Abstract

Genetic tools and especially genetically encoded fluorescent reporters have given a special place to optical microscopy in drosophila neurobiology research. In order to monitor neural networks activity, high speed and sensitive techniques, with high spatial resolution are required. Structured illumination microscopies are wide-field approaches with optical sectioning ability. Despite the large progress made with the introduction of the HiLo principle, they did not meet the criteria of speed and/or spatial resolution for drosophila brain imaging. We report on a new implementation that took advantage of micromirror matrix technology to structure the illumination. Thus, we showed that the developed instrument exhibits a spatial resolution close to that of confocal microscopy but it can record physiological responses with a speed improved by more than an order a magnitude.

© 2014 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

2012

T. N. Ford, D. Lim, J. Mertz, “Fast optically sectioned fluorescence HiLo endomicroscopy,” J Biomed Opt. 13(2), 021105 (2012).
[CrossRef]

2011

F. Christiansen, C. Zube, T. F. M. Andlauer, C. Wichmann, W. Fouquet, D. Owald, S. Mertel, F. Leiss, G. Tavosanis, A. J. F. Luna, A. Fiala, S. Sigrist, “Presynapses in Kenyon Cell Dendrites in the Mushroom Body Calyx of Drosophila,” J. Neurosci. 31(26), 9696–9707 (2011).
[CrossRef] [PubMed]

2010

J. Mertz, J. Kim, “Scanning light-sheet microscopy in the whole mouse brain with HiLo background rejection,” J Biomed Opt. 15(1), 016027 (2010).
[CrossRef] [PubMed]

B. D. Pfeiffer, T. T. Ngo, K. L. Hibbard, C. Murphy, A. Jenett, J. W. Truman, G. M. Rubin, “Refinement of tools for targeted gene expression in Drosophila,” Genetics 186(2), 735–755 (2010).
[CrossRef] [PubMed]

N. Gervasi, P. Tchenio, T. Preat, “PKA dynamics in a Drosophila learning center: coincidence detection by rutabaga adenylyl cyclase and spatial regulation by dunce phosphodiesterase,” Neuron 65(4), 516–529 (2010).
[CrossRef] [PubMed]

2009

S. M. Tomchik, R. L. Davis, “Dynamics of learning-related cAMP signaling and stimulus integration in the Drosophila olfactory pathway,” Neuron 64(4), 510–521 (2009).
[CrossRef] [PubMed]

S. Santos, K. K. Chu, D. Lim, N. Bozinovic, T. N. Ford, C. Hourtoule, A. C. Bartoo, S. K. Singh, J. Mertz, “Optically Sectioned Fluorescence Endomicroscopy with Hybrid-Illumination Imaging through a Flexible Fiber Bundle,” Advances in Imaging 14(3), 30502 (2009).

L. Tian, S. A. Hires, T. Mao, D. Huber, M. E. Chiappe, S. H. Chalasani, L. Petreanu, J. Akerboom, S. A. Kinney, E. R. Schreiter, C. I. Bargmann, V. Jayaraman, K. Svoboda, L. L. Looger, “Imaging neural activity in worms, flies and mice with improved GCaMP calcium indicators,” Nature Methods 6(12), 875–881 (2009).
[CrossRef] [PubMed]

2008

D. Lim, K. K. Chu, J. Mertz, “Wide-field fluorescence sectioning with hybrid speckle and uniform-illumination microscopy,” Opt. Express 33(16), 1819–1821 (2008).

V. Nikolenko, B. O. Watson, R. Araya, A. Woodruff, D. S. Peterka, R. Yuste, “SLM microscopy: scanless two-photon imaging and photostimulation with spatial light modulators,” Front. Neural Circuits 2(5), 1–14 (2008).
[CrossRef]

2007

K. J. Venken, H. J. Bellen, “Transgenesis upgrades for Drosophila melanogaster,” Genetics 134(20), 3571–3584 (2007).

B. Zang, J. Zerubia, J. C. Olivo-Marin, “Gaussian approximations of fluorescence microscope point-spread function models,” Applied Optics 46(10), 1819–1829 (2007).
[CrossRef]

2006

D. Yu, D. B. G. Akalal, R. L. Davis, “Drosophila alpha/beta mushroom body neurons form a branch-specific, long-term cellular memory trace after spaced olfactory conditioning,” Neuron 52(5), 845–855 (2006).
[CrossRef] [PubMed]

2004

R. I. Wilson, G. C. Turner, G. Laurent, “Transformation of Olfactory Representations in the Drosophila Antennal Lobe,” Science 303(5656), 366–370 (2004).
[CrossRef]

L. H. Schaeffer, D. Schuster, J. Schaffer, “Structured illumination microscopy: artefact analysis and reduction utilizing a parameter optimization approach,” J Microsc. 216(2), 165–174 (2004).
[CrossRef]

J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodt, E. H. K. Stelzer, “Optical sectioning deep inside live embryos by selective plane illumination microscopy,” Science 305(5686), 1007–1009 (2004).
[CrossRef] [PubMed]

Y. Wang, H. F. Guo, T. A. Pologruto, F. Hannan, I. Hakker, K. Svoboda, Y. Zhong, “Stereotyped odor-evoked activity in the mushroom body of Drosophila revealed by green fluorescent protein-based Ca2+ imaging,” J Neurosci. 24(29), 6507–6514 (2004).
[CrossRef] [PubMed]

2003

M. Heisenberg, “Mushroom body memoir: from maps to models,” Nat Rev Neurosci. 4(4), 266–275 (2003).
[CrossRef] [PubMed]

2002

J. B. Duffy, “GAL4 system in Drosophila: a fly geneticist’s Swiss army knife,” Genesis 34(1–2), 516–529 (2002).
[CrossRef]

A. Fiala, T. Spall, S. Diegelmann, B. Eisermann, S. Sachse, J. M. Devaud, E. Buchner, C. G. Galizia, “Genetically expressed cameleon in Drosophila melanogaster is used to visualize olfactory information in projection neurons,” Current Biology 12(21), 1877–1884 (2002).
[CrossRef] [PubMed]

A. Nakano, “Spinning-disk confocal microscopy a cutting-edge tool for imaging of membrane traffic,” Cell Struct Funct. 27(5), 349–355 (2002).
[CrossRef] [PubMed]

2001

T. Nielsen, M. Fricke, D. Hellweg, P. Andresen, “High efficiency beam splitter for multifocal multiphoton microscopy,” J Microsc. 201(3), 368–376 (2001).
[CrossRef] [PubMed]

1998

J. Bewersdorf, R. Pick, S. W. Hell, “Multifocal multiphoton microscopy,” Optics Letters 23(9), 655–657 (1998).
[CrossRef]

G. Miesenbock, D. A. De Angelis, J. E. Rothman, “Visualizing secretion and synaptic transmission with pH-sensitive green fluorescent proteins,” Nature 394(6689), 192–195 (1998).
[CrossRef] [PubMed]

1997

A. Bullen, S. S. Patel, P. Saggau, “High-speed, random-access fluorescence microscopy: High-resolution optical recording with voltage-sensitive dyes and ion indicators,” Biophys J. 73(1), 477–491 (1997).
[CrossRef] [PubMed]

M. A. A. Neil, R. Juskaitis, T. Wilson, “Method of obtaining optical sectioning by using structured light in a conventional microscope,” Opt. Express 22(24) 1905–1907 (1997).

1996

R. H. Webb, “Confocal optical microscopy,” Rep. Prog. Phys. 59, 427–471 (1996).
[CrossRef]

1995

T. J. Ebner, G. Chen, “Use of voltage-sensitive dyes and optical recordings in the central nervous system,” Prog Neurobiol. 46(5), 463–506 (1995).
[CrossRef] [PubMed]

1993

A. H. Brand, N. Perrimon, “Targeted gene expression as a means of altering cell fates and generating dominant phenotypes,” Development 118, 401–415 (1993).
[PubMed]

1990

W. Denk, J. H. Strickler, W. W. Webb, “Two-Photon Laser Scanning Fluorescence Microscopy,” Science 248(4951), 73–76 (1990).
[CrossRef] [PubMed]

1987

G. Q. Xiao, G.S. Kino, “A real-time confocal scanning optical microscope,” Proc. SPIE 0809, 107–113(1987).
[CrossRef]

1985

M. Heisenberg, A. Borst, S. Wagner, D. Byers, “Drosophila mushroom body mutants are deficient in olfactory learning,” J Neurogenet. 13, 1–30 (1985).
[CrossRef]

1969

A. Stockseth, “Properties of a Defocused Optical System,” JOSA 59(10), 1314–1321 (1969).
[CrossRef]

Akalal, D. B. G.

D. Yu, D. B. G. Akalal, R. L. Davis, “Drosophila alpha/beta mushroom body neurons form a branch-specific, long-term cellular memory trace after spaced olfactory conditioning,” Neuron 52(5), 845–855 (2006).
[CrossRef] [PubMed]

Akerboom, J.

L. Tian, S. A. Hires, T. Mao, D. Huber, M. E. Chiappe, S. H. Chalasani, L. Petreanu, J. Akerboom, S. A. Kinney, E. R. Schreiter, C. I. Bargmann, V. Jayaraman, K. Svoboda, L. L. Looger, “Imaging neural activity in worms, flies and mice with improved GCaMP calcium indicators,” Nature Methods 6(12), 875–881 (2009).
[CrossRef] [PubMed]

Andlauer, T. F. M.

F. Christiansen, C. Zube, T. F. M. Andlauer, C. Wichmann, W. Fouquet, D. Owald, S. Mertel, F. Leiss, G. Tavosanis, A. J. F. Luna, A. Fiala, S. Sigrist, “Presynapses in Kenyon Cell Dendrites in the Mushroom Body Calyx of Drosophila,” J. Neurosci. 31(26), 9696–9707 (2011).
[CrossRef] [PubMed]

Andresen, P.

T. Nielsen, M. Fricke, D. Hellweg, P. Andresen, “High efficiency beam splitter for multifocal multiphoton microscopy,” J Microsc. 201(3), 368–376 (2001).
[CrossRef] [PubMed]

Araya, R.

V. Nikolenko, B. O. Watson, R. Araya, A. Woodruff, D. S. Peterka, R. Yuste, “SLM microscopy: scanless two-photon imaging and photostimulation with spatial light modulators,” Front. Neural Circuits 2(5), 1–14 (2008).
[CrossRef]

Bargmann, C. I.

L. Tian, S. A. Hires, T. Mao, D. Huber, M. E. Chiappe, S. H. Chalasani, L. Petreanu, J. Akerboom, S. A. Kinney, E. R. Schreiter, C. I. Bargmann, V. Jayaraman, K. Svoboda, L. L. Looger, “Imaging neural activity in worms, flies and mice with improved GCaMP calcium indicators,” Nature Methods 6(12), 875–881 (2009).
[CrossRef] [PubMed]

Bartoo, A. C.

S. Santos, K. K. Chu, D. Lim, N. Bozinovic, T. N. Ford, C. Hourtoule, A. C. Bartoo, S. K. Singh, J. Mertz, “Optically Sectioned Fluorescence Endomicroscopy with Hybrid-Illumination Imaging through a Flexible Fiber Bundle,” Advances in Imaging 14(3), 30502 (2009).

Bellen, H. J.

K. J. Venken, H. J. Bellen, “Transgenesis upgrades for Drosophila melanogaster,” Genetics 134(20), 3571–3584 (2007).

Bewersdorf, J.

J. Bewersdorf, R. Pick, S. W. Hell, “Multifocal multiphoton microscopy,” Optics Letters 23(9), 655–657 (1998).
[CrossRef]

Borst, A.

M. Heisenberg, A. Borst, S. Wagner, D. Byers, “Drosophila mushroom body mutants are deficient in olfactory learning,” J Neurogenet. 13, 1–30 (1985).
[CrossRef]

Bozinovic, N.

S. Santos, K. K. Chu, D. Lim, N. Bozinovic, T. N. Ford, C. Hourtoule, A. C. Bartoo, S. K. Singh, J. Mertz, “Optically Sectioned Fluorescence Endomicroscopy with Hybrid-Illumination Imaging through a Flexible Fiber Bundle,” Advances in Imaging 14(3), 30502 (2009).

Brand, A. H.

A. H. Brand, N. Perrimon, “Targeted gene expression as a means of altering cell fates and generating dominant phenotypes,” Development 118, 401–415 (1993).
[PubMed]

Buchner, E.

A. Fiala, T. Spall, S. Diegelmann, B. Eisermann, S. Sachse, J. M. Devaud, E. Buchner, C. G. Galizia, “Genetically expressed cameleon in Drosophila melanogaster is used to visualize olfactory information in projection neurons,” Current Biology 12(21), 1877–1884 (2002).
[CrossRef] [PubMed]

Bullen, A.

A. Bullen, S. S. Patel, P. Saggau, “High-speed, random-access fluorescence microscopy: High-resolution optical recording with voltage-sensitive dyes and ion indicators,” Biophys J. 73(1), 477–491 (1997).
[CrossRef] [PubMed]

Byers, D.

M. Heisenberg, A. Borst, S. Wagner, D. Byers, “Drosophila mushroom body mutants are deficient in olfactory learning,” J Neurogenet. 13, 1–30 (1985).
[CrossRef]

Chalasani, S. H.

L. Tian, S. A. Hires, T. Mao, D. Huber, M. E. Chiappe, S. H. Chalasani, L. Petreanu, J. Akerboom, S. A. Kinney, E. R. Schreiter, C. I. Bargmann, V. Jayaraman, K. Svoboda, L. L. Looger, “Imaging neural activity in worms, flies and mice with improved GCaMP calcium indicators,” Nature Methods 6(12), 875–881 (2009).
[CrossRef] [PubMed]

Chen, G.

T. J. Ebner, G. Chen, “Use of voltage-sensitive dyes and optical recordings in the central nervous system,” Prog Neurobiol. 46(5), 463–506 (1995).
[CrossRef] [PubMed]

Chiappe, M. E.

L. Tian, S. A. Hires, T. Mao, D. Huber, M. E. Chiappe, S. H. Chalasani, L. Petreanu, J. Akerboom, S. A. Kinney, E. R. Schreiter, C. I. Bargmann, V. Jayaraman, K. Svoboda, L. L. Looger, “Imaging neural activity in worms, flies and mice with improved GCaMP calcium indicators,” Nature Methods 6(12), 875–881 (2009).
[CrossRef] [PubMed]

Christiansen, F.

F. Christiansen, C. Zube, T. F. M. Andlauer, C. Wichmann, W. Fouquet, D. Owald, S. Mertel, F. Leiss, G. Tavosanis, A. J. F. Luna, A. Fiala, S. Sigrist, “Presynapses in Kenyon Cell Dendrites in the Mushroom Body Calyx of Drosophila,” J. Neurosci. 31(26), 9696–9707 (2011).
[CrossRef] [PubMed]

Chu, K. K.

S. Santos, K. K. Chu, D. Lim, N. Bozinovic, T. N. Ford, C. Hourtoule, A. C. Bartoo, S. K. Singh, J. Mertz, “Optically Sectioned Fluorescence Endomicroscopy with Hybrid-Illumination Imaging through a Flexible Fiber Bundle,” Advances in Imaging 14(3), 30502 (2009).

D. Lim, K. K. Chu, J. Mertz, “Wide-field fluorescence sectioning with hybrid speckle and uniform-illumination microscopy,” Opt. Express 33(16), 1819–1821 (2008).

Davis, R. L.

S. M. Tomchik, R. L. Davis, “Dynamics of learning-related cAMP signaling and stimulus integration in the Drosophila olfactory pathway,” Neuron 64(4), 510–521 (2009).
[CrossRef] [PubMed]

D. Yu, D. B. G. Akalal, R. L. Davis, “Drosophila alpha/beta mushroom body neurons form a branch-specific, long-term cellular memory trace after spaced olfactory conditioning,” Neuron 52(5), 845–855 (2006).
[CrossRef] [PubMed]

De Angelis, D. A.

G. Miesenbock, D. A. De Angelis, J. E. Rothman, “Visualizing secretion and synaptic transmission with pH-sensitive green fluorescent proteins,” Nature 394(6689), 192–195 (1998).
[CrossRef] [PubMed]

Del Bene, F.

J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodt, E. H. K. Stelzer, “Optical sectioning deep inside live embryos by selective plane illumination microscopy,” Science 305(5686), 1007–1009 (2004).
[CrossRef] [PubMed]

Denk, W.

W. Denk, J. H. Strickler, W. W. Webb, “Two-Photon Laser Scanning Fluorescence Microscopy,” Science 248(4951), 73–76 (1990).
[CrossRef] [PubMed]

Devaud, J. M.

A. Fiala, T. Spall, S. Diegelmann, B. Eisermann, S. Sachse, J. M. Devaud, E. Buchner, C. G. Galizia, “Genetically expressed cameleon in Drosophila melanogaster is used to visualize olfactory information in projection neurons,” Current Biology 12(21), 1877–1884 (2002).
[CrossRef] [PubMed]

Diegelmann, S.

A. Fiala, T. Spall, S. Diegelmann, B. Eisermann, S. Sachse, J. M. Devaud, E. Buchner, C. G. Galizia, “Genetically expressed cameleon in Drosophila melanogaster is used to visualize olfactory information in projection neurons,” Current Biology 12(21), 1877–1884 (2002).
[CrossRef] [PubMed]

Duffy, J. B.

J. B. Duffy, “GAL4 system in Drosophila: a fly geneticist’s Swiss army knife,” Genesis 34(1–2), 516–529 (2002).
[CrossRef]

Ebner, T. J.

T. J. Ebner, G. Chen, “Use of voltage-sensitive dyes and optical recordings in the central nervous system,” Prog Neurobiol. 46(5), 463–506 (1995).
[CrossRef] [PubMed]

Eisermann, B.

A. Fiala, T. Spall, S. Diegelmann, B. Eisermann, S. Sachse, J. M. Devaud, E. Buchner, C. G. Galizia, “Genetically expressed cameleon in Drosophila melanogaster is used to visualize olfactory information in projection neurons,” Current Biology 12(21), 1877–1884 (2002).
[CrossRef] [PubMed]

Fiala, A.

F. Christiansen, C. Zube, T. F. M. Andlauer, C. Wichmann, W. Fouquet, D. Owald, S. Mertel, F. Leiss, G. Tavosanis, A. J. F. Luna, A. Fiala, S. Sigrist, “Presynapses in Kenyon Cell Dendrites in the Mushroom Body Calyx of Drosophila,” J. Neurosci. 31(26), 9696–9707 (2011).
[CrossRef] [PubMed]

A. Fiala, T. Spall, S. Diegelmann, B. Eisermann, S. Sachse, J. M. Devaud, E. Buchner, C. G. Galizia, “Genetically expressed cameleon in Drosophila melanogaster is used to visualize olfactory information in projection neurons,” Current Biology 12(21), 1877–1884 (2002).
[CrossRef] [PubMed]

Ford, T. N.

T. N. Ford, D. Lim, J. Mertz, “Fast optically sectioned fluorescence HiLo endomicroscopy,” J Biomed Opt. 13(2), 021105 (2012).
[CrossRef]

S. Santos, K. K. Chu, D. Lim, N. Bozinovic, T. N. Ford, C. Hourtoule, A. C. Bartoo, S. K. Singh, J. Mertz, “Optically Sectioned Fluorescence Endomicroscopy with Hybrid-Illumination Imaging through a Flexible Fiber Bundle,” Advances in Imaging 14(3), 30502 (2009).

Fouquet, W.

F. Christiansen, C. Zube, T. F. M. Andlauer, C. Wichmann, W. Fouquet, D. Owald, S. Mertel, F. Leiss, G. Tavosanis, A. J. F. Luna, A. Fiala, S. Sigrist, “Presynapses in Kenyon Cell Dendrites in the Mushroom Body Calyx of Drosophila,” J. Neurosci. 31(26), 9696–9707 (2011).
[CrossRef] [PubMed]

Fricke, M.

T. Nielsen, M. Fricke, D. Hellweg, P. Andresen, “High efficiency beam splitter for multifocal multiphoton microscopy,” J Microsc. 201(3), 368–376 (2001).
[CrossRef] [PubMed]

Galizia, C. G.

A. Fiala, T. Spall, S. Diegelmann, B. Eisermann, S. Sachse, J. M. Devaud, E. Buchner, C. G. Galizia, “Genetically expressed cameleon in Drosophila melanogaster is used to visualize olfactory information in projection neurons,” Current Biology 12(21), 1877–1884 (2002).
[CrossRef] [PubMed]

Gervasi, N.

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Figures (10)

Fig. 1
Fig. 1

Microscope setup. The LED beam (Prizmatix Ultra High Power LED, 460 nm, 2.5 W, 30 kHz) is shaped by a digital micro-mirror array (DLP Texas Instruments Discovery 4100 0.7 XGA 1024×768 micro-mirrors) to generate pattern used to perform optical sectioning. The typical power at the sample plan is about 1.5 mW. Excitation and emission beams are separated thanks to a dichroic mirror. The filtered fluorescence emission is recorded by a sCMOS camera (2560 pixels×2160 pixels, the pixels are square of 6.5 μm long on each side). Dashed lines represent the vertical part of the set-up.

Fig. 2
Fig. 2

Determination of PSF with 100 nm diameter fluorescent beads. (a) Lateral PSF. (b) axial PSF. Experimental results (straight line) and gaussian fits (dotted line) giving lateral and axial FWHM of 440 ± 40 nm and 2.0 ± 0.1 μm respectively after calculations on four beads of the sample. Leica Objective 40× 0.8 NA.

Fig. 3
Fig. 3

(Dashed line) Theoretical optical transfer function for an incoherent system of 2 f0 cut-off frequency with f0 = 31 lines.mm−1. (Straight line) Normalized experimental evolution of contrast on camera images for different line periods: 2, 4, 8, 10, 12, 14, 16, 32 and 64 DLP pixels. The results are presented in spatial frequencies space where 2, 4, 8, 10, 12, 14, 16 and 32 DLP pixels correspond to pattern frequency of 51.6, 25.8, 12.9, 10.3, 8.6, 7.4, 6.5, 3.2 and 1.6 lines.mm−1 respectively. Leica Objective 40× 0.8 NA.

Fig. 4
Fig. 4

Axial HiLo profiles for three line periods: 4 (dotted line), 8 (straight line) and 16 (dashed line) DLP pixels line periods. We got a Full Width Half Maximum (FWHM) of 5.5 μm, 3.3 μm and 2.0 μm for 16, 8 and 4 DLP pixels line periods respectively assuming gaussian fits. Leica objective 40× 0.8 NA.

Fig. 5
Fig. 5

2 μm diameter fluorescent bead HiLo images for 4 DLP pixels line period. (a) Lateral view (X, Y). (b) Reconstruction of an axial view (Z, Y). Optical sections are separated by a step of 0.2 μm. Leica objective 40× NA 0.8.

Fig. 6
Fig. 6

Axial profiles of the 2 μm diameter fluorescent bead for wide-field microscopy (dotted line) and HiLo microscopy (straight line). We got an axial bead size of 5.5 μm and 2.8 μm for wide-field and HiLo microscopy respectively taking account the medium change from water to agarose of respective refractive index of 1.33 and 1.5.

Fig. 7
Fig. 7

Kenyon cells of the MB of a 238Y-Gal4/+; UAS-NLS-GFP/+ labeled fly. (a) Image with uniform illumination, (b) with structured illumination (line of 8 pixels period on the DLP) for optical sectioning with Hilo reconstruction. (Leica 25× 0.95 NA. 512×512 pixels images. Coherent laser 488 nm

Fig. 8
Fig. 8

Kenyon cells of the MB of a 238Y-Gal4/+; UAS-NLS-GFP/+ labeled fly. (a) Hilo image with a 2 reconstruction factor (Leica objective 25× 0.95 NA. 512×512 pixels images). (b) Confocal image (Nikon objective 25 × 0.95 NA. 512×512 pixels images).

Fig. 9
Fig. 9

Kenyon cells of the MB of a 238Y-Gal4/+; UAS-CD8-GFP/+ labeled fly. (a) Hilo image with a 2 reconstruction factor (Leica objective 25× 0.95 NA. 512×512 pixels images). We used an incoherent source of light to avoid laser speckle and correctly image the cell membranes. (b) Confocal image (Olympus objective 25× 1 NA, 512×512 pixels images).

Fig. 10
Fig. 10

Variation of Gcamp3 fluorescence in alpha branch after an electric shock of 6 μA. The shock is delivered during 1 s represented by the gray bar. Data are presented for the region of interest as Δ F F 0 = F F 0 F 0 where F0 is the baseline before the electric stimulus and F represents the background-substracted emission fluorescence HiLo intensity of Gcamp3.

Equations (10)

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I u ( ρ ) = I in ( ρ ) + I out ( ρ ) I s ( ρ ) = I in ( ρ ) 2 + ( 1 + M sin ( 2 π f u . ρ ) + h f ( ρ ) ) + I out ( ρ ) 2
I diff ( ρ ) = I u ( ρ ) I u ρ I s ( ρ ) I s ( ρ ) = I in ( ρ ) I u ( ρ ) ( M sin ( 2 π f u . ρ ) + h f ( ρ ) ) + noise
F 2 g ( k x , k y ) = exp ( ( k x + k g x ) 2 + ( k y + k g y ) 2 2 σ 2 ) + exp ( ( k x k g x ) 2 + ( k y k g y ) 2 2 σ 2 )
I H i L o ( ρ ) = I high ( ρ ) + η I low ( ρ )
Object PSF = Image FWHM object 2 + PSF 2 = FWHM image
FWHM x , y = 0.51 λ NA FWHM z = 0.88 λ n n 2 NA 2
C = σ [ I in ( ρ ) I u ( ρ ) ( M sin ( 2 π f u . ρ ) ) ]
OTF ( f ) = { 2 π [ arccos ( f 2 f 0 ) f 2 f 0 1 ( f 2 f 0 ) 2 ] } 2
f 0 = NA eff λ m = 31 l . mm 1
OTF = { 2 [ 1 0.69 f f 0 + 0.0076 ( f f 0 ) 2 + 0.043 ( f f 0 ) 3 ] J 1 ( 4 π w n λ f f 0 2 π w n λ ( f f 0 ) 2 ) 4 π w n λ f f 0 2 π w n λ ( f f 0 ) 2 } 2 ; where w = f tube m z n n 2 NA eff 2 + [ ( f tube m ) 2 + 2 z f tube m + z 2 ( 1 NA eff 2 n 2 ) ] 1 2

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