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Supercontinuum source tuned by an on-axis monochromator for fluorescence lifetime imaging

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Supercontinuum source tuned by an on-axis monochromator for fluorescence lifetime imaging Raffaella Mercatelli, 2 Silvia Soria, 1,* Giuseppe Molesini, 3 Federica Bianco, 1 Giancarlo Righini, 1 and Franco Quercioli 3 1 IFAC-CNR, Istituto di Fisica Applicata “N. Carrara,” Via Madonna del Piano 10, 50019 Sesto Fiorentino (FI), Italy. 2 ISC-CNR, Istituto dei Sistemi Complessi, Via Madonna del Piano 10, 50019 Sesto Fiorentino (FI), Italy 3 INO-CNR, Istituto Nazionale di Ottica, Sede Principale di Arcetri, Largo Fermi 6, 50125 Firenze, Italy *[email protected] Abstract: We report on the application of an optically tunable coherent white light source, based on the supercontinuum generation from microstructured optical fibres, to fluorescence lifetime imaging (FLIM) microscopy and Foerster resonance energy transfer (FRET). A prototype lens based on monotonic longitudinal chromatic aberration is used for tuning the supercontinuum wavelengths from 400 to 1000 nm and acts as an axial monochromator, suitable for fibre delivery in confocal microscopy. ©2010 Optical Society of America OCIS codes: (180.1790) Confocal Microscopy, (180.2520) Fluorescence Microscopy, (220.3620) Lens System Design. References and links 1. J. R. Lakowicz, Principles of Fluorescence Spectroscopy, 3rd Edition (Springer, 2006). 2. E. A. Jares-Erijman, and T. M. Jovin, “Imaging molecular interactions in living cells by FRET microscopy,” Curr. Opin. Chem. Biol. 10(5), 409–416 (2006). 3. D. M. Owen, E. Auksorius, H. B. Manning, C. B. Talbot, P. A. A. de Beule, C. Dunsby, M. A. A. Neil, and P. M. W. French, “Excitation-resolved hyperspectral fluorescence lifetime imaging using a UV-extended supercontinuum source,” Opt. Lett. 32(23), 3408–3410 (2007). 4. G. McConnell, “Confocal laser scanning fluorescence microscopy with a visible continuum source,” Opt. Express 12(13), 2844–2850 (2004). 5. H. N. Paulsen, K. M. Hilligsøe, J. Thøgersen, S. R. Keiding, and J. J. Larsen, “Coherent anti-Stokes Raman scattering microscopy with a photonic crystal fiber based light source,” Opt. Lett. 28(13), 1123–1125 (2003). 6. J. A. Palero, V. O. Boer, J. C. Vijverberg, H. C. Gerritsen, and H. J. C. M. Sterenborg, “Short-wavelength two- photon excitation fluorescence microscopy of tryptophan with a photonic crystal fiber based light source,” Opt. Express 13(14), 5363–5368 (2005). 7. C. Dunsby, P. M. P. Lanigan, J. McGinty, D. S. Elson, J. Requejo-Isidro, I. Munro, N. Galletly, F. McCann, B. Treanor, B. Onfelt, D. M. Davis, M. A. A. Neil, and P. M. W. French, “An electronically tunable ultrafast laser source applied to fluorescence imaging and fluorescence lifetime imaging microscopy,” J. Phys. D Appl. Phys. 37(23), 3296–3303 (2004). 8. D. M. Grant, J. McGinty, E. J. McGhee, T. D. Bunney, D. M. Owen, C. B. Talbot, W. Zhang, S. Kumar, I. Munro, P. M. P. Lanigan, G. T. Kennedy, C. Dunsby, A. I. Magee, P. Courtney, M. Katan, M. A. A. Neil, and P. M. W. French, “High speed optically sectioned fluorescence lifetime imaging permits study of live cell signaling events,” Opt. Express 15(24), 15656–15673 (2007). 9. P. Blandin, S. Lévêque-Fort, S. Lécart, J. C. Cossec, M.-C. Potier, Z. Lenkei, F. Druon, and P. Georges, “Time- gated total internal reflection fluorescence microscopy with a supercontinuum excitation source,” Appl. Opt. 48(3), 553–559 (2009). 10. A. Gurtler, J. Gilijamse, A. Wetzels, L. Noordam, E. Sali, and M. Bellini, “Frequency selection of supercontinuum ultrashort pulses using a Fresnel zone plate,” Opt. Commun. 270(2), 336–339 (2007). 11. K. Shi, P. Li, S. Yin, and Z. Liu, “Chromatic confocal microscopy using supercontinuum light,” Opt. Express 12(10), 2096–2101 (2004). 12. G. McConnell, S. Poland, and J. M. Girkin, “Fast wavelength multiplexing of a white-light supercontinuum using a digital micromirror device for improved three-dimensional fluorescence microscopy,” Rev. Sci. Instrum. 77(1), 013702 (2006). 13. F. Quercioli, B. Tiribilli, and G. Molesini, “Optical Surface profile transducer,” Opt. Eng. 27, 135–142 (1988). 14. B. J. Bacskai, J. Skoch, G. A. Hickey, R. Allen, and B. T. Hyman, “Fluorescence resonance energy transfer determinations using multiphoton fluorescence lifetime imaging microscopy to characterize amyloid-beta plaques,” J. Biomed. Opt. 8(3), 368–375 (2003). #132160 - $15.00 USD Received 22 Jul 2010; revised 26 Aug 2010; accepted 28 Aug 2010; published 10 Sep 2010 (C) 2010 OSA 13 September 2010 / Vol. 18, No. 19 / OPTICS EXPRESS 20505
Transcript
Page 1: Supercontinuum source tuned by an on-axis monochromator for fluorescence lifetime imaging

Supercontinuum source tuned by an on-axis monochromator for fluorescence lifetime

imaging

Raffaella Mercatelli,2 Silvia Soria,

1,* Giuseppe Molesini,

3 Federica Bianco,

1 Giancarlo

Righini,1 and Franco Quercioli

3

1IFAC-CNR, Istituto di Fisica Applicata “N. Carrara,” Via Madonna del Piano 10, 50019 Sesto Fiorentino (FI), Italy.

2ISC-CNR, Istituto dei Sistemi Complessi, Via Madonna del Piano 10, 50019 Sesto Fiorentino (FI), Italy 3INO-CNR, Istituto Nazionale di Ottica, Sede Principale di Arcetri, Largo Fermi 6, 50125 Firenze, Italy

*[email protected]

Abstract: We report on the application of an optically tunable coherent white light source, based on the supercontinuum generation from microstructured optical fibres, to fluorescence lifetime imaging (FLIM) microscopy and Foerster resonance energy transfer (FRET). A prototype lens based on monotonic longitudinal chromatic aberration is used for tuning the supercontinuum wavelengths from 400 to 1000 nm and acts as an axial monochromator, suitable for fibre delivery in confocal microscopy.

©2010 Optical Society of America

OCIS codes: (180.1790) Confocal Microscopy, (180.2520) Fluorescence Microscopy, (220.3620) Lens System Design.

References and links

1. J. R. Lakowicz, Principles of Fluorescence Spectroscopy, 3rd Edition (Springer, 2006). 2. E. A. Jares-Erijman, and T. M. Jovin, “Imaging molecular interactions in living cells by FRET microscopy,”

Curr. Opin. Chem. Biol. 10(5), 409–416 (2006). 3. D. M. Owen, E. Auksorius, H. B. Manning, C. B. Talbot, P. A. A. de Beule, C. Dunsby, M. A. A. Neil, and P. M.

W. French, “Excitation-resolved hyperspectral fluorescence lifetime imaging using a UV-extended supercontinuum source,” Opt. Lett. 32(23), 3408–3410 (2007).

4. G. McConnell, “Confocal laser scanning fluorescence microscopy with a visible continuum source,” Opt. Express 12(13), 2844–2850 (2004).

5. H. N. Paulsen, K. M. Hilligsøe, J. Thøgersen, S. R. Keiding, and J. J. Larsen, “Coherent anti-Stokes Raman scattering microscopy with a photonic crystal fiber based light source,” Opt. Lett. 28(13), 1123–1125 (2003).

6. J. A. Palero, V. O. Boer, J. C. Vijverberg, H. C. Gerritsen, and H. J. C. M. Sterenborg, “Short-wavelength two-photon excitation fluorescence microscopy of tryptophan with a photonic crystal fiber based light source,” Opt. Express 13(14), 5363–5368 (2005).

7. C. Dunsby, P. M. P. Lanigan, J. McGinty, D. S. Elson, J. Requejo-Isidro, I. Munro, N. Galletly, F. McCann, B. Treanor, B. Onfelt, D. M. Davis, M. A. A. Neil, and P. M. W. French, “An electronically tunable ultrafast laser source applied to fluorescence imaging and fluorescence lifetime imaging microscopy,” J. Phys. D Appl. Phys. 37(23), 3296–3303 (2004).

8. D. M. Grant, J. McGinty, E. J. McGhee, T. D. Bunney, D. M. Owen, C. B. Talbot, W. Zhang, S. Kumar, I. Munro, P. M. P. Lanigan, G. T. Kennedy, C. Dunsby, A. I. Magee, P. Courtney, M. Katan, M. A. A. Neil, and P. M. W. French, “High speed optically sectioned fluorescence lifetime imaging permits study of live cell signaling events,” Opt. Express 15(24), 15656–15673 (2007).

9. P. Blandin, S. Lévêque-Fort, S. Lécart, J. C. Cossec, M.-C. Potier, Z. Lenkei, F. Druon, and P. Georges, “Time-gated total internal reflection fluorescence microscopy with a supercontinuum excitation source,” Appl. Opt. 48(3), 553–559 (2009).

10. A. Gurtler, J. Gilijamse, A. Wetzels, L. Noordam, E. Sali, and M. Bellini, “Frequency selection of supercontinuum ultrashort pulses using a Fresnel zone plate,” Opt. Commun. 270(2), 336–339 (2007).

11. K. Shi, P. Li, S. Yin, and Z. Liu, “Chromatic confocal microscopy using supercontinuum light,” Opt. Express 12(10), 2096–2101 (2004).

12. G. McConnell, S. Poland, and J. M. Girkin, “Fast wavelength multiplexing of a white-light supercontinuum using a digital micromirror device for improved three-dimensional fluorescence microscopy,” Rev. Sci. Instrum. 77(1), 013702 (2006).

13. F. Quercioli, B. Tiribilli, and G. Molesini, “Optical Surface profile transducer,” Opt. Eng. 27, 135–142 (1988). 14. B. J. Bacskai, J. Skoch, G. A. Hickey, R. Allen, and B. T. Hyman, “Fluorescence resonance energy transfer

determinations using multiphoton fluorescence lifetime imaging microscopy to characterize amyloid-beta plaques,” J. Biomed. Opt. 8(3), 368–375 (2003).

#132160 - $15.00 USD Received 22 Jul 2010; revised 26 Aug 2010; accepted 28 Aug 2010; published 10 Sep 2010(C) 2010 OSA 13 September 2010 / Vol. 18, No. 19 / OPTICS EXPRESS 20505

Page 2: Supercontinuum source tuned by an on-axis monochromator for fluorescence lifetime imaging

15. C. Biskup, L. Kelbauskas, T. Zimmer, K. Benndorf, A. Bergmann, W. Becker, J. P. Ruppersberg, C. Stockklausner, and N. Klöcker, “Interaction of PSD-95 with potassium channels visualized by fluorescence lifetime-based resonance energy transfer imaging,” J. Biomed. Opt. 9(4), 753–759 (2004).

1. Introduction

The study of protein dynamics in living cells is of crucial importance in biology and medicine since protein-protein interactions mediate several cellular processes. The identification of specific protein interactions opens up the possibility of understanding their function, their role in pathological processes and the place where biochemical reactions take place. Thus, functional imaging with high spatial resolution is required to study such processes. During the last decade, along with new fluorescent labels, novel confocal microscopy techniques have radically improved the probing capabilities of fluorescence images.

Fluorescence lifetime imaging microscopy (FLIM) determines the fluorescence decay time for each pixel of the acquired image and creates a map of the molecular environment of a fluorophore. FLIM is almost insensitive to intensity artifacts and fluorophores concentration but highly sensitive to local changes in the environment such as variations of pH, physiological ions or interacting partners [1]. FLIM probes the alterations in the immediate vicinity of a fluorescent molecule; among these alterations, of particular interest are the lifetime alterations due to excited state reactions [2]. Hyperspectral FLIM [3] is a technique allowing simultaneously recording of the full emission spectrum and temporal decay curves of a biological specimen and may be useful for Foerster resonance energy transfer (FRET) measurements [2] in order to exclude changes in lifetime due to other local variations. FRET between two fluorescent labels, donor and acceptor, is a well tested spectroscopic technique for measuring distances below 10 nm, which is the order of the distance between proteins bound in a complex [1]. FLIM-FRET has the capability of imaging within cells or tissue, at optical resolution, and detect where in biological sample protein interactions are occurring.

A critical component for a fluorescence microscope is still the excitation source. FLIM requires an ultrafast excitation source and this can be provided by supercontinuum (SC) generation in microstructured fibres (MOF) [4]. SC sources are ideal for many forms of microscopy like coherent anti-Stokes Raman scattering (CARS) microscopy [5], confocal microscopy [4], two photon microscopy [6], FLIM [7,8] and total internal reflection microscopy [9]. SC provides the capability of simultaneous optical imaging and spectroscopy with multiple wavelengths to characterise biological samples. Developing filtering techniques in order to select discrete wavelengths from the SC source has always been of interest. Many different methods have been proposed: among the most innovative ones, we can find Fresnel plates [10], pair of singlet lenses [11], electrically tuneable slits [7], and digital mirror devices [12].

In this work, we have filtered the broadband SC generated from a commercial MOF by means of a special lens, custom-designed to maximize its longitudinal chromatic aberration [13] while keeping all the other aberrations at low value. The intentionally generated aberration has been used as an useful on-axis monochromator for resolving the excitation source in a range from 400 to 1000 nm with a bandwidth comparable to interferometric filters. The monochromator lens is easy to align, tight, accurate and it is specially suitable for interfacing the SC fiber source with the confocal fibre beam delivery system. We have validated our monochromator lens by measuring hyperspectral FLIM-FRET in vivo in human embryonic kidney cells in order to characterize the interaction between two cellular membrane proteins, a potassium channel and integrin-beta1, stained with enhanced Cyan Fluorescence Protein (ECFP) and enhanced Yellow Fluorescent Protein (EYFP), respectively.

2. Experimental setup and characterization

Figure 1 shows the experimental set-up. The multiphoton microscope set up is made up of a Nikon PCM2000 Confocal Laser Scanning Microscope (CLSM), equipped with a Nikon TE2000-U inverted optical microscope. The scanning unit was modified to allow the use of the monochromator lens. The ultrafast laser system is made up of a standard mode locked

#132160 - $15.00 USD Received 22 Jul 2010; revised 26 Aug 2010; accepted 28 Aug 2010; published 10 Sep 2010(C) 2010 OSA 13 September 2010 / Vol. 18, No. 19 / OPTICS EXPRESS 20506

Page 3: Supercontinuum source tuned by an on-axis monochromator for fluorescence lifetime imaging

Ti:Sapphire oscillator (Mira 900 F pumped by Verdi V5 solid-state laser, Coherent Inc., USA). The wavelength is tunable in the range from 700 to 980 nm, with typical pulse duration of 130 fs and 76 MHz repetition rate. A Faraday isolator avoids back reflections going into the laser cavity. A half-wave plate was used to adjust the polarization of the laser relative to the fast axis of the fibre. A wavelength of 800 nm was coupled into the MOF by means of an aspherical lens with a matching numerical aperture. For generating the SC, we used a 30 cm long NL-1.7-670 MOF (Crystal Fibre, 0.24 NA). The generated SC was then collimated by a plano convex lens (20 mm focal length, 25 mm diameter and 0.53 NA) and the excitation wavelength, selected by the axial monochromator, was sent to the confocal microscope. The fluorescent light emission from one of the two microscope channels was sent to a spectrometer (Oriel) and detected by a 16-channel photomultiplier (PML-16C Becker & Hickl) and then processed by the time correlated single photon counting (TCSPC) board (SPC-830 Becker & Hickl).

Fig. 1. Experimental set-up.

Figure 2 shows the SC spectrum of the NL-1.7-670 MOF; it spans from 390 nm to 1500 nm when pumped at 800 nm with 650 mW power. The spectrum was acquired using an Anritsu optical spectrum analyzer MS9030A. Details of the characterization of this fiber can be found in reference [6].

#132160 - $15.00 USD Received 22 Jul 2010; revised 26 Aug 2010; accepted 28 Aug 2010; published 10 Sep 2010(C) 2010 OSA 13 September 2010 / Vol. 18, No. 19 / OPTICS EXPRESS 20507

Page 4: Supercontinuum source tuned by an on-axis monochromator for fluorescence lifetime imaging

Fig. 2. SC spectrum plotted on logarithmic scale for a pumping wavelength of 800 nm. The red line shows the zero dispersion wavelength (670 nm).

The SC light is then filtered by the monochromator lens. Such an axial monochromator provides a longitudinal dispersion of foci along the optical axis as a function of wavelength.

The finite aperture of the microscope input delivery fibre (core diameter: 4 µm) acts as the slit in an off-axis standard monochromator, filtering the out of focused wavelengths. The prototype optical system is made of five optical elements and two different glass materials, BK7 and SF1. It works from infinity to focus, with an Effective Focal Length (EFL) of 22.5 mm and with an f/1.7 (0.28 NA) relative aperture (design data at 633 nm) (Fig. 3.a) and it is optimized over a semifield angle of 3°. Suitable constraints were introduced in order to minimize spherical aberration while intentionally enhancing the longitudinal chromatic aberration. A micrometric axial displacement between the monochromator and the microscope input fibre allows the selection of the spectral line (see Fig. 3.b). The wavelength design range goes from 400 nm up to 1000 nm, while the monochromator lens varies its back focal length (BFL) in a monotonic way from 4.57 to 6.02 mm (see Fig. 3.c), respectively [13]. Table 1 shows, for a number of filtered wavelengths, the calculated diffraction limited spot size, the back focal length, wave aberration parameters (rms and Strehl ratio) of the longitudinally aberrated optical system [13] and the experimental full width half maximum (FWHM) of the filtered spectral line. The monotonic increase of FWHM versus wavelength is due to the inverse proportionality to d(BFL)/dλ. The measured data are in good agreement with the calculated filtered spectrum.

Table 1. Diffraction limited spot, Back Focal Length (BFL), on-axis wave rms, Strehl ratio and measured FWHM at some selected wavelengths

λ (nm)

Diffraction-limited spot

(µm) BFL (mm) Wave rms Strehl ratio FWHM

(nm) 400 1.66 4.57 0.076 0.783 9.9 500 2.07 5.12 0.050 0.905 13.4

600 2.49 5.48 0.035 0.951 14.0 700 2.90 5.71 0.027 0.972 15.7 800 3.32 5.86 0.021 0.982 17.6 900 3.73 5.95 0.017 0.988 22.0

1000 4.15 6.02 0.014 0.992 27.0

#132160 - $15.00 USD Received 22 Jul 2010; revised 26 Aug 2010; accepted 28 Aug 2010; published 10 Sep 2010(C) 2010 OSA 13 September 2010 / Vol. 18, No. 19 / OPTICS EXPRESS 20508

Page 5: Supercontinuum source tuned by an on-axis monochromator for fluorescence lifetime imaging

400 450 500 550 600 650 700 750 800 850 900 950 1000

4.4

4.6

4.8

5.0

5.2

5.4

5.6

5.8

6.0

6.2

Ba

ck

Foc

al L

en

gth

[mm

]

Wavelength [nm]

b)

c)

a)

400 500 600 700 800 900 1000 1100 1200 1300 1400 1500

-90

-80

-70

-60

-50

-40

-30

400 600 800 1000 1200 1400

10-4

10-3

Filt

ere

d S

C

[mW

]

SC

Po

we

r [d

B]

Wavelength [nm]

Fig. 3. a) Plot of the monochromator lens and ray tracing of two spectral components, red line: 1000 nm, blue line: 400 nm, made by CODE V optical design program; b) filtering action of the monochromator lens: the black line indicates the SC spectrum of the NL-1.7-670 MOF, while the color curves show the filtered spectral lines at the wavelengths listed in Table 1; c) monotonical increase of the BFL with wavelength: continuous line: calculated, red squares: experimental.

In order to check the effective tuning performance of our system, we have imaged with the confocal microscope bovine pulmonary artery endothelial (BPAE) cells (Invitrogen). BPAE cells are stained with a combination of fluorescent dyes. Nuclei were labeled with blue-

#132160 - $15.00 USD Received 22 Jul 2010; revised 26 Aug 2010; accepted 28 Aug 2010; published 10 Sep 2010(C) 2010 OSA 13 September 2010 / Vol. 18, No. 19 / OPTICS EXPRESS 20509

Page 6: Supercontinuum source tuned by an on-axis monochromator for fluorescence lifetime imaging

fluorescent DAPI, mitochondria with red-fluorescent MitoTracker® Red CMXRos, and F-actin with green-fluorescent BODIPY® FL phallacidin.

The optimum excitation wavelength for each of the three fluorophores was chosen and Fig. 4 shows the resulting RGB image of a BPAE cell.

Fig. 4. RGB confocal image of a single BPAE cell: blue: DAPI stained nucleus excited at 405 nm; red: MitoTracker® Red CMXRos stained mitrochondria, excited at 550 nm; green: BODIPY® FL phallacidin stained F-actin filaments, excited at 490 nm.

3. Results and discussion

We have developed a tunable pulsed white light source system with the aim of performing hyperspectral FLIM-FRET imaging. The method for determining FRET efficiency by FLIM is based on the measurement of the donor lifetime when the acceptor is present (τDA) and when the acceptor is absent (τD). Since fluorescence lifetime is independent of the actual number of fluorophores in a wide range of concentrations, there is no need to know the fluorophore concentrations in the sample [14,15]. In our measurements, the donor fluorescence decay was well fitted by a single-exponential function. This characteristic allows a simpler FRET analysis devoid of rough approximations. In fact, if the donor decay, in the absence of an acceptor, is well fitted by a single-exponential curve, the bi-exponential decay for donors in the presence of acceptors is easier to interpret. As a matter of fact, the slow lifetime component results from non-interacting (unquenched) donor molecules while the fast component is due to the interacting ones (quenched). The slow lifetime component should be in agreement with the one obtained in absence of acceptor (control sample).

The specificity and sensitivity of FLIM to detect FRET in vivo has been tested using HEK293 stably transfected with β1 integrin- EYFP and potassium channel- ECFP, either as single transfectants or as double transfectants. During all measurements, the samples were kept at room temperature and constant pH. Figure 5.a. shows the lifetime image in false colours corresponding to lifetime values in picoseconds, plotted in the lifetime histogram of a control sample. The resulting curve is well fitted by a mono-exponential curve (χ

2 = 0.88) and

the obtained ECFP lifetime is 2.42 ± 0.07 ns. Figure 5.b. shows an HEK cell transfected with ECFP and EYFP showing FRET. The histogram is shifted to lower values than the control sample, and it is more irregular due to the fact that the protein-protein interaction can vary from point to point in the membrane. The fluorescence decay in the ECFP channel is bi-exponential (χ

2 = 0.9) and the lifetime is shortened, but in the EYFP channel the fluorescence

decay is different: it is mono-exponential and the resulting mean lifetime value is 2.58 ± 0.07 ns. Therefore, we can assume that FRET has occurred.

#132160 - $15.00 USD Received 22 Jul 2010; revised 26 Aug 2010; accepted 28 Aug 2010; published 10 Sep 2010(C) 2010 OSA 13 September 2010 / Vol. 18, No. 19 / OPTICS EXPRESS 20510

Page 7: Supercontinuum source tuned by an on-axis monochromator for fluorescence lifetime imaging

Fig. 5. Lifetime image in false colours corresponding to lifetime values in picoseconds (left) showed in the lifetime histogram (right): a) Cell only transfected with ECFP at room temperature, b) Cell transfected with ECFP and EYFP showing FRET.

4. Conclusions

We have reported the physical principle, design features and performance characteristics of an optical system consisting of a tunable pulsed white light source based on SC generation in a commercial MOF, followed by a practical axial monochromator suitable for interfacing two optical fiber based systems. As a particular application, this unconventional monochromator device has proved excellent in filtering the broadband ultrashort source. We have used this optical system for one-photon imaging, namely confocal imaging, and for hyperspectral FRET-FLIM imaging. The ease and simplicity of tuning are remarkable, as well as the compactness of the monochromator lens compared with other devices.

Acknowledgments

The European NoE “Photonics for Life” (P4L) is acknowledged. F. Quercioli and R. Mercatelli gratefully acknowledge the funding of Ente Cassa di Risparmio of Florence, Italy. HEK cells were generously provided by Prof. A. Arcangeli. Useful discussions with G. Nunzi Conti and S. Pelli are also gratefully acknowledged. F. Bianco is now at the University of Trento, Italy.

#132160 - $15.00 USD Received 22 Jul 2010; revised 26 Aug 2010; accepted 28 Aug 2010; published 10 Sep 2010(C) 2010 OSA 13 September 2010 / Vol. 18, No. 19 / OPTICS EXPRESS 20511


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