Superresolution techniques based on intensity measurements after a spatial mode decomposition can overcome the precision of diffraction-limited direct imaging. However, realistic measurement devices always introduce finite crosstalk in any such mode decomposition. Here, we show that any nonzero crosstalk leads to a breakdown of superresolution when the number N of detected photons is large. Combining statistical and analytical tools, we obtain the scaling of the precision limits for weak, generic crosstalk from a device-independent model as a function of the crosstalk probability and N. The scaling of the smallest distance that can be distinguished from noise changes from N^{-1/2} for an ideal measurement to N^{-1/4} in the presence of crosstalk.
Superresolution techniques based on intensity measurements after a spatial mode decomposition can overcome the precision of diffraction-limited direct imaging. However, realistic measurement devices always introduce finite crosstalk in any such mode decomposition. Here, we show that any nonzero crosstalk leads to a breakdown of superresolution when the number N of detected photons is large. Combining statistical and analytical tools, we obtain the scaling of the precision limits for weak, generic crosstalk from a device-independent model as a function of the crosstalk probability and N. The scaling of the smallest distance that can be distinguished from noise changes from N^{-1/2} for an ideal measurement to N^{-1/4} in the presence of crosstalk.
Superresolution techniques based on intensity measurements after a spatial mode decomposition can overcome the precision of diffraction-limited direct imaging. We present both the experimental implementation of simultaneous spatial multimode demultiplexing as a distance measurement tool and the theoretical analysis of the actual sensitivity limits given the main experimental imperfection: cross-talks between channels. We demonstrate the distance estimation between two incoherent beams in both directions of the transverse plane, and find a perfect accordance with theoretical predictions, given a proper calibration of the demultiplexer. We show that, even though sensitivity is limited by the cross-talk between channels, we can perform measurements in two dimensions much beyond the Rayleigh limit over a large dynamic range. Combining statistical and analytical tools, we obtain the scaling of the precision limits for weak, generic crosstalk from a device-independent model as a function of the crosstalk probability and N.
Superresolution is one of the key issues at the crossroads of contemporary quantum optics and metrology. Recently, it was shown that for an idealized case of two balanced sources, spatial mode demultiplexing (SPADE) achieves resolution better than direct imaging even in the presence of measurement crosstalk [Phys. Rev. Lett. 125, 100501 (2020)]. In this work, we consider arbitrarily unbalanced sources and provide a systematic analysis of the impact of crosstalk on the resolution obtained from SPADE. As we dissect, in this generalized scenario, SPADE's effectiveness depends non-trivially on the strength of crosstalk, relative brightness and the separation between the sources. In particular, for any source imbalance, SPADE performs worse than ideal direct imaging in the asymptotic limit of vanishing source separations. Nonetheless, for realistic values of crosstalk strength, SPADE is still the superior method for several orders of magnitude of source separations.
Sensitivity limits are usually determined using the Cram\'er-Rao bound. Recently, this approach has been used to obtain the ultimate resolution limit for the estimation of the separation between two incoherent point sources. However, methods that saturate these resolution limits usually require the full measurement statistics, which can be challenging to access. In this work we introduce a simple superresolution protocol to estimate the separation between two thermal sources which relies only on the average value of a single accessible observable. We show how optimal observables for this technique may be constructed for arbitrary thermal sources and we study their sensitivities when one has access to spatially resolved intensity measurements (direct imaging) and photon counting after spatial-mode demultiplexing. For demultiplexing, our method is optimal, i.e., it saturates the quantum Cram\'er-Rao bound. We also investigate the impact of noise on the optimal observables, their measurement sensitivity, and the scaling with the number of detected photons of the smallest resolvable separation. For low signals in the image plane, we demonstrate that our method saturates the Cram\'er-Rao bound even in the presence of noise.
Conventional superresolution of closely spaced point sources using image intensity data acquired by noiseless single-photon detectors suffers from Rayleigh’s diffraction curse that can only be overcome at photon numbers that scale quartically with the degree of required superresolution. By contrast, acquiring and processing suitably chosen mode projections of the wavefront, which contain dual information of its intensity and phase, can reduce the photon budget to one that is quadratic in the degree of superresolution and achieve quantum-limited performance. Such dramatic improvements enabled by the wavefront projection (WFP) approach have been realized both in computer simulation and laboratory experiments over the last five years. The invited talk will explore the fundamental, theoretically insuperable limits on superresolution imaging by presenting computations of quantum Fisher information and practical realizations of the novel WFP approach that can reach these limits for a variety of point and extended source geometries and operating conditions.
Precision measurement has been an important research area in sensing and metrology. In classical physics, the Fisher information determines the maximum extractable information from statistically unknown signals, based on a joint probability density function of independently and identically distributed random variables. The Cramer-Rao lower bound (CRLB) indicates the minimum error of the Fisher information, generally known as the shot-noise limit. On the other hand, coherence has pushed the resolution limit further overcoming the diffraction limit using many-wave interference strictly confined to the first-order intensity correlation. However, practical implementation is limited by the lithographic constraints in, e.g., optical gratings. Recently, a coherence technique of superresolution has been introduced to overcome the diffraction limit in phase sensitivity using higher-order intensity correlations of a phase-controlled output field from an interferometer. Here, the superresolution is adopted for precision metrology in an optical spectrometer, whose enhanced frequency resolution is linearly proportional to the intensity-product order, overcoming CRLB. Unlike quantum sensing using entangled photons, this technique is purely classical and offers robust performance against environmental noises, benefiting from the interferometer's scanning mode for fringe counting.
The resolution of optical imaging devices is ultimately limited by the diffraction of light. To circumvent this limit, modern superresolution microscopy techniques employ active interaction with the object by exploiting its optical nonlinearities, nonclassical properties of the illumination beam, or near field probing. Thus, they are not applicable whenever such interaction is not possible, for example, in astronomy or noninvasive biological imaging. Far field, linear optical superresolution techniques based on passive analysis of light coming from the object would cover these gaps. In this Letter, we present the first proof-of-principle demonstration of such a technique for 2D imaging. It works by accessing information about spatial correlations of the image optical field and, hence, about the object itself via measuring projections onto Hermite-Gaussian transverse spatial modes. With a basis of 21 spatial modes in both transverse dimensions, we perform two-dimensional imaging with twofold resolution enhancement beyond the diffraction limit.