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The Fall of Rayleigh’s Curse

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The Hope Diamond; Egypt’s infamous Tutankhamun; Turáni átok in Hungary — all are associated with purported curses that continue to plague believers around the world.

The optics world has a curse of its own, of sorts — one that has recently been disproven thanks to the work of a team of international scientists.

Here are two points separated by Rayleigh’s limit, as demonstrated in the research.

Optical resolution is the ability of an imaging system to distinguish between closely spaced objects. Here are two points separated by Rayleigh’s limit, as demonstrated in the research. Courtesy of Martin Paúr/Palacký University.

Named after English physicist Lord Rayleigh, the so-called Rayleigh’s curse or criterion is a unversally held standard that specifies the minimum separation between two incoherent point sources that may be resolved into distinct objects. It restricts the minimum distance that can be distinguished with visible light, on the order of 0.1 µm, limiting the resolution of cameras, microscopes and telescopes.

This “is a great limitation to our ability to see finer details,” according to Luis Sánchez-Soto, a professor at the Complutense University of Madrid and a researcher at the Max Planck Institute for the Science of Light.

He and a team from Palacký University, Olomouc, in the Czech Republic, have broken this limit, reaching resolutions up to 17 times lower than those previously asserted, and demonstrating that Rayleigh’s is not a fundamental curse, but rather the result of not having chosen a good detection strategy. A model optical system would resolve a point perfectly as a point, according to the researchers, but the wave nature of light prompts diffraction caused by the limiting edges of a system’s apertures. The resulting image points are a blur.

In their experiments — documented in a paper published in OSA’s Optica in October (doi: 10.1364/OPTICA.3.001144) — the researchers found the Rayleigh limitation can be overcome with suitable measurements. They generated two incoherent point-like sources using a digital light projector that employs a digital micromirror chip with square micromirrors, each 7.6 μm in size. This provided precise control of the points’ separation by individually addressing two particular micromirrors. The digital chip was illuminated by an intensity-stabilized HeNe laser equipped with an expander for a sufficiently uniform beam, the researchers said, and the spatial incoherence was ensured by “switching between the two object points so that only one was ON at a time, keeping the switching time well below the detector time resolution.”

“So far, all our telescopes or microscopes directly observed intensity. Here we proposed a scheme that optimizes the information obtainable and can exceed the Rayleigh limit,” Sánchez-Soto said.

The researchers’ methods were found to surpass traditional imaging in resolving two closely spaced point sources. The results of the experiments show that diffraction resolution limits are the consequence of traditional imaging techniques that discard phase information. The researchers note that their findings suggest other directions of research, as well. The point source represents a natural unit for image processing, and other signal units could be further expanded and processed in a similar way.

“Optimal detection can then be tailored to suit the desired target. This clearly provides a novel and not yet explored avenue for image processing protocols,” according to the study. The researchers “firmly believe that this approach will have a broad range of applications in the near future,” calling new applications for their breakthrough “indubitable.”

“Textbook optics should be reconsidered and Rayleigh’s limit shall be placed in a broader context,” Sánchez-Soto said.

Several groups of scientists had the goal of dispelling Rayleigh’s curse, using other techniques. The Madrid/Palacký team is the first to achieve it.

Dec 2016
Rayleigh’s curseimagingRayleigh criterionLord RayleighcamerasmicroscopestelescopesComplutense University of MadridMax Planck Institute for the Science of LightPalacký University Olomoucmicromirrordigital light projectorPicture This

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