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

Turbulence strength parameter in laboratory and natural optical experiments in non-Kolmogorov cases

The basic configuration of free space satellite optical communication includes a transmitter and a receiver. The transmitter satellite must point the optical information beam to the receiver satellite in order to establish communication. An important aspect in satellite optical communication is to obtain minimum bit error rate using minimum power. This aim can be achieved with very small transmitter beam divergence angles. The disadvantages of too narrow a divergence angle are that the transmitter beam may sometimes miss the receiver satellite due to pointing vibrations, and that the transmitter optics aperture required is large and expensive. The optimum value of the received power as a function of the pointing vibration displacement determines the optimum bean divergence angle. The performance of the tracking system determines the amplitude limits of the vibrations of the transmitter beam in the spatial domain. A mathematical model including the performance of the communication system as a function of the performance of the tracking system is derived. From this model we derive the optimum transmitter telescope gain. An example for a practical communication system between a low earth orbit satellite (LEO) and a geostationary earth orbit satellite (GEO) is presented. Using this model makes it possible to choose appropriate optics for the transmitter with reduced size and weight.

Optimum transmitter optics aperture for free space satellite optical communication as a function of tracking system performance

A new method of real-time high resolution imaging through the atmosphere is presented. This technique is based on the knowledge of average atmospheric MTF at the time the image is received. Atmospheric effects are modeled by a noisy spatial frequency filter including an average component described by the average atmospheric modulation transfer function, and a noisy component modeled by the atmospheric point spread function's power spectral density. Analytical results are accompanied by experimental image restoration examples, indicating significant image quality improvement based upon knowledge of average atmospheric MTF. This method can be used to help overcome the jitter characteristics of turbulence, and is capable of yielding real-time image restoration with resolution limited essentially only by the hardware itself.

High-resolution restoration of images distorted by the atmosphere, based upon average atmospheric modulation transfer function

A well-known method for range applications is chirped frequency modulated continuous wave (FMCW) radar. We offer a simple way to measure the distance to the object target with high resolution based on very inexpensive glow discharge detectors (GDDs) at terahertz (THz) band frequencies. Proof of concept of THz FMCW radar using a GDD is experimentally demonstrated in this paper. The advantage of FMCW in the THz band is its better range resolution compared with FMCW radar in the microwave band due to wider frequency swing. Such a system using a GDD has the following advantages: very inexpensive and simple to realize, rigid components, room temperature operation, fast response time, and high power radiation immunity. Those properties are very important in the realization of high resolution 3-D imaging in the THz band. Depth resolution on the order of 7.5 mm can be achieved by the proposed system.

Terahertz Frequency Modulated Continuous Wave Radar Using Glow Discharge Detector

A simple model of photoionization of excited atoms by UV photons from capacitor spark discharges is suggested to explain the improvement in both plasma density production and laser efficiency noticed by several investigators when the proportion of helium in high-pressure CO 2 laser mixtures is increased. Such improvements with increased He proportion take place both with and without seeding with low ionization potential dopants. The model is also applicable to explaining the arc suppression qualities of helium as well as the ability to ignite discharges at higher total pressures when the proportion of helium is increased. Several implications regarding future TEA laser work are suggested.

Norman S. Kopeika

Papers

Turbulence strength parameter in laboratory and natural optical experiments in non-Kolmogorov cases

Optimum transmitter optics aperture for free space satellite optical communication as a function of tracking system performance

High-resolution restoration of images distorted by the atmosphere, based upon average atmospheric modulation transfer function

Terahertz Frequency Modulated Continuous Wave Radar Using Glow Discharge Detector

The role of excited atoms in UV photopreionization TEA lasers