There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

We present a universal statistical model for texture images in the context of an overcomplete complex wavelet transform. The model is parameterized by a set of statistics computed on pairs of coefficients corresponding to basis functions at adjacent spatial locations, orientations, and scales. We develop an efficient algorithm for synthesizing random images subject to these constraints, by iteratively projecting onto the set of images satisfying each constraint, and we use this to test the perceptual validity of the model. In particular, we demonstrate the necessity of subgroups of the parameter set by showing examples of texture synthesis that fail when those parameters are removed from the set. We also demonstrate the power of our model by successfully synthesizing examples drawn from a diverse collection of artificial and natural textures.

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A Parametric Texture Model Based on Joint Statistics of Complex Wavelet Coefficients

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.

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Optical coherence tomography - principles and applications

Optical wireless communication (OWC) refers to transmission in unguided propagation media through the use of optical carriers, i.e., visible, infrared (IR), and ultraviolet (UV) bands. In this survey, we focus on outdoor terrestrial OWC links which operate in near IR band. These are widely referred to as free space optical (FSO) communication in the literature. FSO systems are used for high rate communication between two fixed points over distances up to several kilometers. In comparison to radio-frequency (RF) counterparts, FSO links have a very high optical bandwidth available, allowing much higher data rates. They are appealing for a wide range of applications such as metropolitan area network (MAN) extension, local area network (LAN)-to-LAN connectivity, fiber back-up, backhaul for wireless cellular networks, disaster recovery, high definition TV and medical image/video transmission, wireless video surveillance/monitoring, and quantum key distribution among others. Despite the major advantages of FSO technology and variety of its application areas, its widespread use has been hampered by its rather disappointing link reliability particularly in long ranges due to atmospheric turbulence-induced fading and sensitivity to weather conditions. In the last five years or so, there has been a surge of interest in FSO research to address these major technical challenges. Several innovative physical layer concepts, originally introduced in the context of RF systems, such as multiple-input multiple-output communication, cooperative diversity, and adaptive transmission have been recently explored for the design of next generation FSO systems. In this paper, we present an up-to-date survey on FSO communication systems. The first part describes FSO channel models and transmitter/receiver structures. In the second part, we provide details on information theoretical limits of FSO channels and algorithmic-level system design research activities to approach these limits. Specific topics include advances in modulation, channel coding, spatial/cooperative diversity techniques, adaptive transmission, and hybrid RF/FSO systems.

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Survey on Free Space Optical Communication: A Communication Theory Perspective

In free-space optical communication links, atmospheric turbulence causes fluctuations in both the intensity and the phase of the received light signal, impairing link performance. We describe several communication techniques to mitigate turbulence-induced intensity fluctuations, i.e., signal fading. These techniques are applicable in the regime in which the receiver aperture is smaller than the correlation length of fading and the observation interval is shorter than the correlation time of fading. We assume that the receiver has no knowledge of the instantaneous fading state. When the receiver knows only the marginal statistics of the fading, a symbol-by-symbol ML detector can be used to improve detection performance. If the receiver has knowledge of the joint temporal statistics of the fading, maximum-likelihood sequence detection (MLSD) can be employed, yielding a further performance improvement, but at the cost of very high complexity. Spatial diversity reception with multiple receivers can also be used to overcome turbulence-induced fading. We describe the use of ML detection in spatial diversity reception to reduce the diversity gain penalty caused by correlation between the fading at different receivers.

/pdf/free-space-optical-communication-through-atmospheric-48mj86nu81.pdf

Free-space optical communication through atmospheric turbulence channels

The interaction between W-band radiation and particles and/or aerosols is very important for imaging and remote sensing applications. The reflectance and back scattering of such media are important parameters in the design of active and passive W-band imaging and remote sensing. In order to investigate those parameters we designed and constructed a unique W-band spectroscopic system operating at 92–100 GHz. The system is based upon two parabolic mirrors, two diagonal mirrors, a high power high resolution continuous wave tunable W-band source, and a unique detector. The spectrometer is fully computerized. In order to investigate the interaction with particles we prepared unique samples. The samples were prepared from polyethylene powder mixed with known percentage of 44 μm stainless steel particles. The mixture was heated to about 2000C and 100 mm sample plate was extracted. Samples with different percentage of stainless steel particles were prepared as well as a reference pure polyethylene plate keeping the same volume for all samples. Reflection function measurements of those samples are presented in this work. Back scattering measurements will be carried out in the future.

High resolution remote sensing of particles and aerosols in the W-band (92–100 GHz)

In Chapter 8 the optical transfer function was introduced. It was used first to describe limitations on image quality stemming from diffraction by various shape and size apertures. Such diffraction at aperture edges gives rise to deflection of light incident on such aperture edges. This deflection causes rays incident on aperture edges to take exit paths different from those of rays incident on the middle portions of the aperture. The latter rays behave according to Snell’s law and form the image. The diffracted rays give rise to image blur. In Section 8.9, it was suggested that the transfer function approach can be used to describe image quality in general for an imaging system and for its various components and not only for diffraction-limited imaging.

Modulation Contrast Function

Many properties of the atmosphere affect the quality of images propagating through it. There are atmospheric phenomena that give rise to attenuation of the irradiance of the propagating image, thus reducing the contrast of the final image. There are also atmospheric phenomena that cause blurring of detail. Both types of phenomena prevent small detail from being resolved in the final image, thus degrading image quality.

Phenomena that give rise to attenuation are electromagnetic (EM) wave absorption and scattering by the constituent gases and particulates of the atmosphere and airborne particulates. Scattering of photons by airborne particulates is manifested as deflections of the photons to directions other than that of original propagation. If such scattering causes the deflected photons to miss the imaging receiver, then the scattering is manifested as attenuation. The received irradiance of the image propagated through the atmosphere is correspondingly diminished from that in the object plane. However, if the light scattering is at very small angles with respect to the original directions of propagation, and several such small-angle scattering events take place, then forward-scattered radiation can take round-about paths and still be received by the imaging system together with the unscattered radiation. The net effect is image blurring caused by a multitude of angles of arrival at the imaging receiver of radiation, emanating from the same point in the object plane, for one multiply forward-scattered ray and one unscattered ray. Many such multiple-scattering paths give rise to a relatively large blurred-point image rather than a fine sharp-point image. Several adjacent object plane points can then appear as a single blurred image plane point, thus degrading image resolution.

Optical Properties of the Atmosphere

Using atmospheric modulation contrast function area (mcfa) as a single-valued numerical criterion for image quality propagated through the atmosphere, a statistical study of atmospheric imaging data has led to the determination of regression coefficients with which to quantitatively predict effects of windspeed, air temperature, and relative humidity on image quality propagated through the atmosphere as a function of wavelength for visible and near infrared wavelengths. Utilization of this procedure is quite simple. One simply plugs in expected values for windspeed, air temperature, and relative humidity in the regression coefficient expression for mcfa. The larger the expected mcfa, the better the expected image quality. Data for desert atmospheres have been presented previously. Here, an improved version of that model is presented. Preliminary experimentation indicates the accuracy of the present model is quite good.

Prediction Of Image Quality Through The Desert Atmosphere

Image blurring caused by vibrations is a factor whose influence on resolution is often significant in imaging systems that involve mechanical motion. For example, an unstabilized, airborne system mounted on vibration isolators experiences an angular velocity typically on the order of 60,000 μrad/s. On the other hand, a stabilized system, which obtains image motion corrections by moving optical elements so as to counteract sensor motions, has a residual error typically on the order of 2500 μrad/s involving pitch, roll, yaw, and forward motion compensation errors. The greatest errors result usually from rotational vibration. A stabilized mount-type system has a combined error typically on the order of 100 μrad/s [14.1]. Even where no motion is involved, as in large fixed-position astronomical telescopes, vibrations deriving from thermal gradients in the walls and other parts of the telescope can be the limiting factor in image resolution.

Norman S. Kopeika

Papers

High resolution remote sensing of particles and aerosols in the W-band (92–100 GHz)

Modulation Contrast Function

Optical Properties of the Atmosphere

Prediction Of Image Quality Through The Desert Atmosphere

Optical Transfer Functions for Image Motion and Vibration