Interferometry is a family of techniques in which waves, usually electromagnetic, are superimposed in order to extract information. Interferometry 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, and optometry.:1–2
Interferometers are widely used in science and industry for the measurement of small displacements, refractive index changes and surface irregularities. In analytical science, interferometers are used in continuous wave Fourier transform spectroscopy to analyze light containing features of absorption or emission associated with a substance or mixture. An astronomical interferometer consists of two or more separate telescopes that combine their signals, offering a resolution equivalent to that of a telescope of diameter equal to the largest separation between its individual elements.
Heterodyning is a method for transferring a broadcast signal from its carrier to a fixed local intermediate frequency in the receiver so that most of the receiver does not have to be retuned when you change channels. The interference of any two waves will produce a beat frequency, and this technique provides for the tuning of a radio by forcing it to produce a specific beat frequency called the “intermediate frequency” or IF. Heterodyning is used in the AM radio receiver and played a big part in making AM radio practical for mass communication.
An electromagnetic carrier wave which is carrying a signal by means of amplitude modulation or frequency modulation can transfer that signal to a carrier of different frequency by means of heterodyning. This transfer is accomplished by mixing the original modulated carrier with a sine wave of another frequency. This process produces a beat frequency equal to the difference between the frequencies, and this difference frequency constitutes a third carrier which will be modulated by the original signal.
Heterodyning is extremely important in radio transmission — in fact, the development of heterodyning schemes was one of the major developments which led to mass communication by radio. By fixing the beat frequency between the incoming carrier and the local oscillator to a fixed intermediate frequency (IF), most of a radio receiver can be constructed so that it can be used by any incoming radio signal. When the input radio frequency amplifier is tuned to the station’s carrier frequency, the local oscillator is tuned along with it to produce a beat frequency equal to the fixed IF frequency. We now take for granted that one radio receiver can be tuned to any of the locally broadcast radio stations, but if it were not for heterodyning, you would have to have one receiver for each broadcast station.
Optical heterodyne detection is the implementation of heterodyne detection principle using a nonlinear optical process. In heterodyne detection, a signal of interest at some frequency is non-linearly mixed with a reference “local oscillator” (LO) that is set at a close-by frequency. The desired outcome is the difference frequency, which carries the information (amplitude, phase, and frequency modulation) of the original higher frequency signal, but is oscillating at a lower more easily processed carrier frequency.
Optical heterodyne detection has special temporal and spatial characteristics that pragmatically distinguish it from conventional Radio Frequency(RF) heterodyne detection. Electrical field oscillations in the optical frequency range cannot be directly measured since the relatively high optical frequencies have oscillating fields that are much faster than electronics can respond. Instead, optical photons are detected by energy or equivalently by photon counting, which are proportional to the square of the electric field and thus form a non-linear event. Thus when the LO and the signal beams impinge together on the surface of a photodiode they “mix”, producing heterodyne beat frequencies directly via the physics of energy absorption. While an old technique, key limiting issues were solved only as recently as 1994 with the invention of synthetic array heterodyne detection.
Contrast to conventional radio frequency (RF) heterodyne detection
It is instructive to contrast the practical aspects of optical band detection to radio frequency (RF) band heterodyne detection.
Energy versus electric field detection
Unlike Radio Frequency (RF) band detection, optical frequencies oscillate too rapidly to directly measure and process the electric field electronically. Instead optical photons are (usually) detected by absorbing the photon’s energy, thus only revealing the magnitude, and not by following the electric field phase. Hence the primary purpose of heterodyne mixing is to down shift the signal from the optical band to an electronically tractable frequency range.
In RF band detection, typically, the electromagnetic field drives oscillatory motion of electrons in an antenna; the captured EMF is subsequently electronically mixed with a local oscillator (LO) by any convenient non-linear circuit element with a quadratic term (most commonly a rectifier). In optical detection, the desired non-linearity is embedded in the photon absorption process itself. Conventional light detectors—so called “Square-law detectors”—respond to the photon energy to free bound electrons, and since the energy flux scales as the square of the electric field, so does the rate at which electrons are freed. A difference frequency only appears in the detector output current when both the LO and signal illuminate the detector at the same time, causing the square of their combined fields to have a cross term or “difference” frequency modulating the average rate at which free electrons are generated.
Wideband local oscillators for coherent detection
Another point of contrast is the expected bandwidth of the signal and local oscillator. Typically, an RF local oscillator is a pure frequency; pragmatically, “purity” means that a local oscillator’s frequency bandwidth is much much less than the difference frequency. With optical signals, even with a laser, it is not simple to produce a reference frequency sufficiently pure to have either an instantaneous bandwidth or long term temporal stability that is less than a typical megahertz or kilohertz scale difference frequency. For this reason, the same source is often used to produce the LO and the signal so that their difference frequency can be kept constant even if the center frequency wanders.
As a result, the mathematics of squaring the sum of two pure tones, normally invoked to explain RF heterodyne detection, is an oversimplified model of optical heterodyne detection. Nevertheless, the intuitive pure-frequency heterodyne concept still holds perfectly for the wideband case provided that the signal and LO are mutually coherent. Indeed, one can obtain narrow-band interference from coherent broadband sources: this is the basis for white light interferometry and optical coherence tomography. Mutual coherence permits the rainbow in Newton’s rings, and supernumerary rainbows.
Consequently, optical heterodyne detection is usually performed as interferometry where the LO and signal share a common origin, rather than, as in radio, a transmitter sending to a remote receiver. The remote receiver geometry is uncommon because generating a local oscillator signal that is coherent with a signal of independent origin is technologically difficult at optical frequencies. However, lasers of sufficiently narrow linewidth to allow the signal and LO to originate from different lasers do exist.
My photos around 9am Octber 28, 2016