Completely passive method of speckle reduction utilizing static multimode optical fibre and two-dimensional diffractive optical element

ABSTRACT

In this paper, we present experimental results on speckle noise suppression using a completely passive method. The passivity of the method is achieved owing to the absence of any mechanical, electronic, or other dynamic influences on the optical scheme elements. In the experiment, a multimode semiconductor 520?±?5-nm laser with a spectral bandwidth of 2?nm, static two-dimensional (2D) and 2?×?1D diffractive optical elements (DOEs), as well as multimode single-core optical fibre and multimode optical fibre bundle were used. The dependence of the speckle reduction efficiency as a function of the optical fibre type and optical fibre length was measured for different DOEs. A speckle contrast of 0.148 and speckle reduction coefficient of 2.38 were obtained for a 2.5-m-long multimode optical fibre bundle. The experimental results confirmed that it is possible to construct completely passive optical circuits with reduced speckle noises using static multimode optical fibres and diffraction optical elements.     

Spatial and Temporal Coherence of Light in a Fibre Waveguide

Abstract

A general expression for the mutual coherence function of an electromagnetic field propagating in a fibre waveguide is presented by means of classical coherence formalism and the guided modes field representation. Moreover, this expression is applied to a limiting case of the fibre waveguide excitation by cross-spectrally pure, spatially coherent and quasi-monochromatic source with a symmetrical spectrum. In particular, the complex degree of both spatial and temporal coherence at the exit face of a two-mode, weakly-guiding, step-index fibre waveguide is discussed as a function of an exciting condition of guided modes, an intermodal dispersion and a temporal coherence of the source, respectively.     

Complex Degree of Coherence Due to Tilted Planar Sources

Abstract

The complex degree of coherence (CDC) due to a quasi-monochromatic spatially incoherent source can be displayed by performing a two-step procedure. The CDC information is encoded in the spectral content of the speckle pattern produced via a diffuser placed at the plane where the CDC is to be studied. In a second step, the recorded speckle is Fourier analysed. We apply this method to the study of tilted incoherent sources, for which the CDC is no longer an homogeneous function. A relationship is found that links the size of the speckle halo in the Fourier plane (where CDC information exists), and the tilt angle of the source plane. Some experimental results are shown in order to illustrate the method. Finally, some possible extensions and applications of our study are mentioned.     

Analysis of time-domain and spectral-domain two-beam interference including the effect of a variable spectral bandpass of a detecting system

Abstract

The effect of a variable Gaussian response function of a monochromator in a detecting system with a broadband detector is included in the theoretical and experimental analysis of time-domain and spectral-domain interference of two light beams from a source of a multimode Gaussian spectrum. The time-domain theoretical analysis gives the analytic expressions for the measured complex degree of temporal coherence of the light with and without the effect of variable spectral bandpass of the detecting system. The spectral-domain theoretical analysis of the two-beam interference gives the spectral interference law from which the visibility of the spectral interference fringes resolved for a given delay in the interferometer by a spectrometer is expressed as a function of the bandpass of the spectrometer. The theoretical conclusions are confirmed experimentally in the Michelson interferometer configuration using a laser diode operated below the threshold, a prism monochromator and a p-i-n photodetector. From the width of the central peak in the measured visibility dependence that narrows with increasing slit width of the monochromator, the spectral bandpass of the monochromator is evaluated. It is also shown how the visibility of the spectral interference fringes decreases as the slit width of the prism spectrometer increases.     

Measuring dispersion between two modes of an optical fibre using time-domain and spectral-domain low-coherence interferometry

Abstract

Group optical path difference (OPD) between two modes of an optical fibre excited by a low-coherence source characterized by a multimode spectrum is evaluated measuring both the visibility dependence in the Michelson interferometer configuration and the spectral modulation at the output of the optical fibre. Using the Fourier-transform method in processing the measured spectral modulations, a slight wavelength dependence in the group OPD between two modes of the optical fibre is resolved. Comparing the group OPD corresponding to a central wavelength of the measured spectral region with the group OPD obtained from the measured visibility dependence, good agreement between results of the measurements in the spectral domain and in the time domain is achieved.     

Experimental demonstration of the spectral interference between two linearly polarized modes at the output of a fibre waveguide excited by a low-coherence source

Abstract

The mutual interference of two linearly polarized (LP) modes in the frequency domain has been demonstrated experimentally at the output of a fibre waveguide excited by a low-coherence source when the optical path difference between both LP modes exceeds the coherence length of the source. The spectral interference between two LP modes, which shows up a periodic modulation of the source spectrum, serves as an illustration of the experimental verification of conclusions we have made in previous theoretical works. Consequently, the feasibility of a novel experimental method utilizing a high-resolution spectrometer in the evaluation of the group-delay time difference between both LP modes has been confirmed.     

Using light scattering to measure the temporal coherence of optical sources

We demonstrate a simple and robust method for characterizing the temporal coherence of statistically stationary optical sources by using dynamic light scattering. Measurement of the contrast of the fluctuating speckle pattern produced by two counterpropagating beams incident on a scattering medium is used to evaluate their mutual coherence. Important features of this method are high statistical accuracy, the ability to compensate for imperfect spatial coherence, and the possibility of characterizing milliwatt-level optical beams with a wide range of spectral widths. As an example, the squared magnitude of the field autocorrelation function for light emitted by a broadband argon-ion laser is obtained.     

Simple model for image-plane polychromatic speckle contrast.

A simple geometrical model was developed for calculation of the contrast of a polychromatic image-plane speckle pattern from a source of light with high spatial coherence. It is based on counting the number of independent speckle patterns that contribute to a given point in the image plane. This results in a simple equation for the contrast as a function of imaging geometry; relative orientation of the projection direction, observation direction, and specimen normal; bandwidth of the light source; and surface roughness. Its validity was established by comparison with an exact solution: rms errors in the calculated contrast were only 0.033 over a wide range of parameter values likely to be encountered in practice.     

Quantitative temporal speckle contrast imaging for tissue mechanics

We demonstrate through a series of simulations that by parameterizing the temporal speckle contrast statistic from a sequence of translating speckle images on a number of experimental constants, the local temporal contrast can be used to quantitatively assess local motion, provided that the spatial and temporal Nyquist sampling criteria are both met. We develop a simple exponential model for quantifying speckle motion for speckle patterns that display arbitrary intensity statistics and provide suggestions for optimizing both the experimental acquisition of speckle data and the temporal contrast analysis of the data. The confounding effects of uncorrelated noise are also discussed. The model is demonstrated by applying it to an optical coherence tomography image sequence of an engineered tissue construct undergoing dynamic compression. Applications to tissue mechanics are shown, although the discussion is equally relevant for fluid motion studies.     

Advanced analysis of coupled buffeting response of bridges: a complex modal decomposition approach

This paper presents a framework based on a complex modal decomposition technique for predicting coupled buffeting response of bridges in both time and frequency domains. The coupled equations of motion in structural modal coordinates with frequency dependent aeroelastic self-excited terms are approximated by frequency independent state-space equations, without augmented aerodynamic states, which retain the complex modal properties of the original system. These equations are then decomposed into a set of uncoupled equations of motion for buffeting response analysis. The frequency dependent unsteady buffeting characteristics and their spanwise correlation are considered in both frequency and time domain analyses instead of invoking the customary quasi-steady assumption. This framework significantly enhances computational efficiency in the frequency domain analysis by avoiding system matrix inversion at each discretized frequency when evaluating the transfer function matrix. Furthermore, it also offers simulation of buffeting response in the time domain that includes frequency dependence of buffeting and self-excited forces. A detailed discussion concerning the complex modal frequencies, damping ratios, mode shapes, and the significance of structural modes on the multimode coupled buffeting response is provided. This helps to glean additional insight and to improve our understanding of the underlying physics of wind–structure interactions. Examples of long span suspension bridges are provided to illustrate the proposed scheme and to demonstrate its effectiveness.     

Simulation of Time-evolving Speckle Patterns Using Kolmogorov Statistics

Abstract

We present a new approach for simulating time-evolving speckle patterns, by combining the shift of a rigid phase screen with its evolution. Thus, the two time-scales associated with speckle boiling and speckle motion can be adjusted independently. The statistical properties of the phase perturbation and the speckle pattern are investigated by using the temporal phase structure function and the temporal intensity correlation. We found a very good agreement with experimental results.     

Mean and variance of energy reflected from a diffuse object illuminated by radiation with partial temporal coherence

Closed-form integral expressions are developed for the mean and variance of power and energy received from a diffusely reflective object upon illumination by laser radiation with partial temporal coherence. Expressions are presented in dimensionless form and analytic approximations to the integrals are given for signal variations at a receiver caused by fully developed laser speckle. Results are presented in terms of three parameters: the mutual Fresnel number of the receiver and object, the number of longitudinal modes of the illuminating source, and the dimensionless mode spacing of the illuminating source. The calculations assume high light levels and free-space geometry.     

Experimental and numerical investigations for the free vibration of cantilever trapezoidal plates

Abstract

Based on the advantages of non‐contact and full field measurement, the optical technique called amplitude‐fluctuation electronic speckle pattern interferometry (AFESPI) with an out‐of‐plane setup is employed to investigate the free vibration of cantilever trapezoidal plates with various taper ratios and sweep‐back angles. Twenty different plate configurations are analyzed, including triangular and trapezoidal plates, and the first seven vibration modes of each plate are measured. The AF‐ESPI method is very convenient for measuring vibrating objects because no contact is required in contrast to classical modal analysis using accelerometers. Based on the fact that clear fringe patterns will appear only in resonance, both resonant frequencies and corresponding mode shapes can be obtained experimentally using the present technique. Numerical calculations by finite element method are also performed and the results are compared with the experimental measurements. Excellent agreements are obtained for both results of resonant frequencies and mode shapes. The influences of taper ratios and sweep‐back angles on the vibration behavior of cantilever trapezoidal plates are also demonstrated in terms of the dimensionless frequency parameter.     

Influence of geometry on polychromatic speckle contrast

Understanding speckle behavior is very important in speckle metrology application. The contrast of a polychromatic speckle depends not only on surface roughness and the coherence length of a light source, as shown in previous works, but also on optical geometry. We applied the Fresnel approach of diffraction theory for the free-space geometry and derived a simple analytical relationship between contrast, coherence length, size of illuminated spot, and distances between source, object, and observation plane. The effect of contrast reduction is found to be significant for low-coherence light sources.     

Statistical model for fading return signals in coherent lidars

A statistical model for the return signal in a coherent lidar is derived from the fundamental principles of atmospheric scattering and turbulent propagation. The model results in a three-parameter probability distribution for the coherent signal-to-noise ratio in the presence of atmospheric turbulence and affected by target speckle. We consider the effects of amplitude and phase fluctuations, in addition to local oscillator shot noise, for both passive receivers and those employing active modal compensation of wavefront phase distortion. We obtain exact expressions for statistical moments for lidar fading and evaluate the impact of various parameters, including the ratio of receiver aperture diameter to the wavefront coherence diameter, the speckle effective area, and the number of modes compensated.     

On the Properties of Surface Plasmon Polarization Beam Splitters

Abstract

The transmission and cross-coupling characteristics of a surface-plasmon-based polarization beam splitter with multimode interlay between two polished optical fibre blocks are presented. Through the continuous monitoring of the characteristics as a function of interlay refractive index and wavelength it was found that the device is symmetrical in terms of optical power coupling in the cross direction and asymmetrical in terms of transmission, with respect to input launch direction. The fibre fixed in the metal-coated block has a transverse electric (TE) mode transmission which is independent of the refractive index of interlay. The transmission of the other (uncovered) block shows resonance-type interaction for both TE and transverse magnetic modes owing to evanescent field coupling to the multimode interlay.     

Phase measurement in temporal speckle pattern interferometry: comparison between the phase-shifting and the Fourier transform methods

The measurement of dynamic displacements by use of speckle pattern interferometry and temporal phase unwrapping allows for the evaluation of large-object displacement fields without the propagation of spatial unwrapping errors. If a temporal carrier is introduced in one of the beams of the interferometer, phase data for whole-object displacement can be retrieved by use of a temporal phase-shifting method or a temporal Fourier transformation approach. We present a comparison between both methods of temporal phase measurement in terms of precision and execution speed. We performed the analysis by using computer-simulated speckle interferograms, an approach that allowed us to know precisely the original phase distribution and also to determine the spatial rms phase error as a function of the phase change introduced between two consecutive speckle interferograms. The performance of both methods to process experimental data is also illustrated by use of the results from a high-speed speckle interferometry study of a carbon fiber panel.     

Spatial coherence wavelets

Abstract

It is shown that the cross-spectral density at a plane in the Fresnel—Fraunhofer domain can be expressed as a certain diffraction pattern, which is generated by the superposition of second-order spatial coherence wavelets that emerge from the aperture. The amplitude of each coherence wavelet exhibits units of power density (average energy) and the power spectrum at the far zone plane will be the summation of the amplitudes of such wavelets. Thus, the spatial coherence wavelet constitutes a vehicle for both correlation and energy transport in free space. Some simulation results are discussed to illustrate these ideas.     

Difference in the Definitions of Coherence in the Space-time Domain and in the Space-frequency Domain

Abstract

Coherence in the space-time domain and in the space-frequency domain are compared and found to be non-equivalent. Coherence in the space-time domain is sufficient for coherence in the space-frequency domain. Coherence in the space-frequency domain is not sufficient for coherence in the space-time domain. The source spectrum as well as coherence in the space-frequency domain effect coherence in the space-time domain. The coherence in the radiation field from two very different localized sources is studied. It is found that the fields are coherent throughout the far field region only if the sources are monochromatic.     

Experimental demonstration of Klyshko’s advanced-wave picture using a coincidence-count based,camera-enabled imaging system

The Klyshko advanced-wave picture is a well-known tool useful in the conceptualisation of parametric down-conversion (SPDC) experiments. Despite being well-known and understood, there have been few experimental demonstrations illustrating its validity. Here, we present an experimental demonstration of this picture using a time-gated camera in an image-based coincidence measurement. We show an excellent agreement between the spatial distributions as predicted by the Klyshko picture and those obtained using the SPDC photon pairs. An interesting speckle feature is present in the Klyshko predictive images due to the spatial coherence of the back-propagated beam in the multi-mode fibre. This effect can be removed by mechanically twisting the fibre, thus degrading the spatial coherence of the beam and time-averaging the speckle pattern, giving an accurate correspondence between the predictive and SPDC images.