EDP Sciences
Free Access
Erratum
This article is an erratum for: [this article]

Issue
A&A
Volume 582, October 2015
Article Number C3
Number of page(s) 1
Section Astronomical instrumentation
DOI https://doi.org/10.1051/0004-6361/201322665e
Published online 16 October 2015

In Sect. 3.3 of Kellerer (2014) I suggested detector read-out times below the coherence time of photons. If one assumes, instead, read-out times not less than the coherence time, Δt = λ2/(c Δλ), the spontaneous photons exceed, even for a very small field-of-view, the number of stimulated photons per incoming photon.

With the notation employed in  Kellerer (2014) the mean number of cloned photons per incoming photon is: (1)where I is the number of excited atoms, σ is the cross-section of excited atoms and S is the aperture- and amplifier-area. A field of angular diameter θ = 2.44 λ/D – where D is the aperture diameter – corresponds to the Airy disc up to its first minimum. Within the read-out time Δt = λ2/ (c Δλ), equal to the photon coherence time, this “diffraction area” receives a mean number of spontaneous photons: (2)A is the spontaneous emission rate.

From these relations one obtains the average fluence ratio of spontaneous and stimulated photons on the diffraction area: (3)

in line with calculations by Prasad (1994) and his conclusions that the spontaneous emissions dominate the stimulated ones. On the other hand, on average 0.64 N cloned photons end up on the central standard deviation range of diameter 1/3 of the Airy disc. This area is 9 times smaller than the Airy disc considered above. Thus the ratio of spontaneous to stimulated fluence is not 7.3 but merely 7.3/(9 × 0.64) ~ 1.3 in this region around the centre of the cloned photons.

The spontaneous photons will prevent a large improvement of resolution as long as our set-up lacks a stage to recognize events where the stimulated emissions dominate. Such a stage is in principle possible, see notably the probabilistic noiseless amplification processes discussed by Duan & Guo (1998), Ralph & Lund (2009). The main message of my article remains: it is fundamentally possible to improve the resolution of a telescope beyond the diffraction limit at the price of sensitivity, i.e. it is possible to trade sensitivity against resolution. The set-up that I have suggested will be incomplete unless it is given a suitable heralding stage.

References


© ESO, 2015

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.