According to the widely accepted Rayleigh criterion, in order to resolve two distant point sources, their angular separation must be larger than 1.22 (the wavelength of light divided by the telescope’s aperture diameter. To achieve higher resolutions, telescope systems with ever larger primary mirrors are therefore being designed, making them extremely expensive and technologically challenging to build.
By calculating the Fisher information for the case of conventional image-plane photon counting, it has been shown that the information drops to zero as the separation of the point sources goes to zero – a phenomenon that has been dubbed Rayleigh’s curse. Nevertheless, by changing the measurement scheme, it is possible to have a non-zero Fisher information for every source separation and rendering the Rayleigh criterion moot. Limitations on our ability to resolve two incoherent point sources is therefore not a fundamental constraint, but rather a consequence of the most commonly applied measurement technique – wherein a pixelated detector is used to measure the light intensity distribution in the image plane of the system.
Stephen Felming and colleagues has an improved measurement scheme uses spatial light demultiplexing, in which the electric field in the image plane is decomposed into a set of spatially independent modes – for example HermiteGaussian (also TEM) modes. By measuring the corresponding signal in a number of lower order modes, it is then possible to extract information about the separation and brightness of the two point sources, even for separations below the conventional resolution limit. By decomposing the image field into a symmetric and an antisymmetric mode, the method has already been experimentally tested and proven to work for two equally bright incoherent point sources.
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