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SPIE Conference on Nonlinear Optics and its Applications

Separation estimation of two incoherent point sources using sum frequency generation.

Maxime Mertens, Ilya Karuseichyk, Romain Demur, Luc Leviandier, Arnaud Grisard, Nicolas Treps

Published Jun 20, 2024• 0 citations
Publisher

Abstract

In the context of separation estimation between two incoherent point sources, it has recently been shown that an optimal measurement strategy, which saturates the quantum Cramer-Rao bound, involves the use of spatial mode demultiplexing method (SPADE). To realize mode selective measurement required for SPADE, we propose a new approach based on sum frequency generation (SFG). The conversion of infrared light coming from two incoherent point sources is performed in a periodically-poled lithium niobate (PPLN) crystal by mean of a spatially shaped pump laser. By analyzing the converted images obtained with pump beams shaped as Hermite-Gaussian (HG) modes, we demonstrate the mode-sorting capabilities of this system. Our experiment, shows that our measurement method can estimate separations in sub-Rayleigh regime with improved accuracy compared to the traditional direct imaging method.

DOI
10.1117/12.3017599

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In the context of separation estimation between two incoherent point sources, it has recently been shown that an optimal measurement strategy, which saturates the quantum Cramer-Rao bound, involves the use of spatial mode demultiplexing method (SPADE). To realize mode selective measurement required for SPADE, we propose a new approach based on sum frequency generation (SFG). The conversion of infrared light coming from two incoherent point sources is performed in a periodically-poled lithium niobate (PPLN) crystal by mean of a spatially shaped pump laser. By analyzing the converted images obtained with pump beams shaped as Hermite-Gaussian (HG) modes, we demonstrate the mode-sorting capabilities of this system. Our experiment, shows that our measurement method can estimate separations in sub-Rayleigh regime with improved accuracy compared to the traditional direct imaging method.
Abstract Achieving resolution in the sub-Rayleigh regime (superresolution) is one of the rapidly developing topics in quantum optics and metrology. Recently, it was shown that perfect measurement based on spatial mode demultiplexing (SPADE) in Hermite–Gauss modes allows one to reach the quantum limit of precision for estimation of separation between two weak incoherent stationary sources. Since then, different imperfections such as misalignment or crosstalk between modes have been studied to check how this result translates into more realistic experimental setups. In this paper, we consider another deviation from the perfect setup by discarding the assumption about the stationarity of the sources. This is relevant for example for astrophysical applications where planets necessarily orbit around the star. We analyze two examples of dynamics: rotations and oscillations, showing the robustness of the SPADE-based measurement against them. The analysis is based on Fisher information, which allows one to obtain the precision limit through Cramér–Rao bound. Furthermore, we formulate a measurement algorithm that allows for the reduction of one parameter for estimation (system orientation angle) in the stationary sources scenario, maintaining the measurement precision despite the lack of knowledge about this parameter.
Spatial-mode demultiplexing (SPADE) has recently been adopted to measure the separation in the transverse plane between two incoherent point-like sources with sub-wavelength separation. It has been argued that this approach may yield extraordinary performances in the photon-counting regime. Here, we explore SPADE as a tool for precision measurements in the regime of bright, incoherent sources. First we analyze the general problem of estimating the second moments of the source's intensity distribution, for an extended incoherent source of any shape. Our theory predicts a substantial improvement in signal-to-noise ratio (SNR) of SPADE over direct imaging in the sub-wavelength regime. Second, we present an experimental application of SPADE to the case of two point-like, bright sources. We demonstrate the use of this setup for the estimation of the transverse separation and for the estimation of the relative intensity, confirming the expected improvement in SNR.
Resolving light sources below the diffraction limit is a fundamental task both for astronomy and microscopy. Several recent works analysed this problem through the lens of quantum parameter estimation theory and proved that the separation between two point sources can be estimated at the quantum limit using intensity measurements after spatial-mode demultiplexing. We implement this technique and provide an optimal estimator based on a linear combination of demultiplexed intensity measurements [1]–[3]. Our experimental setup (see Fig. 1 (left)) allows for the generation of the images of two sources, with tunable mutual coherence, as well as for spatial mode demultiplexing to estimate their separation [4].
Resolving light sources below the diffraction limit is a fundamental task both for astronomy and microscopy. Several recent works analysed this problem through the lens of quantum parameter estimation theory and proved that the separation between two point sources can be estimated at the quantum limit using intensity measurements after spatial-mode demultiplexing. We implement this technique and provide an optimal estimator based on a linear combination of demultiplexed intensity measurements [1–3]. Our experimental setup allows for the generation of the images of two sources, with tunable mutual coherence, as well as for spatial mode demultiplexing to estimate their separation [4].
The development of super-resolution techniques, i.e., allowing for efficient resolution below the Rayleigh limit, became one of the important branches in contemporary optics and metrology. Recent findings show that perfect spatial mode demultiplexing (SPADE) into Hermite-Gauss modes followed by photon counting enables one to reach the quantum limit of precision in the task of estimation of separation between two weak stationary sources in the sub-Rayleigh regime. In order to check the limitations of the method, various imperfections such as misalignment or crosstalk between the modes were considered. Possible applications of the method in microscopy call for the adaptive measurement scheme, as the position of the measured system can evolve in time, causing non-negligible misalignment. In this paper, we examine the impact of Brownian motion of the center of the system of two weak incoherent sources on adaptive SPADE measurement precision limits. The analysis is carried out using Fisher information, from which the limit of precision can be obtained by Cramér-Rao bound. As a result, we find that Rayleigh's curse is present in such a scenario; however, SPADE measurement can outperform perfect direct imaging. What is more, a suitable adjustment of the measurement time between alignments allows measurement with near-optimal precision.