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

There are basically two techniques used to correct for turbulence degradation. One is adaptive optics, whose purpose is to prevent turbulence-derived distortions from being recorded in the image. The other technique is image restoration using typically digital computers. In the latter case, turbulence-derived blur has already been recorded in the image but is removed through image processing.

Turbulence Modulation Transfer Function

Atmospheric Blur and Image Restoration

The recently developed atmospheric Wiener filter, which corrects for turbulence and aerosol blur and path radiance simultaneously, is implemented in digital restoration of AVHR imagery over the five wavelength bands of the satellite instrumentation. Restoration is most impressive for higher optical depth situations which cause more blur, with improvement in regard to both smallness of size of resolvable detail and contrast. Turbulence modulation transfer function (MTF) is calculated from meteorological data. Aerosol MTF is consistent with optical depth, measured with a sum-photometer. The product of the two yields atmospheric MTF which is implemented in the atmospheric Wiener filter. Turbulence blur, aerosol blur, and path radiance contrast loss are all corrected simultaneously, as if there were no intervening atmosphere. Image restorations with accompanying atmospheric MTF curves are presented. However, restoration results using a simple inverse atmospheric MTF filter were quite similar. This indicates the satellite images were characterized by very low noise and that turbulence jitter was very limited which, in turn, indicates that the turbulence MTFs integrated upwards over the path length wee not significant when compared to aerosol MTFs. Restorations are shown for various wavelength bands and are quite apparent even under clear weather conditions.

Imaging through the atmosphere from satellites: restoration of images based on atmospheric MTF

The properties of terahertz (THz) radiation are well known. They penetrate well most nonconducting
media; there are no known biological hazards, and atmospheric attenuation and scattering is
lower than for visual and IR radiation.
Recently we have found that common miniature commercial neon glow discharge detector
(GDD) lamps costing typically about 30 cents each exhibit high sensitivity to THz radiation, with
microsecond order rise times, thus making them excellent candidates for such focal plane arrays.
Based on this technology we designed, built and tested 4X4 and 8X8 GDD focal plane arrays.
A line vector of 32 GDD pixels is being designed in order to increase the number of pixels in such
arrays and thus the image resolution. Unique large aperture quasi optic mirrors were design and tested
experimentally in this work. A new technology of light weight large aperture mirrors is proposed in this
work. In this case a metal coating on plastic substrate is demonstrated. According to first experiments
this technology proves to reliable with minimal deformation in LAB conditions. THz Images at 100
GHz were taken using this new inexpensive technology with good quality and resolution.

THz imaging using Glow Discharge Detector (GDD) focal plane arrays and large aperture quasi optic mirrors

Imaging quality of optical systems in a turbid environment is influenced not only by the contents of the turbid layer between the object and the optical receiver but also by the inhomogeneity of that medium. This is important particularly when imaging is performed through clouds, non homogeneous layers of dust, or over vertical or slant paths through the atmosphere. Forward small angle scattering influences more severely image quality and blur when the scattering layer is closer to the receiver. In this study the influence of the position of the scattering layer along the optical axis on the image quality and modulation transfer function (MTF) is investigated. The scattering layer was in controlled laboratory experiments consisted of calibrated polystyrene particles of known size and quantity. A point source was imaged by a computerized imaging system through a layer containing polystyrene particles and the point spread function (PSF) was recorded. The scattering MTF was calculated using the measured PSF. The MTF was measured as a function of the relative distance of the layer from the receiver. The experimental results were compared to theoretical models based on the solution of the radiative transfer theory under the small angle approximation.

Norman S. Kopeika

Papers

Turbulence Modulation Transfer Function

Atmospheric Blur and Image Restoration

Imaging through the atmosphere from satellites: restoration of images based on atmospheric MTF

THz imaging using Glow Discharge Detector (GDD) focal plane arrays and large aperture quasi optic mirrors

Investigation of the influence of inhomogenous scattering media on image quality: the shower curtain effect