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

We present an algorithm to realign images distorted by motion and vibrations captured in cameras that use a scanning vector sensor with an interlaced scheme. In particular, the method is developed for images captured by a staggered time delay and integration camera distorted by motion. The algorithm improves the motion-distorted image by adjusting its fields irrespective of the type of motion that occurs during the exposure. The algorithm performs two tasks: estimation of the field relative motion during the exposure by a normal least-squares estimation technique and improvement of the degraded image from such motion distortion. The algorithm uses matrix computations; therefore it has a computation advantage over algorithms based on the technique of searching for a match. The algorithm is successfully demonstrated on both simulated and real images.

Registration of motion-distorted interlaced images captured by a scanning vector imaging sensor.

Any image acquired by optical, electro-optical, or electronic means is likely to be degraded by the environment. The resolution of the acquired image depends on the total modulation transfer function (MTF) of the system and the additive noise. Image restoration techniques can improve image resolution significantly; however, as the noise increases, improvements via image processing become more limited because im- age restoration increases the noise level in the image. We characterize the influence of the MTF and noise level on human target acquisition probability to ascertain the advantages, if any, of image restoration. Con- ditions when restoration would be advisable are determined. © 1998 So- ciety of Photo-Optical Instrumentation Engineers. (S0091-3286(98)01007-1)

Relative effects of distortion and noise on target acquisition: the advisability of image restoration

Different views of the significance of aerosol MTF have been reported. For example, one recent paper [OE, 52(4)/2013, pp. 046201] claims that the aerosol MTF "contrast reduction is approximately independent of spatial frequency, and image blur is practically negligible". On the other hand, another recent paper [JOSA A, 11/2013, pp. 2244-2252] claims that aerosols "can have a non-negligible effect on the atmospheric point spread function". We present clear experimental evidence of common significant aerosol blur and evidence that aerosol contrast reduction can be extremely significant. In the IR, it is more appropriate to refer to such phenomena as aerosol-absorption MTF. The role of imaging system instrumentation on such MTF is addressed too.

Aerosol MTF revisited

Photoconductive detectors with relatively flat response to wavelengths as short as 2500 A have been fabricated in thin films of zinc phosphide deposited by the close-space-transport method on to mica substrates. Responsivity at 2527 A was 0.13 A/W.

Ultraviolet photoconductive detectors in Zn3P2

The rise time of a gas-filled photodiode at blue-green wavelengths is found to be less than that at red wavelengths. As photoionization of excited atoms in such devices increases response to light of decreasing wavelength over that provided by the photocathode, spectral differences in rise time are also attributed to the same mechanism. It is suggested that these phenomena decrease parasitic inductance of the tube. This implies that rise times in glow discharge detectors of EM radiation can be improved through miniaturization of inter-electrode spacing.

Spectral Dependence of Rise Time in Gas Filled Phototubes: Implications concerning Possible Miniaturization of Gas Discharge Detectors of Electromagnetic Radiation

Norman S. Kopeika

Papers

Registration of motion-distorted interlaced images captured by a scanning vector imaging sensor.

Relative effects of distortion and noise on target acquisition: the advisability of image restoration

Aerosol MTF revisited

Ultraviolet photoconductive detectors in Zn3P2

Spectral Dependence of Rise Time in Gas Filled Phototubes: Implications concerning Possible Miniaturization of Gas Discharge Detectors of Electromagnetic Radiation