Some fundamental properties of speckle
01 Nov 1976-Journal of the Optical Society of America (Optical Society of America)-Vol. 66, Iss: 11, pp 1145-1150
TL;DR: In this paper, the distribution of scale sizes in a speckle pattern (i.e., the Wiener spectrum) is investigated from a physical point of view, and it is shown that adding M uncorrelated speckles on an intensity basis can reduce the contrast by 1/√M.
Abstract: A speckle pattern formed in polarized monochromatic light may be regarded as resulting from a classical random walk in the complex plane. The resulting irradiance fluctuations obey negative exponential statistics, with ratio of standard deviation to mean (i.e., contrast) of unity. Reduction of this contrast, or smoothing of the speckle, requires diversity in polarization, space, frequency, or time. Addition of M uncorrelated speckle patterns on an intensity basis can reduce the contrast by 1/√M. However, addition of speckle patterns on a complex amplitude basis provides no reduction of contrast. The distribution of scale sizes in a speckle pattern (i.e., the Wiener spectrum) is investigated from a physical point of view.
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16 Nov 1992
TL;DR: Optical coherence tomography (OCT) has developed rapidly since its first realisation in medicine and is currently an emerging technology in the diagnosis of skin disease as mentioned in this paper, where OCT is an interferometric technique that detects reflected and backscattered light from tissue.
Abstract: Optical coherence tomography (OCT) has developed rapidly since its first realisation in medicine and is currently an emerging technology in the diagnosis of skin disease. OCT is an interferometric technique that detects reflected and backscattered light from tissue and is often described as the optical analogue to ultrasound. The inherent safety of the technology allows for in vivo use of OCT in patients. The main strength of OCT is the depth resolution. In dermatology, most OCT research has turned on non-melanoma skin cancer (NMSC) and non-invasive monitoring of morphological changes in a number of skin diseases based on pattern recognition, and studies have found good agreement between OCT images and histopathological architecture. OCT has shown high accuracy in distinguishing lesions from normal skin, which is of great importance in identifying tumour borders or residual neoplastic tissue after therapy. The OCT images provide an advantageous combination of resolution and penetration depth, but specific studies of diagnostic sensitivity and specificity in dermatology are sparse. In order to improve OCT image quality and expand the potential of OCT, technical developments are necessary. It is suggested that the technology will be of particular interest to the routine follow-up of patients undergoing non-invasive therapy of malignant or premalignant keratinocyte tumours. It is speculated that the continued technological development can propel the method to a greater level of dermatological use.
6,095 citations
TL;DR: Initial results of several phantom and excised animal tissue experiments are reported which demonstrate the ability of this technique to quantitatively image strain and elastic modulus distributions with good resolution, sensitivity and with diminished speckle.
3,636 citations
TL;DR: OCT as discussed by the authors synthesises cross-sectional images from a series of laterally adjacent depth-scans, which can be used to assess tissue and cell function and morphology in situ.
Abstract: There have been three basic approaches to optical tomography since the early 1980s: diffraction tomography, diffuse optical tomography and optical coherence tomography (OCT). Optical techniques are of particular importance in the medical field, because these techniques promise to be safe and cheap and, in addition, offer a therapeutic potential. Advances in OCT technology have made it possible to apply OCT in a wide variety of applications but medical applications are still dominating. Specific advantages of OCT are its high depth and transversal resolution, the fact, that its depth resolution is decoupled from transverse resolution, high probing depth in scattering media, contact-free and non-invasive operation, and the possibility to create various function dependent image contrasting methods. This report presents the principles of OCT and the state of important OCT applications. OCT synthesises cross-sectional images from a series of laterally adjacent depth-scans. At present OCT is used in three different fields of optical imaging, in macroscopic imaging of structures which can be seen by the naked eye or using weak magnifications, in microscopic imaging using magnifications up to the classical limit of microscopic resolution and in endoscopic imaging, using low and medium magnification. First, OCT techniques, like the reflectometry technique and the dual beam technique were based on time-domain low coherence interferometry depth-scans. Later, Fourier-domain techniques have been developed and led to new imaging schemes. Recently developed parallel OCT schemes eliminate the need for lateral scanning and, therefore, dramatically increase the imaging rate. These schemes use CCD cameras and CMOS detector arrays as photodetectors. Video-rate three-dimensional OCT pictures have been obtained. Modifying interference microscopy techniques has led to high-resolution optical coherence microscopy that achieved sub-micrometre resolution. This report is concluded with a short presentation of important OCT applications. Ophthalmology is, due to the transparent ocular structures, still the main field of OCT application. The first commercial instrument too has been introduced for ophthalmic diagnostics (Carl Zeiss Meditec AG). Advances in using near-infrared light, however, opened the path for OCT imaging in strongly scattering tissues. Today, optical in vivo biopsy is one of the most challenging fields of OCT application. High resolution, high penetration depth, and its potential for functional imaging attribute to OCT an optical biopsy quality, which can be used to assess tissue and cell function and morphology in situ. OCT can already clarify the relevant architectural tissue morphology. For many diseases, however, including cancer in its early stages, higher resolution is necessary. New broad-bandwidth light sources, like photonic crystal fibres and superfluorescent fibre sources, and new contrasting techniques, give access to new sample properties and unmatched sensitivity and resolution.
1,914 citations
Cites background from "Some fundamental properties of spec..."
...Suppression of speckle in OCT. Adding up M uncorrelated fully developed speckle patterns yields a compound speckle pattern with a gamma-distributed probability density and speckle contrast C = M−1/2 (Goodman 1965, 1976)....
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...The corresponding statistics of the sample intensity is negative exponential and the probability density function is (Goodman 1965, 1976) pIS(IS) = 1 〈IS〉 exp ( − IS〈IS〉 ) , if IS 0, 0, otherwise, (2.22) with moments 〈I n〉 = n!...
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...Therefore, the corresponding gain in the SNR is M1/2....
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TL;DR: A model for the radar imaging process is derived and a method for smoothing noisy radar images is presented and it is shown that the filter can be easily implemented in the spatial domain and is computationally efficient.
Abstract: Standard image processing techniques which are used to enhance noncoherent optically produced images are not applicable to radar images due to the coherent nature of the radar imaging process. A model for the radar imaging process is derived in this paper and a method for smoothing noisy radar images is also presented. The imaging model shows that the radar image is corrupted by multiplicative noise. The model leads to the functional form of an optimum (minimum MSE) filter for smoothing radar images. By using locally estimated parameter values the filter is made adaptive so that it provides minimum MSE estimates inside homogeneous areas of an image while preserving the edge structure. It is shown that the filter can be easily implemented in the spatial domain and is computationally efficient. The performance of the adaptive filter is compared (qualitatively and quantitatively) with several standard filters using real and simulated radar images.
1,906 citations
Cites background from "Some fundamental properties of spec..."
...If noncoherent averaging is performed, then the pdf for the power follows a gamma distribution [2], i....
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...Obviously, it is applicable for coherent speckle reduction in general, as the noise processes are similar for all coherent sensors [2] ....
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TL;DR: In this article, a review of the technology and signal theoretical aspects of InSAR is presented, where the phase differences of at least two complex-valued SAR images acquired from different orbit positions and/or at different times are exploited to measure several geophysical quantities, such as topography, deformations, glacier flows, ocean currents, vegetation properties, etc.
Abstract: Synthetic aperture radar (SAR) is a coherent active microwave imaging method. In remote sensing it is used for mapping the scattering properties of the Earth's surface in the respective wavelength domain. Many physical and geometric parameters of the imaged scene contribute to the grey value of a SAR image pixel. Scene inversion suffers from this high ambiguity and requires SAR data taken at different wavelength, polarization, time, incidence angle, etc. Interferometric SAR (InSAR) exploits the phase differences of at least two complex-valued SAR images acquired from different orbit positions and/or at different times. The information derived from these interferometric data sets can be used to measure several geophysical quantities, such as topography, deformations (volcanoes, earthquakes, ice fields), glacier flows, ocean currents, vegetation properties, etc. This paper reviews the technology and the signal theoretical aspects of InSAR. Emphasis is given to mathematical imaging models and the statistical properties of the involved quantities. Coherence is shown to be a useful concept for system description and for interferogram quality assessment. As a key step in InSAR signal processing two-dimensional phase unwrapping is discussed in detail. Several interferometric configurations are described and illustrated by real-world examples. A compilation of past, current and future InSAR systems concludes the paper.
1,563 citations
Cites background from "Some fundamental properties of spec..."
...(21) The fluctuations of pixel intensities described by thesepdf s are known as thespeckle effect in the context of coherent imaging of rough surfaces (see, e.g. Dainty (1975), Goodman (1976), Madsen (1986, 1987))....
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References
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01 Dec 1963
TL;DR: In this article, the first order statistics of the observed electric-field strength, the observed light intensity, and observed light phase are examined, and the autocorrelation functions of the complex field and intensity processes are investigated, and that of the electric field is found to be proportional to the Fourier transform of the light intensity distribution incident on the scattering surface.
Abstract: : When laser light strikes a diffuse object, such as paper, the scattered light has been observed to possess a granular spatial structure. The statistical properties of these so-called 'sparkle patterns,' as seen by an observer in the far field of the scattering spot, are investigated. The first order statistics of the observed electric-field strength, the observed light intensity, and the observed light phase are examined. The electric field is reasoned to be a complex normal random variable; the intensity a real, exponentially distributed random variable; and the phase a uniformly distributed random variable. Higher order statistics of these random processes are also discussed. The autocorrelation functions of the complex field and the intensity processes are investigated, and that of the electric field is found to be proportional to the Fourier transform of the light-intensity distribution incident on the scattering surface. Spatial averages of the light intensity are considered and are found to converge to corresponding ensemble averages when either the area of the scattering spot or the average area grows large.
1,526 citations
01 Jan 1975
TL;DR: In this article, the first-order statistics of the complex amplitude, intensity and phase of speckle are derived for a free-space propagation geometry and for an imaging geometry.
Abstract: Since speckle plays an important role in many physical phenomena, it is essential to fully understand its statistical properties. Starting from the basic idea of a random walk in the complex plane, we derive the first-order statistics of the complex amplitude, intensity and phase of speckle. Sums of speckle patterns are also considered, the addition being either on an amplitude or on an intensity basis, with partially polarized speckle being a special case. Next we consider the sum of a speckle pattern and a coherent background, deriving the first-order probability density functions of intensity and phase. Attention is then turned to second-order statistics. The autocorrelation function and power spectral density are derived, both for a free-space propagation geometry and for an imaging geometry. In some cases the recorded speckle pattern may be spatially integrated or blurred, and accordingly consideration is given to the statistics of such patterns. Finally, the relationship between detailed surface structure and the resulting speckle pattern is explored, with emphasis on the effects of the surface autocorrelation function and the effects of finite surface roughness.
1,217 citations
TL;DR: In this paper, the Fourier approach is extended to deal with problems of ''random'' diffraction, for which purpose the use of auto-correlation functions is introduced and explained in physical terms.
Abstract: In Part I the `Fourier' approach to diffraction theory is outlined in such a way as to emphasize its physical significance. Particular attention is paid to diffraction phenomena of the Fresnel type, and to diffraction from screens which alter both the phase and the amplitude of the incident wave. The `Fourier' approach is extended to deal with problems of `random' diffraction, for which purpose the use of auto-correlation functions is introduced and explained in physical terms. In Part II measurements made on radio waves reflected from, or transmitted through, the ionosphere are discussed. The nature of the radio diffraction pattern observed at the ground is first summarized and deductions are then made about the ionosphere which has given rise to this diffraction. There are few references in the text, but the bibliography provides brief abstracts of the more important papers on the subject.
461 citations
01 Jan 2017
TL;DR: In this article, the Fourier approach is extended to deal with problems of ''random'' diffraction, for which purpose the use of auto-correlation functions is introduced and explained in physical terms.
Abstract: In Part I the `Fourier' approach to diffraction theory is outlined in such a way as to emphasize its physical significance. Particular attention is paid to diffraction phenomena of the Fresnel type, and to diffraction from screens which alter both the phase and the amplitude of the incident wave. The `Fourier' approach is extended to deal with problems of `random' diffraction, for which purpose the use of auto-correlation functions is introduced and explained in physical terms. In Part II measurements made on radio waves reflected from, or transmitted through, the ionosphere are discussed. The nature of the radio diffraction pattern observed at the ground is first summarized and deductions are then made about the ionosphere which has given rise to this diffraction. There are few references in the text, but the bibliography provides brief abstracts of the more important papers on the subject.
444 citations
TL;DR: In this article, the resultant of a large number of vibrations of the same pitch and of arbitrary phase is discussed. But the authors focus on the effect of the phase of the vibrations.
Abstract: (1880). XII. On the resultant of a large number of vibrations of the same pitch and of arbitrary phase. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science: Vol. 10, No. 60, pp. 73-78.
403 citations