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.

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Free-space optical communication through atmospheric turbulence channels

The role of the atmosphere in target acquisition modeling is investigated experimentally. Three models are compared to experimental results measured on the Golan Heights, Israel. Concepts considered are atmospheric attenuation versus atmospheric blur, and contrast limited (blur-limited) versus noise limited imaging. Results indicate that the role of the atmosphere in target acquisition is blur rather than attenuation, and that for ranges on the order of a kilometer or more, target acquisition is limited by atmospheric blur rather than by hardware. A significant portion of the atmospheric blur derives from small angle forward scattering by aerosols, which actually increases measured temperature differences for ranges up to a few kilometers.

Role of the atmosphere in target acquisition: models versus experiment

After a brief introduction to Fourier optics in the previous chapter, we now return to imaging with incoherent light. In Chapter 2 geometrical optics was used to describe image formation and location. Diffraction effects were neglected, and distortions from ideal image quality were attributed to chromatic and spherical aberrations. At this point, another limitation to image quality can be considered, namely, diffraction. Diffraction causes parallel light rays incident on the edges of optical elements such as lenses or mirrors to be deflected away from the focal point, thus degrading image quality. This causes spreading of point images and loss of resolution as described on p. 244 and in Section 7.4 for coherent light. Here we consider primarily incoherent light which is normally used in imaging.

Diffraction-limited imaging refers to a situation in which image quality is limited by such diffraction. It is very common, particularly when geometrical optics aberrations are minimized through use of achromatic elements and parabolic rather than spherical surfaces. Moreover, diffraction-limited imaging is a convenient method in which to introduce the use of system concepts such as impulse response and transfer function to characterize image quality. These system concepts are introduced here and emphasized throughout the remainder of this book.

Diffraction-Limited Imaging

Recently several investigators proposed an extension of the Navy Aerosol Model (NAM) based on analysis of an extensive series of measurements at the Irish Atlantic Coast and at the French Mediterranean Coast. This work extends NAM by use of a similar analysis using data collected at three different Middle East Coastal areas: the Negev Desert (Eilat) Red Sea Coast, the Sea of Galilee (Tiberias) Coast, and the Mediterranean (Haifa) Coast. Results of the aerosol size distribution are compared with those obtained through measurements carried out over the Atlantic Ocean and Mediterranean Coasts. An analysis of these different results allows a better understanding of the similarities and differences between different coastal and open ocean zones. Parameterization is introduced. The aerosol particle concentrations and their dependences on wind speed for these coastal zones are analyzed and discussed.

Aerosol models for Middle East coastal zones: a modified NAM model

In many high-resolution photographic and photoelectronic imaging systems, resolution is limited by image motion and vibration and, as a result, the high-resolution capability of the sensor may be wasted. In normal reconnaissance and robotics the sensor moves during the exposure. Some of the resulting image motion can be removed by mechanical compensation, but not all of it. The residual motion blurs the image, and usually this blur becomes the limiting factor for many high-quality imaging systems. The ever-increasing altitudes and coverage requirements of modern imaging have put a premium on high resolution. An application of this paper is the recovery of the original image by inverse filtering that depends on the modulation transfer function (MTF) of the real-time relative motion between the object and the imaging system. An original method developed here for numerically calculating MTF for any type of image motion is the basis of the paper.

Numerical calculation of image motion and vibration modulation transfer function

The differential multiply subtractive Kramers-Kronig (DMSKK) method is utilized for deriving the optical spectral response of a 1D scattering medium The technique is based on the multiply subtractive Kramers-Kronig technique, where the phase spectrum is reconstructed from the amplitude spectrum in a finite spectral range with the aid of one or more phase-anchoring values We employ a new phase-anchoring technique in the DMSKK method to partially mitigate the finite-range effects This method incorporates spectral ballistic imaging to anchor the phase difference (instead of the phase directly) at one or more reference wavelengths The simplicity of phase derivative measurements and its utilization in the DMSKK method are emphasized by a simple experiment

Norman S. Kopeika

Papers

Role of the atmosphere in target acquisition: models versus experiment

Diffraction-Limited Imaging

Aerosol models for Middle East coastal zones: a modified NAM model

Numerical calculation of image motion and vibration modulation transfer function

Spectral analysis of a one-dimensional scattering medium with the differential multiply subtractive Kramers-Kronig method