Abstract

Optimization of illumination and detection optics is pivotal for multiphoton imaging in highly scattering tissue and the objective lens is the central component in both of these pathways. To better understand how basic lens parameters (NA, magnification, field number) affect fluorescence collection and image quality, a two-detector setup was used with a specialized sample cell to separate measurement of total excitation from epifluorescence collection. Our data corroborate earlier findings that low-mag lenses can be superior at collecting scattered photons, and we compare a set of commonly used multiphoton objective lenses in terms of their ability to collect scattered fluorescence, providing guidance for the design of multiphoton imaging systems. For example, our measurements of epi-fluorescence beam divergence in the presence of scattering reveal minimal beam broadening, indicating that often-advocated over-sized collection optics are not as advantageous as previously thought. These experiments also provide a framework for choosing objective lenses for multiphoton imaging by relating the results of our measurements to various design parameters of the objectives lenses used.

© 2015 Optical Society of America

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References

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2013 (2)

N. G. Horton, K. Wang, D. Kobat, C. G. Clark, F. W. Wise, C. B. Schaffer, and C. Xu, “In vivo three-photon microscopy of subcortical structures within an intact mouse brain,” Nat. Photonics 7(3), 205–209 (2013).
[Crossref] [PubMed]

S. L. Jacques, “Optical properties of biological tissues: a review,” Phys. Med. Biol. 58(11), R37–R61 (2013).
[Crossref] [PubMed]

2011 (3)

D. Kobat, N. G. Horton, and C. Xu, “In vivo two-photon microscopy to 1.6-mm depth in mouse cortex,” J. Biomed. Opt. 16(10), 106014 (2011).
[Crossref] [PubMed]

J. D. McMullen, A. C. Kwan, R. M. Williams, and W. R. Zipfel, “Enhancing collection efficiency in large field of view multiphoton microscopy,” J. Microsc. 241(2), 119–124 (2011).
[Crossref] [PubMed]

J. P. Zinter and M. J. Levene, “Maximizing fluorescence collection efficiency in multiphoton microscopy,” Opt. Express 19(16), 15348–15362 (2011).
[Crossref] [PubMed]

2010 (1)

2009 (1)

2007 (1)

C. A. Combs, A. V. Smirnov, J. D. Riley, A. H. Gandjbakhche, J. R. Knutson, and R. S. Balaban, “Optimization of multiphoton excitation microscopy by total emission detection using a parabolic light reflector,” J. Microsc. 228(3), 330–337 (2007).
[Crossref] [PubMed]

2006 (2)

2005 (1)

A. Diaspro, G. Chirico, and M. Collini, “Two-photon fluorescence excitation and related techniques in biological microscopy,” Q. Rev. Biophys. 38(2), 97–166 (2005).
[Crossref] [PubMed]

2003 (2)

W. R. Zipfel, R. M. Williams, and W. W. Webb, “Nonlinear magic: multiphoton microscopy in the biosciences,” Nat. Biotechnol. 21(11), 1369–1377 (2003).
[Crossref] [PubMed]

P. Theer, M. T. Hasan, and W. Denk, “Two-photon imaging to a depth of 1000 microm in living brains by use of a Ti:Al2O3 regenerative amplifier,” Opt. Lett. 28(12), 1022–1024 (2003).
[Crossref] [PubMed]

2002 (1)

2001 (3)

A. Hopt and E. Neher, “Highly Nonlinear Photodamage in Two-Photon Fluorescence Microscopy,” Biophys. J. 80(4), 2029–2036 (2001).
[Crossref] [PubMed]

M. Oheim, E. Beaurepaire, E. Chaigneau, J. Mertz, and S. Charpak, “Two-photon microscopy in brain tissue: parameters influencing the imaging depth,” J. Neurosci. Methods 111(1), 29–37 (2001).
[Crossref] [PubMed]

E. Beaurepaire, M. Oheim, and J. Mertz, “Ultra-deep two-photon fluorescence excitation in turbid media,” Opt. Commun. 188(1-4), 25–29 (2001).
[Crossref]

2000 (2)

1998 (1)

1990 (2)

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248(4951), 73–76 (1990).
[Crossref] [PubMed]

W. Cheong, S. A. Prahl, and A. J. Welch, “A Review of the Optical Properties of Biological Tissues,” IEEE J. Quantum Electron. 26(12), 2166–2185 (1990).
[Crossref]

1987 (1)

1959 (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

Balaban, R. S.

C. A. Combs, A. V. Smirnov, J. D. Riley, A. H. Gandjbakhche, J. R. Knutson, and R. S. Balaban, “Optimization of multiphoton excitation microscopy by total emission detection using a parabolic light reflector,” J. Microsc. 228(3), 330–337 (2007).
[Crossref] [PubMed]

Bartol, T. M.

Beaurepaire, E.

E. Beaurepaire and J. Mertz, “Epifluorescence collection in two-photon microscopy,” Appl. Opt. 41(25), 5376–5382 (2002).
[Crossref] [PubMed]

M. Oheim, E. Beaurepaire, E. Chaigneau, J. Mertz, and S. Charpak, “Two-photon microscopy in brain tissue: parameters influencing the imaging depth,” J. Neurosci. Methods 111(1), 29–37 (2001).
[Crossref] [PubMed]

E. Beaurepaire, M. Oheim, and J. Mertz, “Ultra-deep two-photon fluorescence excitation in turbid media,” Opt. Commun. 188(1-4), 25–29 (2001).
[Crossref]

Berns, M. W.

Chaigneau, E.

M. Oheim, E. Beaurepaire, E. Chaigneau, J. Mertz, and S. Charpak, “Two-photon microscopy in brain tissue: parameters influencing the imaging depth,” J. Neurosci. Methods 111(1), 29–37 (2001).
[Crossref] [PubMed]

Charpak, S.

M. Oheim, E. Beaurepaire, E. Chaigneau, J. Mertz, and S. Charpak, “Two-photon microscopy in brain tissue: parameters influencing the imaging depth,” J. Neurosci. Methods 111(1), 29–37 (2001).
[Crossref] [PubMed]

Cheong, W.

W. Cheong, S. A. Prahl, and A. J. Welch, “A Review of the Optical Properties of Biological Tissues,” IEEE J. Quantum Electron. 26(12), 2166–2185 (1990).
[Crossref]

Chirico, G.

A. Diaspro, G. Chirico, and M. Collini, “Two-photon fluorescence excitation and related techniques in biological microscopy,” Q. Rev. Biophys. 38(2), 97–166 (2005).
[Crossref] [PubMed]

Clark, C. G.

N. G. Horton, K. Wang, D. Kobat, C. G. Clark, F. W. Wise, C. B. Schaffer, and C. Xu, “In vivo three-photon microscopy of subcortical structures within an intact mouse brain,” Nat. Photonics 7(3), 205–209 (2013).
[Crossref] [PubMed]

Coleno, M.

Collini, M.

A. Diaspro, G. Chirico, and M. Collini, “Two-photon fluorescence excitation and related techniques in biological microscopy,” Q. Rev. Biophys. 38(2), 97–166 (2005).
[Crossref] [PubMed]

Combs, C. A.

C. A. Combs, A. V. Smirnov, J. D. Riley, A. H. Gandjbakhche, J. R. Knutson, and R. S. Balaban, “Optimization of multiphoton excitation microscopy by total emission detection using a parabolic light reflector,” J. Microsc. 228(3), 330–337 (2007).
[Crossref] [PubMed]

Denk, W.

Diaspro, A.

A. Diaspro, G. Chirico, and M. Collini, “Two-photon fluorescence excitation and related techniques in biological microscopy,” Q. Rev. Biophys. 38(2), 97–166 (2005).
[Crossref] [PubMed]

Dunn, A. K.

Engelbrecht, C. J.

Gandjbakhche, A. H.

C. A. Combs, A. V. Smirnov, J. D. Riley, A. H. Gandjbakhche, J. R. Knutson, and R. S. Balaban, “Optimization of multiphoton excitation microscopy by total emission detection using a parabolic light reflector,” J. Microsc. 228(3), 330–337 (2007).
[Crossref] [PubMed]

Göbel, W.

Hasan, M. T.

Hell, S. W.

Helmchen, F.

Hopt, A.

A. Hopt and E. Neher, “Highly Nonlinear Photodamage in Two-Photon Fluorescence Microscopy,” Biophys. J. 80(4), 2029–2036 (2001).
[Crossref] [PubMed]

Horton, N. G.

N. G. Horton, K. Wang, D. Kobat, C. G. Clark, F. W. Wise, C. B. Schaffer, and C. Xu, “In vivo three-photon microscopy of subcortical structures within an intact mouse brain,” Nat. Photonics 7(3), 205–209 (2013).
[Crossref] [PubMed]

D. Kobat, N. G. Horton, and C. Xu, “In vivo two-photon microscopy to 1.6-mm depth in mouse cortex,” J. Biomed. Opt. 16(10), 106014 (2011).
[Crossref] [PubMed]

Jacques, S. L.

S. L. Jacques, “Optical properties of biological tissues: a review,” Phys. Med. Biol. 58(11), R37–R61 (2013).
[Crossref] [PubMed]

Knutson, J. R.

C. A. Combs, A. V. Smirnov, J. D. Riley, A. H. Gandjbakhche, J. R. Knutson, and R. S. Balaban, “Optimization of multiphoton excitation microscopy by total emission detection using a parabolic light reflector,” J. Microsc. 228(3), 330–337 (2007).
[Crossref] [PubMed]

Kobat, D.

N. G. Horton, K. Wang, D. Kobat, C. G. Clark, F. W. Wise, C. B. Schaffer, and C. Xu, “In vivo three-photon microscopy of subcortical structures within an intact mouse brain,” Nat. Photonics 7(3), 205–209 (2013).
[Crossref] [PubMed]

D. Kobat, N. G. Horton, and C. Xu, “In vivo two-photon microscopy to 1.6-mm depth in mouse cortex,” J. Biomed. Opt. 16(10), 106014 (2011).
[Crossref] [PubMed]

Kwan, A. C.

J. D. McMullen, A. C. Kwan, R. M. Williams, and W. R. Zipfel, “Enhancing collection efficiency in large field of view multiphoton microscopy,” J. Microsc. 241(2), 119–124 (2011).
[Crossref] [PubMed]

Levene, M. J.

Matthews, H. J.

McMullen, J. D.

J. D. McMullen, A. C. Kwan, R. M. Williams, and W. R. Zipfel, “Enhancing collection efficiency in large field of view multiphoton microscopy,” J. Microsc. 241(2), 119–124 (2011).
[Crossref] [PubMed]

J. D. McMullen and W. R. Zipfel, “A multiphoton objective design with incorporated beam splitter for enhanced fluorescence collection,” Opt. Express 18(6), 5390–5398 (2010).
[Crossref] [PubMed]

Mertz, J.

E. Beaurepaire and J. Mertz, “Epifluorescence collection in two-photon microscopy,” Appl. Opt. 41(25), 5376–5382 (2002).
[Crossref] [PubMed]

M. Oheim, E. Beaurepaire, E. Chaigneau, J. Mertz, and S. Charpak, “Two-photon microscopy in brain tissue: parameters influencing the imaging depth,” J. Neurosci. Methods 111(1), 29–37 (2001).
[Crossref] [PubMed]

E. Beaurepaire, M. Oheim, and J. Mertz, “Ultra-deep two-photon fluorescence excitation in turbid media,” Opt. Commun. 188(1-4), 25–29 (2001).
[Crossref]

Neher, E.

A. Hopt and E. Neher, “Highly Nonlinear Photodamage in Two-Photon Fluorescence Microscopy,” Biophys. J. 80(4), 2029–2036 (2001).
[Crossref] [PubMed]

Oheim, M.

M. Oheim, E. Beaurepaire, E. Chaigneau, J. Mertz, and S. Charpak, “Two-photon microscopy in brain tissue: parameters influencing the imaging depth,” J. Neurosci. Methods 111(1), 29–37 (2001).
[Crossref] [PubMed]

E. Beaurepaire, M. Oheim, and J. Mertz, “Ultra-deep two-photon fluorescence excitation in turbid media,” Opt. Commun. 188(1-4), 25–29 (2001).
[Crossref]

Patterson, G. H.

G. H. Patterson and D. W. Piston, “Photobleaching in Two-Photon Excitation Microscopy,” Biophys. J. 78(4), 2159–2162 (2000).
[Crossref] [PubMed]

Piston, D. W.

G. H. Patterson and D. W. Piston, “Photobleaching in Two-Photon Excitation Microscopy,” Biophys. J. 78(4), 2159–2162 (2000).
[Crossref] [PubMed]

Prahl, S. A.

W. Cheong, S. A. Prahl, and A. J. Welch, “A Review of the Optical Properties of Biological Tissues,” IEEE J. Quantum Electron. 26(12), 2166–2185 (1990).
[Crossref]

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

Riley, J. D.

C. A. Combs, A. V. Smirnov, J. D. Riley, A. H. Gandjbakhche, J. R. Knutson, and R. S. Balaban, “Optimization of multiphoton excitation microscopy by total emission detection using a parabolic light reflector,” J. Microsc. 228(3), 330–337 (2007).
[Crossref] [PubMed]

Schaffer, C. B.

N. G. Horton, K. Wang, D. Kobat, C. G. Clark, F. W. Wise, C. B. Schaffer, and C. Xu, “In vivo three-photon microscopy of subcortical structures within an intact mouse brain,” Nat. Photonics 7(3), 205–209 (2013).
[Crossref] [PubMed]

Schönle, A.

Sejnowski, T. J.

Sheppard, C. J. R.

Smirnov, A. V.

C. A. Combs, A. V. Smirnov, J. D. Riley, A. H. Gandjbakhche, J. R. Knutson, and R. S. Balaban, “Optimization of multiphoton excitation microscopy by total emission detection using a parabolic light reflector,” J. Microsc. 228(3), 330–337 (2007).
[Crossref] [PubMed]

Strickler, J. H.

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248(4951), 73–76 (1990).
[Crossref] [PubMed]

Theer, P.

Tromberg, B. J.

Vucinic, D.

Wallace, V. P.

Wang, K.

N. G. Horton, K. Wang, D. Kobat, C. G. Clark, F. W. Wise, C. B. Schaffer, and C. Xu, “In vivo three-photon microscopy of subcortical structures within an intact mouse brain,” Nat. Photonics 7(3), 205–209 (2013).
[Crossref] [PubMed]

Webb, W. W.

W. R. Zipfel, R. M. Williams, and W. W. Webb, “Nonlinear magic: multiphoton microscopy in the biosciences,” Nat. Biotechnol. 21(11), 1369–1377 (2003).
[Crossref] [PubMed]

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248(4951), 73–76 (1990).
[Crossref] [PubMed]

Welch, A. J.

W. Cheong, S. A. Prahl, and A. J. Welch, “A Review of the Optical Properties of Biological Tissues,” IEEE J. Quantum Electron. 26(12), 2166–2185 (1990).
[Crossref]

Williams, R. M.

J. D. McMullen, A. C. Kwan, R. M. Williams, and W. R. Zipfel, “Enhancing collection efficiency in large field of view multiphoton microscopy,” J. Microsc. 241(2), 119–124 (2011).
[Crossref] [PubMed]

W. R. Zipfel, R. M. Williams, and W. W. Webb, “Nonlinear magic: multiphoton microscopy in the biosciences,” Nat. Biotechnol. 21(11), 1369–1377 (2003).
[Crossref] [PubMed]

Wise, F. W.

N. G. Horton, K. Wang, D. Kobat, C. G. Clark, F. W. Wise, C. B. Schaffer, and C. Xu, “In vivo three-photon microscopy of subcortical structures within an intact mouse brain,” Nat. Photonics 7(3), 205–209 (2013).
[Crossref] [PubMed]

Wolf, E.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

Xu, C.

N. G. Horton, K. Wang, D. Kobat, C. G. Clark, F. W. Wise, C. B. Schaffer, and C. Xu, “In vivo three-photon microscopy of subcortical structures within an intact mouse brain,” Nat. Photonics 7(3), 205–209 (2013).
[Crossref] [PubMed]

D. Kobat, N. G. Horton, and C. Xu, “In vivo two-photon microscopy to 1.6-mm depth in mouse cortex,” J. Biomed. Opt. 16(10), 106014 (2011).
[Crossref] [PubMed]

Zinter, J. P.

Zipfel, W. R.

J. D. McMullen, A. C. Kwan, R. M. Williams, and W. R. Zipfel, “Enhancing collection efficiency in large field of view multiphoton microscopy,” J. Microsc. 241(2), 119–124 (2011).
[Crossref] [PubMed]

J. D. McMullen and W. R. Zipfel, “A multiphoton objective design with incorporated beam splitter for enhanced fluorescence collection,” Opt. Express 18(6), 5390–5398 (2010).
[Crossref] [PubMed]

W. R. Zipfel, R. M. Williams, and W. W. Webb, “Nonlinear magic: multiphoton microscopy in the biosciences,” Nat. Biotechnol. 21(11), 1369–1377 (2003).
[Crossref] [PubMed]

Appl. Opt. (2)

Biophys. J. (2)

G. H. Patterson and D. W. Piston, “Photobleaching in Two-Photon Excitation Microscopy,” Biophys. J. 78(4), 2159–2162 (2000).
[Crossref] [PubMed]

A. Hopt and E. Neher, “Highly Nonlinear Photodamage in Two-Photon Fluorescence Microscopy,” Biophys. J. 80(4), 2029–2036 (2001).
[Crossref] [PubMed]

IEEE J. Quantum Electron. (1)

W. Cheong, S. A. Prahl, and A. J. Welch, “A Review of the Optical Properties of Biological Tissues,” IEEE J. Quantum Electron. 26(12), 2166–2185 (1990).
[Crossref]

J. Biomed. Opt. (1)

D. Kobat, N. G. Horton, and C. Xu, “In vivo two-photon microscopy to 1.6-mm depth in mouse cortex,” J. Biomed. Opt. 16(10), 106014 (2011).
[Crossref] [PubMed]

J. Microsc. (2)

C. A. Combs, A. V. Smirnov, J. D. Riley, A. H. Gandjbakhche, J. R. Knutson, and R. S. Balaban, “Optimization of multiphoton excitation microscopy by total emission detection using a parabolic light reflector,” J. Microsc. 228(3), 330–337 (2007).
[Crossref] [PubMed]

J. D. McMullen, A. C. Kwan, R. M. Williams, and W. R. Zipfel, “Enhancing collection efficiency in large field of view multiphoton microscopy,” J. Microsc. 241(2), 119–124 (2011).
[Crossref] [PubMed]

J. Neurosci. Methods (1)

M. Oheim, E. Beaurepaire, E. Chaigneau, J. Mertz, and S. Charpak, “Two-photon microscopy in brain tissue: parameters influencing the imaging depth,” J. Neurosci. Methods 111(1), 29–37 (2001).
[Crossref] [PubMed]

J. Opt. Soc. Am. A (2)

Nat. Biotechnol. (1)

W. R. Zipfel, R. M. Williams, and W. W. Webb, “Nonlinear magic: multiphoton microscopy in the biosciences,” Nat. Biotechnol. 21(11), 1369–1377 (2003).
[Crossref] [PubMed]

Nat. Photonics (1)

N. G. Horton, K. Wang, D. Kobat, C. G. Clark, F. W. Wise, C. B. Schaffer, and C. Xu, “In vivo three-photon microscopy of subcortical structures within an intact mouse brain,” Nat. Photonics 7(3), 205–209 (2013).
[Crossref] [PubMed]

Opt. Commun. (1)

E. Beaurepaire, M. Oheim, and J. Mertz, “Ultra-deep two-photon fluorescence excitation in turbid media,” Opt. Commun. 188(1-4), 25–29 (2001).
[Crossref]

Opt. Express (3)

Opt. Lett. (3)

Phys. Med. Biol. (1)

S. L. Jacques, “Optical properties of biological tissues: a review,” Phys. Med. Biol. 58(11), R37–R61 (2013).
[Crossref] [PubMed]

Proc. R. Soc. Lond. A Math. Phys. Sci. (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

Q. Rev. Biophys. (1)

A. Diaspro, G. Chirico, and M. Collini, “Two-photon fluorescence excitation and related techniques in biological microscopy,” Q. Rev. Biophys. 38(2), 97–166 (2005).
[Crossref] [PubMed]

Science (1)

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248(4951), 73–76 (1990).
[Crossref] [PubMed]

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Figures (5)

Fig. 1
Fig. 1 (a) Diagram of illumination photons propagating from the Objective Front Aperture (OFA) to the objective focus. The flux through a ring of radius R(θ) at the OFA propagates a total distance of wd / cos θ, of which L(θ) = z0 / cos θ is below the specimen surface, where θ ranges from 0 to θNA. (b) Schematic of the fluorescence beam exiting the Objective Back Aperture (OBA), showing a relatively collimated beam when imaging in a clear specimen and a more divergent beam when imaging in turbid samples.
Fig. 2
Fig. 2 (a) Experimental apparatus used to measure lens transmittance. A small pinhole was used to create a thin “beam” of white light which was incident on the OFA of an objective lens. Light transmitted through the objective was collected by an integrating sphere and relayed to a spectrometer using an optical fiber. (b) Transmittance curves were generated by taking a ratio of the spectrometer counts at each wavelength when the objective was in place and removed from the apparatus. Newer lenses show substantially better transmission than the earliest version of the Olympus 20x/0.95W we used in these measurements.
Fig. 3
Fig. 3 (a) Experimental setup for two-channel detection of epi-collected and transmitted fluorescence. Laser illumination was focused through a scattering medium into a solution of fluorescein. Emissions were collected in both epifluorescence and transmission channels. A confocal pinhole in the lower path was used to reject any back-scattered light from the bead layer. An iris in the upper channel was adjusted to controllably vignette the beam in order to measure the emission beam divergence. (b) Plot of fluorescence detected in the transmitted light channel as a function of power out of the objective lens without added scatterer. All data (with and without scatterer) fit well to F = aP2, where a = ηγ2. η is the fraction of emission collected by the lower channel times excitation-related parameters (Eq. (4)) and γ is the fraction of ballistic photons lost (squared for two-photon excitation). For the data in 3b without added scatterer, γ = 1. (c) Calculated two-photon excitation potential within the focal volume as a function of NA for diffraction limited and under-filled back apertures demonstrating the NA-dependence of nonlinear excitation for a diffraction limited focal volume. The intensity PSF was calculated using the method of Richards and Wolf [16] modified to take OBA under-filling into account. The 3D intensity PSF was then squared, integrated and divided by the focal plane beam area (Eq. (6)). Data is normalized to the diffraction-limited (β = 0) case for lowest NA used in the calculation (0.25). β = 3 approaches the expected paraxial limit under which the two-photon excitation is independent of NA. Inset: Predicted relative net epifluorescence collection for the diffraction-limited (black line) and paraxial (blue line) cases, calculated as the fractional solid angle x two-photon excitation potential as a function of NA. (d) Comparison of experimental values for the ballistic fraction of illumination squared (γ2) for two different values of zs and zs’ to the theory presented in Eq. (3). Black lines and symbols (X’s) are calculations and measurements, respectively, made with scattering conditions of zs = 1.6 (dotted line) and zs’ = 0.16 (g = 0.9, solid line) at 800 nm. Blue lines and symbols are for scattering conditions of zs = 2.7 (dotted line) and zs’ = 0.27 (solid line) at 800 nm.
Fig. 4
Fig. 4 Epi-collection objective lens characteristics in scattering media. (a) Ratios of counts in the epifluorescence channel to counts in the transmission channel for each lens at zs = 0 (water), 3 and 5, showing the decrease in epi-collection efficiencies as a function of sample scattering. (b) Normalized ratios (relative to zs = 0 value for each lens) with data taken over a larger number of zs values. Error bars are SEM (n = 4). (c and d) Correlation between the scattering dependent epi-collected signal decay with objective lens OBA/OFA ratios (c) and objective field number (d). Signal decay lengths for each objective lens were obtained from fits of the data in (b) to a single exponential decay model: y0 + exp(-(zs-zs,0)/ε) to parametrize the scattering loses through each lens. Each lens is colored coded as indicated by the key in (b). (e) Measured epi-collected fluorescence emission beam 1/e2 radius 100 mm from the OBA as a function of solution scattering (zs = 0, 3, and 5) and objective lens. The corresponding angular divergence values are noted at top of each bar. (f and g) Correlation between the measured emission divergence angle and the OBA/OFA ratio (f) and field number (g). (h) Diagram illustrating the effect of the divergence for each lens measured at zs = 5 (worst case scenario) 200 mm from the OBA (where a detector might typically be placed).
Fig. 5
Fig. 5 (a) Excitation power needed to achieve 500,000 counts/second in the epifluorescence channel as a function of zs. (b) Drop-off in integrated bead intensity (n = 3) when imaging fluorescent beads embedded in agarose with added polystyrene microspheres to vary zs.

Tables (1)

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Table 1 Objective lens properties of lenses used in this study.

Equations (7)

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F= 1 2 ϕ F σ 2P C(r) < I 2 (r,t)>dr= C avg σ 2P * g p Rτ ( Pλ hc ) 2 ( area PSF(x,y,0,NA,λ)dxdy ) 2 ( volume PSF (x,y,z,NA,λ) 2 dxdydz )
γ= 2π 0 r OFA R(θ) I 0 e L(θ) l s ( λ exc ) dR 2π 0 r OFA R(θ) I 0 dR
γ= 0 θ NA tanθ sec 2 θ e z 0 l s ( λ exc )cosθ dθ 0 θ NA tanθ sec 2 θdθ = 2 tan 2 ( θ NA ) [ ( 1+ z 0 l s ( λ exc )cos( θ NA ) ) e Z 0 l s ( λ exc )cos( θ NA ) ( 1+ z 0 l s ( λ exc ) ) e Z 0 l s ( λ exc ) ]
F= C avg σ 2P * g p Rτ ( γPλ hc ) 2 ( area PSF(x,y,0,NA,λ)dxdy ) 2 ( volume PSF (x,y,z,NA,λ) 2 dxdydz )
Ω f ( NA,n )= 1 1 ( NA n ) 2 2
Focal volume 2P excitation potential volume PSF (x,y,z,NA,λ) 2 dxdydz ( area PSF(x,y,0,NA,λ)dxdy ) 2
OBA OFA = 2NA f obj 2wdtan( θ NA ) = f reftubelens n 1 ( NA n ) 2 Mag×wd

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