Book contents
- Frontmatter
- Contents
- Preface to the first edition
- Preface to the second edition
- 1 Introduction
- 2 Theoretical foundations
- 3 Propagation and focusing of optical fields
- 4 Resolution and localization
- 5 Nanoscale optical microscopy
- 6 Localization of light with near-field probes
- 7 Probe–sample distance control
- 8 Optical interactions
- 9 Quantum emitters
- 10 Dipole emission near planar interfaces
- 11 Photonic crystals, resonators, and cavity optomechanics
- 12 Surface plasmons
- 13 Optical antennas
- 14 Optical forces
- 15 Fluctuation-induced interactions
- 16 Theoretical methods in nano-optics
- Appendix A Semi-analytical derivation of the atomic polarizability
- Appendix B Spontaneous emission in the weak-coupling regime
- Appendix C Fields of a dipole near a layered substrate
- Appendix D Far-field Green functions
- Index
- References
4 - Resolution and localization
Published online by Cambridge University Press: 05 November 2012
Book contents
- Frontmatter
- Contents
- Preface to the first edition
- Preface to the second edition
- 1 Introduction
- 2 Theoretical foundations
- 3 Propagation and focusing of optical fields
- 4 Resolution and localization
- 5 Nanoscale optical microscopy
- 6 Localization of light with near-field probes
- 7 Probe–sample distance control
- 8 Optical interactions
- 9 Quantum emitters
- 10 Dipole emission near planar interfaces
- 11 Photonic crystals, resonators, and cavity optomechanics
- 12 Surface plasmons
- 13 Optical antennas
- 14 Optical forces
- 15 Fluctuation-induced interactions
- 16 Theoretical methods in nano-optics
- Appendix A Semi-analytical derivation of the atomic polarizability
- Appendix B Spontaneous emission in the weak-coupling regime
- Appendix C Fields of a dipole near a layered substrate
- Appendix D Far-field Green functions
- Index
- References
Summary
Localization refers to the precision with which the position of an object can be defined. Spatial resolution, on the other hand, is a measure of the ability to distinguish two separated point-like objects from a single object. The diffraction limit implies that optical resolution is ultimately limited by the wavelength of light. Before the advent of near-field optics it was believed that the diffraction limit imposes a hard boundary and that physical laws strictly prohibit resolution significantly better than λ/2. It was then found that this limit is not as strict as assumed and that access to evanescent modes of the spatial spectrum offers a direct route to overcome the diffraction limit. However, further critical analysis of the diffraction limit revealed that “super-resolution” can also be obtained by pure far-field imaging under certain constraints. In this chapter we analyze the diffraction limit and discuss the principles of different imaging modes with resolutions near or beyond the diffraction limit.
The point-spread function
The point-spread function is a measure of the resolving power of an optical system. The narrower the point-spread function the better the resolution will be. As the name implies, the point-spread function defines the spread of a point source. If we have a radiating point source then the image of that source will appear to have a finite size. This broadening is a direct consequence of spatial filtering. A point in space is characterized by a delta function that has an infinite spectrum of spatial frequencies kx and ky.
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- Principles of Nano-Optics , pp. 86 - 130Publisher: Cambridge University PressPrint publication year: 2012
References
[1] and , “The image of a single point in microscopes of large numerical aperture,” Proc. Roy. Soc.A 379, 145–158 (1982).Google Scholar
[2] , “Theoretical study of detection of a dipole emitter through an objective with high numerical aperture,” Opt. Lett. 25, 634–636 (2000).Google Scholar
[3] , , and , “Simultaneous imaging of individual molecules aligned both parallel and perpendicular to the optic axis,” Phys. Rev. Lett. 81, 5322–5325 (1998).Google Scholar
[4] , , and , “Single molecule orientations determined by direct emission pattern imaging,” J. Opt. Soc.B 21, 1210–1215 (2004).Google Scholar
[5] , “Beiträge zur Theorie des Mikroskops und des mikroskopischen Wahrnehmung,” Arch. Mikrosk. Anat. 9, 413–468 (1873).Google Scholar
[6] , “On the theory of optical images with special reference to the microscope,” Phil. Mag. 5, 167–195 (1896).Google Scholar
[8] , , and , “Time-multiplexed multifocal multiphoton microscope,” Opt. Lett. 26, 75–77 (2001).Google Scholar
[9] , , , , and , “Fluorescence microscopy with diffraction resolution barrier broken by stimulated emission,” Proc. Nat. Acad. Sci. 97, 8206–8210 (2000).Google Scholar
[10] , “Memoir on inventing the confocal scanning microscope,” Scanning 10, 128–138 (1988).Google Scholar
[11] , , and , Confocal Laser Scanning Microscopy. New York: BIOS Scientific Publishers (1997).Google Scholar
[12] and , Confocal Scanning Optical Microscopy and Related Imaging Systems. New York: Academic Press (1997).Google Scholar
[14] , “Position measurement with a resolution and noise-limited instrument,” Rev. Sci. Instrum. 57, 1152–1157 (1986).Google Scholar
[15] , , and , “Precise nanometer localization analysis for individual fluorescent probes,” Biophys. J. 82, 2775–2783 (2002).Google Scholar
[16] , , and , “Localization accuracy in single-molecule microscopy,” Biophys. J. 86, 1185–1200 (2004).Google Scholar
[17] , , , et al., “Myosin V walks hand-over-hand: single fluorophore imaging with 1.5-nm localization,” Science 300, 2061–2065 (2003). Reprinted with permission from AAAS.Google Scholar
[18] , , , et al., “Statistical analysis of single-molecule colocalization assays,” Anal. Chem. 73, 1100–1105 (2001).Google Scholar
[19] , , , et al., “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).Google Scholar
[20] , , and , “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nature Methods 3, 793–795 (2006).Google Scholar
[21] , , and , “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91, 4258–4272 (2006).Google Scholar
[22] and , Data Reduction and Error Analysis for the Physical Sciences. New York: McGraw-Hill, p. 212 (1994).Google Scholar
[23] , , and , “Parameter estimation in X-ray astronomy,” Astrophys. J. 208, 177–190 (1976).Google Scholar
[25] , “On Bethe's theory of diffraction by small holes,” Philips Res. Rep. 5, 321–332 (1950).Google Scholar
[26] , , and , “Optical characterization of nanosources used in scanning near-field optical microscopy,” J. Opt. Soc. Am.A 12, 695–703 (1995).Google Scholar
[27] and , “Scanning tunneling optical microscopy: theoretical study of polarization effects with two models of tip,” in Near-field Optics, ed. and . Dordrecht: Kluwer, pp. 179–188 (1993).Google Scholar
[28] and , “Image formation in near-field optics,” Prog. Surf. Sci. 56, 133–237 (1997).Google Scholar
[29] , , , , and , “Influence of detection conditions on near-field optical imaging,” J. Appl. Phys. 84, 5873–5882 (1998).Google Scholar
[30] , , , , and , “Facts and artifacts in near-field optical microscopy,” J. Appl. Phys. 81, 2492–2498 (1997).Google Scholar
[32] and ,“Optische Abbildung unter Überschreitung der beugungsbedingten Auflösungsgrenze,” J. Mod. Opt. 10, 241–255 (1963).Google Scholar
[33] , , and , “Method and apparatus for three-dimensional microscopy with enhanced depth resolution,” US patent 5671085, cols. 23–25 (1997).Google Scholar
[34] , “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198, 82–87 (2000).Google Scholar
[35] and , “Laterally modulated excitation microscopy: improvement of resolution by using a diffraction grating,” Proc. SPIE 3568, 185–196 (1999).Google Scholar
[36] , , and , “True optical resolution beyond the Rayleigh limit achieved by standing wave illumination,” Proc. Nat. Acad. Sci. 97, 7232–7236 (2000).Google Scholar
[37] , , and , “Method of obtaining optical sectioning by using structured light in a conventional microscope,” Opt. Lett. 22, 1905–1907 (1997).Google Scholar
[39] , “Nonlinear structured-illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution,” Proc. Nat. Acad. Sci. 102, 13081–13086 (2005). Copyright 2005 National Academy of Sciences, U.S.A.Google Scholar
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