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1. H. Volkmann, “ Ernst Abbe and his work,” Appl. Opt. 5, 17201731 (1966).
2. L. Rayleigh, “ On the theory of optical images, with special reference to the microscope,” The London, Edinburgh, Dublin Philos. Mag. J. Sci. 42(XV), 167195 (1896).
3. A. B. Porter, “ On the diffraction theory of microscopic vision,” The London, Edinburgh, Dublin Philos. Mag. J. Sci. 11, 154166 (1906).
4. G. Toraldo di Francia, “ Super-gain antennas and optical resolving power,” Nuovo Cimento Suppl. 9, 426438 (1952).
5. J. W. Goodman, Introduction to Fourier Optics, 3rd ed. ( Roberts and Company Publishers, Greenwood Village, CO, 2005). The first edition was published in 1968.
6. F. M. Huang and N. I. Zheludev, “ Super-resolution without evanescent waves,” Nano Lett. 9, 12491254 (2009). The authors give a modern implementation of the aperture schemes pioneered by Toraldo Di Francia (Ref. 4).
7. “Superresolution” is also sometimes used to describe sub-pixel resolution in an imaging detector. Since pixels are not necessarily related to intrinsic resolution, we do not consider such techniques here.
8. J.-B. Sibarita, “ Deconvolution microscopy,” Adv. Biochem. Engin. Biotechnol. 95, 201243 (2005).
9. Superresolution fluorescence microscopy was the 2008 “Method of the Year” for Nature Methods, and its January 2009 issue contains commentary and interviews with scientists playing a principal role in its development. This is a good “cultural” reference.
10. B. O. Leung and K. C. Chou, “ Review of superresolution fluorescence microscopy for biology,” Appl. Spectrosc. 65, 967980 (2011).
11. For example, a STED microscope is sold by the Leica Corporation.
12. C. J. R. Sheppard, “ Fundamentals of superresolution,” Micron 38, 165169 (2007). Sheppard introduces three classes rather than two: Improved superresolution boosts spatial frequency response but leaves the cutoff frequency unchanged. Restricted superresolution includes tricks that increase the cut-off by up to a factor of two. We use “pseudo” superresolution for both cases. Finally, unrestricted superresolution refers to what we term “true” superresolution.
13. J. Mertz, Introduction to Optical Microscopy ( Roberts and Co., Greenwood Village, CO, 2010), Chap. 18. Mertz follows Sheppard's classification, giving a simple but broad overview.
14. J. L. Harris, “ Resolving power and decision theory,” J. Opt. Soc. Am. 54, 606611 (1964).
15.An updated treatment of the one-point-source-or-two decision problem is given by A. R. Small, “ Theoretical limits on errors and acquisition rates in localizing switchable fluorophores,” Biophys. J. 96, L16L18 (2009).
16.For a more formal Bayesian treatment, see S. Prasad, “ Asymptotics of Bayesian error probability and source super-localization in three dimensions,” Opt. Express 22, 1600816028 (2014).
17. S. W. Hell, “ Far-field optical nanoscopy,” Springer Ser. Chem. Phys. 96, 365398 (2010).
18. B. Huang, H. Babcock, and X. Zhuang, “ Breaking the diffraction barrier: Superresolution imaging of cells,” Cell 143, 10471058 (2010).
19. C. Cremer and B. R. Masters, “ Resolution enhancement techniques in microscopy,” Eur. Phys. J. H 38, 281344 (2013).
20. E. Hecht, Optics, 4th ed. ( Addison-Wesley, Menlo Park, CA, 2002), Chap. 13.
21. G. Brooker, Modern Classical Optics ( Oxford U.P., New York, 2002), Chap. 12.
22. A. Lipson, S. G. Lipson, and H. Lipson, Optical Physics, 4th ed. ( Cambridge U.P., Cambridge, UK, 2011), Chap. 12. This edition of a well-established text adds a section on superresolution techniques, with a view that complements the one presented here.
23. Equation (1) gives the lateral resolution. The resolution along the optical axis is poorer: .
24. However, the magnification of an objective does not determine its resolution.
25. P. M. Duffieux, The Fourier Transform and Its Applications to Optics, 2nd ed. ( John Wiley & Sons, Hoboken, NJ, 1983). The first edition, in French, was published in 1946. Duffieux formulated the idea of the optical transfer function in the 1930s.
26. J. Lindberg, “ Mathematical concepts of optical superresolution,” J. Opt. 14, 083001 (2012).
27. A subtle point: The modulation transfer function is zero beyond a finite spatial frequency; yet the response in Fig. 3 is non-zero at all frequencies. The explanation is that an object of finite extent has a Fraunhofer diffraction pattern (Fourier transform) that is analytic, neglecting noise. Analytic functions are determined by any finite interval (analytic continuation), meaning that one can, in principle, extrapolate the bandwidth and deduce the exact behavior beyond the cutoff from that inside the cutoff. In practice, noise cuts off the information (Fig. 3). See Lucy (Ref. 28) for a brief discussion and Goodman's book (Ref. 5) for more detail.
28. L. B. Lucy, “ Statistical limits to superresolution,” Astron. Astrophys. 261, 706710 (1992). Lucy does not assume the PSF width to be known and thus reaches the more pessimistic conclusion that Δx ∼ N−1∕8 . Since the second moments are then matched, one has to use the variance of the fourth moment to distinguish the images.
29. K. Piché, J. Leach, A. S. Johnson, J. Z. Salvail, M. I. Kolobov, and R. W. Boyd, “ Experimental realization of optical eigenmode superresolution,” Opt. Express 20, 26424 (2012). Instruments with finite aperture sizes have discrete eigenmodes (that are not simple sines and cosines), which should be used for more accurate image restoration.
30. E. Ramsay, K. A. Serrels, A. J. Waddie, M. R. Taghizadeh, and D. T. Reid, “ Optical superresolution with aperture-function engineering,” Am. J. Phys. 76, 10021006 (2008).
31. G. Toraldo di Francia, “ Resolving power and information,” J. Opt. Soc. Am. 45, 497501 (1955).
32. S. G. Lipson, “ Why is superresolution so inefficient?Micron 34, 309312 (2003).
33. W. Lukosz, “ Optical systems with resolving powers exceeding the classical limit,” J. Opt. Soc. Am. 56, 14631472 (1966).
34. W. Lukosz, “ Optical systems with resolving powers exceeding the classical limit. II,” J. Opt. Soc. Am. 57, 932941 (1967).
35. E. A. Mukamel and M. J. Schnitzer, “ Unified resolution bounds for conventional and stochastic localization fluorescence microscopy,” Phys. Rev. Lett. 109, 168102-1–5 (2012).
36. J. E. Fitzgerald, J. Lu, and M. J. Schnitzer, “ Estimation theoretic measure of resolution for stochastic localization microscopy,” Phys. Rev. Lett. 109, 048102-1–5 (2012).
37. R. P. J. Nieuwenhuizen, K. A. Lidke, M. Bates, D. L. Puig, D. Grönwald, S. Stallinga, and B. Rieger, “ Measuring image resolution in optical nanoscopy,” Nat. Methods 10, 557562 (2013).
38. D. S. Sivia and J. Skilling, Data Analysis: A Bayesian Tutorial, 2nd ed. ( Oxford U.P., New York, 2006), Chap. 5.
39. N. Bobroff, “ Position measurement with a resolution and noise-limited instrument,” Rev. Sci. Instrum. 57, 11521157 (1986).
40. R. J. Ober, S. Ram, and E. S. Ward, “ Localization accuracy in single-molecule microscopy,” Biophys. J. 86, 11851200 (2004).
41. K. I. Mortensen, L. S. Churchman, J. A. Spudich, and H. Flyvbjerg, “ Optimized localization analysis for single-molecule tracking and superresolution microscopy,” Nat. Methods 7, 377381 (2010). Gives a useful assessment of various position estimators.
42. H. Deschout, F. C. Zanacchi, M. Mlodzianoski, A. Diaspro, J. Bewersdorf, S. T. Hess, and K. Braeckmans, “ Precisely and accurately localizing single emitters in fluorescence microscopy,” Nat. Methods 11, 253266 (2014).
43. A. Yildiz and P. R. Selvin, “ Fluorescence imaging with one nanometer accuracy: Application to molecular motors,” Acc. Chem. Res. 38, 574582 (2005).
44. G. Patterson, M. Davidson, S. Manley, and J. Lippincott-Schwartz, “ Superresolution imaging using single-molecule localization,” Annu. Rev. Phys. Chem. 61, 345367 (2010).
45. One should set the errors to be the square root of the smooth distribution value deduced from the initial fit and then iterate the fitting process (Ref. 46). The conclusions however, would not change, in this case.
46. S. F. Nørrelykke and H. Flyvbjerg, “ Power spectrum analysis with least-squares fitting: Amplitude bias and its elimination, with application to optical tweezers and atomic force microscope cantilevers,” Rev. Sci. Inst. 81, 075103-1–16 (2010).
47. E. Betzig and R. J. Chichester, “ Single molecules observed by near-field scanning optical microscopy,” Science 262, 14221425 (1993).
48. T. Ha, T. A. Laurence, D. S. Chemla, and S. Weiss, “ Polarization spectroscopy of single fluorescent molecules,” J. Phys. Chem. B 103, 68396850 (1999).
49. J. Engelhardt, J. Keller, P. Hoyer, M. Reuss, T. Staudt, and S. W. Hell, “ Molecular orientation affects localization accuracy in superresolution far-field fluorescence microscopy,” Nano. Lett. 11, 209213 (2011).
50. P. Frantsuzov, M. Kuno, B. Jankó, and R. A. Marcus, “ Universal emission intermittency in quantum dots, nanorods and nanowires,” Nat. Phys. 4, 519522 (2008).
51. 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, 16421645 (2006).
52. M. J. Rust, M. Bates, and X. Zhuang, “ Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3, 793795 (2006).
53. Important precursors in using sequential localization to develop stochastic localization techniques such as PALM and STORM were Qu et al. (Ref. 54) and Lidke et al. (Ref. 55) Stochastic localization was also independently developed by Hess et al. (Ref. 56).
54. X. Qu, D. Wu, L. Mets, and N. F. Scherer, “ Nanometer-localized multiple single-molecule fluorescence microscopy,” Proc. Natl. Acad. Sci. U.S.A 101, 1129811303 (2004).
55. K. A. Lidke, B. Rieger, T. M. Jovin, and R. Heintzmann, “ Superresolution by localization of quantum dots using blinking statistics,” Opt. Express 13, 70527062 (2005).
56. S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “ Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91, 42584272 (2006).
57. Sparseness can improve resolution in other ways, as well. For example, the new field of compressive sensing also uses a priori knowledge that a sparse representation exists in a clever way to improve resolution (Ref. 58).
58. H. P. Babcock, J. R. Moffitt, Y. Cao, and X. Zhuang, “ Fast compressed sensing analysis for super-resolution imaging using L1-homotopy,” Opt. Express 21, 2858328596 (2013).
59. T. Dertinger, R. Colyer, G. Iyer, S. Weiss, and J. Enderlein, “ Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI),” Proc. Natl. Acad. Sci. U.S.A 106, 2228722292 (2009). This clever technique uses intensity fluctuations due to multiple switching between two states of different brightness.
60. A. J. Berro, A. J. Berglund, P. T. Carmichael, J. S. Kim, and J. A. Liddle, “ Super-resolution optical measurement of nanoscale photoacid distribution in lithographic materials,” ACS Nano 6, 94969502 (2012). If one knows that vertical stripes are present, one can sum localizations by column to get a higher-resolution horizontal cross-section.
61. S. W. Hell and J. Wichmann, “ Breaking the diffraction resolution limit by stimulated emission: Stimulated-emission-depletion fluorescence microscopy,” Opt. Lett. 19, 780782 (1994).
62. B. Harke, J. Keller, C. K. Ullal, V. Westphal, A. Schönle, and S. W. Hell, “ Resolution scaling in STED microscopy,” Opt. Express 16, 41544162 (2008).
63. M. Dyba, J. Keller, and S. W. Hell, “ Phase filter enhanced STED-4Pi fluorescence microscopy: Theory and experiment,” New J. Phys. 7, Article 134 (2005), pp. 21.
64. J. B. Pawley, Handbook of Biological Confocal Microscopy, 2nd ed. ( Springer, New York, 2006).
65. A. Diaspro, G. Chirico, and M. Collini, “ Two-photon fluorescence excitation and related techniques in biological microscopy,” Quart. Rev. Biophys. 38, 97166 (2005).
66. C. Cremer and T. Cremer, “ Considerations on a laser-scanning-microscope with high resolution and depth of field,” Microsc. Acta 81, 3144 (1978).
67. S. Hell and E. H. K. Stelzer, “ Fundamental improvement of resolution with a 4Pi-confocal fluorescence microscope using two-photon excitation,” Opt. Commun. 93, 277282 (1992).
68. E. H. Synge, “ A suggested method for extending microscopic resolution into the ultra-microscopic region,” Philos. Mag. 6, 356362 (1928).
69. E. Betzig, A. Lewis, A. Harootunian, M. Isaacson, and E. Kratschmer, “ Near-field scanning optical microscopy (NSOM): Development and biophysical applications,” Biophys. J. 49, 269279 (1986).
70. L. Novotny and B. Hecht, Principles of Nano-Optics, 2nd ed. ( Cambridge U.P., Cambridge, UK, 2012).
71. F. Simonetti, “ Multiple scattering: The key to unravel the subwavelength world from the far-field pattern of a scattered wave,” Phys. Rev. E 73, 036619-1–13 (2006).
72. R. Heintzmann, T. M. Jovin, and C. Cremer, “ Saturated patterned excitation microscopy—a concept for optical resolution improvement,” J. Opt. Soc. Am. A 19, 15991609 (2002).
73. K. Fujita, M. Kobayashi, S. Kawano, M. Yamanaka, and S. Kawata, “ High-resolution confocal microscopy by saturated excitation of fluorescence,” Phys. Rev. Lett. 99, 228105-1–4 (2007).
74. J. B. Pendry, “ Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 39663969 (2000).
75. N. Fang, H. Lee, C. Sun, and X. Zhang, “ Sub-diffraction-limited optical imaging with a silver superlens,” Science 308, 534537 (2005).
76. M. G. L. Gustafsson, “ Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198, 8287 (2000).
77. M. G. L. Gustafsson, “ Nonlinear structured-illumination microscopy: Wide-field fluorescence imaging with theoretically unlimited resolution,” Proc. Natl. Acad. Sci. U.S.A 102, 1308113086 (2005).
78. A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “ Quantum interferometric optical lithography: Exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 27332736 (2000).
79. L. A. Rozema, J. D. Bateman, D. H. Mahler, R. Okamoto, A. Feizpour, A. Hayat, and A. M. Steinberg, “ Scalable spatial superresolution using entangled photons,” Phys. Rev. Lett. 112, 223602-1–5 (2014).
80. J. N. Oppenheim and M. O. Magnasco, “ Human time-frequency acuity beats the Fourier Uncertainty principle,” Phys. Rev. Lett. 110, 044301-1–5 (2013).

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In this paper, we discuss what , what is , and what is only superresolution microscopy. We begin by considering optical resolution, first in terms of diffraction theory, then in terms of linear-systems theory, and finally in terms of techniques that use prior information, nonlinearity, and other tricks to improve resolution. This discussion reveals two classes of superresolution microscopy, “pseudo” and “true.” The former improves images up to the diffraction limit, whereas the latter allows for substantial improvements beyond the diffraction limit. The two classes are distinguished by their scaling of resolution with photon counts. Understanding the limits to imaging resolution involves concepts that pertain to almost any measurement problem, implying a framework with applications beyond optics.


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