Super-Resolution Meets Quantum Optics
Applying Photon Correlations for Super-Resolution Microscopy
- Fig. 1: A Hanbury-Brown and Twiss experiment. Illustration of a photon stream in an HBT experiment split into two detectors for the case of (a) one single photon emitter and (b) two equal intensity single photon emitters. The graphs below show the second order correlation function for each case. While for a single marker for two markers.
- Fig. 2: Super-resolution imaging through photon antibunching. (a) Experimental setup scheme. Laser light is focused onto a sample through an objective lens. The resulting fluorescence photons are collected with the same objective, filtered and imaged onto an EMCCD camera synced to the laser source pulses. (b) From left to right: The fluorescence, 2nd order photon correlation and 3rd order photon correlation images, produced from the same data set, show the resolution improvement enabled by measuring antibunching. Scalebar length is 1μm and 0.4μm for the large area and zoom-in images respectively. Adapted with permission from .
- Fig. 3: Applying photon correlation as extra information in localization microscopy. (a) Monitoring the normalized photon pair probability , in an experiment with two quantum dots. Red markers signify events in which indicates, with a high statistical significance, a single active emitter. (b) Using the periods marked in red in (a) we accurately locate the emitters. The color of a point represents the time of localization from the beginning of the measurement. The movement here is only due to sample drift with time and therefore the two emitters move in a coordinated fashion. Adapted from “Y. Israel, R. Tenne, D. Oron, & Y. Silberberg: Quantum correlation enhanced super-resolution localization microscopy enabled by a fibre bundle camera, Nat. Commun. 8, 1–5 (2017) doi 10.1038/ncomms14786”.
Super-resolution is a general term for methods surpassing the diffraction limit in optical microscopy, imaging details finer than half of the visible wavelength. Each of these methods employs a different source of extra information such as non-linearity or a time dependent scene. We present here two methods, which for the first time apply the quantum nature of light as a source of extra information in order to break the diffraction limit.
Quantum optics is based on the notion that light is made out of particles, termed photons, rather than classical waves. A manifestation of the quantum character of light is, nowadays, routinely measured with a Hanbury-Brown and Twiss setup. When a stream of single photons is split between two sensitive detectors (fig. 1a) only one of the detectors will register a detection each time. The two detectors are thus completely anti-correlated. If we could fully describe light with classical waves, splitting it into two identical copies and sending each to a different detector will surely not generate this type of correlation. This phenomena, named photon antibunching, is therefore one of the hallmarks of the non-classicality of light. Measurement of antibunching was, correspondingly, a milestone in the study of light [1-3].
Light microscopy is one of the earliest applications of optics. As such, basic progress in various scientific fields in optics, such as non-linear optics, laser and detector technologies, was applied to enhance the performance and overcome the limitations of light microscopes. Although quantum optics developed into a vast research field with fascinating discoveries, only a few intriguing ideas and pioneering experiments managed to use quantum optics principles in the context of optical microscopy .
Perhaps the most fundamental limitation of optical microscopy is due to the diffraction limit of spatial resolution. As first stated by Ernst Abbe, an infinitely small point object becomes a blurry circle in the image, termed the point spread function (PSF) of the system . As a result, one cannot resolve objects closer than about half of the visible light’s wavelength.
In biology, were light microscopy is the most popular imaging technique used in almost every lab, this means, for example, that many sub-cellular features cannot be imaged. Super-resolution microscopy is the general name for techniques that combat this harsh consequence. The Nobel prize in Chemistry from 2014 recognized the important breakthroughs in this field and in particular those achieved by Moerner, Betzig and Hell . Super-resolution techniques can be classified according to the assumptions they violate in Abbe’s analysis. For example, photoactivated localization microscopy (PALM) and stochastic optical reconstruction microscopy (STORM) rely on a fluorescent scene fluctuating with time, breaching the assumption of a stationary image. Until recently, the aforementioned classification of super-resolution methods pointed to an interesting fact: all but one of the basic assumptions in Abbe’s analysis have been violated, the implicit assumption that light is described by classical waves.
A Super-Resolved Image from Quantum Correlations
Since the diffraction limit was mathematically formulated in the 19th century, prior to the discovery of quantum mechanics, it contained the implicit assumption that light can be described by classical waves. We were the first to suggest , and later experimentally demonstrate , how a Hanbury-Brown and Twiss antibunching measurement, as described above, can be used to construct a super-resolved image. To date, there are several different experimental implementations of variations on this idea, detailed below [9, 10].
Figure 2a shows the method used in reference 8 schematically. When a scene is labelled with fluorescent markers that emit a single photon at a time, such as dye molecules and quantum dots, the light collected by the camera is inherently non-classic. To observe the quantum nature of light the sample is excited with a short laser pulse and one camera frame is taken for each pulse with a single-photon sensitive camera (EMCCD). The light from each marker spreads according to the diffraction limit (the PSF) onto a few pixels and each photon is detected stochastically by one of them. This is precisely the same experiment described above to measure photon antibunching. Two neighboring pixels observing the same marker will be anti-correlated; if one measures a photon in the current frame, the other surely does not. In more accurate terms, it is possible to measure an image of the second order correlation function of the photon stream; the PSF in such an image is a second power of the original PSF and therefore narrower by a factor of √2. Notably, one can measure higher order (n) anti-correlation. The absence of simultaneous n-photon detection events leads to gain of a √n in resolution. Figure 2b displays, from left to right, a series images for the same scene with a standard microscope, second and third order antibunching presenting a noticeable resolution improvement. While this approach can theoretically allow unlimited resolution enhancement by measuring high orders of correlation, each additional anti-correlation order relies on events that are less frequent by roughly the collection efficiency of emitted photons, corresponding to an order of magnitude. As a result, the long exposure times required to enhance the resolution merely by a factor of √3 limit the application of this method alone to biological samples.
The Extra Information Contained in Photon Correlations
As described in the previous section, while one can construct a super-resolved image by measuring quantum photon correlations alone, their acquisition is very slow. Relying solely on photon anti-bunching yields only a modest resolution improvement in reasonable acquisition times. An alternative approach would be to complement an existing super-resolution technique with the extra information stored in photon correlation data.
STORM and PALM, mentioned above, are excellent candidates for such a combination since they can be performed with single photon emitters, organic dye molecules. In these super-resolution methods, subsequent images of a fluctuating scene are acquired, containing only a sparse subset of active markers in each frame [11, 12]. Since the emitters in the subset are, on-average, well separated one can pinpoint their position with high accuracy by locating the center of the emission pattern (the PSF).
However, a problem arises when we want to acquire images at high rates. To do so one must increase the density of active markers per frame. Yet, already at rather low densities markers will frequently spatially overlap. To find their position one should preferably know the number of overlapping emitters. Without this knowledge, even a sophisticated computer algorithm fails to construct a trustworthy image, adding many false extra markers. A possible relief could be a source of extra information about the number of markers in each frame.
Photon correlations can add information about the number of markers contributing to the image . Figuratively, each emitter is a source of missing photon pairs. Therefore, multiple single photon emitters will produce a photon pair with a reduced probability compared to a classical (coherent) state of light. This is quantitatively estimated by , the factor of reduced probability to detect a photon pair with respect to the Poisson distribution (fig. 1). M identical single photon emitters produce photon pairs with a probability multiplied by a factor . As an example, when only one emitter is present (fig. 1a) and when two emitters contribute to the image (fig. 1b).
While a sensitive camera was sufficient for a proof-of-principle demonstration as described in the previous section, the inherently low time resolution of a camera (< 1KHz) limits the laser pulse rate and thus the rate of photons detected from a single photon emitter. To overcome this limitation a new type of detector is needed, having both single-photon sensitivity and an effective high frame rate. Monolithic arrays of single-photon avalanche detectors (SPADs) could be used for this end, but typically suffer from a low fill factor . Instead, we replaced the camera with a fiber bundle; an array of fibers arranged in a honey-comb lattice, 15 of which were connected to a SPADs . Each fiber functions as a pixel in a small area imaging sensor with a very high (nanosecond) temporal resolution. One can use the acquired data in two ways: integrating over time we can produce a spatial image whereas integrating over the entire array we can monitor photon correlation, over the measurement time.
Illuminating a fluctuating scene of two markers, in the example shown in Fig. 3a, we can observe ‘blinking’ stochastically between two states: When both emitters are active is ~0.5 while it is substantially lower when only one of the markers is in a bright state. The simplest way to apply this extra data is to filter-in only photons detected within single emitter periods (red dots in fig. 3a). Using these detections, we form images and find the center of the emission pattern in each; a similar analysis to the one performed in STORM \ PALM. Figure 3b shows how, using this method, we track two particles (quantum dots) moving together with ~20nm resolution even though they are much closer than the diffraction limit.
Monitoring the number of active emitters, one can decipher a dense frame without risking errors. Provided this method can work in the demanding conditions of biological imaging, one could perform STORM \ PALM imaging with much denser frames and therefore shorter acquisition times.
After decades of research in quantum optics, its application in practical measurements is still quite challenging. We have shown that one important phenomenon in quantum optics, photon antibunching, can be used in super-resolution microscopy. Two ways to extract extra information from the same type of measurement, photon correlation, were explored. In the first the absence of photon pairs served as the imaging contrast itself whereas in the second it was used as additional information about the number of markers enhancing a classical super-resolution microscopy, STORM\PALM.
While both of these experiments have not yet reached the level of applicability required from light microscopy methods, we believe that there is sufficient room for improvement. Since it only adds information without compromising the classical data, photon correlation signal can complement additional super-resolution methods to gain better performance. One such intriguing recent suggestion is combining antibunching information into structured illumination microscopy . In addition, the rapid progress in EMCCD, CMOS cameras and on-chip SPAD array imaging sensors technology will enable better use of the time domain in optical microscopy. In particular, this progress may enable photon correlation measurements in a widefield setup at fast rates, substantially speeding-up the acquisition process of super-resolution images based on quantum optics principles.
Ron Tenne1 and Dan Oron1
1Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot ,Israel
 H. J. Kimble, M. Dagenais & L. Mandel, Photon Antibunching in Resonance Fluorescence: Phys. Rev. Lett. 39, 691–695 (1977) doi 10.1103/PhysRevLett.39.691
 P. Michler, et al: A quantum dot single-photon turnstile device. Science 290, 2282–5 (2000) doi 10.1126/science.290.5500.2282
 T. Basche, W. E. Moerner, M. Orrit, & H. Talon: Photon Antihunching in the Fluorescence of a Single Dye Molecule Trapped in a Solid. 69, (1992) doi 10.1103/PhysRevLett.69.1516
 M. A. Taylor, & W. P. Bowen: Quantum metrology and its application in biology. Phys. Rep. 615, 1–59 (2016) doi 10.1016/j.physrep.2015.12.002
 E. Abbe: Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung. Arch. für Mikroskopische Anat. 9, 413–418 (1873)
 Nobelprize.org. The Nobel Prize in Chemistry 2014 - Advanced Information. Nobel Media (2014) at <http://www.nobelprize.org/nobel_prizes/chemistry/laureates/2014/advanced.html>
 O. Schwartz, & D. Oron: Improved resolution in fluorescence microscopy using quantum correlations, Phys. Rev. A 85, 033812 (2012) doi 10.1103/PhysRevA.85.033812
 O. Schwartz, et al.: Superresolution microscopy with quantum emitters, Nano Lett. 13, 5832–6 (2013) doi 10.1021/nl402552m
 J.-M. Cui, F.-W. Sun, X.-D. Chen, Z.-J. Gong, & G.-C. Guo: Quantum Statistical Imaging of Particles without Restriction of the Diffraction Limit, Phys. Rev. Lett. 110, 153901 (2013) doi 10.1103/PhysRevLett.110.153901
 D. Gatto Monticone, et al.: Beating the Abbe Diffraction Limit in Confocal Microscopy via Nonclassical Photon Statistics, Phys. Rev. Lett. 113, 143602 (2014) doi 10.1103/PhysRevLett.113.143602
 E. Betzig, et al.: Imaging intracellular fluorescent proteins at nanometer resolution, Science 313, 1642–5 (2006) doi 10.1126/science.1127344
 M. J. Rust, M. Bates, & X. Zhuang: Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM), Nat. Methods 3, 793–5 (2006) doi 10.1038/nmeth929
 H. Ta, A. Kiel, M. Wahl & D.-P. Herten: Experimental approach to extend the range for counting fluorescent molecules based on photon-antibunching, Phys. Chem. Chem. Phys. 12, 10295 (2010) doi 10.1039/c0cp00363h
 C. Gerry & P. Knight: Introductory Quantum Optics., Cambridge University Press, (2005)
 C. Bruschini, H. Homulle, & E. Charbon: Ten years of biophotonics single-photon SPAD imager applications: retrospective and outlook. in (eds. Periasamy, A., So, P. T. C., König, K. & Xie, X. S.) 10069, 100691S (International Society for Optics and Photonics, 2017)
 Y. Israel, R. Tenne, D. Oron, & Y. Silberberg: Quantum correlation enhanced super-resolution localization microscopy enabled by a fibre bundle camera, Nat. Commun. 8, 1–5 (2017) doi 10.1038/ncomms14786
 A. Classen, J. von Zanthier, M. O. Scully, & G. S. Agarwal: Superresolution via structured illumination quantum correlation microscopy, Optica 4, 580 (2017) doi 10.1364/OPTICA.4.000580