Speckle Intensity Research Articles

White-light interferometry on rough surfaces--measurement uncertainty caused by surface roughness

White-light interferometry measuring an optically rough surface commonly does not resolve the lateral structure of the surface. This means that there are height differences within one resolution cell that exceed one-fourth of the wavelength of the light used. Thus the following questions arise: Which height is measured by white-light interferometry? How does the surface roughness affect the measurement uncertainty? The goal of the presented paper is to answer these questions by means of numerical simulations. Before the aforementioned questions can be answered, the distribution of the intensity of individual speckles, the influence of surface roughness, and the spectral width of the light source used are discussed.

Effects of clipping threshold on the scaling property of clipped fractal speckle intensities

The effect of clipping threshold on the scaling property of clipped fractal speckles is investigated theoretically. To evaluate this effect, we consider a quantity of total deviation, which is defined as the summation of the squared differences between slopes in the bilogarithmic plots of autocorrelation coefficients of nonclipped and clipped fractal speckles. The total deviation depends on three parameters related to the clipping process and the correlation coefficient of fractal speckles. The optimal clipping threshold for best retaining the fractal property of clipped fractal speckles is defined as one giving the minimum total deviation for various values of these parameters. To confirm the theoretical analysis, experimental data were also examined and found to give the optimal clipping threshold corresponding well with the theoretical prediction.

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.

X-ray-scattering information obtained from near-field speckle

Whenever coherent radiation impinges on a scattering object, a speckled intensity pattern is produced. In the far field the speckle size and shape do not mirror any properties of the object. Here we show that, in spite of the limited spatial coherence of synchrotron radiation, speckles with remarkable properties can be observed when the sensor is placed in the near field. The statistical analysis of these speckles generates static and dynamic X-ray-scattering data, and the results from two typical scattering samples are given. When compared with conventional far-field techniques, the method enables a substantial increase of around four orders of magnitude in the beam size and power and opens the way to a previously inaccessible region of scattering angles. It also offers the possibility of tracking the spatio-temporal evolution of complex fluids and other inhomogeneous systems.

Speckle with a finite number of steps

The statistical properties of classical, fully developed speckle must be modified when the speckle is generated by a random walk with a finite number of steps. It is shown that for such speckle, the standard negative-exponential probability density function for speckle intensity often overestimates the probability that the intensity exceeds a given threshold. In addition, while any linear transformation of the fields in a classical speckle pattern does not change the intensity statistics, the same is not true for finite-step speckle. The implications of these facts in certain applications are discussed.

Speckle size, intensity and contrast measurement application in micron-size particle concentration assessment

A transmission type of experiment was set-up to investigate coherent light scattering on suspensions with scattering centers having a wider size distribution. For each sample the contrast, the average intensity and the average speckle size of the far interference field were calculated using an alternative simple algorithm that is presented in detail. The variation of the far field parameters with the scattering centers concentration is presented. A possible application in measuring the scattering centers concentration in the very small values range is suggested and the range is indicated.

Use of an intensity threshold to improve the visibility of ghost images produced by incoherent light

In thermal light ghost imaging, the transparent mask, located in the object arm of the optical setup, is numerically reconstructed by correlating the speckle patterns acquired by the video camera with the output of a bucket detector placed behind the mask. We show that the visibility of images can be significantly improved by discarding every speckle pattern whose bucket output falls below a certain threshold. We also demonstrate that the efficiency of the conventional method strongly decreases when the speckle statistics deviate from the negative exponential, whereas the threshold method is more robust against changes in the statistical distribution of the speckle intensity. We also provide reasonable statistical explanations for these results.

Estimation of the phase error in interferometric measurements by evaluation of the speckle field intensity

Intensities recorded with CCD or CMOS sensors represent spatially averaged values of the intensity across the area of a pixel. In this work we investigate the influence of spatial averaging in interferograms on the evaluated phase from an object wave with well resolved, fully developed speckles. Based on an analytical description of the averaging process, a procedure is developed to create a quality map for the evaluated phase, in order to give an estimation of the expected error at each point. The proposed method uses only the local intensity distribution of the object wave for the qualification of the phase values. The theoretical results are tested and verified by means of numerically generated objective and subjective speckle fields.

Multifractal analysis of speckle intensities produced by power-law illumination of diffusers

Speckle patterns produced by computer simulations on the assumption of a power-law illumination of scattering objects are investigated on the basis of multifractal analysis. This analysis provides us with more detailed information on a fractal structure than conventional methods yielding a simple dimension. To examine multifractal properties of simulated speckle intensities, their generalized dimensions and singularity spectra are calculated by means of the method of moments. The results show that the multifractal description of the speckles characterizes clustering behaviour of the speckle intensities.

Absolute Measurement of Surface Vibrational Distribution in Piezoelectric Devices Using Burst-Wave Driving

A non mechanical scanning method is developed for mapping absolute vibrational patterns of piezoelectric devices based on a burst-wave resonator drive and the laser speckle method. By taking into account the statistical treatment for the distributions of the speckle intensity, absolute vibrational shapes can be visualized. This method is based on a simple relationship of coherent light interference on device surfaces and the linear relationship of piezoelectricity. To derive the interference factor γ, which is mandatory for determining absolute displacement, a polynomial approximation is applied to an expression of the difference in the brightness caused by the interference condition between the resonator-resting and resonator-driving states. This is because γ cannot be directly obtained from the interference equations when the device being tested is excited by the burst signal. Although the sensitivity of this method is less than that of the synchronized laser speckle method, its simple measurement system and wide frequency range more than offset this disadvantage. An experimental result for a 23 MHz AT-cut quartz resonator is also presented.

Multiscale analysis of the intensity fluctuation in a time series of dynamic speckle patterns

We propose the application of a method based on the discrete wavelet transform to detect, identify, and measure scaling behavior in dynamic speckle. The multiscale phenomena presented by a sample and displayed by its speckle activity are analyzed by processing the time series of dynamic speckle patterns. The scaling analysis is applied to the temporal fluctuation of the speckle intensity and also to the two derived data sets generated by its magnitude and sign. The application of the method is illustrated by analyzing paint-drying processes and bruising in apples. The results are discussed taking into account the different time organizations obtained for the scaling behavior of the magnitude and the sign of the intensity fluctuation.

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.

B217 オフセット印刷における湿し水供給自動化に関する研究

In this paper, the correlation between the amount of dampening water on an offset printing plate and the intensity of speckle patterns generated on the plate is examined by experiment and numerical simulation. In experiment, speckle pattern observation is performed for two different conditions that the plate is at rest and dynamically move attached to a rotating cylinder to evaluate the feasibility of speckle intensity method in offset printing system. In numerical simulation, time variation of speckle intensity is simulated with the model of the distribution of dampening water on an offset printing plate, considering the reflection factors on water surface and the printing plate. From the results, it is seen that the speckle intensity method has usability on dynamic condition and speckle intensity depends on observation angle.

OS2-2-7 Application of statistical interferometry to monitor biological activity of plant under environmental stress

In this study, a novel optical interferometric technique called 'statistical interferometry'^<1-3> has been developed. In contrast to the conventional interferometry where the phase is determined in a completely deterministic way, we consider the interference of completely random wave fronts, i.e., speckle fields, and it has been proved that the complete randomness of the speckle field can play the role of a standard phase in a statistical sense. The advantage of the method is that since the phase of the object under testing can be derived in a statistical way, the accuracy of the measurement depends only on the number of data taken to calculate a probability density distribution of speckle phase. This feature permits a simple optical system to achieve measurements with an extremely high accuracy. According to a computer simulation, the accuracy of λ/1000 can be achieved using 40,000 data of the speckle intensity. Statistical interferometry was applied to monitor biological activity or growth rate of plant, aiming to investigate the influence of the environmental pollutions. In the experiments, the plants were exposed to ozone that is the main substance of photochemical oxidant, and the growth rates were measured before and after the exposure. It was clearly observed that the fluctuation of growth rate as well as its mean rate was dramatically affected by the exposure of ozone. By the observation of growth rate of plant with the accuracy of sub-nanometer scale and a time scale of second, it was newly revealed that the fluctuation of the growth rate reflects the biological activity of the plant.

Generation of fractal speckles by means of a spatial light modulator

It was shown in previous studies that, when a diffuser is illuminated by coherent light with an average spatial intensity distribution obeying a negative power function, the scattered field in the Fraunhofer diffraction region exhibits random fractal properties. The method employed so far for producing such fields has a disadvantage in that generated speckle intensities are low due to small transmittance of fractal apertures used in the illumination optics. To overcome this disadvantage, a generation of fractal speckles by means of a spatial light modulator is proposed. The principle is explained and experimental results are also shown.

Speckle activity images based on the spatial variance of the phase

We propose the display of the local spatial variance of the temporal variations of the phase as an activity descriptor in dynamic speckle images. The spatial autocorrelation of the speckle intensity is calculated in sliding windows, and an estimation of the variance of the phase variations in each region of the sample is determined. The activity images obtained in this way depict some interesting features and in some cases they could be related to physical magnitudes in the samples. A simulation is presented, and examples corresponding to usual study cases are also shown, namely, fruit bruising and paint drying.

Polarized temporal impulse response for scattering media from third-order frequency correlations of speckle intensity patterns

Second- and third-order frequency correlations of speckle intensity patterns are used to characterize scattering media for multiple polarization states. The polarized temporal responses thus obtained are sensitive to the degree of scatter, with results being predictable by a diffusion model with sufficiently strong scatter. Experimental data are used to reconstruct various transfer functions.

Reconstructing spatial phase distributions and object images from speckle intensity patterns of the diffraction field

A method of reconstruction of the spatial phase distribution and the image of a scattering object from a recorded speckle pattern of the diffraction field has been developed and verified on test objects. The proposed method is based on an assumption that, for objects of a certain class, the phase difference between adjacent speckles in the far zone is equal to π. Digital records of Fourier speckle patterns and the corresponding digitally reconstructed images are presented.

The gated integration technique for the accurate measurement of the autocorrelation function of speckle intensities scattered from random phase screens

A new approach based on the gated integration technique is proposed for the accurate measurement of the autocorrelation function of speckle intensities scattered from a random phase screen. The Boxcar used for this technique in the acquisition of the speckle intensity data integrates the photoelectric signal during its sampling gate open, and it repeats the sampling by a preset number, m. The average analog of the m samplings output by the Boxcar enhances the signal-to-noise ratio by m , because the repeated sampling and the average make the useful speckle signals stable, while the randomly varied photoelectric noise is suppressed by 1 / m . In the experiment, we use an analog-to-digital converter module to synchronize all the actions such as the stepped movement of the phase screen, the repeated sampling, the readout of the averaged output of the Boxcar, etc. The experimental results show that speckle signals are better recovered from contaminated signals, and the autocorrelation function with the secondary maximum is obtained, indicating that the accuracy of the measurement of the autocorrelation function is greatly improved by the gated integration technique.