Autocorrelator
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Autocorrelator
A real time interferometric autocorrelator is an electronic tool used to examine the autocorrelation of, among other things, optical beam intensity and spectral components through examination of variable beam path differences. ''See Optical autocorrelation.'' Description In an interferometric autocorrelator, the input beam is split into a fixed path beam and a variable path beam using a standard beamsplitter. The fixed path beam travels a known and constant distance, whereas the variable path beam has its path length changed via rotating mirrors or other path changing mechanisms. At the end of the two paths, the beams are ideally parallel, but slightly separated, and using a correctly positioned lens, the two beams are crossed inside a second-harmonic generating (SHG) crystal. The autocorrelation term of the output is then passed into a photomultiplying tube (PMT) and measured. Details Considering the input beam as a single pulse with envelope E(t), the constant fixed path dist ...
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Autocorrelation
Autocorrelation, sometimes known as serial correlation in the discrete time case, is the correlation of a signal with a delayed copy of itself as a function of delay. Informally, it is the similarity between observations of a random variable as a function of the time lag between them. The analysis of autocorrelation is a mathematical tool for finding repeating patterns, such as the presence of a periodic signal obscured by noise, or identifying the missing fundamental frequency in a signal implied by its harmonic frequencies. It is often used in signal processing for analyzing functions or series of values, such as time domain signals. Different fields of study define autocorrelation differently, and not all of these definitions are equivalent. In some fields, the term is used interchangeably with autocovariance. Unit root processes, trend-stationary processes, autoregressive processes, and moving average processes are specific forms of processes with autocorrelation. A ...
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Optical Autocorrelation
In optics, various autocorrelation functions can be experimentally realized. The field autocorrelation may be used to calculate the spectrum of a source of light, while the intensity autocorrelation and the interferometric autocorrelation are commonly used to ''estimate'' the duration of ultrashort pulses produced by modelocked lasers. The laser pulse duration cannot be easily measured by optoelectronic methods, since the response time of photodiodes and oscilloscopes are at best of the order of 200 femtoseconds, yet laser pulses can be made as short as a few femtoseconds. In the following examples, the autocorrelation signal is generated by the nonlinear process of second-harmonic generation (SHG). Other techniques based on two-photon absorption may also be used in autocorrelation measurements, as well as higher-order nonlinear optical processes such as third-harmonic generation, in which case the mathematical expressions of the signal will be slightly modified, but the basi ...
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Interferometry
Interferometry is a technique which uses the ''interference'' of superimposed waves to extract information. Interferometry typically uses electromagnetic waves and is an important investigative technique in the fields of astronomy, fiber optics, engineering metrology, optical metrology, oceanography, seismology, spectroscopy (and its applications to chemistry), quantum mechanics, nuclear and particle physics, plasma physics, remote sensing, biomolecular interactions, surface profiling, microfluidics, mechanical stress/strain measurement, velocimetry, optometry, and making holograms. Interferometers are devices that extract information from interference. They are widely used in science and industry for the measurement of microscopic displacements, refractive index changes and surface irregularities. In the case with most interferometers, light from a single source is split into two beams that travel in different optical paths, which are then combined again to produce interfer ...
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Second-harmonic Generation
Second-harmonic generation (SHG, also called frequency doubling) is a nonlinear optical process in which two photons with the same frequency interact with a nonlinear material, are "combined", and generate a new photon with twice the energy of the initial photons (equivalently, twice the frequency and half the wavelength), that conserves the coherence of the excitation. It is a special case of sum-frequency generation (2 photons), and more generally of harmonic generation. The second-order nonlinear susceptibility of a medium characterizes its tendency to cause SHG. Second-harmonic generation, like other even-order nonlinear optical phenomena, is not allowed in media with inversion symmetry (in the leading electric dipole contribution). However, effects such as the Bloch–Siegert shift (oscillation), found when two-level systems are driven at Rabi frequencies comparable to their transition frequencies, will give rise to second harmonic generation in centro-symmetric systems. ...
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Photomultiplier
A photomultiplier is a device that converts incident photons into an electrical signal. Kinds of photomultiplier include: * Photomultiplier tube, a vacuum tube converting incident photons into an electric signal. Photomultiplier tubes (PMTs for short) are members of the class of vacuum tubes, and more specifically vacuum phototubes, which are extremely sensitive detectors of light in the ultraviolet, visible, and near-infrared ranges of the electromagnetic spectrum. ** Magnetic photomultiplier, developed by the Soviets in the 1930s. ** Electrostatic photomultiplier, a kind of photomultiplier tube demonstrated by Jan Rajchman of RCA Laboratories in Princeton, NJ in the late 1930s which became the standard for all future commercial photomultipliers. The first mass-produced photomultiplier, the Type 931, was of this design and is still commercially produced today. * Silicon photomultiplier, a solid-state device converting incident photons into an electric signal. Silicon photomultiplie ...
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Autocorrelation Technique
The autocorrelation technique is a method for estimating the dominating frequency in a complex signal, as well as its variance. Specifically, it calculates the first two moments of the power spectrum, namely the mean and variance. It is also known as the pulse-pair algorithm in radar theory. The algorithm is both computationally faster and significantly more accurate compared to the Fourier transform, since the resolution is not limited by the number of samples used. Derivation The autocorrelation of lag 1 can be expressed using the inverse Fourier transform of the power spectrum S(\omega): : R(1) = \frac \int_^ S(\omega) e^ d\omega. If we model the power spectrum as a single frequency S(\omega) \ \stackrel\ \delta(\omega - \omega_0), this becomes: : R(1) = \frac \int_^ \delta(\omega - \omega_0) e^ d\omega : R(1) = \frac e^ where it is apparent that the phase of R(1) equals the signal frequency. Implementation The mean frequency is calculated based on the autocorrelation w ...
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:Category:Nonlinear Optics
Nonlinear optics is the branch of optics that describes the behaviour of light in ''nonlinear media'', that is, media in which the polarization P responds nonlinearly to the electric field E of the light. This nonlinearity is typically only observed at very high light intensities such as provided by pulsed laser A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The fir ...s. {{Cat main, Nonlinear optics Optics ...
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Signal Processing
Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing ''signals'', such as audio signal processing, sound, image processing, images, and scientific measurements. Signal processing techniques are used to optimize transmissions, Data storage, digital storage efficiency, correcting distorted signals, subjective video quality and to also detect or pinpoint components of interest in a measured signal. History According to Alan V. Oppenheim and Ronald W. Schafer, the principles of signal processing can be found in the classical numerical analysis techniques of the 17th century. They further state that the digital refinement of these techniques can be found in the digital control systems of the 1940s and 1950s. In 1948, Claude Shannon wrote the influential paper "A Mathematical Theory of Communication" which was published in the Bell System Technical Journal. The paper laid the groundwork for later development of information c ...
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