Reduction of Speckle in Coherent Imaging by Spatial Frequency Sampling
TL;DR: In this paper, an expression for the average power spectrum of the speckle in the image of a coherently illuminated diffusing object was derived when a number of exposures are superimposed with a shift of the sampling aperture located in the spatial frequency plane between successive exposures.
Abstract: One method which has been suggested for reducing speckle in the holographically reconstructed image of a diffusing object is the use of a moving aperture in the pupil plane of the imaging lens (this is equivalent to sampling the spatial frequency spectrum of the object). An expression is derived for the average power spectrum of the speckle in the image of a coherently illuminated diffusing object when a number of exposures are superimposed with a shift of the sampling aperture located in the spatial frequency plane between successive exposures, and experimental results are presented which confirm that an appreciable reduction in speckle can be obtained even when the shift of the sampling aperture between two exposures is less than its dimensions. This analysis is then extended to the case of a rectangular sampling aperture which is moving continuously for the duration of the exposure. The results show that, for a given range of movement, an exposure with a continuously moving aperture should be more effe...
Citations
More filters
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
TL;DR: Modelling of the monocular, steady-state, accommodation response to sinusoidal grating targets suggests that the accommodation to a target with a complex spatial frequency spectrum cannot be predicted from a knowledge of that spectrum and of the observer's response to its component frequencies, under the same viewing conditions.
190 citations
TL;DR: A digital signal processing technique that reduces the speckle content in reconstructed digital holograms based on sequential sampling of the discrete Fourier transform of the reconstructed image field is presented.
Abstract: We present a digital signal processing technique that reduces the speckle content in reconstructed digital holograms. The method is based on sequential sampling of the discrete Fourier transform of the reconstructed image field. Speckle reduction is achieved at the expense of a reduced intensity and resolution, but this trade-off is shown to be greatly superior to that imposed by the traditional mean and median filtering techniques. In particular, we show that the speckle can be reduced by half with no loss of resolution (according to standard definitions of both metrics).
129 citations
01 May 1996
TL;DR: In this article, a survey of the research works in the field of speckle reduction techniques involving four categories 1)-4) which have been conducted in the past 30 years is presented.
Abstract: Speckle reduction techniques have been developed as one of the most active research fields in coherent optical information processing, together with the investigations of speckle statistics and coherence theory. The principles of speckle reduction are classified to five categories: 1) control of spatial coherence, 2) control of temporal coherence, 3) spatial sampling, 4) spatial averaging, and 5) digital image processing. This paper surveys the research works in the field of speckle reduction techniques involving four categories 1)-4) which have been conducted in the past 30 years.
105 citations
TL;DR: It is shown that high-quality images can be obtained from binary holograms when speckle reduction is performed, and it is shown how the resultant noise in the reconstructed image, as well as theSpeckle that is inherent in digital holography, can be conveniently suppressed by standard speckles reduction techniques.
Abstract: Digital holography is an imaging technique that enables recovery of topographic 3D information about an object under investigation. In digital holography, an interference pattern is recorded on a digital camera. Therefore, quantization of the recorded hologram is an integral part of the imaging process. We study the influence of quantization error in the recorded holograms on the fidelity of both the intensity and phase of the reconstructed image. We limit our analysis to the case of lensless Fourier off-axis digital holograms. We derive a theoretical model to predict the effect of quantization noise and we validate this model using experimental results. Based on this, we also show how the resultant noise in the reconstructed image, as well as the speckle that is inherent in digital holography, can be conveniently suppressed by standard speckle reduction techniques. We show that high-quality images can be obtained from binary holograms when speckle reduction is performed.
51 citations
Cites background from "Reduction of Speckle in Coherent Im..."
...The image quality of objects containing speckle can be considerably improved by performing speckle reduction [44,45]....
[...]
References
More filters
Book•
01 Jan 1965
TL;DR: This chapter discusses the concept of a Random Variable, the meaning of Probability, and the axioms of probability in terms of Markov Chains and Queueing Theory.
Abstract: Part 1 Probability and Random Variables 1 The Meaning of Probability 2 The Axioms of Probability 3 Repeated Trials 4 The Concept of a Random Variable 5 Functions of One Random Variable 6 Two Random Variables 7 Sequences of Random Variables 8 Statistics Part 2 Stochastic Processes 9 General Concepts 10 Random Walk and Other Applications 11 Spectral Representation 12 Spectral Estimation 13 Mean Square Estimation 14 Entropy 15 Markov Chains 16 Markov Processes and Queueing Theory
13,886 citations
Book•
01 Jan 2002
TL;DR: In this paper, the meaning of probability and random variables are discussed, as well as the axioms of probability, and the concept of a random variable and repeated trials are discussed.
Abstract: Part 1 Probability and Random Variables 1 The Meaning of Probability 2 The Axioms of Probability 3 Repeated Trials 4 The Concept of a Random Variable 5 Functions of One Random Variable 6 Two Random Variables 7 Sequences of Random Variables 8 Statistics Part 2 Stochastic Processes 9 General Concepts 10 Random Walk and Other Applications 11 Spectral Representation 12 Spectral Estimation 13 Mean Square Estimation 14 Entropy 15 Markov Chains 16 Markov Processes and Queueing Theory
12,407 citations
TL;DR: A general theorem is provided for the moments of a complex Gaussian video process that states that an n th order central product moment is zero if n is odd and is equal to a sum of products of covariances when n is even.
Abstract: A general theorem is provided for the moments of a complex Gaussian video process. This theorem is analogous to the well-known property of the multivariate normal distribution for real variables, which states that an n th order central product moment is zero if n is odd and is equal to a sum of products of covariances when n is even.
411 citations
TL;DR: In this paper, the properties of the amplitude and illuminance of the images of coherently illuminated diffuse objects are studied, where uniform and non-uniform objects are considered and a linear transformation of a nonstationary gaussian stochastic process followed by a square-law detection is considered.
Abstract: The properties of the amplitude and illuminance of the images of coherently illuminated diffuse objects are studied. Uniform and nonuniform objects are considered. The image illuminance is considered to result from a linear transformation of a nonstationary gaussian stochastic process followed by a square-law detection. Expressions are obtained for the mean, autocorrelation, variance, and spatial power spectral density of the amplitude and of the illuminance. Interpretation of the results led to conclusions concerning the speckle size, the noise power in the image, and the transfer function of an optical system when the object diffuses coherent light. When the autocorrelation width of the random fluctuations of the object amplitude is small compared to the impulse response of the system, the mean illuminance in the image plane is that which would be given by an incoherent object having the same luminance as the object considered; the average speckle size is equal to that of the impulse response of the system; the average transfer function of the system is the incoherent transfer function; and the distribution of the noise spatial frequencies does not depend upon the form of the signal, but only upon its total energy. Other results concerning the image statistics have also been obtained.
138 citations
TL;DR: In this paper, the mean-square value of the fluctuation in the image intensity is equal to the square of the mean intensity and the autocorrelation junction of the noise-like fluctuations.
Abstract: Holographic and other imaging systems utilizing coherent light introduce a speckled or noise-like pattern in the image of a diffuse object which severely degrades image quality It is desirable to understand this effect quantitatively Intelligent design in many cases requires knowledge of the mean-square value, spatial power spectral density, and autocorrelation junction of the noise-like fluctuations These quantities have been determined for the image of a uniform diffuse object Major results are: (i) The mean-square value of the fluctuation in the image intensity is equal to the square of the mean intensity (ii) One can decrease the relative magnitude of the noise-like fluctuations at the cost of a corresponding increase in the aperture required of the optical system (or hologram) over that required to resolve the desired image in a spatial frequency sense In a holographic facsimile or TV system, this calls for a corresponding increase in electrical bandwidth (iii) The improvement in (ii) is not possible for direct viewing with the human eye, since the resolution of a healthy eye is known to be limited by diffraction at the iris
78 citations