Abstract

An environmental cell with a 50-nm-thick cathodolumi-nescent window was attached to a scanning electron microscope, and diffraction-unlimited near-field optical imaging of unstained living human lung epithelial cells in liquid was demonstrated. Electrons with energies as low as 0.8 – 1.2 kV are sufficiently blocked by the window without damaging the specimens, and form a sub-wavelength-sized illumination light source. A super-resolved optical image of the specimen adhered to the opposite window surface was acquired by a photomultiplier tube placed below. The cells after the observation were proved to stay alive. The image was formed by enhanced dipole radiation or energy transfer, and features as small as 62 nm were resolved.

© 2013 Optical Society of America

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2013

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics7, 113–117 (2013).
[CrossRef]

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[CrossRef]

A. Chiba, S. Tanaka, W. Inami, A. Sugita, K. Takada, and Y. Kawata, “Amorphous silicon nitride thin films implanted with cerium ions for cathodoluminescent light source,” Opt. Mater.35, 1887–1889 (2013).
[CrossRef]

2012

2011

N. de Jonge and F. M. Ross, “Electron miocroscopy of specimens in liquid,” Nat. Nanotechnol.6, 695–704 (2011).
[CrossRef] [PubMed]

D. B. Peckys, P. Mazur, K. L. Gould, and N. de Jonge, “Fully hydrated yeast cells imaged with electron microscopy,” Biophys. J.100, 2522–2529 (2011).
[CrossRef] [PubMed]

H. Niioka, T. Furukawa, M. Ichimiya, M. Ashida, T. Araki, and M. Hashimoto, “Multicolor cathodoluminescence microscopy for biological imaging with nanophosphors,” Appl. Phys. Express4, 112402 (2011).
[CrossRef]

N. Hanagata, F. Zhuang, S. Connolly, J. Li, N. Ogawa, and M. Xu, “Molecular responses of human lung epithelial cells to the toxicity of copper oxide nanoparticles inferred from whole genome expression analysis,”ACS Nano5, 9326–9338 (2011).
[CrossRef] [PubMed]

2010

T. Oto, R. G. Banal, K. Kataoka, M. Funato, and Y. Kawakami, “100 mW deep-ultraviolet emission from aluminium-nitride-based quantum wells pumped by an electron beam,”Nat. Photonics4, 767–771 (2010).
[CrossRef]

M. Xu, D. Fujita, S. Kajiwara, T. Minowa, X. Li, T. Takemura, H. Iwai, and N. Hanagata, “Contribution of physicochemical characteristics of nano-oxides to cytotoxicity,” Biomaterials31, 8022–8031 (2010).
[CrossRef] [PubMed]

W. Inami, K. Nakajima, A. Miyakawa, and Y. Kawata, “Electron beam excitation assisted optical microscope with ultra-high resolution,” Opt. Express18, 12897–12902 (2010).
[CrossRef] [PubMed]

H. Nishiyama, M. Suga, T. Ogura, Y. Maruyama, M. Koizumi, K. Mio, S. Kitamura, and C. Sato, “Atmospheric scanning electron microscope observes cells and tissues in open medium through silicon nitride film,” J. Struct. Biol.169, 438–449 (2010).
[CrossRef] [PubMed]

2009

T. Ogura, “Measurement of the unstained biological sample by a novel scanning electron generation X-ray microscope based on SEM,” Biochem. Biophys. Res. Commun.385, 624–629 (2009).
[CrossRef] [PubMed]

R. R. Lunt, N. C. Giebink, A. A. Belak, J. B. Benziger, and S. R. Forrest, “Exciton diffusion lengths of organic semiconductor thin films measured by spectrally resolved photoluminescence quenching,” J. Appl. Phys.105, 053711 (2009).
[CrossRef]

B. Barwick, D. J. Flannigan, and A. H. Zewail, “Photon-induced near-field electron microscopy,” Nature462, 902–906 (2009).
[CrossRef] [PubMed]

N. de Jonge, D. B. Peckys, G. J. Kremers, and D. W. Piston, “Electron microscopy of whole cells in liquid with nanometer resolution,” Proc. Natl. Acad. Sci. U. S. A.106, 2159–2164 (2009).
[CrossRef] [PubMed]

R. Böhme, M. Richter, D. Cialla, P. Rösch, V. Deckert, and J. Popp, “Towards a specific characterisation of components on a cell surface – combined TERS – investigations of lipids and human cells,” J. Raman Spectrosc.40, 1452–1457 (2009).
[CrossRef]

J. Han, J. An, R. N. Jana, K. Jung, J. Do, S. Pyo, and C. Im, “Charge carrier photogeneration and hole transport properties of blends of a π-conjugated polymer and an organic-inorganic hybrid material,” Macromol. Res.17, 894–900 (2009).
[CrossRef]

2008

K.-L. Liu, C.-C. Wu, Y.-J. Huang, H.-L. Peng, W.-Y. Chang, P. Chang, L. Hsu, and T.-R. Yew, “Novel microchip for in situ TEM imaging of living organisms and bio-reactions in aqueous conditions,” Lab Chip8, 1915–1921 (2008).
[CrossRef] [PubMed]

C. Höppener and L. Novotny, “Imaging of membrane proteins using antenna-based optical microscopy,” Nanotechnology19, 384012 (2008).
[CrossRef] [PubMed]

2007

S. W. Hell, “Far-field optical nanoscopy,” Science316, 1153–1158 (2007).
[CrossRef] [PubMed]

J. Nelayah, M. Kociak, O. Stéphan, F. J. García de Abajo, M. Tencé, L. Henrard, D. Taverna, I. Pastoriza-Santos, L. M. Liz-Marzán, and C. Colliex, “Mapping surface plasmons on a single metallic nanoparticle,” Nat. Phys.3, 348–353 (2007).
[CrossRef]

D. Drouin, A. R. Couture, D. Joly, X. Tastet, V. Aimez, and R. Gauvin, “CASINO V2.42—a fast and easy-to-use modeling tool for scanning electron microscopy and microanalysis users,” Scanning29, 92–101 (2007).
[CrossRef] [PubMed]

H. Mertens, A. F. Koenderink, and A. Polman, “Plasmon-enhanced luminescence near noble-metal nanospheres: comparison of exact theory and an improved Gersten and Nitzan model,” Phys. Rev. B76, 115123 (2007).
[CrossRef]

2006

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent protains at nanometer resolution,” Science313, 1642–1645 (2006).
[CrossRef] [PubMed]

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods3, 793–795 (2006).
[CrossRef] [PubMed]

2005

M. G. L. Gustafsson, “Nonlinear structured-illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution,” Proc. Natl. Acad. Sci. U. S. A.102, 13081–13086 (2005).
[CrossRef] [PubMed]

J. Niitsuma, H. Oikawa, E. Kimura, T. Ushiki, and T. Sekiguchi, “Cathodoluminescence investigation of organic materials,” J. Electron Microsc.54, 325–330 (2005).
[CrossRef]

A. Kubo, K. Onda, H. Petek, Z. Sun, Y. S. Jung, and H. K. Kim, “Femtosecond imaging of surface plasmon dynamics in a nanostructured silver film,” Nano Lett.5, 1123–1127 (2005).
[CrossRef] [PubMed]

2004

S. Thiberge, A. Nechushtan, D. Sprinzak, O. Gileadi, V. Behar, O. Zik, Y. Chowers, S. Michaeli, J. Schlessinger, and E. Moses, “Scanning electron microscopy of cells and tissues under fully hydrated conditions,” Proc. Natl. Acad. Sci. U. S. A.101, 3346–3351 (2004).
[CrossRef] [PubMed]

M. Koopman, A. Cambi, B. I. de Bakker, B. Joosten, C. G. Figdor, N. F. van Hulst, and M. F. Garcia-Parajo, “Near-field scanning optical microscopy in liquid for high resolution single molecule detection on dendritic cells,” FEBS Lett.573, 6–10 (2004).
[CrossRef] [PubMed]

E. Kimura, T. Sekiguchi, H. Oikawa, J. Niitsuma, Y. Nakayama, H. Suzuki, M. Kimura, K. Fujii, and T. Ushiki, “Cathodoluminescence imaging for identifying uptaken fluorescence materials in Kupffer cells using scanning electron microscopy,” Arch. Histol. Cytol.67, 263–270 (2004).
[CrossRef] [PubMed]

K. Nakaoka, J. Ueyama, and K. Ogura, “Photoelectrochemical behavior of electrodeposited CuO and Cu2O thin films on conducting substrates,” J. Electrochem. Soc.151, C661–C665 (2004).
[CrossRef]

2001

N. Yamamoto, K. Araya, and F. J. García de Abajo, “Photon emission from silver particles induced by a high-energy electron beam,” Phys. Rev. B64, 205419 (2001).
[CrossRef]

2000

N. Hayazawa, Y. Inouye, Z. Sekkat, and S. Kawata, “Metallized tip amplification of near-field Raman scattering,” Opt. Commun.183, 333–336 (2000).
[CrossRef]

T. A. Klar, S. Jakobs, M. Dyba, A. Egner, and S. W. Hell, “Fluorescence microscopy with diffraction resolution barrier broken by stimulated emission,” Proc. Natl. Acad. Sci. U. S. A.97, 8206–8210 (2000).
[CrossRef] [PubMed]

K. Postava, H. Sueki, M. Aoyama, T. Yamaguchi, Ch. Ino, Y. Igasaki, and M. Horie, “Spectroscopic ellipsometry of epitaxial ZnO layer on sapphire substrate,” J. Appl. Phys.87, 7820–7824 (2000).
[CrossRef]

1998

T. Saiki, K. Nishi, and M. Ohtsu, “Low temperature near-field photoluminescence spectroscopy of InGaAs single quantum dots,”Jpn. J. Appl. Phys.37, 1638–1642 (1998).
[CrossRef]

1996

A. Stoffel, A. Kovács, W. Kronast, and B. Müller, “LPCVD against PECVD for micromechanical applications,” J. Micromech. Microeng.6, 1–13 (1996).
[CrossRef]

1995

T. Funatsu, Y. Harada, M. Tokunaga, K. Saito, and T. Yanagida, “Imaging of single fluorescent molecules and individual ATP turnovers by single myosin molecules in aqueous solution,” Nature374, 555–559 (1995).
[CrossRef] [PubMed]

J. Kido, H. Shionoya, and K. Nagai, “Single-layer white light-emitting organic electroluminescent devices based on dye-dispersed poly(N-vinylcarbazole),” Appl. Phys. Lett.67, 2281–2283 (1995).
[CrossRef]

1984

D. W. Pohl, W. Denk, and M. Lanz, “Optical stethoscopy: image recording with resolution λ/20,” Appl. Phys. Lett.44, 651–653 (1984).
[CrossRef]

A. Lewis, M. Isaacson, A. Harootunian, and A. Muray, “Development of a 500 Å spatial resolution light microscope,” Ultramicroscopy13, 227–232 (1984).
[CrossRef]

1978

R. Herbst and D. Hoder, “Cathodoluminescence in biological studies,” Scanning1, 35–41 (1978).
[CrossRef]

V. E. Cosslett, “Radiation damage in the high resolution electron microscopy of biological materials: a review,” J. Microsc.113, 113–129 (1978).
[CrossRef] [PubMed]

1974

D. F. Parsons, V. R. Matricardi, R. C. Moretz, and J. N. Turner, “Electron microscopy and diffraction of wet unstained and unfixed biological objects,” Adv. Biol. Med. Phys.15, 161–270 (1974).
[PubMed]

1973

1972

K. Kanaya and S. Okayama, “Penetration and energy-loss theory of electrons in solid targets,” J. Phys. D Appl. Phys.5, 43–58 (1972).
[CrossRef]

J. E. Mazurkiewicz and P. K. Nakane, “Light and electron microscopic localization of antigens in tissues embedded in polyethylene glycol with a peroxidase-labeled antibody method,” J. Histochem. Cytochem.20, 969–974 (1972).
[CrossRef] [PubMed]

Aimez, V.

D. Drouin, A. R. Couture, D. Joly, X. Tastet, V. Aimez, and R. Gauvin, “CASINO V2.42—a fast and easy-to-use modeling tool for scanning electron microscopy and microanalysis users,” Scanning29, 92–101 (2007).
[CrossRef] [PubMed]

An, J.

J. Han, J. An, R. N. Jana, K. Jung, J. Do, S. Pyo, and C. Im, “Charge carrier photogeneration and hole transport properties of blends of a π-conjugated polymer and an organic-inorganic hybrid material,” Macromol. Res.17, 894–900 (2009).
[CrossRef]

Aoyama, M.

K. Postava, H. Sueki, M. Aoyama, T. Yamaguchi, Ch. Ino, Y. Igasaki, and M. Horie, “Spectroscopic ellipsometry of epitaxial ZnO layer on sapphire substrate,” J. Appl. Phys.87, 7820–7824 (2000).
[CrossRef]

Araki, T.

H. Niioka, T. Furukawa, M. Ichimiya, M. Ashida, T. Araki, and M. Hashimoto, “Multicolor cathodoluminescence microscopy for biological imaging with nanophosphors,” Appl. Phys. Express4, 112402 (2011).
[CrossRef]

Araya, K.

N. Yamamoto, K. Araya, and F. J. García de Abajo, “Photon emission from silver particles induced by a high-energy electron beam,” Phys. Rev. B64, 205419 (2001).
[CrossRef]

Ashida, M.

H. Niioka, T. Furukawa, M. Ichimiya, M. Ashida, T. Araki, and M. Hashimoto, “Multicolor cathodoluminescence microscopy for biological imaging with nanophosphors,” Appl. Phys. Express4, 112402 (2011).
[CrossRef]

Banal, R. G.

T. Oto, R. G. Banal, K. Kataoka, M. Funato, and Y. Kawakami, “100 mW deep-ultraviolet emission from aluminium-nitride-based quantum wells pumped by an electron beam,”Nat. Photonics4, 767–771 (2010).
[CrossRef]

Barwick, B.

B. Barwick, D. J. Flannigan, and A. H. Zewail, “Photon-induced near-field electron microscopy,” Nature462, 902–906 (2009).
[CrossRef] [PubMed]

Bass, M.

M. Bass, Handbook of Optics II, 2 (McGraw-Hill, 1995).

Bates, M.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods3, 793–795 (2006).
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Figures (12)

Fig. 1
Fig. 1

(a) Setup of SEOM. The EC placed under vacuum maintains an arbitrary environment between the entrance and exit windows. The cathodoluminescent entrance window is scanned with an EB, and light modulated by the specimen passes through the exit window and is detected by the PMT beneath. The SiN membrane is supported by a rigid Si frame. (b) Photographs of the detection unit attached to the specimen stage of the SEM. In the inset, the EC unit is removed and the photocathode can be seen. (c) Left: the entrance and the exit windows. Right: the exit side of the assembled state. There are two vent holes on either side of the exit window to drain excess liquid during assembly. After tightening the screws, each hole is sealed with polyimide film and an instant glue. (d) For culturing cells on the entrance window, a silicone ring is attached and filled with culture medium. Scale bars in (b) and (c): 10 mm.

Fig. 2
Fig. 2

(a) Electron penetration through the entrance windows with tm = 20 nm and different te as a function of electron energy E. Experimental threshold energies are indicated by arrows. The threshold for tm = 15 nm and te = 35 nm was 0.8 kV (data not shown). Inset: magnification around the thresholds. The results of Monte Carlo simulation are shown as broken lines whose colors correspond to those of the experimental results. The theoretical thresholds are denoted by asterisks. (b) Simulated distributions of the absorbed energy at the theoretical threshold energies for te = 0, 30, and 60 nm (E = 0.9, 1.3, and 1.7 kV, respectively). These cases correspond to the experimental results for E = 0.6, 0.9, and 1.0 kV, respectively. (c) E dependence of the emission spectra of the entrance windows for tm = 20 nm and te = 30 nm. The spectra shown were acquired without the exit window, but those for enclosed cells filled with water were similar (data not shown).

Fig. 3
Fig. 3

(a) Angular distribution of the radiation at λ = 550 nm from a single dipole placed at a position Δz = 10 nm from the top of a sphere. As shown above the panel, the sphere is embedded in a medium with a refractive index n1. Upper: radiation modulated by spheres with a diameter 2a = 100 nm and various refractive indices n2 placed in water. We considered polystyrene (PS), SiO2, ZnO, and CuO. Lower: radiation modulated by PS spheres with various diameters placed in water. Even when the sphere is absent, a constant intensity is detected since a dipole always radiates homogeneously. The presence of the sphere enhances the radiation and gives a positive contrast. (b) Intensity profile at λ = 550 nm for the EB scanning. Left: single PS spheres. Right: two PS spheres in contact with various diameters. In the calculation hereafter, the distribution of the electrons is taken into account (red lower hemisphere above the panels). (c) Contrast change as a function of the distance d of the PS sphere from the surface of the emitting layer for several diameters and wavelengths. The dominant exponential terms are indicated by the lines. See Appendix A for details on the calculation.

Fig. 4
Fig. 4

Images of NPs for evaluating the resolution. (a) – (d): CL (cathodoluminescence) images by SEOM system. (e) – (h): SE (secondary electron) images. (i) – (l): intensity profiles (red: CL, blue: SE) between the arrowheads in the CL/SE images for four particles. (a), (e), and (i): PS (diameter: 100 nm), (b), (f), and (j): SiO2 (100 nm), (c), (g), and (k): ZnO (< 100 nm), and (d), (h), and (l): CuO (< 50 nm). In the profiles, FWHM or peak distance is shown. In the SE images in (e) – (h), particles on the flipped entrance window were directly observed at E = 3 or 5 kV, as shown to the right of the images, and the flipped images are shown. Observation conditions of the CL images (E, pixel size Xp, dwell time Td) for each panel are (a) 0.9 kV, 20 nm, 10 ms, (b) 0.8 kV, 20 nm, 10 ms, (c) 0.8 kV, 20 nm, 10 ms, and (d) 1.0 kV, 15 nm, 5 ms. The CL images are lowpass filtered at a cutoff of 1/3 pixel−1. Though ZnO is a typical phosphor material, the CL from the ZnO NPs does not contribute to the image, since the EB is sufficiently blocked. Scale bars: 1 μm.

Fig. 5
Fig. 5

Images of unstained cells in PBS. (a) CL (cathodoluminescence) image by SEOM system and (b) PC (phase contrast) image of a part of a fixed cell. The upper half of a vertically oriented long cell is shown. (c) Intensity profiles (red: CL, black: PC) between the arrowheads denoted by A in (a) and (b). (d) Raw CL image and (e) PC image of an unstained living cell in PBS. The PC image was recorded 40 min before the CL image. (f) Enhanced CL image spatially bandpass-filtered at 1/150 – 1/34 pixel−1 and (g) major features traced from (f). Observation conditions of the CL images (E, Xp, Td) are (a) 1.0 kV, 37.5 nm, 1 ms and (d) 0.8 kV, 60 nm, 1 ms. Scale bars: 10 μm.

Fig. 6
Fig. 6

Typical images of unstained fixed cells in PBS. (a) Raw CL (cathodoluminescence) image by SEOM system and (b) PC (phase contrast) image of a cell that has taken up CuO NPs. (c) EDS (X-ray spectrometry) spectra measured at a dark CL area (upper) and at a blank area (lower). EDS data were recorded for a similar cell. Cu is detected in only the dark areas. In blank areas, O, C, Cl, Na, Al, Si are detected. Al comes from the specimen holder; Cl and Na are from the PBS. (d) Raw CL image and (e) PC image of a cell observed at E = 1.2 kV. (f) CL image spatially bandpass-filtered at 1/100 – 1/75 pixel−1. Both bright cytoplasmic granules (A and B) and dark CuO NPs (C) are visible in (d). However, another feature should be noted here; microstructures of the adhesion surface can be seen even in (d), but are very clear in the filtered image in (f). Cell D in (e) is not seen in (d), because the cell is spherical and in contact with the emitting layer at only a small point. Observation conditions of the CL images (E, Xp, Td) are (a) 1.0 kV, 40 nm, 0.5 ms and (d) 1.2 kV, 60 nm, 1 ms. Scale bars: (a) and (b) 5 μm, (d) – (f) 10 μm.

Fig. 7
Fig. 7

Typical CL intensity distributions for inorganic and organic emitting materials: (a) ZnS:Ag (0.6 wt%) annealed at 1000°C for 0.5 h, (b) ZnS:Ag (0.6 wt%) treated with rapid thermal annealing (RTA) at 800°C for 10 s, (c) ZnO treated with RTA at 700°C for 50 s, and (d) PVK:C6 (1 wt%). The CL image in (d) shows the intensity distribution only due to the shot noise, and is suited to a plain screen for visualizing nanometric features of the specimen. The film thicknesses tm and te, and observation conditions E, Xp, and Td are as follows: (a) 100 nm, 40 nm, 3 kV, 15 nm, 10 ms; (b) 100 nm, 40 nm, 5 kV, 15 nm, 1 ms; (c) 100 nm, 40 nm, 5 kV, 15 nm, 10 ms; and (d) 20 nm, 44 nm, 0.9 kV, 30 nm, 16 ms. Scale bars: 500 nm.

Fig. 8
Fig. 8

(a) Rays in the xz plane with an intensity higher than 0.2 of that of the original rays are shown for θ = 0, 5, ..., 90°. Right: magnification around the membrane. Emission at high angles is reflected off the sloped surfaces of the Si frame and directed toward the PMT. The coordinate system is shown in the inset of (b). The rays that reach the detector are shown in red, and those do not in blue. Due to the total internal reflection in the exit window, rays at θ ≃ 45° cannot be captured. The shield window on the PMT is a quartz plate coated with an indium tin oxide for shielding the electric field caused by the high voltage applied to the photocathode of the PMT; however, this also contributes to guide the rays to the PMT. (b) The fraction of the power that reaches the PMT compared to rays with a unit intensity emitted in the direction of (ϕ, θ). Right: intensity integrated over ϕ, I(θ), is plotted in the form of I(θ)sinθ. The area surrounded by the curve gives the total detected power.

Fig. 9
Fig. 9

Dependence of the image contrast (upper) and peak width (lower) for spheres with a diameter 2a = 100 nm on the refractive index contrast at λ = 550 nm. The values of the index contrast correspond to PS or SiO2 spheres in water or vacuum, as denoted in the lower panel. The particle size 2a = 100 nm is also shown by the horizontal line in the lower panel. Spheres placed on the emitting surface (d = 0 nm) are observed as their actual sizes irrespective of the refractive indices of the sphere and the surrounding medium.

Fig. 10
Fig. 10

Viability of 165 cells observed under various EB conditions. The data are plotted with small horizontal shifts so that all the results can be seen. Typical beam current was 45 – 85 pA, and the values of D were adjusted by changing Td in the range of 0.02 – 4 ms. The dose was determined by the measured electron transmittance. The pixel size was Xp = 60 nm. Results for cells filled with both PBS and DMEM are shown in the figure, as there was no difference between them. The cells in this work were observed under EB conditions within the green line.

Fig. 11
Fig. 11

(a) The PC image after the acquisition of the CL image, (b) that after the double staining, (c) the fluorescence image for calcein-AM, and (d) that for PI. The cell shrank at each stage but it was found to be alive. During the disassembly of the EC and the double staining, another cell nearby was detached and moved into the field of view. (e) – (h) A cell observed using an EB with E = 3 kV and D = 28 electrons/nm2. (e) The PC image before the acquisition of the CL image, (f) that after the CL observation, (g) the fluorescence image for calcein-AM, and (h) that for PI. The fluorescence images were obtained and displayed under the same conditions as (c) and (d). The nucleus of the cell is stained by PI, and this cell is found to be dead. (i) The CL and (j) SE images obtained by EB scanning in the square area in (e). Xp = 60 nm and Td = 1 ms. Scale bars: 10 μm.

Fig. 12
Fig. 12

Typical CL image of dried cells. The square area in (a) is magnified in (b). The profiles between the arrowheads denoted by A and B in (b) are shown in (c). Observation conditions are E = 1.2 kV, Xp = 60 nm, and Td = 1 ms. Scale bars: (a) 10 μm, (b) 5 μm.

Equations (1)

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η tot = η e l × ( E / E l ) × η p h × η ext × η col × η det ,

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