Abstract
This article explores the possibility of another kind of superresolution functionality that exists in superoscillatory functions besides the “faster than Fourier” feature. We posit the ability to resolve images with resolution beyond the wavelength of light used via the exponentially rising and falling parts of superoscillatory and related functions. We give some preliminary results that this technique can indeed be useful using intensity contrast imaging. The exponential growth or decay of these functions can give higher resolution of the image, provided the rate of falloff is faster than the smallest wavenumber of the light that is used: “supergrowth”. One limitation of this proposal is the high dynamic range the detector would need to possess to map out several decades of intensity. An outstanding question is to find the optimal image reconstruction method using a superoscillatory point spread function that makes optimal use of the function’s unique properties. We give a number of conjectures about this new kind of supergrowth imaging technique as an outlook for future research.
Similar content being viewed by others
References
Aharonov, Y., Popescu, S., Rohrlich, D.: How can an infra-red photon behave as a gamma ray?. Tel-Aviv University Preprint TAUP 1847–90
Berry, M.V., Popescu, S.: Evolution of quantum superoscillations and optical superresolution without evanescent waves. J. Phys. A Math. Gen. 39(22), 6965 (2006)
Berry, M.V.: Evanescent and real waves in quantum billiards and Gaussian beams. J. Phys. A Math. Gen. 27(11), L391 (1994)
Berry, M., Zheludev, N., Aharonov, Y., Colombo, F., Sabadini, I., Struppa, D.C., Tollaksen, J., Rogers, E.T., Qin, F., Hong, M., et al.: Roadmap on superoscillations. J. Opt. 21(5), 053002 (2019)
Aharonov, Y., Colombo, F., Sabadini, I., Struppa, D.C., Tollaksen, J.: Some mathematical properties of superoscillations. J. Phys. A Math. Theor. 44(36), 365304 (2011)
Popescu, S.: Multi-time and non-local measurements in quantum mechanics. Ph.D. thesis, PhD Thesis (1991)
Lipson, A., Lipson, S.G., Lipson, H.: Optical Physics. Cambridge University Press, Cambridge (2010)
Tsang, M., Nair, R., Lu, X.M.: Quantum theory of superresolution for two incoherent optical point sources. Phys. Rev. X 6, 031033 (2016)
Pendharker, S., Shende, S., Newman, W., Ogg, S., Nazemifard, N., Jacob, Z.: Axial super-resolution evanescent wave tomography. Opt. Lett. 41(23), 5499 (2016)
Boto, A.N., Kok, P., Abrams, D.S., Braunstein, S.L., Williams, C.P., Dowling, J.P.: Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit. Phys. Rev. Lett. 85, 2733 (2000)
Huang, F.M., Chen, Y., de Abajo, F.J.G., Zheludev, N.I.: Optical super-resolution through super-oscillations. J. Opt. A Pure Appl. Opt. 9(9), S285 (2007)
Kozawa, Y., Matsunaga, D., Sato, S.: Superresolution imaging via superoscillation focusing of a radially polarized beam. Optica 5(2), 86 (2018)
McCutchen, C.: Optical systems for observing surface topography by frustrated total internal reflection and by interference. Rev. Sci. Instrum. 35(10), 1340 (1964)
Guerra, J.M.: Photon tunneling microscopy. Appl. Opt. 29(26), 3741 (1990)
Pohl, D.W., Denk, W., Lanz, M.: Optical stethoscopy: image recording with resolution \(\lambda \)/20. Appl. Phys. Lett. 44(7), 651 (1984)
Born, M., Wolf, E.: Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light. Elsevier, Amsterdam (2013)
Motka, L., Stoklasa, B., D’Angelo, M., Facchi, P., Garuccio, A., Hradil, Z., Pascazio, S., Pepe, F., Teo, Y., Řeháček, J., et al.: Optical resolution from Fisher information. Eur. Phys. J. Plus 131(5), 130 (2016)
Acknowledgements
I thank Marc Lopez for discussions and encouragement in this project. This work was supported by Chapman University during the Superoscillations—Theoretical Aspects and Applications Symposium, held in Cetraro, Italy from June 15 to 16, 2019. I thank Daniele Struppa for the invitation.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Jordan, A.N. Superresolution using supergrowth and intensity contrast imaging. Quantum Stud.: Math. Found. 7, 285–292 (2020). https://doi.org/10.1007/s40509-019-00214-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40509-019-00214-5