Abstract

In the past decade, quantitative phase imaging gave a new dimension to optical microscopy, and the recent extension of digital holography techniques to nonlinear microscopy appears very promising, for the phase of nonlinear signal provides additional information, inaccessible to incoherent imaging schemes. In this work, we show that the position of second harmonic generation (SHG) emitters can be determined from their respective phase, at the nanometer scale, with single-shot off-axis digital holography, making possible real-time nanometric 3D-tracking of SHG emitters such as nanoparticles.

© 2010 OSA

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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
  4. J. Panyam and V. Labhasetwar, “Biodegradable nanoparticles for drug and gene delivery to cells and tissue,” Adv. Drug Delivery Rev. 55, 329–347 (2003).
    [Crossref]
  5. W. H. De Jong and P. J. A. Borm, “Drug delivery and nanoparticles: Applications and hazards,” Internat. J. Nanomed. 3, 133–149 (2008).
    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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2010 (1)

Y. Pu, R. Grange, C. L. Hsieh, and D. Psaltis, “Nonlinear optical properties of core-shell nanocavities for enhanced second-harmonic generation,” Phys. Rev. Lett. 104, 207402 (2010).
[Crossref] [PubMed]

2009 (3)

2008 (2)

M. Atlan, M. Gross, P. Desbiolles, E. Absil, G. Tessier, and M. Coppey-Moisan, “Heterodyne holographic microscopy of gold particles,” Opt. Lett. 33, 500–502 (2008).
[Crossref] [PubMed]

W. H. De Jong and P. J. A. Borm, “Drug delivery and nanoparticles: Applications and hazards,” Internat. J. Nanomed. 3, 133–149 (2008).
[Crossref]

2007 (5)

S. S. Rogers, T. A. Waigh, X. B. Zhao, and J. R. Lu, “Precise particle tracking against a complicated background: polynomial fitting with gaussian weight,” Phys. Biology 4, 220–227 (2007).
[Crossref]

S. H. Lee and D. G. Grier, “Holographic microscopy of holographically trapped three-dimensional structures,” Opt. Express 15, 1505–1512 (2007).
[Crossref] [PubMed]

S. H. Lee, Y. Roichman, G. R. Yi, S. H. Kim, S. M. Yang, A. van Blaaderen, P. van Oostrum, and D. G. Grier, “Characterizing and tracking single colloidal particles with video holographic microscopy,” Opt. Express 15, 18275–18282 (2007).
[Crossref] [PubMed]

K. T. Thurn, E. M. B. Brown, A. Wu, S. Vogt, B. Lai, J. Maser, T. Paunesku, and G. E. Woloschak, “Nanoparticles for applications in cellular imaging,” Nanoscale Res. Lett. 2, 430–441 (2007).
[Crossref] [PubMed]

K. Kim and J. P. Fisher, “Nanoparticle technology in bone tissue engineering,” J. Drug Targeting 15, 241–252 (2007).
[Crossref]

2006 (1)

H. W. Gu, K. M. Xu, C. J. Xu, and B. Xu, “Biofunctional magnetic nanoparticles for protein separation and pathogen detection,” Chemical Communications 37, 941–949 (2006).
[Crossref]

2005 (1)

2003 (1)

J. Panyam and V. Labhasetwar, “Biodegradable nanoparticles for drug and gene delivery to cells and tissue,” Adv. Drug Delivery Rev. 55, 329–347 (2003).
[Crossref]

2002 (1)

U. Schnars and W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms,” Measurement Scie. Technol. 13, R85–R101 (2002).
[Crossref]

2001 (1)

M. K. Cheezum, W. F. Walker, and W. H. Guilford, “Quantitative comparison of algorithms for tracking single fluorescent particles,” Biophys. J. 81, 2378–2388 (2001).
[Crossref] [PubMed]

2000 (1)

L. N. Bohs, B. J. Geiman, M. E. Anderson, S. C. Gebhart, and G. E. Trahey, “Speckle tracking for multidimensional flow estimation,” Ultrasonics 38, 369–375 (2000).
[Crossref] [PubMed]

1999 (1)

1997 (2)

G. J. Schutz, H. Schindler, and T. Schmidt, “Single-molecule microscopy on model membranes reveals anomalous diffusion,” Biophys. J. 73, 1073–1080 (1997).
[Crossref] [PubMed]

K. Konig, P. T. C. So, W. W. Mantulin, and E. Gratton, “Cellular response to near-infrared femtosecond laser pulses in two-photon microscopes,” Opt. Lett. 22, 135–136 (1997).
[Crossref] [PubMed]

1994 (1)

R. N. Ghosh and W. W. Webb, “Automated detection and tracking of individual and clustered cell surface low density lipoprotein receptor,” Biophys. J. 66, 1301–1318 (1994).
[Crossref] [PubMed]

1992 (1)

C. M. Anderson, G. N. Georgiou, I. E. G. Morrison, G. V. W. Stevenson, and R. J. Cherry, “Tracking of cell surface receptors by fluorescence digital imaging microscopy using a charge-coupled device - low-density-lipoprotein and influenza-virus receptor mobility at 4 degrees c,” J. Cell Scie. 101, 415–425 (1992).

1988 (1)

J. Gelles, B. J. Schnapp, and M. P. Sheetz, “Tracking kinesin-driven movements with nanometer-scale precision,” Nature 331, 450–453 (1988).
[Crossref] [PubMed]

Absil, E.

Anderson, C. M.

C. M. Anderson, G. N. Georgiou, I. E. G. Morrison, G. V. W. Stevenson, and R. J. Cherry, “Tracking of cell surface receptors by fluorescence digital imaging microscopy using a charge-coupled device - low-density-lipoprotein and influenza-virus receptor mobility at 4 degrees c,” J. Cell Scie. 101, 415–425 (1992).

Anderson, M. E.

L. N. Bohs, B. J. Geiman, M. E. Anderson, S. C. Gebhart, and G. E. Trahey, “Speckle tracking for multidimensional flow estimation,” Ultrasonics 38, 369–375 (2000).
[Crossref] [PubMed]

Atlan, M.

Bevilacqua, F.

Bohs, L. N.

L. N. Bohs, B. J. Geiman, M. E. Anderson, S. C. Gebhart, and G. E. Trahey, “Speckle tracking for multidimensional flow estimation,” Ultrasonics 38, 369–375 (2000).
[Crossref] [PubMed]

Borm, P. J. A.

W. H. De Jong and P. J. A. Borm, “Drug delivery and nanoparticles: Applications and hazards,” Internat. J. Nanomed. 3, 133–149 (2008).
[Crossref]

Brown, E. M. B.

K. T. Thurn, E. M. B. Brown, A. Wu, S. Vogt, B. Lai, J. Maser, T. Paunesku, and G. E. Woloschak, “Nanoparticles for applications in cellular imaging,” Nanoscale Res. Lett. 2, 430–441 (2007).
[Crossref] [PubMed]

Cheezum, M. K.

M. K. Cheezum, W. F. Walker, and W. H. Guilford, “Quantitative comparison of algorithms for tracking single fluorescent particles,” Biophys. J. 81, 2378–2388 (2001).
[Crossref] [PubMed]

Cherry, R. J.

C. M. Anderson, G. N. Georgiou, I. E. G. Morrison, G. V. W. Stevenson, and R. J. Cherry, “Tracking of cell surface receptors by fluorescence digital imaging microscopy using a charge-coupled device - low-density-lipoprotein and influenza-virus receptor mobility at 4 degrees c,” J. Cell Scie. 101, 415–425 (1992).

Colomb, T.

Coppey-Moisan, M.

Cuche, E.

Day, E. S.

E. S. Day, J. G. Morton, and J. L. West, “Nanoparticles for thermal cancer therapy,” J. Biomechan. Engin.-transactions of the Asme 131, 074001 (2009).
[Crossref]

De Jong, W. H.

W. H. De Jong and P. J. A. Borm, “Drug delivery and nanoparticles: Applications and hazards,” Internat. J. Nanomed. 3, 133–149 (2008).
[Crossref]

Depeursinge, C.

Desbiolles, P.

Emery, Y.

Fisher, J. P.

K. Kim and J. P. Fisher, “Nanoparticle technology in bone tissue engineering,” J. Drug Targeting 15, 241–252 (2007).
[Crossref]

Gebhart, S. C.

L. N. Bohs, B. J. Geiman, M. E. Anderson, S. C. Gebhart, and G. E. Trahey, “Speckle tracking for multidimensional flow estimation,” Ultrasonics 38, 369–375 (2000).
[Crossref] [PubMed]

Geiman, B. J.

L. N. Bohs, B. J. Geiman, M. E. Anderson, S. C. Gebhart, and G. E. Trahey, “Speckle tracking for multidimensional flow estimation,” Ultrasonics 38, 369–375 (2000).
[Crossref] [PubMed]

Gelles, J.

J. Gelles, B. J. Schnapp, and M. P. Sheetz, “Tracking kinesin-driven movements with nanometer-scale precision,” Nature 331, 450–453 (1988).
[Crossref] [PubMed]

Georgiou, G. N.

C. M. Anderson, G. N. Georgiou, I. E. G. Morrison, G. V. W. Stevenson, and R. J. Cherry, “Tracking of cell surface receptors by fluorescence digital imaging microscopy using a charge-coupled device - low-density-lipoprotein and influenza-virus receptor mobility at 4 degrees c,” J. Cell Scie. 101, 415–425 (1992).

Ghosh, R. N.

R. N. Ghosh and W. W. Webb, “Automated detection and tracking of individual and clustered cell surface low density lipoprotein receptor,” Biophys. J. 66, 1301–1318 (1994).
[Crossref] [PubMed]

Grange, R.

Y. Pu, R. Grange, C. L. Hsieh, and D. Psaltis, “Nonlinear optical properties of core-shell nanocavities for enhanced second-harmonic generation,” Phys. Rev. Lett. 104, 207402 (2010).
[Crossref] [PubMed]

C.-L. Hsieh, R. Grange, Y. Pu, and D. Psaltis, “Three-dimensional harmonic holographic microcopy using nanoparticles as probes for cell imaging,” Opt. Express 17, 2880–2891 (2009).
[Crossref] [PubMed]

Gratton, E.

Grier, D. G.

Gross, M.

Gu, H. W.

H. W. Gu, K. M. Xu, C. J. Xu, and B. Xu, “Biofunctional magnetic nanoparticles for protein separation and pathogen detection,” Chemical Communications 37, 941–949 (2006).
[Crossref]

Guilford, W. H.

M. K. Cheezum, W. F. Walker, and W. H. Guilford, “Quantitative comparison of algorithms for tracking single fluorescent particles,” Biophys. J. 81, 2378–2388 (2001).
[Crossref] [PubMed]

Hermanson, G. T.

G. T. Hermanson, Bioconjugate Techniques (Academic Press, New York, NY, USA, 1996).

Hsieh, C. L.

Y. Pu, R. Grange, C. L. Hsieh, and D. Psaltis, “Nonlinear optical properties of core-shell nanocavities for enhanced second-harmonic generation,” Phys. Rev. Lett. 104, 207402 (2010).
[Crossref] [PubMed]

Hsieh, C.-L.

Jüptner, W. P. O.

U. Schnars and W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms,” Measurement Scie. Technol. 13, R85–R101 (2002).
[Crossref]

Kim, K.

K. Kim and J. P. Fisher, “Nanoparticle technology in bone tissue engineering,” J. Drug Targeting 15, 241–252 (2007).
[Crossref]

Kim, S. H.

Konig, K.

Kühn, J.

E. Shaffer, N. Pavillon, J. Kühn, and C. Depeursinge, “Digital holographic microscopy investigation of second harmonic generated at a glass/air interface,” Opt. Lett. 34, 2450–2452 (2009).
[Crossref] [PubMed]

E. Shaffer, N. Pavillon, J. Kühn, and C. Depeursinge, “Second harmonic and fundamental wavelength digital holographic microscopy,” in “OSA Technical Digest (CD),” (Optical Society of America, 2009), pp. JTuA3-.

Labhasetwar, V.

J. Panyam and V. Labhasetwar, “Biodegradable nanoparticles for drug and gene delivery to cells and tissue,” Adv. Drug Delivery Rev. 55, 329–347 (2003).
[Crossref]

Lai, B.

K. T. Thurn, E. M. B. Brown, A. Wu, S. Vogt, B. Lai, J. Maser, T. Paunesku, and G. E. Woloschak, “Nanoparticles for applications in cellular imaging,” Nanoscale Res. Lett. 2, 430–441 (2007).
[Crossref] [PubMed]

Lee, S. H.

Lu, J. R.

S. S. Rogers, T. A. Waigh, X. B. Zhao, and J. R. Lu, “Precise particle tracking against a complicated background: polynomial fitting with gaussian weight,” Phys. Biology 4, 220–227 (2007).
[Crossref]

Magistretti, P. J.

Mantulin, W. W.

Marquet, P.

Maser, J.

K. T. Thurn, E. M. B. Brown, A. Wu, S. Vogt, B. Lai, J. Maser, T. Paunesku, and G. E. Woloschak, “Nanoparticles for applications in cellular imaging,” Nanoscale Res. Lett. 2, 430–441 (2007).
[Crossref] [PubMed]

Morrison, I. E. G.

C. M. Anderson, G. N. Georgiou, I. E. G. Morrison, G. V. W. Stevenson, and R. J. Cherry, “Tracking of cell surface receptors by fluorescence digital imaging microscopy using a charge-coupled device - low-density-lipoprotein and influenza-virus receptor mobility at 4 degrees c,” J. Cell Scie. 101, 415–425 (1992).

Morton, J. G.

E. S. Day, J. G. Morton, and J. L. West, “Nanoparticles for thermal cancer therapy,” J. Biomechan. Engin.-transactions of the Asme 131, 074001 (2009).
[Crossref]

Panyam, J.

J. Panyam and V. Labhasetwar, “Biodegradable nanoparticles for drug and gene delivery to cells and tissue,” Adv. Drug Delivery Rev. 55, 329–347 (2003).
[Crossref]

Paunesku, T.

K. T. Thurn, E. M. B. Brown, A. Wu, S. Vogt, B. Lai, J. Maser, T. Paunesku, and G. E. Woloschak, “Nanoparticles for applications in cellular imaging,” Nanoscale Res. Lett. 2, 430–441 (2007).
[Crossref] [PubMed]

Pavillon, N.

E. Shaffer, N. Pavillon, J. Kühn, and C. Depeursinge, “Digital holographic microscopy investigation of second harmonic generated at a glass/air interface,” Opt. Lett. 34, 2450–2452 (2009).
[Crossref] [PubMed]

E. Shaffer, N. Pavillon, J. Kühn, and C. Depeursinge, “Second harmonic and fundamental wavelength digital holographic microscopy,” in “OSA Technical Digest (CD),” (Optical Society of America, 2009), pp. JTuA3-.

Psaltis, D.

Y. Pu, R. Grange, C. L. Hsieh, and D. Psaltis, “Nonlinear optical properties of core-shell nanocavities for enhanced second-harmonic generation,” Phys. Rev. Lett. 104, 207402 (2010).
[Crossref] [PubMed]

C.-L. Hsieh, R. Grange, Y. Pu, and D. Psaltis, “Three-dimensional harmonic holographic microcopy using nanoparticles as probes for cell imaging,” Opt. Express 17, 2880–2891 (2009).
[Crossref] [PubMed]

Pu, Y.

Y. Pu, R. Grange, C. L. Hsieh, and D. Psaltis, “Nonlinear optical properties of core-shell nanocavities for enhanced second-harmonic generation,” Phys. Rev. Lett. 104, 207402 (2010).
[Crossref] [PubMed]

C.-L. Hsieh, R. Grange, Y. Pu, and D. Psaltis, “Three-dimensional harmonic holographic microcopy using nanoparticles as probes for cell imaging,” Opt. Express 17, 2880–2891 (2009).
[Crossref] [PubMed]

Rappaz, B.

Rogers, S. S.

S. S. Rogers, T. A. Waigh, X. B. Zhao, and J. R. Lu, “Precise particle tracking against a complicated background: polynomial fitting with gaussian weight,” Phys. Biology 4, 220–227 (2007).
[Crossref]

Roichman, Y.

Schindler, H.

G. J. Schutz, H. Schindler, and T. Schmidt, “Single-molecule microscopy on model membranes reveals anomalous diffusion,” Biophys. J. 73, 1073–1080 (1997).
[Crossref] [PubMed]

Schmidt, T.

G. J. Schutz, H. Schindler, and T. Schmidt, “Single-molecule microscopy on model membranes reveals anomalous diffusion,” Biophys. J. 73, 1073–1080 (1997).
[Crossref] [PubMed]

Schnapp, B. J.

J. Gelles, B. J. Schnapp, and M. P. Sheetz, “Tracking kinesin-driven movements with nanometer-scale precision,” Nature 331, 450–453 (1988).
[Crossref] [PubMed]

Schnars, U.

U. Schnars and W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms,” Measurement Scie. Technol. 13, R85–R101 (2002).
[Crossref]

Schutz, G. J.

G. J. Schutz, H. Schindler, and T. Schmidt, “Single-molecule microscopy on model membranes reveals anomalous diffusion,” Biophys. J. 73, 1073–1080 (1997).
[Crossref] [PubMed]

Shaffer, E.

E. Shaffer, N. Pavillon, J. Kühn, and C. Depeursinge, “Digital holographic microscopy investigation of second harmonic generated at a glass/air interface,” Opt. Lett. 34, 2450–2452 (2009).
[Crossref] [PubMed]

E. Shaffer, N. Pavillon, J. Kühn, and C. Depeursinge, “Second harmonic and fundamental wavelength digital holographic microscopy,” in “OSA Technical Digest (CD),” (Optical Society of America, 2009), pp. JTuA3-.

Sheetz, M. P.

J. Gelles, B. J. Schnapp, and M. P. Sheetz, “Tracking kinesin-driven movements with nanometer-scale precision,” Nature 331, 450–453 (1988).
[Crossref] [PubMed]

So, P. T. C.

Stevenson, G. V. W.

C. M. Anderson, G. N. Georgiou, I. E. G. Morrison, G. V. W. Stevenson, and R. J. Cherry, “Tracking of cell surface receptors by fluorescence digital imaging microscopy using a charge-coupled device - low-density-lipoprotein and influenza-virus receptor mobility at 4 degrees c,” J. Cell Scie. 101, 415–425 (1992).

Tessier, G.

Thurn, K. T.

K. T. Thurn, E. M. B. Brown, A. Wu, S. Vogt, B. Lai, J. Maser, T. Paunesku, and G. E. Woloschak, “Nanoparticles for applications in cellular imaging,” Nanoscale Res. Lett. 2, 430–441 (2007).
[Crossref] [PubMed]

Trahey, G. E.

L. N. Bohs, B. J. Geiman, M. E. Anderson, S. C. Gebhart, and G. E. Trahey, “Speckle tracking for multidimensional flow estimation,” Ultrasonics 38, 369–375 (2000).
[Crossref] [PubMed]

van Blaaderen, A.

van Oostrum, P.

Vogt, S.

K. T. Thurn, E. M. B. Brown, A. Wu, S. Vogt, B. Lai, J. Maser, T. Paunesku, and G. E. Woloschak, “Nanoparticles for applications in cellular imaging,” Nanoscale Res. Lett. 2, 430–441 (2007).
[Crossref] [PubMed]

Waigh, T. A.

S. S. Rogers, T. A. Waigh, X. B. Zhao, and J. R. Lu, “Precise particle tracking against a complicated background: polynomial fitting with gaussian weight,” Phys. Biology 4, 220–227 (2007).
[Crossref]

Walker, W. F.

M. K. Cheezum, W. F. Walker, and W. H. Guilford, “Quantitative comparison of algorithms for tracking single fluorescent particles,” Biophys. J. 81, 2378–2388 (2001).
[Crossref] [PubMed]

Webb, W. W.

R. N. Ghosh and W. W. Webb, “Automated detection and tracking of individual and clustered cell surface low density lipoprotein receptor,” Biophys. J. 66, 1301–1318 (1994).
[Crossref] [PubMed]

West, J. L.

E. S. Day, J. G. Morton, and J. L. West, “Nanoparticles for thermal cancer therapy,” J. Biomechan. Engin.-transactions of the Asme 131, 074001 (2009).
[Crossref]

Woloschak, G. E.

K. T. Thurn, E. M. B. Brown, A. Wu, S. Vogt, B. Lai, J. Maser, T. Paunesku, and G. E. Woloschak, “Nanoparticles for applications in cellular imaging,” Nanoscale Res. Lett. 2, 430–441 (2007).
[Crossref] [PubMed]

Wu, A.

K. T. Thurn, E. M. B. Brown, A. Wu, S. Vogt, B. Lai, J. Maser, T. Paunesku, and G. E. Woloschak, “Nanoparticles for applications in cellular imaging,” Nanoscale Res. Lett. 2, 430–441 (2007).
[Crossref] [PubMed]

Xu, B.

H. W. Gu, K. M. Xu, C. J. Xu, and B. Xu, “Biofunctional magnetic nanoparticles for protein separation and pathogen detection,” Chemical Communications 37, 941–949 (2006).
[Crossref]

Xu, C. J.

H. W. Gu, K. M. Xu, C. J. Xu, and B. Xu, “Biofunctional magnetic nanoparticles for protein separation and pathogen detection,” Chemical Communications 37, 941–949 (2006).
[Crossref]

Xu, K. M.

H. W. Gu, K. M. Xu, C. J. Xu, and B. Xu, “Biofunctional magnetic nanoparticles for protein separation and pathogen detection,” Chemical Communications 37, 941–949 (2006).
[Crossref]

Yang, S. M.

Yi, G. R.

Zhao, X. B.

S. S. Rogers, T. A. Waigh, X. B. Zhao, and J. R. Lu, “Precise particle tracking against a complicated background: polynomial fitting with gaussian weight,” Phys. Biology 4, 220–227 (2007).
[Crossref]

Adv. Drug Delivery Rev. (1)

J. Panyam and V. Labhasetwar, “Biodegradable nanoparticles for drug and gene delivery to cells and tissue,” Adv. Drug Delivery Rev. 55, 329–347 (2003).
[Crossref]

Biophys. J. (3)

R. N. Ghosh and W. W. Webb, “Automated detection and tracking of individual and clustered cell surface low density lipoprotein receptor,” Biophys. J. 66, 1301–1318 (1994).
[Crossref] [PubMed]

G. J. Schutz, H. Schindler, and T. Schmidt, “Single-molecule microscopy on model membranes reveals anomalous diffusion,” Biophys. J. 73, 1073–1080 (1997).
[Crossref] [PubMed]

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Figures (5)

Fig. 1.
Fig. 1.

(a) Experimental setup schematics: BS beamsplitter, BE beam expander, C condenser lens, S specimen, MO 100× microscope objective, M mirror, FL field lens, F filter, L lens and FDC frequency doubler crystal. O designates the object arm, while R designates the reference arm. (b) Illustration, at a given instantaneous time, that the second harmonic field generated by the FDC crystal inserted in the object arm (O1) and the second harmonic field generated by the nanoparticle (O2) both interfere with the tilted second harmonic reference field (R), but on different regions of the detector because of the dispersion induced by the condenser lens that delays O1 with respect to O2, thus making the two mutually incoherent.

Fig. 2.
Fig. 2.

Cartoon depicting the relation between the axial position of the SHG emitter (in the object space) and that of its image plane (in the image space). Method 1 deduces the axial position of a nanoparticle from the hologram reconstruction distance d that brings the image into focus. See Section 3 for more details.

Fig. 3.
Fig. 3.

Second harmonic generation (SHG) by a nanoparticle. (a) and (b) Transverse (xy) cross-section of the intensity of the SHG field, respectively in the hologram plane and after hologram reconstruction in the image plane. Scale bars are 2 microns. (c) Intensity of the SHG field along the dashed white line trace in (a) and (b) for hologram reconstruction distances (d) varying between −8 and −15 cm. (d) Color-coded in jet is the maximum SHG field intensity vs reconstruction distance, for different axial positions of the specimen, when scanned with a piezoelectric stage. Blue squares indicates the reconstruction distance maximizing the SHG field intensity and black line represents the linear fit of Eq. (1).

Fig. 4.
Fig. 4.

(a) Cartoon depicting how the observed SHG phase depends on the position of the emitter. Method 2 deduces the axial position of a nanoparticle directly from the phase of the second harmonic field it generates. See section 4 for more details. (b) Same principle as in (a), but for a nanoparticle deposited on a glass cover slip, and with the addition of a SHG background that serves as constant phase reference.

Fig. 5.
Fig. 5.

(a) Intensity (left) and phase (right) of the SHG field retrieved in the hologram plane, i.e. without numerical propagation to the image plane. The transverse position of the nanoparticle, corresponding to the maximum SHG field intensity is located at the intersection of the white dashed lines. Scale bars are 2 microns. (b) Phase of the SHG field, taken at the intersection of the white dashed lines in (a), plotted against the axial position of the nanoparticle, as returned by the piezoelectric stage.

Equations (3)

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M L = M T 2 .
Δ φ ( Δ z ) = z z 0 + Δ z 2 π ( n ( λ 0 2 ) λ 0 2 n ( λ 0 ) λ 0 ) dz .
Δ φ ( Δ z ) = 2 π λ 0 n Δ z .

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