Abstract

We show that the position of single molecules in all three spatial dimensions can be estimated alongside its emission color by diffractive optics based design of the Point Spread Function (PSF). The phase in a plane conjugate to the aperture stop of the objective lens is modified by a diffractive structure that splits the spot on the camera into closely spaced diffraction orders. The distance between and the size of these sub-spots are a measure of the emission color. Estimation of the axial position is enabled by imprinting aberrations such as astigmatism and defocus onto the orders. The overall spot shape is fitted with a fully vectorial PSF model. Proof-of-principle experiments on quantum dots indicate that a spectral precision of 10 to 20 nm, an axial localization precision of 25 to 50 nm, and a lateral localization precision of 10 to 30 nm can be achieved over a 1 μm range of axial positions for on average 800 signal photons and 17 background photons/pixel. The method appears to be rather sensitive to PSF model errors such as aberrations, giving in particular rise to biases in the fitted wavelength of up to 15 nm.

© 2016 Optical Society of America

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2015 (6)

C. C. Valley, S. Liu, D. S. Lidke, and K. A. Lidke, “Sequential superresolution imaging of multiple targets using a single fluorophore,” PLoS One 10, e0123941 (2015).
[Crossref] [PubMed]

Z. Zhang, S. J. Kenny, M. Hauser, W. Li, and K. Xu, “Ultrahigh-throughput single-molecule spectroscopy and spectrally resolved super-resolution microscopy,” Nat. Meth. 12, 935–938 (2015).
[Crossref]

Y. Shechtman, L. E. Weiss, A. S. Backer, S. J. Sahl, and W. E. Moerner, “Precise 3D scan-free multiple-particle tracking over large axial ranges with tetrapod point spread functions,” Nano Lett. 15, 4194–4199 (2015).
[Crossref] [PubMed]

S. Stallinga, “Single emitter localization analysis in the presence of background,” Proc. SPIE 9630, 96300V (2015).
[Crossref]

C. S. Smith, S. Stallinga, K. A. Lidke, B. Rieger, and D. Grünwald, “Probability-based particle detection that enables threshold-free and robust in vivo single molecule tracking,” Mol. Biol. Cell. 26(22), 4057–4062 (2015).
[Crossref] [PubMed]

S. Stallinga, “Effect of rotational diffusion in an orientational potential well on the point spread function of electric dipole emitters,” J. Opt. Soc. Am. A,  32, 213–223 (2015).
[Crossref]

2014 (8)

M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, and W. E. Moerner, “The role of molecular dipole orientation in single-molecule fluorescence microscopy and implications for super-resolution imaging,” Chem. Phys. Chem. 15, 587–599 (2014).
[PubMed]

C. Roider, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “Axial super-localisation using rotating point spread functions shaped by polarisation-dependent phase modulation,” Opt. Express 22, 4029–4037 (2014).
[Crossref] [PubMed]

J. Broeken, B. Rieger, and S. Stallinga, “Simultaneous measurement of position and color of single fluorescent emitters using diffractive optics,” Opt. Lett. 39, 3352–3355 (2014).
[Crossref] [PubMed]

B. Rieger and S. Stallinga, “The lateral and axial localization uncertainty in super-resolution light microscopy,” Chem. Phys. Chem. 15, 664–670, (2014).

Y. Shechtman, S. J. Sahl, A. S. Backer, and W. E. Moerner, “Optimal point spread function design for 3D imaging,” Phys. Rev. Lett. 113, 133902 (2014).
[Crossref] [PubMed]

S. Jia, J. C. Vaugan, and X. Zhuang, “Isotropic 3D super-resolution imaging with a self-bending point spread function,” Nat. Photonics 8, 302–306 (2014).
[Crossref] [PubMed]

A. S. Backer and W. E. Moerner, “Extending single-molecule microscopy using optical Fourier processing,” J. Phys. Chem. B 118, 8313–8329 (2014).
[Crossref] [PubMed]

J. Tam, G. A. Cordier, J. S. Borbely, Á. S. Álvarez, and M. Lakadamyali, “Cross-talk-free multi-color STORM imaging using a single fluorophore,” PLoS One 9, e101772 (2014).
[Crossref] [PubMed]

2013 (5)

P. J. Cutler, M. D. Malik, S. Liu, J. M. Byars, D. S. Lidke, and K. A. Lidke, “Multi-color quantum dot tracking using a high-speed hyperspectral line-scanning microscope,” PLoS One 8, e64320 (2013).
[Crossref] [PubMed]

R. P. J. Nieuwenhuizen, K. A. Lidke, M. Bates, D. Leyton Puig, D. Grünwald, S. Stallinga, and B. Rieger, “Measuring image resolution in optical nanoscopy,” Nat. Meth. 10, 557–562 (2013).
[Crossref]

F. Huang, T. M. P. Hartwich, F. E. Rivera-Molina, Y. Lin, W. C. Duim, J. J. Long, P. D. Uchil, J. R. Myers, M. A. Baird, W. Mothes, M. W. Davidson, D. Toomre, and J. Bewersdorf, “Video-rate nanoscopy using sCMOS cameraspecific single-molecule localization algorithms,” Nat. Meth. 10, 653–658 (2013).
[Crossref]

S. Prasad, “Rotating point spread function via pupil-phase engineering,” Opt. Lett. 38, 585–587 (2013).
[Crossref] [PubMed]

S. Abrahamsson, J. Chen, B. Haij, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Meth. 10, 60–63 (2013).
[Crossref]

2012 (3)

2011 (1)

D. Baddeley, M. B. Cannell, and C. Soeller, “Three-dimensional sub-100 nm super-resolution imaging of biological samples using a phase ramp in the objective pupil,” Nano Res. 4, 589–598 (2011).
[Crossref]

2010 (5)

K. I. Mortensen, L. Stirling Churchman, J. A. Spudich, and H. Flyvbjerg, “Optimized localization analysis for single-molecule tracking and super-resolution microscopy,” Nat. Meth. 7, 377–381 (2010).
[Crossref]

C. S. Smith, N. Joseph, B. Rieger, and K. A. Lidke, “Fast, single-molecule localization that achieves theoretically minimum uncertainty,” Nat. Meth. 7, 373–375 (2010).
[Crossref]

I. Testa, C. A. Wurm, R. Medda, E. Rothermel, C. von Middendorf, J. Fölling, S. Jakobs, A. Schönle, S. W. Hell, and C. Eggeling, “Multicolor fluorescence nanoscopy in fixed and living cells by exciting conventional fluorophores with a single wavelength,” Biophys. J. 99, 2686–2694 (2010).
[Crossref] [PubMed]

D. Grünwald and R. H. Singer, “In vivo imaging of labelled endogenous β-actin mRNA during nucleocytoplasmic transport,” Nature 467, 604–607 (2010).
[Crossref]

S. Stallinga and B. Rieger, “Accuracy of the Gaussian point spread function model in 2D localization microscopy,” Opt. Express 18, 24461–24476 (2010).
[Crossref] [PubMed]

2009 (3)

M. J. Mlodzianoski, M. F. Juette, G. L. Beane, and J. Bewersdorf, “Experimental characterization of 3D localization techniques for particle-tracking and super-resolution microscopy,” Opt. Express 17, 8264–8277 (2009).
[Crossref] [PubMed]

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 106, 2995–2999 (2009).
[Crossref] [PubMed]

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. 106, 3125–3130 (2009).
[Crossref] [PubMed]

2008 (5)

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319, 810–813 (2008).
[Crossref] [PubMed]

S. Ram, P. Prabhat, J. Chao, E. S. Ward, and R. J. Ober, “High accuracy 3D quantum dot tracking with multifocal plane microscopy for the study of fast intracellular dynamics in live cells,” Biophys. J. 95, 6025–6043 (2008).
[Crossref] [PubMed]

M.F. Juette, T.J. Gould, M.D. Lessard, M.J. Mlodzianoski, B.S. Nagpure, B.T. Bennett, S.T. Hess, and J. Bewersdorf, “Three-dimensional sub-100nm resolution fluorescence microscopy of thick samples,” Nat. Meth. 5, 527–530 (2008).
[Crossref]

M. Bossi, J. Folling, V. N. Belov, V. P. Boyarskiy, R. Medda, A. Egner, C. Eggeling, A. Schonle, and S. W. Hell, “Multicolor far-field fluorescence nanoscopy through isolated detection of distinct molecular species,” Nano Lett. 8, 2463–2468 (2008).
[Crossref] [PubMed]

S. R. P. Pavani and R. Piestun, “Three dimensional tracking of fluorescent microparticles using a photon-limited double-helix response system,” Opt. Express 16, 22048–22057 (2008).
[Crossref] [PubMed]

2007 (5)

S. W. Hell, “Far-field optical nanoscopy,” Science 316, 1153–1158 (2007).
[Crossref] [PubMed]

H. Shroff, C. G. Galbraith, J. A. Galbraith, H. White, J. Gillette, S. Olenych, M. W. Davidson, and E. Betzig, “Dual-color superresolution imaging of genetically expressed probes within individual adhesion complexes,” Proc. Natl. Acad. Sci. U.S.A. 104, 20308–20313 (2007).
[Crossref] [PubMed]

M. Bates, B. Huang, G. T. Dempsey, and X. Zhuang, “Multicolor super-resolution imaging with photo-switchable fluorescent probes,” Science 317, 1749–1753 (2007).
[Crossref] [PubMed]

L. Holtzer, T. Meckel, and T. Schmidt, “Nanometric three-dimensional tracking of individual quantum dots in cells,” Appl. Phys. Lett. 90, 053902 (2007).
[Crossref]

E. Toprak, H. Balci, B. H. Blehm, and P. R. Selvin, “Three-dimensional particle tracking via bifocal imaging,” Nano Lett. 7, 2043–2045 (2007).
[Crossref] [PubMed]

2006 (5)

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 proteins at nanometer resolution,” Science 313, 1643–1645 (2006).
[Crossref]

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Meth. 3, 793–795 (2006).
[Crossref]

S. T. Hess, T. P. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91, 4258–4272 (2006).
[Crossref] [PubMed]

J. Enderlein, E. Toprak, and P. R. Selvin, “Polarization effect on position accuracy of fluorophore localization,” Opt. Express 14, 8111–8120 (2006).
[Crossref] [PubMed]

M. Leutenegger, R. Rao, R. A. Leitgeb, and T. Lasser, “Fast focus field calculations,” Opt. Express 14, 11277–11291 (2006).
[Crossref] [PubMed]

2004 (1)

R. J. Ober, S. Ram, and E. S. Ward, “Localization accuracy in single-molecule microscopy,” Biophys. J. 86, 1185–1200 (2004).
[Crossref] [PubMed]

2002 (1)

J. L. Bakx, “Efficient computation of opical disk readout by use of the chirp z transform,” Appl. Opt. 41, 4879–4903 (2002).
[Crossref]

2000 (2)

R. G. Neuhauser, K. T. Shimizu, W. K. Woo, S. A. Empedocles, and M. G. Bawendi, “Correlation between Fluorescence Intermittency and Spectral Diffusion in Single Semiconductor Quantum Dots,” Phys. Rev. Lett. 85, 3301 (2000).
[Crossref] [PubMed]

X. Deng, B. Bihari, J. Gan, F. Zhao, and R.T. Chen, “Fast algorithm for chirp transforms with zooming-in ability and its applications,” J. Opt. Soc. Am. A,  17, 762–771 (2000).
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Supplementary Material (2)

NameDescription
» Visualization 1: AVI (407 KB)      Through-focus PSFs
» Visualization 2: AVI (544 KB)      QD mix analysis

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Figures (8)

Fig. 1
Fig. 1

Principle of 3D+λ measurement for single emitters. (a) Schematic of the microscope setup. A 4f-relay path is added to the detection branch of a microscope, the SLM is placed conjugate to the back focal plane of the objective lens. (b) The shape of the zones is curved for inducing aberrations to the sub-spots (diffraction orders) captured at the camera. The profile shown is a binary phase profile with phase step close to π in the visible spectrum for splitting the spot into −1st and +1st diffraction order sub-spots, and with zone shapes inducing astigmatism. (c) Modeled spots at the camera plane for different axial positions and emission wavelengths of the emitter. The computation of the spots is over a 2.5μm×1.5μm region discretized with a 125 × 75 grid for a medium refractive index n = 1.33 and a numerical aperture NA = 1.25, with a pupil discretized with a 164 × 164 grid.

Fig. 2
Fig. 2

Phase profile and spot shapes of existing axial localization principles for fitting the emission wavelength λ from the scale of the spot. (a) Double helix PSF, (b) astigmatic PSF. The computation of the spots is over a 1.5μm×1.5μm region discretized with a 75 × 75 grid for a medium refractive index n = 1.33 and a numerical aperture NA = 1.25, with a pupil discretized with a 164 × 164 grid.

Fig. 3
Fig. 3

CRLB in emitter 3D-position and emission wavelength as a function of the z-position of the emitter and the emission wavelength λ for 1500 signal photons and 10 background photons/pixel. (abcd) Diffractive astigmatic PSF using two diffraction orders. (efgh): Double helix PSF. (qrst): astigmatic PSF.

Fig. 4
Fig. 4

Numerically determined fit error and CRLB in the x, y and z-position of the emitter and in the emission wavelength λ as a function of signal photon count for two background levels, (abcd) Diffractive astigmatic PSF case. (efgh) Double helix PSF case, (ijkl) astigmatic PSF case.

Fig. 5
Fig. 5

Simulated effect of non-zero emission bandwidth and of unknown aberrations on fit precision in the x, y and z-position of the emitter and in the emission wavelength λ. (abcd) Precision and CRLB averaged over 100 random instances as a function of the width of Gaussian emission spectrum. (efgh) Precision and CRLB averaged over 100 random instances as a function of the rms value of unknown aberrations.

Fig. 6
Fig. 6

Results on experiments on quantum dots emitting at 525 nm and 585 nm. (abcd) Experimental precision in xyzλ determined from repeated fits of the same quantum dot compared to the CRLB for the fitted parameter values. (ef): Fitted z position and fitted wavelength as a function of stage position, showing a z-dependent bias in the fitted wavelength of up to 15 nm. (g) Histogram of fitted wavelengths for all repeated acquisitions at all focus levels of all QDs (30 × 9 × 5 = 1350 data points).

Fig. 7
Fig. 7

First frame of Visualization 1 showing a focal slice of the experimental through-focus PSF and the corresponding model through-focus PSF for the QD525 and the QD585 species. The orientational misalignment of the SLM with respect to the camera (over an angle of 14 deg) has been incorporated to the fitting routine. The asymmmetry in spot shape between positive and negative defocus is due to spherical aberration (estimated as 0.06λ rms).

Fig. 8
Fig. 8

Frame of Visualization 2 showing the recorded images for different axial positions (left), and the 6 indicated ROIs (right). All images are first contrast stretched and then rendered with an RGB colormap corresponding to the fitted wavelength, so they do not accurately represent the actual signal level. QDs 1, 2, and 4 have the red-amber appearance of the species with emission peak at 585 nm, QDs 4,5, and 6 have the green-yellow appearance of the species with emission peak at 525 nm.

Equations (23)

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j λ 0 K ( ρ ) < ( j + 1 ) λ 0 ,
t = K ( ρ ) λ 0 j = K ( ρ ) λ 0 floor ( K ( ρ ) λ 0 ) ,
W ( ρ ) = f ( t ) = f ( K ( ρ ) λ 0 floor ( K ( ρ ) λ 0 ) ) .
T ( ρ ) = exp ( 2 π λ f ( K ( ρ ) λ 0 floor ( K ( ρ ) λ 0 ) ) ) = 0 1 d t δ ( K ( ρ ) λ 0 floor ( K ( ρ ) λ 0 ) t ) exp ( 2 π i f ( t ) λ ) = 0 1 d t [ m = + exp ( 2 π i m ( K ( ρ ) λ 0 floor ( K ( ρ ) λ 0 ) t ) ) ] exp ( 2 π i f ( t ) λ ) = m = + C m exp ( 2 π i W m ( ρ ) λ ) ,
C m = 0 1 d t exp ( 2 π i m t ) exp ( 2 π i f ( t ) λ ) ,
W m ( ρ ) = m K ( ρ ) λ λ 0 .
K ( ρ ) = A 11 ρ x + 2 A 2 2 ρ x ρ y ,
K ( ρ ) = A 11 ρ x + A 20 ( 2 ( ρ x 2 + ρ y 2 ) 1 ) ,
K ( ρ ) = ( 2 l + 1 ) ϕ / ( 2 π ) ,
log L = k [ ( n k + σ 2 ) log ( μ k + σ 2 ) ( μ k + σ 2 ) log Γ ( n k + σ 2 + 1 ) ] ,
n k = μ k ,
n k 2 n k 2 = μ k + σ 2 .
log L θ j = k n k μ k μ k + σ 2 μ k θ j ,
2 log L θ j θ l = k n k + σ 2 ( μ k + σ 2 ) 2 μ k θ j μ k θ l + k n k μ k μ k + σ 2 2 μ k θ j θ l .
F j l = log L θ j log L θ l = k 1 μ k + σ 2 μ k θ j μ k θ l .
CRLB j = F 1 j j ,
μ k = 𝒟 k d x d y H ( r r 0 ) ,
H ( r ) = N 3 l = x , y j = x , y , z | w i j ( r ) | 2 + b a 2 ,
w l j ( r ) = 1 w n | ρ | 1 d 2 ρ A ( ρ ) exp ( 2 π i W ( ρ ) λ ) q l j ( ρ ) exp ( i k ( ρ ) r ) ,
k ( ρ ) = 2 π λ ( NA ρ x , NA ρ y , n 2 NA 2 ρ 2 ) ,
μ k θ m = 2 N 3 l = x , y j = x , y , z 𝒟 k d x d y Re { w l j ( r r 0 ) * w l j ( r r 0 ) θ m } .
w l j ( r r 0 ) r 0 = i w n | ρ | 1 d 2 ρ A ( ρ ) exp ( 2 π i W ( ρ ) λ ) q l j ( ρ ) k ( ρ ) exp ( i k ( ρ ) ( r r 0 ) ) ,
w l j ( r r 0 ) λ = 2 π i w n λ 2 | ρ | 1 d 2 ρ A ( ρ ) exp ( 2 π i W ( ρ ) λ ) q l j ( ρ ) W ( ρ ) exp ( i k ( ρ ) ( r r 0 ) ) + 1 λ ( r r 0 ) w k j ( r r 0 ) r 0 ,

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