Photon Shot Noise Research Articles

Monte Carlo Diffusion-Enhanced Photon Inference: Distance Distributions and Conformational Dynamics in Single-Molecule FRET.

Single-molecule Förster resonance energy transfer (smFRET) is utilized to study the structure and dynamics of many biomolecules, such as proteins, DNA, and their various complexes. The structural assessment is based on the well-known Förster relationship between the measured efficiency of energy transfer between a donor (D) and an acceptor (A) dye and the distance between them. Classical smFRET analysis methods called photon distribution analysis (PDA) take into account photon shot-noise, D-A distance distribution, and, more recently, interconversion between states in order to extract accurate distance information. It is known that rapid D-A distance fluctuations on the order of the D lifetime (or shorter) can increase the measured mean FRET efficiency and thus decrease the estimated D-A distance. Nonetheless, this effect has been so far neglected in smFRET experiments, potentially leading to biases in estimated distances. Here we introduce a PDA approach dubbed Monte Carlo diffusion-enhanced photon inference (MC-DEPI). MC-DEPI recolor detected photons of smFRET experiments taking into account dynamics of D-A distance fluctuations, multiple interconverting states, and photoblinking. Using this approach, we show how different underlying conditions may yield identical FRET histograms and how the additional information from fluorescence decays helps in distinguishing between the different conditions. We also introduce a machine learning fitting approach for retrieving the D-A distance distribution, decoupled from the above-mentioned effects. We show that distance interpretation of smFRET experiments of even the simplest dsDNA is nontrivial and requires decoupling the effects of rapid D-A distance fluctuations on FRET in order to avoid systematic biases in the estimation of the D-A distance distribution.

Evaluation of EUV mask impacts on wafer line-width roughness using aerial and SEM image analyses

As more aggressive EUV imaging techniques and resists with lower intrinsic roughness are developed for patterning at 7- and 5-nm technology nodes, EUV mask roughness will contribute an increasing portion of the total printed line-width roughness (LWR). We perform a comprehensive characterization of the EUV mask impacts on wafer LWR using actinic aerial images and wafer SEM images. Analytical methods are developed to properly separate and compare the LWR effects from EUV masks, photon shot noise, and resist stochastics. The use of EUV AIMS™ to emulate and measure incident photon shot noise effects is explored and demonstrated. A sub 10-nm EUV mask is qualified using EUV AIMS™ with scanner equivalent dose settings that are required for patterning 16- and 18-nm half-pitch L/S features. Typical chemically amplified EUV resists with low- and high-dose sensitivities are patterned and characterized with SEM metrology. The variance and spectral components contributing to wafer LWR are quantified and compared. Our analysis shows that speckle-induced aerial LWR is not a significant factor at the experimental imaging conditions when ML roughness is 50-pm rms. At the current scanner dose levels, mask absorber pattern roughness is a major factor in aerial LWR, but not as significant a contributor to wafer LWR where resist stochastics still dominate.

A convex 3D deconvolution algorithm for low photon count fluorescence imaging

Deconvolution is widely used to improve the contrast and clarity of a 3D focal stack collected using a fluorescence microscope. But despite being extensively studied, deconvolution algorithms can introduce reconstruction artifacts when their underlying noise models or priors are violated, such as when imaging biological specimens at extremely low light levels. In this paper we propose a deconvolution method specifically designed for 3D fluorescence imaging of biological samples in the low-light regime. Our method utilizes a mixed Poisson-Gaussian model of photon shot noise and camera read noise, which are both present in low light imaging. We formulate a convex loss function and solve the resulting optimization problem using the alternating direction method of multipliers algorithm. Among several possible regularization strategies, we show that a Hessian-based regularizer is most effective for describing locally smooth features present in biological specimens. Our algorithm also estimates noise parameters on-the-fly, thereby eliminating a manual calibration step required by most deconvolution software. We demonstrate our algorithm on simulated images and experimentally-captured images with peak intensities of tens of photoelectrons per voxel. We also demonstrate its performance for live cell imaging, showing its applicability as a tool for biological research.

Josephson Parametric Reflection Amplifier with Integrated Directionality

A directional superconducting parametric amplifier in the GHz frequency range is designed and analyzed, suitable for low-power read-out of microwave kinetic inductance detectors employed in astrophysics and when combined with a nonreciprocal device at its input also for circuit quantum electrodynamics (cQED). It consists of an one wavelength long nondegenerate Josephson parametric reflection amplifier circuit. The device has two Josephson junction oscillators, connected via a tailored impedance to an on-chip passive circuit which directs the in- to the output port. The amplifier provides a gain of 20 dB over a bandwidth of 220 MHz on the signal as well as on the idler portion of the amplified input and the total photon shot noise referred to the input corresponds to maximally 1.3 photons per second per Hertz of bandwidth. We predict a factor of four increase in dynamic range compared to conventional Josephson parametric amplifiers.

Complementary aspects of spatial resolution and signal-to-noise ratio in computational imaging

A generic computational imaging setup is considered which assumes sequential illumination of a semi-transparent object by an arbitrary set of structured illumination patterns. For each incident illumination pattern, all transmitted light is collected by a photon-counting bucket (single-pixel) detector. The transmission coefficients measured in this way are then used to reconstruct the spatial distribution of the object's projected transmission. It is demonstrated that the squared spatial resolution of such a setup is usually equal to the ratio of the image area to the number of linearly independent illumination patterns. If the noise in the measured transmission coefficients is dominated by photon shot noise, then the ratio of the spatially-averaged squared mean signal to the spatially-averaged noise variance in the "flat" distribution reconstructed in the absence of the object, is equal to the average number of registered photons when the illumination patterns are orthogonal. The signal-to-noise ratio in a reconstructed transmission distribution is always lower in the case of non-orthogonal illumination patterns due to spatial correlations in the measured data. Examples of imaging methods relevant to the presented analysis include conventional imaging with a pixelated detector, computational ghost imaging, compressive sensing, super-resolution imaging and computed tomography.

Detection of small-amplitude periodic surface pressure fluctuation by pressure-sensitive paint measurements using frequency-domain methods

Image measurement using pressure-sensitive paint (PSP) is an effective tool for analyzing the unsteady pressure field on the surface of a body in a low-speed air flow, which is associated with wind noise. In this study, the surface pressure fluctuation due to the tonal trailing edge (TE) noise for a two-dimensional NACA 0012 airfoil was quantitatively detected using a porous anodized aluminum PSP (AA-PSP). The emission from the PSP upon illumination by a blue laser diode was captured using a 12-bit high-speed complementary metal-oxide-semiconductor (CMOS) camera. The intensities of the captured images were converted to pressures using a standard intensity-based method. Three image-processing methods based on the fast Fourier transform (FFT) were tested to determine their efficiency in improving the signal-to-noise ratio (SNR) of the unsteady PSP data. In addition to two fundamental FFT techniques (the full data and ensemble averaging FFTs), a technique using the coherent output power (COP), which involves the cross correlation between the PSP data and the signal measured using a pointwise sound-level meter, was tested. Preliminary tests indicated that random photon shot noise dominates the intensity fluctuations in the captured PSP emissions above 200 Hz. Pressure fluctuations associated with the TE noise, whose dominant frequency is approximately 940 Hz, were successfully measured by analyzing 40,960 sequential PSP images recorded at 10 kfps. Quantitative validation using the power spectrum indicates that the COP technique is the most effective method of identification of the pressure fluctuation directly related to TE noise. It is possible to distinguish power differences with a resolution of 10 Pa $$^2$$ (4 Pa in amplitude) when the COP was employed without use of another wind-off data. This resolution cannot be achieved by the ensemble averaging FFT because of an insufficient elimination of the background noise.

Gravitational wave detection using laser interferometry beyond the standard quantum limit.

Interferometric gravitational wave detectors (such as advanced LIGO) employ high-power solid-state lasers to maximize their detection sensitivity and hence their reach into the universe. These sophisticated light sources are ultra-stabilized with regard to output power, emission frequency and beam geometry; this is crucial to obtain low detector noise. However, even when all laser noise is reduced as far as technically possible, unavoidable quantum noise of the laser still remains. This is a consequence of the Heisenberg Uncertainty Principle, the basis of quantum mechanics: in this case, it is fundamentally impossible to simultaneously reduce both the phase noise and the amplitude noise of a laser to arbitrarily low levels. This fact manifests in the detector noise budget as two distinct noise sources-photon shot noise and quantum radiation pressure noise-which together form a lower boundary for current-day gravitational wave detector sensitivities, the standard quantum limit of interferometry. To overcome this limit, various techniques are being proposed, among them different uses of non-classical light and alternative interferometer topologies. This article explains how quantum noise enters and manifests in an interferometric gravitational wave detector, and gives an overview of some of the schemes proposed to overcome this seemingly fundamental limitation, all aimed at the goal of higher gravitational wave event detection rates.This article is part of a discussion meeting issue 'The promises of gravitational-wave astronomy'.

Coherence properties of the 0-π qubit

Superconducting circuits rank among some of the most interesting architectures for the implementation of quantum information processing devices. The recently proposed 0-π qubit (Brooks et al 2013 Phys. Rev. A 87 52306) promises increased protection from spontaneous relaxation and dephasing. In this paper we present a detailed theoretical study of the coherence properties of the 0-π device, investigate relevant decoherence channels, and show estimates for achievable coherence times in multiple parameter regimes. In our analysis, we include disorder in circuit parameters, which results in the coupling of the qubit to a low-energy, spurious harmonic mode. We analyze the effects of such coupling on decoherence, in particular dephasing due to photon shot noise, and outline how such a noise channel can be mitigated by appropriate parameter choices. In the end we find that the 0-π qubit performs well and may become an attractive candidate for the implementation of the next-generation superconducting devices for uses in quantum computing and information.

Multi-Aperture-Based Probabilistic Noise Reduction of Random Telegraph Signal Noise and Photon Shot Noise in Semi-Photon-Counting Complementary-Metal-Oxide-Semiconductor Image Sensor.

A probabilistic method to remove the random telegraph signal (RTS) noise and to increase the signal level is proposed, and was verified by simulation based on measured real sensor noise. Although semi-photon-counting-level (SPCL) ultra-low noise complementary-metal-oxide-semiconductor (CMOS) image sensors (CISs) with high conversion gain pixels have emerged, they still suffer from huge RTS noise, which is inherent to the CISs. The proposed method utilizes a multi-aperture (MA) camera that is composed of multiple sets of an SPCL CIS and a moderately fast and compact imaging lens to emulate a very fast single lens. Due to the redundancy of the MA camera, the RTS noise is removed by the maximum likelihood estimation where noise characteristics are modeled by the probability density distribution. In the proposed method, the photon shot noise is also relatively reduced because of the averaging effect, where the pixel values of all the multiple apertures are considered. An extremely low-light condition that the maximum number of electrons per aperture was the only 2 was simulated. PSNRs of a test image for simple averaging, selective averaging (our previous method), and the proposed method were 11.92 dB, 11.61 dB, and 13.14 dB, respectively. The selective averaging, which can remove RTS noise, was worse than the simple averaging because it ignores the pixels with RTS noise and photon shot noise was less improved. The simulation results showed that the proposed method provided the best noise reduction performance.

Subdiffraction incoherent optical imaging via spatial-mode demultiplexing: Semiclassical treatment

I present a semiclassical analysis of a spatial-mode demultiplexing (SPADE) measurement scheme for far-field incoherent optical imaging under the effects of diffraction and photon shot noise. Building on previous results that assume two point sources or the Gaussian point-spread function, I generalize SPADE for a larger class of point-spread functions and evaluate its errors in estimating the moments of an arbitrary subdiffraction object. Compared with the limits to direct imaging set by the Cram\'er-Rao bounds, the results show that SPADE can offer far superior accuracy in estimating the second and higher-order moments.

Model-assisted measuring method for periodical sub-wavelength nanostructures.

This paper describes a scatterometry approach designed by simulations for the in-line characterization of sub-wavelength sinusoidal gratings, which are formed on a transparent foil in a roll-to-roll procedure. Currently used methods are based on series of in situ measurements of the specular optical response at different incident angles or wavelengths for acquiring dimensional information on the gratings. The capability of single measurements of the first diffraction maxima at a fixed incident angle and wavelength to accurately measure the height of the sub-wavelength sinusoidal gratings is investigated in this work. The relation between the scattered powers of the diffraction maxima and the grating height is extracted from light scattering simulations, i.e., the inverse problem is solved. Optimal setup parameters for the measurement of grating heights ranging from 100nm to 300nm are derived from simulations. Limits of measurability and the measurement uncertainty are evaluated for different instrumentation and simulation parameters. When using laser light in the visible wavelength range, the measurement uncertainty is physically limited by the photon shot noise to the picometer range, but the systematic contributions dominate the uncertainty. As a result, the measurement uncertainty for the grating height is estimated to ≤12 nm, with a potential for <4 nm. Large-area scanning measurements performed offline and reference atomic force microscopy measurements verify the sensitivity of the presented measurement approach for identifying local variations of the spatial surface properties. Depending on the chosen detection system, sampling rates up to the MHz range are feasible, meeting the requirements of in-line process control of the roll-to-roll production process.

Appropriate Probe Condition for Absorption Imaging of Ultracold6Li Atoms

One of the readily accessible observables in trapped cold-atom experiments is the column density, which is determined from optical depth (OD) obtained from absorption imaging and the absorption cross-section ($\sigma_{\rm abs}$). Here we report on simple and accurate determination of OD for dense gases of light atoms such as lithium-6. We investigate theoretically and experimentally an appropriate condition for the probe intensity and duration to achieve good signal-to-noise ratio by considering the influences of photon recoils and photon shot noises. As a result, we have succeeded in measuring OD which reached 2.5 with a signal-to-noise ratio of 10 under spatial resolution of 1.7 $\mu$m.

Determination of extracellular matrix collagen fibril architectures and pathological remodeling by polarization dependent second harmonic microscopy

Polarization dependence second harmonic generation (P-SHG) microscopy is gaining increase popularity for in situ quantification of fibrillar protein architectures. In this report, we combine P-SHG microscopy, new linear least square (LLS) fitting and modeling to determine and convert the complex second-order non-linear optical anisotropy parameter ρ of several collagen rich tissues into a simple geometric organization of collagen fibrils. Modeling integrates a priori knowledge of polyhelical organization of collagen molecule polymers forming fibrils and bundles of fibrils as well as Poisson photonic shot noise of the detection system. The results, which accurately predict the known sub-microscopic hierarchical organization of collagen fibrils in several tissues, suggest that they can be subdivided into three classes according to their microscopic and macroscopic hierarchical organization of collagen fibrils. They also show, for the first time to our knowledge, intrahepatic spatial discrimination between genuine fibrotic and non-fibrotic vessels. CCl4-treated livers are characterized by an increase in the percentage of fibrotic vessels and their remodeling involves peri-portal compaction and alignment of collagen fibrils that should contribute to portal hypertension. This integrated P-SHG image analysis method is a powerful tool that should open new avenue for the determination of pathophysiological and chemo-mechanical cues impacting collagen fibrils organization.

Detecting Friedel oscillations in ultracold Fermi gases

Investigating Friedel oscillations in ultracold gases would complement the studies performed on solid state samples with scanning-tunneling microscopes. In atomic quantum gases interactions and external potentials can be tuned freely and the inherently slower dynamics allow to access non-equilibrium dynamics following a potential or interaction quench. Here, we examine how Friedel oscillations can be observed in current ultracold gas experiments under realistic conditions. To this aim we numerically calculate the amplitude of the Friedel oscillations which are induced by a potential barrier in a 1D Fermi gas and compare it to the expected atomic and photonic shot noise in a density measurement. We find that to detect Friedel oscillations the signal from several thousand one-dimensional systems has to be averaged. However, as up to 100 parallel one-dimensional systems can be prepared in a single run with present experiments, averaging over about 100 images is sufficient.Graphical abstract

Fundamental uncertainty limit for speckle displacement measurements.

The basic metrological task in speckle photography is to quantify displacements of speckle patterns, allowing for instance the investigation of the mechanical load and modification of objects with rough surfaces. However, the fundamental limit of the measurement uncertainty due to photon shot noise is unknown. For this reason, the Cramér-Rao bound (CRB) is derived for speckle displacement measurements, representing the squared minimal achievable measurement uncertainty. As result, the CRB for speckle patterns is only two times the CRB for an ideal point light source. Hence, speckle photography is an optimal measurement approach for contactless displacement measurements on rough surfaces. In agreement with a derivation from Heisenberg's uncertainty principle, the CRB depends on the number of detected photons and the diffraction limit of the imaging system described by the speckle size. The theoretical results are verified and validated, demonstrating the capability for displacement measurements with nanometer resolution.

Magnetometry via spin-mechanical coupling in levitated optomechanics.

We analyze magnetometry using an optically levitated nanodiamond. We consider a configuration where a magnetic field gradient couples the mechanical oscillation of the diamond with its spin degree of freedom provided by a nitrogen vacancy center. First, we investigate the measurement of the position spectrum of the mechanical oscillator. We find that conditions of ultrahigh vacuum and feedback cooling allow a magnetic field gradient sensitivity of 1μTm-1/Hz. At high pressure and room temperature, this sensitivity degrades and can attain a value of the order of 100mTm-1/Hz. Subsequently, we characterize the magnetic field gradient sensitivity obtainable by maneuvering the spin degrees of freedom using Ramsey interferometry. We find that this technique can offer photon-shot noise and spin-projection noise limited magnetic field gradient sensitivity of 100μTm-1/Hz. We conclude that this hybrid levitated nanomechanical magnetometer provides a favorable and versatile platform for sensing applications.

A noise-immune cavity-assisted non-destructive detection for an optical lattice clock in the quantum regime

We present and implement a non-destructive detection scheme for the transition probability readout of an optical lattice clock. The scheme relies on a differential heterodyne measurement of the dispersive properties of lattice-trapped atoms enhanced by a high finesse cavity. By design, this scheme offers a 1st order rejection of the technical noise sources, an enhanced signal-to-noise ratio, and an homogeneous atom-cavity coupling. We theoretically show that this scheme is optimal with respect to the photon shot noise limit. We experimentally realise this detection scheme in an operational strontium optical lattice clock. The resolution is on the order of a few atoms with a photon scattering rate low enough to keep the atoms trapped after detection. This scheme opens the door to various different interrogations protocols, which reduce the frequency instability, including atom recycling, zero-dead time clocks with a fast repetition rate, and sub quantum projection noise frequency stability.

Resistive flow sensing of vital mitochondria with nanoelectrodes

We report label-free detection of single mitochondria with high sensitivity using nanoelectrodes. Measurements of the conductance of carbon nanotube transistors show discrete changes of conductance as individual mitochondria flow over the nanoelectrodes in a microfluidic channel. Altering the bioenergetic state of the mitochondria by adding metabolites to the flow buffer induces changes in the mitochondrial membrane potential detected by the nanoelectrodes. During the time when mitochondria are transiently passing over the nanoelectrodes, this (nano) technology is sensitive to fluctuations of the mitochondrial membrane potential with a resolution of 10mV with temporal resolution of order milliseconds. Fluorescence based assays (in ideal, photon shot noise limited setups) are shown to be an order of magnitude less sensitive than this nano-electronic measurement technology. This opens a new window into the dynamics of an organelle critical to cellular function and fate.

Thresholds and noise limitations of colour vision in dim light.

Colour discrimination is based on opponent photoreceptor interactions, and limited by receptor noise. In dim light, photon shot noise impairs colour vision, and in vertebrates, the absolute threshold of colour vision is set by dark noise in cones. Nocturnal insects (e.g. moths and nocturnal bees) and vertebrates lacking rods (geckos) have adaptations to reduce receptor noise and use chromatic vision even in very dim light. In contrast, vertebrates with duplex retinae use colour-blind rod vision when noisy cone signals become unreliable, and their transition from cone- to rod-based vision is marked by the Purkinje shift. Rod-cone interactions have not been shown to improve colour vision in dim light, but may contribute to colour vision in mesopic light intensities. Frogs and toads that have two types of rods use opponent signals from these rods to control phototaxis even at their visual threshold. However, for tasks such as prey or mate choice, their colour discrimination abilities fail at brighter light intensities, similar to other vertebrates, probably limited by the dark noise in cones.This article is part of the themed issue 'Vision in dim light'.

Rydberg-atom based radio-frequency electrometry using frequency modulation spectroscopy in room temperature vapor cells.

Rydberg atom-based electrometry enables traceable electric field measurements with high sensitivity over a large frequency range, from gigahertz to terahertz. Such measurements are particularly useful for the calibration of radio frequency and terahertz devices, as well as other applications like near field imaging of electric fields. We utilize frequency modulated spectroscopy with active control of residual amplitude modulation to improve the signal to noise ratio of the optical readout of Rydberg atom-based radio frequency electrometry. Matched filtering of the signal is also implemented. Although we have reached similarly, high sensitivity with other read-out methods, frequency modulated spectroscopy is advantageous because it is well-suited for building a compact, portable sensor. In the current experiment, ∼3 µV cm-1 Hz-1/2 sensitivity is achieved and is found to be photon shot noise limited.