref]

A. Yariv, Optical Electronics (Oxford University, 1990).

M. Schnell, P. S. Carney, and R. Hillenbrand, “Synthetic optical holography for rapid nanoimaging,” Nat. Commun.5 (2014).
[Crossref] [PubMed]

P. Hariharan, Basics of Holography (Cambridge University, 2002).
[Crossref]

U. Schnars and W. Jüptner, Digital Holography: Digital Hologram Recording, Numerical Reconstruction, and Related Techniques (Springer, 2004), 2005 ed.

T.-C. Poon, Digital Holography and Three-Dimensional Display: Principles and Applications (Springer, 2011), softcover reprint of hardcover 1st ed. 2006 ed.

A. V. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing (Prentice Hall, 2009), 3rd ed.

Y. Wang, Optimization and Regularization for Computational Inverse Problems and Applications (Higher Education, 2011).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1 Sketch of setup for synthetic optical holography. The sample is scanned while the reference mirror moves, creating a time-dependent reference phase. A point detector is used to assemble a holographic intensity map.
Fig. 2
Fig. 2 Simulations of SOH with linear- and sinusoidal-phase reference waves. The real and imaginary part of the original complex-valued image are shown in panels (a) and (b) respectively. The mirror position in radians as a function of position in the scanned image is shown in (c) and the resulting hologram is shown in (d) with a 41× zoom inset. The Fourier transform of the hologram is shown in (e) demonstrating the separation of the direct and conjugate images with the filter used indicated by the red box. The recovered images are shown in panels (f) and (g). The mirror position for sinusoidal-phase SOH is shown in panel (h) with resulting hologram and 41× zoom showing the fringe pattern in (i). The Fourier transform of the hologram is shown in (j) with the two filters used to recover the real and imaginary parts of the field indicated by red boxes. The recovered images are shown in (k) and (l).
Fig. 3
Fig. 3 Experimental results for both linear- and sinusoidal-phase reference waves. The hologram for the linear case is shown in panel (a) with logarithm of the absolute values of the Fourier transform in panel (b). The magnitude and phase of the linear case reconstructions are shown in panels (c) and (d). The hologram for the sinusoidal case is shown in panel (e) with logarithm of the absolute values of the Fourier transform in panel (f). The inverse Fourier transforms of the data shown in the red boxes, corresponding to X and Y are shown in the call-outs. The resultant magnitude and phase of the sinusoidal case reconstructions are shown in panels (g) and (h).
Fig. 4
Fig. 4 Reconstructions computed from the second and third order terms of the sinusoidal-phase hologram as indicated by the red boxes in the Fourier domain image (left), resulting in the amplitude (center) and phase (right) images shown.
Fig. 5
Fig. 5 Example of multiple-term reconstruction with simulated noise. Top row: Original data with 6-term reconstruction. Middle row: Two-term reconstructed with simulated Gaussian white noise added to interferogram in the spatial domain. The noise is mostly evident in the phase reconstruction. Bottom row: Eight term reconstruction with simulated noise and α = 1. The result is improved over the two-term case.

Equations (20)

Equations on this page are rendered with MathJax. Learn more.

U S , a , b = U S ( x a x ^ + y b y ^ ) .
I a , b = | U S , a , b + U R , a , b | 2 = | U S , a , b | 2 + | U R , a , b | 2 + U S , a , b * U R , a , b + U S , a , b U R , a , b *
I ˜ p , q = | A R | 2 δ p , q + C ˜ p , q + A R U ˜ S , x p , y q * + A R * U ˜ S , x + p , y + q ,
U R ( t ) = A R e i γ sin ( 2 π f t + ϕ ) ,
U R , a , b = A R exp [ i γ sin ( 2 π ( ( f N f s , x ) x a / v x + ( f M f s , y ) y b / v y ) + ϕ ) ] ,
U R , a , b = A R e i γ sin ( k r + ϕ ) = A R n = J n ( γ ) e in ( k r + ϕ ) .
I a , b = | U S , a , b | 2 + | A R | 2 + A R U S , a , b * n = J n ( γ ) e in ϕ e in k r a , b + c . c .
I ˜ p , q = | U S , a , b | 2 δ p , q + C ˜ p , q + A R n = J n ( γ ) e in ϕ U ˜ S , n x p , n y q * + A R * n = J n ( γ ) e in ϕ U ˜ S , n x + p , n y + q .
I ˜ p , q = | U R , a , b | 2 δ p , q + C ˜ p , q + n = J n ( γ ) e in ϕ ( A R U ˜ S , n x p , n y q * + ( 1 ) n A R * U ˜ S , p n x , q n y ) .
I ˜ 2 m 1 , p , q = J 2 m 1 ( γ ) e i ( 2 m 1 ) ϕ ( A R U ˜ S , p , q * A R * U ˜ S , p , q ) ,
I ˜ 2 m = A R J 2 m ( γ ) e i ( 2 m ) ϕ ( A R U ˜ S , p , q * + A R * U ˜ S , p , q ) .
Y = I 2 m 1 2 J 2 m 1 ( γ ) exp ( i ϕ ^ 2 m 1 ) = Im { A R * U S } ,
X = I 2 m 2 J 2 m ( γ ) exp ( i ϕ ^ 2 m ) = Re { A R * U S } .
U S = A R ( X + i Y ) | A R | 2 .
k y = 2 π ( f M f s , y ) / v y = 2 π ( f M f s , y ) ( n x v f + n x v b + T w ) .
I a , b = I 0 , a , b ( 1 + ε 1 , a , b ) + ε 2 , a , b ,
I ˜ p , q = I ˜ 0 , p , q + I ˜ 0 , p , q * ε ˜ 1 , p , q + ε ˜ , 2 , p , q .
U S = X α + i Y α
Y α = 1 2 m I m J m ( γ ) exp [ i ϕ ^ m ] α | J m ( γ ) | + 1 α m ( α | J m ( γ ) | + 1 α )
X α = 1 2 n 𝒩 I n J n ( γ ) exp [ i ϕ ^ n ] α | J n ( γ ) | + 1 α n ( α | J n ( γ ) | + 1 α ) .

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