A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

We describe a method to estimate the capacity limit of fiber-optic communication systems (or ?fiber channels?) based on information theory. This paper is divided into two parts. Part 1 reviews fundamental concepts of digital communications and information theory. We treat digitization and modulation followed by information theory for channels both without and with memory. We provide explicit relationships between the commonly used signal-to-noise ratio and the optical signal-to-noise ratio. We further evaluate the performance of modulation constellations such as quadrature-amplitude modulation, combinations of amplitude-shift keying and phase-shift keying, exotic constellations, and concentric rings for an additive white Gaussian noise channel using coherent detection. Part 2 is devoted specifically to the "fiber channel.'' We review the physical phenomena present in transmission over optical fiber networks, including sources of noise, the need for optical filtering in optically-routed networks, and, most critically, the presence of fiber Kerr nonlinearity. We describe various transmission scenarios and impairment mitigation techniques, and define a fiber channel deemed to be the most relevant for communication over optically-routed networks. We proceed to evaluate a capacity limit estimate for this fiber channel using ring constellations. Several scenarios are considered, including uniform and optimized ring constellations, different fiber dispersion maps, and varying transmission distances. We further present evidences that point to the physical origin of the fiber capacity limitations and provide a comparison of recent record experiments with our capacity limit estimation.

Capacity Limits of Optical Fiber Networks

We present theoretical and experimental results which demonstrate the superior sensitivity of swept source (SS) and Fourier domain (FD) optical coherence tomography (OCT) techniques over the conventional time domain (TD) approach. We show that SS- and FD-OCT have equivalent expressions for system signal-to-noise ratio which result in a typical sensitivity advantage of 20-30dB over TD-OCT. Experimental verification is provided using two novel spectral discrimination (SD) OCT systems: a differential fiber-based 800nm FD-OCT system which employs deep-well photodiode arrays, and a differential 1300nm SS-OCT system based on a swept laser with an 87nm tuning range.

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Sensitivity advantage of swept source and Fourier domain optical coherence tomography

We review the field of femtosecond pulse shaping, in which Fourier synthesis methods are used to generate nearly arbitrarily shaped ultrafast optical wave forms according to user specification. An emphasis is placed on programmable pulse shaping methods based on the use of spatial light modulators. After outlining the fundamental principles of pulse shaping, we then present a detailed discussion of pulse shaping using several different types of spatial light modulators. Finally, new research directions in pulse shaping, and applications of pulse shaping to optical communications, biomedical optical imaging, high power laser amplifiers, quantum control, and laser-electron beam interactions are reviewed.

Femtosecond pulse shaping using spatial light modulators

Course Description This is an advanced course in which we explore the field of Statistical Optics. Topics covered include such subjects as the statistical properties of natural (thermal) and laser light, spatial and temporal coherence, effects of partial coherence on optical imaging instruments, effects on imaging due to randomly inhomogeneous media, and a statistical treatment of the detection of light. Development of this more comprehensive model of the behavior of light draws upon the use of tools traditionally available to the electrical engineer, such as linear system theory and the theory of stochastic processes.

http://ieeexplore.ieee.org/iel5/3/23094/01073023.pdf

Statistical optics

We investigate experimental limitations in the accuracy of Fourier-transform spectral interferometry, a widely used technique for determining the spectral phase difference between two light beams consisting of, for example, femtosecond light pulses. We demonstrate that the spectrometer's finite spectral resolution, pixel aliasing, and frequency-interpolation error can play an important role, and we provide a new and more accurate recipe for recovering the spectral phase from the experimental data. Cop. 2000 Optical Society of America

Spectral resolution and sampling issues in Fourier-transform spectral interferometry

Ultrafast optics has undergone a revolution in the past two decades, driven by new
methods of pulse generation, amplification, manipulation, and measurement. We review
the advances made in the latter field over this period, indicating the general
principles involved, how these have been implemented in various experimental
approaches, and how the most popular methods encode the temporal electric field of a
short optical pulse in the measured signal and extract the field from the data.

Characterization of ultrashort electromagnetic pulses

In this article, we review the phenomenon of dispersion, paying particular attention to its impact in the optics of ultrashort pulses, as well as its measurement and management. At present, lasers generating coherent bandwidths of several hundred nanometers have been demonstrated and correspondingly short pulses of 10 fs or so are quite usual. The limits to the breadth of optical spectra and brevity of pulse durations that may be achieved are often set by the dispersive properties of the linear optical elements of which the source is constructed. Progress in ultrafast optics to date has therefore relied extensively on the development of ways to characterize and manipulate dispersion. The means by which this can be accomplished are significantly different for laser oscillators and laser amplifiers, as well as for nonlinear interactions that are used to extend the range of frequencies at which short optical pulses are available, but in all cases it is this phenomenon that determines the output of current optical sources.

The role of dispersion in ultrafast optics

We demonstrate a simple technique for simultaneous and complete characterization of the optical pulses and temporal modulators commonly used in telecommunication. The electric field of a pulse and the response of a modulator are obtained from the analysis of the two-dimensional spectrogram of the pulse gated by the modulator. The measurement sensitivity is greatly improved compared with the conventional nonlinear optical techniques. Trains of picosecond pulses as weak as 10-17 J are accurately characterized with an electroabsorption modulator as the temporal gate. The time-resolved transmission and phase of the modulator are also presented.

Simultaneous temporal characterization of telecommunication optical pulses and modulators by use of spectrograms

We demonstrate the measurement of waveforms and eye diagrams at high bit rates by optical sampling using coherent detection. By simultaneously recording two orthogonal quadratures of the interference between the data stream and a sampling pulse with two balanced detectors, we are able to cancel the phase sensitivity inherent to linear optics. As the device is based on linear optics and square-law low-speed photodetectors, its sensitivity is 1000 times better than nonlinear optical sampling techniques, which makes it attractive for optical signal characterization and monitoring. This new diagnostic tool was used to measure eye diagrams at 10, 40, and 80 Gb/s, and is projected to operate at 160 Gb/s and higher.

Christophe Dorrer

Papers

Spectral resolution and sampling issues in Fourier-transform spectral interferometry

Characterization of ultrashort electromagnetic pulses

The role of dispersion in ultrafast optics

Simultaneous temporal characterization of telecommunication optical pulses and modulators by use of spectrograms

Linear optical sampling