Single Speckle Research Articles

Space–time design of the tangled C-points and optical vortex chain and loop reactions in paraxial dynamic elliptic speckle fields

The unique effect of ‘optical damage’ in photorefractive LiNbO3:Fe crystals produces a developing speckle field in the propagating beam of a He–Ne laser (0.63 μm). Elliptic developing speckle fields were created and investigated thoroughly by means of the Stokes polarimetry and monstardom (Dennis 2008 Opt. Lett. 33 2572). The ergodicity of elliptic speckle fields under the index (star, monstar, lemon) and contour (elliptic, hyperbolic) classifications was revealed experimentally by our measurements for developing speckle fields, measurements for static elliptic speckle fields, as well as theory (Flossmann et al 2008 Phys. Rev. Lett. 100 203902). Both hyperbolic (H) and elliptic (E) diabolos were fixed. All the probable topological structures for the neighbour diabolos in the developing elliptic speckle field were measured. All the measured nucleation/annihilation events occur as H(S)+H(M) reactions. The evolution of the singularities occurs separately in the speckle-field areas with fixed handedness and is realized through minimizing the changes needed for the developing speckle fields at each moment. The general regularities of the elliptic speckle-field development were revealed and confirmed. They occur through the time-limited loop and continuous chain reactions in both single and multiple speckles in 1:4 proportion. Strict morphological scenarios for their evolution were found. Applications of the methods of dynamical singular optics are discussed.

Topological dynamics of optical singularities in speckle-fields induced by photorefractive scattering in a LiNbO3 : Fe crystal

A natural singular dynamics of elliptically polarised speckle-fields induced by the 'optical damage' effect in a photorefractive crystal of lithium niobate by a passing beam of a helium — neon laser is studied by the developed methods of singular optics. For the polarisation singularities (C points), a new class of chain reactions, namely, singular chain reactions are discovered and studied. It is shown that they obey the topological charge and sum Poincare index conservation laws. In addition, they exist for all the time of crystal irradiation. They consist of a series of interlocking chains, where singularity pairs arising in a chain annihilate with singularities from neighbouring independently created chains. Less often singular 'loop' reactions are observed where arising pairsof singularities annihilate after reversible transformations in within the boundaries of a single speckle. The type of a singular reaction is determined by a topology and dynamics of the speckles, in which the reactions are developing.

Simultaneous measurement of deformation and the first derivative with spatial phase-shift digital shearography

This paper presents a spatial phase-shift digital shearography system based on a modified Michelson Interferometer, which is capable of measuring out-of-plane deformation and its first derivative simultaneously. A reference beam is introduced into the Michelson Interferometer using an optical fiber. Two sheared images from the Michelson Interferometer are combined with the reference beam to generate two holograms and one shearogram. The Fourier Transform method is utilized to calculate the phase difference. To separate the spectrum in the Fourier Domain, the reference beam is tilted a small angle to create a spatial phase shift. An out-of-plane deformation and its first derivative can then be determined simultaneously from a single speckle interferogram by properly selecting filters for the spectrum image. The theory and the experimental results are presented.

Computational polarization imaging from a single speckle image

We experimentally demonstrate that imaging of the degree of polarization (DOP) can be achieved from a single intensity image acquired under coherent illumination. This computational technique is based on the analysis of the speckle characteristics in a statistically homogeneous neighborhood of the pixel. Over a variety of samples obtained experimentally, we show that a simple calibration step allows this method to quickly and simply provide correct estimated values of the DOP, with precision in agreement with theoretical predictions. It is shown that unlike linear polarimetric contrast imaging, this method remains valid on birefringent samples.

Oral Abstract Sessions: Young Investigator Award session * Thursday 8 December 2011, 12:45-13:45 * Location: Pecs

Oral Abstract Sessions: Young Investigator Award session * Thursday 8 December 2011, 12:45-13:45 * Location: Pecs

Application of the radial basis function interpolation to phase extraction from a single electronic speckle pattern interferometric fringe

In this paper, we introduce the radial basis function (RBF) interpolation method to electronic speckle pattern interferometry (ESPI) and propose the RBF interpolation method to obtain unwrapped phase values based on a skeleton map. Because of the excellent approximation properties of the RBF interpolation, the proposed method can extract accurate phase values from a single fringe pattern effectively, even using a simple 3×3 mean filter as preprocessing. Using our method, both special filtering methods for ESPI fringes as preprocessing and postprocessing, including a dilatation and erosion algorithm for pruning and connecting and the smooth algorithm for improving the phase values are not needed. We test our method on a computer-simulated and two experimentally obtained poor-quality fringe patterns. The results have demonstrated that our RBF interpolation method works well even under a seriously disconnected skeleton map where it is impossible to apply the widely used, Matlab function grid data interpolation or the backpropagation neural networks method [Appl. Opt. 46, 7475 (2007)].

Influence of binary Coulomb collisions on nonlinear stimulated Raman backscatter in the kinetic regime

The influence of binary Coulomb collisions on trapped particle nonlinearities related to stimulated Raman scatter (SRS) in a single laser speckle is examined using one-dimensional particle-in-cell simulations. Binary Coulomb collisions are incorporated using a numerical particle-pairing algorithm that reproduces a collision integral of the Landau form. The onset of nonlinearly enhanced levels of SRS reflectivity is shown to coincide with electron trapping in the daughter plasma wave and is sensitive to the collisional scattering rate. Relaxation of trapping-induced perturbations to the electron velocity distribution via collisional velocity space diffusion is predicted to have the largest effect on the onset of SRS when the amplitude of the daughter plasma wave is smallest, and trapping-induced perturbations to the electron velocity distribution function are also small. In the absence of higher dimensional detrapping mechanisms (e.g., electron side-loss), it is shown that the onset threshold for enhanced SRS reflectivity is determined predominantly by the parallel diffusion of trapped electrons scattering from bulk thermal electrons, and that for the conditions studied here, the contribution to detrapping from perpendicular diffusion is non-negligible. Additionally, inverse bremsstrahlung heating of the bulk electrons is shown to shift the daughter plasma wave spectrum upward along the Stoke’s resonance to larger wave frequency and smaller wave number, changing the linear parametric coupling conditions to SRS backscatter as a function of time. The reduction in SRS reflectivity from binary Coulomb collisions is greatest for laser intensities near the collisionless onset threshold, ulimately leading to an increase in the onset threshold laser intensity for enhanced SRS reflectivity in the kinetic regime.

Turnover Dynamics of Diffuse Actin and Regulators At the Leading Edge

The lamellipodium at the leading edge of motile cells is a dynamic structure consisting of a dense network of branched actin filaments. These actin filaments polymerize in a region close to the leading edge and undergo retrograde flow towards the main body of the cell. A large number of experimental techniques have been used to monitor the structural aspects of actin networks at the leading edge. However, the role of concentration gradients and local heterogeneity of soluble actin, actin oligomers, and actin regulators in the crowded filament network is little explored. We combined single molecule fluorescence microscopy with image analysis and modeling to quantify the role of diffuse actin species and their gradients in actin reorganization at the leading edge of motile cells. Actin, capping protein, and Arp 2/3 complex, were marked with fluorescent probes at low concentrations and imaged at high spatiotemporal resolution in XTC fibroblasts. Particle tracking was used to mark the appearance and disappearance of bright spots that correspond to proteins becoming associated to, or dissociated from,the actin network. Image correlation analysis was used to quantify the motion of proteins in the cytoplasm. We developed conditional image correlation methods to study local dynamics prior to assembly and immediately following disassembly. From these data we create a map of the lamellipodium showing the dynamics of lamellipodium proteins and their turnover. Bounds on the fraction of actin that leaves the filament network as oligomers was determined by measuring the distribution of diffusion coefficients which correspond to different oligomer lengths. We used numerical simulations to model these turnover dynamics and to simulate FRAP experiments. These results help resolve apparenty disparities in measurements found through FRAP and single molecule speckle microscopy.

Experimental Evidence of Predominantly Transverse Electron Plasma Waves Driven by Stimulated Raman Scattering of Picosecond Laser Pulses

We report on highly time- and space-resolved measurements of the evolution of electron plasma waves driven by stimulated Raman scattering of a picosecond, single laser speckle propagating through a preformed underdense plasma. Two-dimensional Thomson scatter spectra indicate that the dominant waves have significant transverse components. These results are supported by particle-in-cell simulations which pinpoint the dominant role of the wave front bowing and of secondary nonlinear electrostatic instabilities in the evolution of the plasma waves.

Estimation of the degree of polarization from a single speckle intensity image with photon noise

It is demonstrated that, if not appropriately taken into account, photon noise leads to a biased estimation of the degree of polarization from a single speckle intensity image. A new method for estimating the degree of polarization from a single speckle intensity image acquired at low photon flux level is thus proposed. Its precision and the limit critical photon level that does not deteriorate the performance up to a given precision are determined.

Precision of moment-based estimation of the degree of polarization in coherent imagery without polarization device

We propose and analyze a statistical method to estimate the degree of polarization of light from a single speckle intensity image by analyzing the statistical distribution of the light intensity. The optimal precision of such an estimation method is evaluated by computing the Cramer-Rao bounds for several speckle degrees. Two moment-based estimators of the square degree of polarization are introduced and characterized. For the first time to our knowledge, it is shown theoretically and through simulations that the estimators are almost efficient for high orders of speckle. The robustness of the method is discussed for the case when the intensity fluctuations do not follow the standard speckle model.

Confidence Level and Sensitivity Limits in High‐Contrast Imaging

In long adaptive optics corrected exposures, exoplanet detections are currently limited by speckle noise originating from the telescope and instrument optics, and it is expected that such noise will also limit future high-contrast imaging instruments for both ground and space-based telescopes. Previous theoretical analysis have shown that the time intensity variations of a single speckle follows a modified Rician. It is first demonstrated here that for a circular pupil this temporal intensity distribution also represents the speckle spatial intensity distribution at a fix separation from the point spread function center; this fact is demonstrated using numerical simulations for coronagraphic and non-coronagraphic data. The real statistical distribution of the noise needs to be taken into account explicitly when selecting a detection threshold appropriate for some desired confidence level. In this paper, a technique is described to obtain the pixel intensity distribution of an image and its corresponding confidence level as a function of the detection threshold. Using numerical simulations, it is shown that in the presence of speckles noise, a detection threshold up to three times higher is required to obtain a confidence level equivalent to that at 5sigma for Gaussian noise. The technique is then tested using TRIDENT CFHT and angular differential imaging NIRI Gemini adaptive optics data. It is found that the angular differential imaging technique produces quasi-Gaussian residuals, a remarkable result compared to classical adaptive optic imaging. A power-law is finally derived to predict the 1-3*10^-7 confidence level detection threshold when averaging a partially correlated non-Gaussian noise.

Simultaneous measurement of out-of-plane displacement and slope using a multiaperture DSPI system and fast Fourier transform

The simultaneous quantitative measurement of out-of-plane displacement and slope using the fast Fourier transform method with a single three-aperture digital speckle pattern interferometry (DSPI) arrangement is demonstrated. The method coherently combines two sheared object waves with a smooth reference wave at the CCD placed at the image plane of an imaging lens with a three-aperture mask placed in front of it. The apertures also introduce multiple spatial carrier fringes within the speckle. A fast Fourier transform of the image generates seven distinct diffraction halos in the spectrum. By selecting the appropriate halos, one can directly obtain two independent out-of-plane displacement phase maps and a slope phase map from the two speckle images, one before and the second after loading the object. It is also demonstrated that by subtracting the out-of-plane displacement phase maps one can generate the same slope phase map. Experimental results are presented for a circular diaphragm clamped along the edges and loaded at the center.

Estimation precision of the degree of polarization from a single speckle intensity image

We address the problem of the estimation of the degree of polarization from a single intensity image. For that purpose, one considers the case of coherent active imagery that leads to speckle fluctuations and assumes that the measured intensity image corresponds to a fully developed speckle for each polarized component of the electric field. In particular, we determine the Cramer-Rao bound of the degree of polarization estimation and propose to illustrate this result by analyzing the variance of different simple estimators.

Inflation threshold: A nonlinear trapping-induced threshold for the rapid onset of stimulated Raman scattering from a single laser speckle

The rapid onset, with increasing laser intensity, of levels of backward stimulated Raman scattering (BSRS) exceeding linear convective predictions, from single laser hot spots was predicted by simulations [Vu et al., Phys. Plasmas 9, 1745 (2002)], and has been observed [Montgomery et al., Phys. Plasmas 9, 2311 (2002)] in nonlinear regimes dominated by electron trapping. A theory for this inflation threshold is given here. The threshold is the result of competition between velocity diffusion and trapping, and is exceeded when the convectively amplified SRS Langmuir wave (LW) achieves an amplitude for which the coherent trapping velocity increment of electrons in the LW (the half-width of the trapping separatrix) exceeds the rms diffusion velocity (resulting from background plasma fluctuations), accumulated in one bounce time, for electrons with mean velocities near the phase velocity of the LW. The results of this theory, when the kinetic theory of the one-dimensional (1D) reduced-description particle-in-cell (RPIC) simulation is used, are in good agreement with a series of 1D RPIC simulations. The theory is naturally generalized to three dimensions, and is compatible with macroscopic laser interaction codes such as pF3d [Berger et al., Phys. Plasmas 5, 4337 (1998)]. Comparison of the LW trapping-induced inflation threshold to the LW threshold for the Langmuir decay instability provides an estimate for the transition between nonlinear saturation regimes. In an independent hot spot model of many hot spots, statistics suggests that the inflation threshold intensity will control the rapid onset of strong BSRS in laser beams smoothed by random phase plates.

Grinding surface roughness measurement based on the co-occurrence matrix of speckle pattern texture

Surface speckle pattern intensity distribution resulting from laser light scattering from a rough surface contains various information about the surface geometrical and physical properties. A surface roughness measurement technique based on the texture analysis of surface speckle pattern texture images is put forward. In the surface roughness measurement technique, the speckle pattern texture images are taken by a simple setup configuration consisting of a laser and a CCD camera. Our experimental results show that the surface roughness contained in the surface speckle pattern texture images has a good monotonic relationship with their energy feature of the gray-level co-occurrence matrices. After the measurement system is calibrated by a standard surface roughness specimen, the surface roughness of the object surface composed of the same material and machined by the same method as the standard specimen surface can be evaluated from a single speckle pattern texture image. The robustness of the characterization of speckle pattern texture for surface roughness is also discussed. Thus the surface roughness measurement technique can be used for an in-process surface measurement.

Nonlinear Spectral Signatures and Spatiotemporal Behavior of Stimulated Raman Scattering from Single Laser Speckles

Simulations are reported of the Thomson scatter spectrum of electrostatic waves (ESWs) excited in single laser hot spots by backward stimulated Raman scattering (BSRS). Under conditions similar those in the recent experiments of Kline et al. [Phys. Rev. Lett. 94, 175003 (2005)], a spectral streak, resulting from the trapping-induced frequency shift of the ESW, is found for high wave-number ESWs, similar to the observations. This shift and parametric frequency matching lead to isolated BSRS pulses. Modes with acoustic dispersion, resulting from the trapping-modified electron velocity distribution, can enhance the frequency range of the streak.

Tracking quasi‐stationary flow of weak fluorescent signals by adaptive multi‐frame correlation

We have developed a novel cross-correlation technique to probe quasi-stationary flow of fluorescent signals in live cells at a spatial resolution that is close to single particle tracking. By correlating image blocks between pairs of consecutive frames and integrating their correlation scores over multiple frame pairs, uncertainty in identifying a globally significant maximum in the correlation score function has been greatly reduced as compared with conventional correlation-based tracking using the signal of only two consecutive frames. This approach proves robust and very effective in analysing images with a weak, noise-perturbed signal contrast where texture characteristics cannot be matched between only a pair of frames. It can also be applied to images that lack prominent features that could be utilized for particle tracking or feature-based template matching. Furthermore, owing to the integration of correlation scores over multiple frames, the method can handle signals with substantial frame-to-frame intensity variation where conventional correlation-based tracking fails. We tested the performance of the method by tracking polymer flow in actin and microtubule cytoskeleton structures labelled at various fluorophore densities providing imagery with a broad range of signal modulation and noise. In applications to fluorescent speckle microscopy (FSM), where the fluorophore density is sufficiently low to reveal patterns of discrete fluorescent marks referred to as speckles, we combined the multi-frame correlation approach proposed above with particle tracking. This hybrid approach allowed us to follow single speckles robustly in areas of high speckle density and fast flow, where previously published FSM analysis methods were unsuccessful. Thus, we can now probe cytoskeleton polymer dynamics in living cells at an entirely new level of complexity and with unprecedented detail.

Periodic Patterns of Actin Turnover in Lamellipodia and Lamellae of Migrating Epithelial Cells Analyzed by Quantitative Fluorescent Speckle Microscopy

We measured actin turnover in lamellipodia and lamellae of migrating cells, using quantitative Fluorescent Speckle Microscopy. Lamellae disassembled at low rates from the front to the back. However, the dominant feature in their turnover was a spatially random pattern of periodic polymerization and depolymerization moving with the retrograde flow. Power spectra contained frequencies between 0.5 and 1 cycle/min. The spectra remained unchanged when applying Latrunculin A and Jasplakinolide in low doses, except that additional frequencies occurred beyond 1cycle/min. Whereas Latrunculin did not change the rate of mean disassembly, Jasplakinolide halted it completely, indicating that the steady state and the dynamics of actin turnover are differentially affected by pharmacological agents. Lamellipodia assembled in recurring bursts at the leading edge and disassembled ∼2.5μm behind. Events of polymerization correlated spatially and temporally with transient formation of Arp2/3 clusters. In lamellae, Arp2/3 accumulation and polymerization correlated only spatially, suggesting an Arp2/3-independent mechanism for filament nucleation. To acquire these data we had to enhance the resolution of quantitative Fluorescent Speckle Microscopy to the submicron level. Several algorithmic advances in speckle image processing are described enabling the analysis of kinetic and kinematic activities of polymer networks at the level of single speckles.

Coupling the dynamics of two actin networks – new views on the mechanics of cell protrusion

We study how mechanical forces integrate spatially and temporally with regulatory signals at the leading edge of migrating cells. To probe the dynamics of this system, we developed quantitative fluorescent speckle microscopy, which maps out actin cytoskeleton transport, assembly and disassembly with high spatial resolution. Statistical processing of single speckle properties revealed two kinetically, kinematically and molecularly distinct, yet spatially overlapping, actin arrays at the leading edge of migrating epithelial cells. The first network, referred to as the lamellipodium, polymerizes and depolymerizes 1-2 microm from the edge in an Arp2/3 (actin-related protein 2/3)- and cofilin-dependent fashion. The second network, referred to as the lamella, exhibits Arp2/3-independent polymerization. To elucidate the dynamic relationship between the two networks, we have begun to examine how assembly and flow are temporally modulated with respect to a protrusion event. In control cells we found bursts of protrusion preceding bursts of F-actin assembly. The time lag disappears in cells where Arp2/3-function is impaired. This and other results allowed us to propose a model in which tropomyosin protects lamella filaments from branching and severing, and to conjecture that Arp2/3-mediated lamellipodium assembly is a natural consequence of lamella expansion, but not the initiator of cell protrusion.