# Subdiffraction incoherent optical imaging via spatial-mode demultiplexing

@article{Tsang2017SubdiffractionIO, title={Subdiffraction incoherent optical imaging via spatial-mode demultiplexing}, author={Mankei Tsang}, journal={New Journal of Physics}, year={2017}, volume={19} }

I propose a spatial-mode demultiplexing (SPADE) measurement scheme for the far-field imaging of spatially incoherent optical sources. For any object too small to be resolved by direct imaging under the diffraction limit, I show that SPADE can estimate its second or higher moments much more precisely than direct imaging can fundamentally do in the presence of photon shot noise. I also prove that SPADE can approach the optimal precision allowed by quantum mechanics in estimating the location and…

## 78 Citations

### Efficient superoscillation measurement for incoherent optical imaging

- Physics
- 2020

A superoscillation measurement method for subdiffraction incoherent optical sources, with potential applications in astronomy, remote sensing, fluorescence microscopy, and spectroscopy, that can capture all the light on the aperture in principle, perform better than direct imaging with image processing on statistical terms, and approach the fundamental quantum limit.

### Quantum limit to subdiffraction incoherent optical imaging. II. A parametric-submodel approach

- Physics, MathematicsPhysical Review A
- 2021

In a previous paper [M. Tsang, Phys. Rev. A 99, 012305 (2019)], I proposed a quantum limit to the estimation of object moments in subdiffraction incoherent optical imaging. In this sequel, I prove…

### Semiparametric bounds for subdiffraction incoherent optical imaging: a parametric-submodel approach

- Physics
- 2020

I derive classical and quantum lower error bounds for moment estimation in subdiffraction incoherent optical imaging. While the end results are similar to earlier ones [Tsang, Phys. Rev. Res. 1,…

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- Physics
- 2020

We present the experimental implementation of simultaneous spatial multimode demultiplexing as a distance measurement tool. We first show a simple and intuitive derivation of the Fisher information…

### Superresolution Linear Optical Imaging in the Far Field

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- 2021

The resolution of optical imaging devices is ultimately limited by the diffraction of light. To circumvent this limit, modern super-resolution microscopy techniques employ active interaction with the…

### Multiparameter quantum metrology of incoherent point sources: Towards realistic superresolution

- Physics
- 2017

We establish the multiparameter quantum Cram\'er-Rao bound for simultaneously estimating the centroid, the separation, and the relative intensities of two incoherent optical point sources using…

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- Physics
- 2016

The Rayleigh limit has so far applied to all microscopy techniques that rely on linear optical interaction and detection in the far field. Here we demonstrate that detecting the light emitted by an…

### Quantum-limited estimation of the axial separation of two incoherent point sources

- PhysicsOptica
- 2019

Spatial mode demultiplexing has recently been proposed as a method to overcome the diffraction limits and can be used to precisely measure the transverse separation between two point sources. Here we…

### Towards Superresolution Surface Metrology: Quantum Estimation of Angular and Axial Separations.

- PhysicsPhysical review letters
- 2019

Using quantum metrology techniques, it is shown that a simultaneous estimation of the two separations is achievable by a single quantum measurement, with a precision saturating the ultimate limit stemming from the quantum Cramér-Rao bound.

### Quantum Limits to Incoherent Imaging are Achieved by Linear Interferometry.

- PhysicsPhysical review letters
- 2020

Insight is provided into the phenomenon of superresolution through incoherent imaging that has attracted much attention recently and will find a wide range of applications over a broad spectrum of frequencies, from fluorescence microscope to stellar interferometry.

## References

SHOWING 1-10 OF 142 REFERENCES

### Multiparameter quantum metrology of incoherent point sources: Towards realistic superresolution

- Physics
- 2017

We establish the multiparameter quantum Cram\'er-Rao bound for simultaneously estimating the centroid, the separation, and the relative intensities of two incoherent optical point sources using…

### Quantum theory of superresolution for two incoherent optical point sources

- Physics
- 2015

Rayleigh's criterion for resolving two incoherent point sources has been the most influential measure of optical imaging resolution for over a century. In the context of statistical image processing,…

### Far-field linear optical superresolution via heterodyne detection in a higher-order local oscillator mode

- Physics
- 2016

The Rayleigh limit has so far applied to all microscopy techniques that rely on linear optical interaction and detection in the far field. Here we demonstrate that detecting the light emitted by an…

### Interferometric superlocalization of two incoherent optical point sources.

- PhysicsOptics express
- 2016

A novel interferometric method for estimating the separation of two incoherent point sources with a mean squared error that does not deteriorate as the sources are brought closer, demonstrating the superlocalization effect for separations well below that set by the Rayleigh criterion.

### Far-Field Superresolution of Thermal Electromagnetic Sources at the Quantum Limit.

- PhysicsPhysical review letters
- 2016

It is shown via the quantum Cramér-Rao bound that, contrary to the Rayleigh limit in conventional direct imaging, quantum mechanics does not mandate any loss of precision in estimating even deep sub-Rayleigh separations.

### Conservative classical and quantum resolution limits for incoherent imaging

- Physics
- 2016

Abstract I propose classical and quantum limits to the statistical resolution of two incoherent optical point sources from the perspective of minimax parameter estimation. Unlike earlier results…

### Superresolving scanning optical microscopy using holographic optical processing

- Physics
- 1993

Two novel superrresolving scanning microscopes, one of which uses coherent imaging and the other incoherent imaging, are described. The optical arrangement used in the coherent microscope is similar…

### Beating Rayleigh's Curse by Imaging Using Phase Information.

- PhysicsPhysical review letters
- 2017

A simple scheme is experimentally demonstrated that captures most of the information in the full electromagnetic field in the image plane and has a greatly improved ability to estimate the distance between a pair of closely separated sources, achieving near-quantum-limited performance and immunity to Rayleigh's curse.

### MICADO: first light imager for the E-ELT

- PhysicsAstronomical Telescopes + Instrumentation
- 2016

MICADO will equip the E-ELT with a first light capability for diffraction limited imaging at near-infrared wavelengths. The instrument’s observing modes focus on various flavours of imaging,…

### Ultimate Precision Bound of Quantum and Subwavelength Imaging.

- PhysicsPhysical review letters
- 2016

The ultimate precision bound for resolving two pointlike sources in an arbitrary quantum state is established, with a simple formula for the specific case of two thermal sources, finding that quantum-correlated sources can be superresolved at the sub-Rayleigh scale.