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.

/pdf/a-parametric-texture-model-based-on-joint-statistics-of-2p5nbgtfy6.pdf

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.

/pdf/optical-coherence-tomography-principles-and-applications-17y32cabbm.pdf

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.

/pdf/survey-on-free-space-optical-communication-a-communication-239v68hfyw.pdf

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

Development of focal plane arrays (FPA) for mm wavelength and THz radiation is presented in this paper. The FPA is
based upon inexpensive neon indicator lamp Glow Discharge Detectors (GDDs) that serve as pixels in the FPA. It was
shown in previous investigations that inexpensive neon indicator lamps GDDs are quite sensitive to mm wavelength and
THz radiation. The diameter of GDD lamps are typically 3-6 mm and thus the FPA can be diffraction limited.
Development of an FPA using such devices as detectors is advantageous since the costs of such a lamp is around 30-50
cents per lamp, and it is a room temperature detector sufficiently fast for video frame rates. Recently a new 8×8 GDD
FPA VLSI board was designed, constructed, and experimentally tested. First THz images as well as DSP methods using
this GDD FPA are demonstrated. Super resolution was achieved by moving the 8×8 pixel board appropriately in the
image plane so that 32X32 pixel images are also obtained and shown here, with much improved image quality because
of much reduced pixelization distortion.

mm wave and THz imaging using very inexpensive neon-indicator lamp detector focal-plane arrays

Atmospheric modulation transfer function (MTF) measurements carried out simultaneously in both thermal imaging atmospheric windows using both passive and actively heated targets are presented. Results indicate rather significant angular spatial frequency dependence of the MTF, in contradiction to the conventional approach, which assumes contrast transfer is atmospheric transmission only. A theoretical explanation is discussed, based on aerosol forward scattering and absorption effects, which is shown to be angular spatial frequency dependent and yields MTF results similar to those measured. This means that small details are blurred much more than large details by the atmosphere, thus also affecting target acquisition probabilities.

Thermal imaging through the atmosphere : atmospheric modulation transfer function theory and verification

A method and device for real time processing of analog signals, such as video signals, representative of frames of data acquired in row order in a two dimensional field. The incoming signal is processed (for example filtered) by analog means, transposed to column order, processed again by analog means, and transposed back to row order. The transpositions are done by digitizing each frame of the signal, transposing the digital signal, and converting the transposed digital signal back to analog form. The process can be pipelined to be accomplished in real time with only a constant delay of two frames.

Real-time two-dimensional filtering of video signals

New exact numerical calculations as well as exact calculations in J. Opt. Soc. Am. A10, 172 ( 1993) indicate that the approximations in the Comment in J. Opt. Soc. Am. A11, 1175 ( 1994) are based on faulty perceptions of basic scattering phenomena and on a misreading of our paper. The Comment does not sufficiently consider effects of instrumentation. Whereas our model refers to the aerosol modulation transfer function (MTF) in the image plane, the values of maximum angles for scattered (θS) and unscattered (θ0) light used in the Comment refer to the optics plane. The Comment does not consider the fact that dynamic range limits (θS) in the image, whereas limited spatial-frequency bandwidth broadens θ0 in the image, each by orders of magnitude. Therefore the Comment’s conclusion contradicts experimental results obtained by numerous researchers. The Comment’s conclusion that aerosol MTF is insignificant is based on that author’s own experiments, in which clear weather and haze atmospheric MTF (composed of turbulence and aerosol MTF’s) could not be measured, the reason being insufficient equipment resolution, rather than insignificant turbulence or aerosol MTF. Furthermore, the claim in our original paper that aerosol MTF is extremely significant has since been supported by many different types of experiments that included short and long exposures, thermal imaging, and image restoration based on atmospheric MTF, including a highly significant practical, uniquely shaped, aerosol MTF.

Imaging through the atmosphere: practical instrumentation-based theory and verification of aerosol modulation transfer function: reply to comment

At present, system design usually assumes the Kolmogorov model of refractive index fluctuation spectra in the
atmosphere. However, experimental data indicates that in the atmospheric boundary layer and at higher altitudes the
turbulence can be different from Kolmogorov's type.
In optical communications, analytical models of mean irradiance and scintillation index have been developed for a
traditional Kolmogorov spectrum and must be revised for non-Kolmogorov turbulence.
The image quality (resolution, MTF, etc.) is essentially dependent on the properties of turbulent media. Turbulence MTF
must be generalized to include non-Kolmogorov statistics. The change in fluctuation correlations of the refractive index
can lead to a considerable change in both the MTF form and the resolution value.
In this work, on the basis of experimental observations and modeling, generalized atmospheric turbulence statistics
including both Kolmogorov and non-Kolmogorov path components are discussed, and their influence on imaging and
communications through the atmosphere estimated for different scenarios of vertical and slant-path propagation. The
atmospheric model of an arbitrary (non-Kolmogorov) spectrum is applied to estimate the statistical quantities associated
with optical communication links (e.g., scintillation and fading statistics) and imaging systems.
Implications can be significant for optical communication, imaging through the atmosphere, and remote sensing.

Norman S. Kopeika

Papers

mm wave and THz imaging using very inexpensive neon-indicator lamp detector focal-plane arrays

Thermal imaging through the atmosphere : atmospheric modulation transfer function theory and verification

Real-time two-dimensional filtering of video signals

Imaging through the atmosphere: practical instrumentation-based theory and verification of aerosol modulation transfer function: reply to comment

Generalized atmospheric turbulence: implications regarding imaging and communications