Near-field Speckle Patterns Research Articles

Rendering near-field speckle statistics in scattering media

We introduce rendering algorithms for the simulation of speckle statistics observed in scattering media under coherent near-field imaging conditions. Our work is motivated by the recent proliferation of techniques that use speckle correlations for tissue imaging applications: The ability to simulate the image measurements used by these speckle imaging techniques in a physically-accurate and computationally-efficient way can facilitate the widespread adoption and improvement of these techniques. To this end, we draw inspiration from recently-introduced Monte Carlo algorithms for rendering speckle statistics under far-field conditions (collimated sensor and illumination). We derive variants of these algorithms that are better suited to the near-field conditions (focused sensor and illumination) required by tissue imaging applications. Our approach is based on using Gaussian apodization to approximate the sensor and illumination aperture, as well as von Mises-Fisher functions to approximate the phase function of the scattering material. We show that these approximations allow us to derive closed-form expressions for the focusing operations involved in simulating near-field speckle patterns. As we demonstrate in our experiments, these approximations accelerate speckle rendering simulations by a few orders of magnitude compared to previous techniques, at the cost of negligible bias. We validate the accuracy of our algorithms by reproducing ground truth speckle statistics simulated using wave-optics solvers, and real-material measurements available in the literature. Finally, we use our algorithms to simulate biomedical imaging techniques for focusing through tissue.

Auto-alignment of X-ray focusing mirrors with speckle-based at-wavelength metrology.

Significant improvements have been made in the fabrication of diffraction-limited X-ray optics used to pursue an aberration-free wavefront. Alignment of these optics plays a crucial role in the resultant beam quality. Here, we present a simple and fast alignment method based on imaging X-ray near-field speckle patterns, with experimental demonstration using a pair of Kirkpatrick-Baez mirrors. The proposed technique has the potential to be an alternative to conventional methods. It loosens the stringent demand for high-resolution scanning stages compared to conventional knife-edge scan and, hence, can be applied to nano-focusing optics. The flexibility and straightforward implementation of the method allow it to be applied to a wide range of experiments at synchrotron facilities and laboratory-based sources.

Near-field speckle imaging of light localization in disordered photonic systems

Optical localization in strongly disordered photonic media is an attractive topic for proposing novel cavity-like structures. Light interference can produce random modes confined within small volumes, whose spatial distribution in the near-field is predicted to show hot spots at the nanoscale. However, these near-field speckles have not yet been experimentally investigated due to the lack of a high spatial resolution imaging techniques. Here, we study a system where the disorder is induced by random drilling air holes in a GaAs suspended membrane with internal InAs quantum dots. We perform deep-subwavelength near-field experiments in the telecom window to directly image the spatial distribution of the electric field intensity of disordered-induced localized optical modes. We retrieve the near-field speckle patterns that extend over few micrometers and show several single speckles of the order of λ/10 size. The results are compared with the numerical calculations and with the recent findings in the literature of disordered media. Notably, the hot spots of random modes are found in proximity of the air holes of the disordered system.

Near-field to far-field characterization of speckle patterns generated by disordered nanomaterials.

We study the intensity spatial correlation function of optical speckle patterns above a disordered dielectric medium in the multiple scattering regime. The intensity distributions are recorded by scanning near-field optical microscopy (SNOM) with sub-wavelength spatial resolution at variable distances from the surface in a range which spans continuously from the near-field (distance ≪ λ) to the far-field regime (distance ≫ λ). The non-universal behavior at sub-wavelength distances reveals the connection between the near-field speckle pattern and the internal structure of the medium.

Two-dimensional transverse coherence measurement of hard-x-ray beams using near-field speckle

Knowledge of the transverse coherence of hard x rays is essential, not only for understanding the source properties, but also to study the impact of x-ray optics. However, the precise measurement of transverse coherence in the x-ray regime is more difficult than in the visible light regime since it often involves complex experimental setups or sophisticated x-ray optics. In this paper, we present a model-free method to measure transverse coherence properties of x-ray beams by using a simple phase membrane. Our method allows one to map the two-dimensional source distribution in the transverse plane by analyzing the power spectrum of x-ray near-field speckle patterns, which are collected at a single distance only. The method has been validated by performing measurements for a range of source sizes, which was achieved by varying the vertical coupling of the electron beam in the Diamond storage ring. We expect that this method will be widely used in transverse coherence measurements for both synchrotron sources and x-ray free-electron lasers.

Subwavelength spatial correlations in near-field speckle patterns

At subwavelength distance from the exit surface of a disordered medium, speckle patterns generated by multiple scattering of waves exhibit nonuniversal near-field correlations. A calculation of the field spatial correlation function shows that the correlation length is driven by the microscopic structure of the medium. The averaged speckle spot size can be smaller than the wavelength, even for nonresonant dielectric media.

Far-field angular distribution of the mean scattered intensity from strong diffusers by means of a near-field intensity pattern

The speckle grain close to a diffuser medium carries information about the angles at which light is scattered. We propose the extension of a technique that allows obtaining the angular distribution of the scattered intensity in the far-field speckle pattern from the near-field speckle pattern produced by strong diffusers (whose roughness is greater than the illuminating wavelength). To illustrate this technique we applied it to the light scattered from ground glass diffusers. The experimental results are compared with those obtained by direct measurement of the angular distribution of the mean scattered intensity in the far field showing good agreement with each other. The advantages over the classical far-field methods are outlined.

Anisotropy of near-field speckle patterns

In the vicinity of a rough interface under normal illumination the speckle field has been found to be anisotropic; that is, its correlation length is much larger in the direction of polarization than in the perpendicular direction, forming stripe-shaped speckle patterns in the near-field region. Furthermore, with increasing distance from the interface, the anisotropy of the near-field speckles decays rapidly, while the speckle size increases drastically in all directions. Based on detailed analysis, it was found that the anisotropy of the near-field speckle patterns can be attributed to polarization-dependent coupling among the evanescent waves from different surface diffusers.

Statistical properties of the near-field speckle patterns of thin films with slightly rough boundaries

In this theoretical paper the basic statistical quantities of the light intensity above thin-film systems with randomly rough boundaries are studied in the near-field. This means that formulae for the mean intensity, standard deviation of the intensity, correlation function of the intensity and the speckle contrast are derived for the systems mentioned in the near-field. It is assumed that the boundaries of the systems are slightly rough, i.e. that the rms values of heights of the irregularities of the boundaries are much smaller than the wavelength of incident light. The Rayleigh–Rice approach is employed for deriving the formulae expressing the quantities specified. In conclusion a brief numerical analysis of the theoretical results is presented.

Relationship between the near-field speckle pattern and the statistical properties of a surface

The scattering of light by a random rough surface is studied in the near field. We define a correlation function for the near-field intensity. Using a perturbative approach, we show that the power spectral density of the intensity is obtained by multiplying the power spectral density of the random rough surface by a transfer function. The explicit form of the transfer function is derived. We also show that the speckle contrast is proportional to the root mean square (rms) height of the surface. Finally, we present some simulations showing the modifications on the images produced when reducing either the temporal or the spatial coherence of the incident beam.

Development of laser speckle and its application to surface inspections

The growth of granularity in partially developed speckle patterns produced in the near field of wave object surfaces under illumination of laser light has been experimentally investigated. The average contrast of intensity variations in near-field speckle patterns due to three kinds of objects having different surface qualities has been measured as a function of the receiving distance from the object surface. It is found that a variation of the speckle contrast against the receiving distance is closely related to the surface waviness of objects. On the basis of this relation, a new and simple method is proposed to inspect the surface quality of objects.

Use of a Laser-Produced Speckle Pattern to Determine Surface Roughness*

Correlation and spectral-density functions for the film records of speckle patterns have been calculated. The reflections from both a random and a deterministic reflecting surface were examined, and in each case, the resultant spectral-density function consisted of an aperture function multipled by a function dependent upon the reflecting surface. The near-field speckle pattern was found to differ from that obtained in the far field. This difference is an inconvenience only because a method was shown whereby the far-field pattern could be obtained in the near field.