Quantum Super-resolution Imaging
in Fluorescence Microscopy
Osip Schwartz, Dan Oron, Jonathan M. Levitt, Ron Tenne,
Stella Itzhakov and Dan Oron
Dept. of Physics of Complex Systems
Weizmann Institute of Science, Israel
FRISNO 12, Ein Gedi (February 2013)
Microscopy and resolution
Resolution of far-field optical microscopes is limited by about half wavelength.
(Ernst Abbe, 1873)
Workarounds:
• Nonlinear optical methods: use nonlinear optical response to
produce narrower point spread function
• Stochastic methods: use fluorophores turning on and off randomly
• Quantum optics?
o Multi-photon interference
o Entangled images
o Sub shot noise imaging
o Resolution enhancement?
Slide 2 of 18
Afek et al., Science 328 (2010)
Walther et al., Nature 429 (2004)
Boyer et al., Science 321 (2008)
Brida et al., Nat. Photonics 4 (2010)
Quantum super-resolution
•
Quantum Limits on Optical Resolution
•
Wolf equations for two-photon light
•
Quantum Imaging beyond the Diffraction Limit by Optical Centroid Measurements
•
Quantum spatial superresolution by optical centroid measurements
•
Quantum imaging with incoherent photons,
Thiel et al., PRL 2007
•
Sub-Rayleigh quantum imaging using single-photon sources
Thiel et al., PRA 2009
•
Sub-Rayleigh-diffraction-bound quantum imaging,
•
Sub-Rayleigh Imaging via N-Photon Detection,
Quantum
light
Slide 3 of 18
Kolobov, Fabre, PRL2000
Saleh et al., PRL 2005
Object
M.Tsang PRL 2009
Shin et al., PRL 2011
Giovannetti, PRA 2009
Guerrieri et al., PRL 2010
Imaging
system
Light
detector
Quantum emitters
Classical light
Quantum light
Quantum
emitters
Imaging
system
Light
detector
What if we had an emitter that would always emit photon pairs?
S.W. Hell et al., Bioimaging (1995)
Slide 4 of 18
Multi-photon detection microscopy
Photon pair
τ1
τ2
τ1>>τ2
cascaded
emitters
Imaging
system
Photon pair
detector
Point spread function: h2phot(x) = h2(x)
Spatial distribution of photon pairs carries high spatial
frequency information (up to double resolution)
Similarly, in N-photon detection microscopy hNphot(x) = hN(x)
Slide 5 of 18
Antibunching microscopy
Observations of antibunching:
Number of photons emitted
after excitation:
Organic dyes:
W. Ambrose et al. (1997)
Quantum dots:
B. Lounis et al. (2000).
1
NV centers:
R. Brouri et al. (2000).
0.5
Classical
0
Fluorescence intensity autocorrelation
g(2)
0
1
2
Pair source
3
1
0.5
0
0
1
2
3
Single photon source
1
0.5
0
10 μs interval between pulses
Slide 6 of 18
0
1
2
3
Instead of actual photon pairs,
consider ‘missing’ pairs.
Antibunching-induced correlations
Two adjacent detectors in the image plane:
x0
For individual fluorophore:
For multiple fluorophores:
Sum over fluorophores
Slide 7 of 18
Emitters
Fluorescence saturation
CdSe / ZnSe / ZnS
quantum dots
1
0.8
0.6
0.4
0.2
0
450
Slide 8 of 18
500
550
600
Wavelength, nm
650
Schwartz et al.,ACS Nano 6 (2012)
At 1 kHz:
Slide 9 of 18
Schwartz et al.,ACS Nano 6 (2012)
Photon counting with a CCD
Pixel signal distribution
Read noise
threshold
CCD ADC units
More signal
Slide 10 of 18
Less noise
arXiv:1212.6003
Computing correlations
2nd order:
Quantifies the missing pairs
3rd order:
• compute correlations for all pixel configurations
• Fourier-interpolate the resulting images
• Sum the interpolated images
Slide 11 of 18
Missing 3-photon events
(except those due to missing
pairs, already accounted for)
arXiv:1212.6003
Antibunching with a CCD
Third order:
g(3)(τ1, τ2)=
=<n(t)n(t+τ1)n(t+ τ2)>
τ, ms
τ, ms
τ2, ms
g(2)(τ)=<n(t)n(t+ τ)>
Classical signal
τ2, ms
Second order
autocorrelation function:
Quantum dot
τ1, ms
Slide 12 of 18
τ1, ms
arXiv:1212.6003
1
8000
2
Fluorescence
image
6000
3
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4000
5
2000
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0
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1
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100
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1
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3
15
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10
5
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6
5
7
0
2
4
6
8
10
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arXiv:1212.6003
1
8000
2
Fluorescence
image
6000
3
4
4000
5
2000
6
7
0
2
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6
8
10
12
1
2nd order
antibunching
500
2
400
3
300
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200
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100
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arXiv:1212.6003
1
8000
2
Fluorescence
image
6000
3
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4000
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2000
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0
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1
2nd order
antibunching
500
2
400
3
300
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200
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100
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0
2
4
6
8
10
order
antibunching
25
2
20
3
15
4
181 nm FWHM
(x1.50)
10
5
Slide 15 of 18
216 nm FWHM
(x1.26)
12
1
3rd
Resolution:
271 nm FWHM
6
5
7
0
2
4
6
8
10
12
arXiv:1212.6003
Optical sectioning
Defocused image of a quantum dot:
Fluorescence
imaging
400
300
200
2nd order
antibunching
imaging
400
300
200
15
10
5
15
10
5
1
1
0.8
0.8
0.6
Optical signal integrated
over the field of view:
0.4
0.6
0.4
0.2
0.2
0
Slide 16 of 18
-1
0
-0.5
0
-1
0.5
-0.5
1
0
0.5
Defocusing, μm
1
Summary
•Far-field super-resolution imaging demonstrated by using quantum
properties of light naturally present in fluorescence microscopy
•The experiment was performed with commercially available
equipment, at room temperature, with commonly used quantum dot
fluorophores
•With further development of detector technology, antibunching
imaging may become feasible as a practical imaging method
Slide 17 of 18
The team
Jonathan M. Levitt
Stella Itzhakov
Ron Tenne
Slide 18 of 18
Zvicka Deutsch
Dan Oron
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Superresolved images
Reconstructed high resolution images
Regular (photon
counting) image
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Second order correlations
Third order correlations
Superresolved images
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arXiv:1212.6003
Superresolved images
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Superresolved images
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Quantum super-resolution
Conceptual difficulty: an absorptive grating with subwavelength period acts as an attenuator for every photon
• Transmitted light contains no information on the grating phase or period
• Any linear absorber mask is a superposition of gratings
• High spatial frequency components of the mask are lost
Slide 25 of 18