Optical heterodyne detection
Encyclopedia
Optical heterodyne detection is an important special case of heterodyne detection
. 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 characteristics and special problems that distinguish it from conventional RF heterodyne detection. The electrical field cannot be directly measured, since the relatively high optical frequencies have oscillating fields that are much faster than electronics can respond. As such, the LO and the reference are typically mixed on a photodiode While an old technique, key limiting issues were solved only as recently as 1994 with the invention of synthetic array heterodyne detection.
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 cross term or "difference" frequency modulating the average rate at which free electrons are generated.
As a result, the mathematics of squaring the sum of two pure tones, normally invoked to explain RF heterodyne mixing, 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. That is to say, the remote receiver geometry is unusual because generating a local oscillator signal that is mutually 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.
systems can discriminate wind velocities with a resolution better than 1 meter per second, which is less than a part in a billion shift in the optical frequency. Likewise small coherent phase shifts can be measured even for nominally incoherent light, allowing optical coherence tomography
to image micrometer-sized features. Moreover, an electronic filter can define an effective optical bandwidth that is narrower than any realizable wavelength filter operating on the light itself, and thereby enable background light rejection and hence the detection of weak signals.
One of the virtues of heterodyne detection is that the difference frequency is generally far removed spectrally from the potential noises radiated during the process of generating either the signal or the LO signal, thus making the spectral region near the difference frequency relatively quiet. Hence, narrow electronic filtering near the difference frequency is highly effective at removing the remaining, generally broadband, noise sources.
The primary remaining source of noise is photon shot noise from the nominally constant level of the Local Oscillator (LO) on the optical detector. Since the Shot noise
scales as the amplitude of the LO electric field level, and the heterodyne gain also scales the same way, the ratio of the shot noise to the mixed signal is constant no matter how large the LO.
Thus in practice one increases the LO level, until the gain on the signal raises it above all other noise sources, leaving only the shot noise. At that point there is no change in the signal to noise as the gain is raised further. (Of course, this is a highly idealized description.)
To solve this problem, synthetic array heterodyne detection was developed. In SAHD, large imaging arrays can be multiplex
ed into virtual pixels on a single element detector with single readout lead, single electrical filter, and single recording system. The time domain conjugate of this approach is Fourier transform heterodyne detection, which also has the multiplex advantage and also allows a single element detector to act like an imaging array. SAHD has been implemented as Rainbow heterodyne detection in which instead of a single frequency LO, many narrowly-spaced frequencies are spread out across the detector element surface like a rainbow. The physical position where each photon arrived is encoded in the resulting difference frequency itself, making a virtual 1D array on a single element detector. If the frequency comb is evenly spaced then, conveniently, the Fourier transform
of the output waveform is the image itself. Arrays in 2D can be created as well, and since the arrays are virtual, the number of pixels, their size, and their individual gains can be adapted dynamically. Because this technique uses more total LO power (spread over multiple pixels) it has more total shot noise than a single pixel detector at the same pixel power density.
s that are spatially incoherent. In laser scattering this is known as speckle.
In RF detection the antenna is rarely larger than the wavelength so all excited electrons move coherently within the antenna, whereas in optics the detector is usually much larger than the wavelength and thus can intercept a distorted phase front, resulting in destructive interference by out-of-phase photo-generated electrons within the detector.
Interestingly, while destructive interference dramatically reduces the signal level, the summed amplitude of a spatially incoherent mixture does not approach zero but rather the mean amplitude of a single speckle. However, since the standard deviation of the coherent sum of the speckles is exactly equal to the mean speckle intensity, optical heterodyne detection of scrambled phase fronts can never measure the absolute light level with an error bar less than the size of the signal itself. This upper bound signal-to-noise ratio of unity is only for absolute magnitude measurement: it can have signal-to-noise ratio
better than unity for phase, frequency or time-varying relative-amplitude measurements in a stationary speckle field.
In RF detection, "diversity reception" is often used when the primary antenna is coincidentally located at an interference null point: by having more than one antenna one can adaptively switch to whichever antenna has the strongest signal or even incoherently add all of the antenna signals. Simply adding the antenna coherently can produce destructive interference just as happens in the optical realm.
The analogous diversity reception for optical heterodyne has been demonstrated with arrays of photon-counting detectors. For incoherent addition of the multiple element detectors in a random speckle field, the ratio of the mean to the standard deviation will scale as the square root of the number of independently measured speckles. This improved signal-to-noise ratio makes absolute amplitude measurements feasible in heterodyne detection.
However, as noted above, scaling physical arrays to large element counts is challenging for heterodyne detection due to the oscillating or even multi-frequency nature of the output signal. Instead, a single-element optical detector can also act like diversity receiver via synthetic array heterodyne detection or Fourier transform heterodyne detection. With a virtual array one can then either adaptively select just one of the LO frequencies, track a slowly moving bright speckle, or add them all in post-processing by the electronics.
.
Heterodyne detection
Heterodyne detection is a method of detecting radiation by non-linear mixing with radiation of a reference frequency. It is commonly used in telecommunications and astronomy for detecting and analysing signals....
. 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 characteristics and special problems that distinguish it from conventional RF heterodyne detection. The electrical field cannot be directly measured, since the relatively high optical frequencies have oscillating fields that are much faster than electronics can respond. As such, the LO and the reference are typically mixed on a photodiode 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 heterodyneHeterodyne
Heterodyning is a radio signal processing technique invented in 1901 by Canadian inventor-engineer Reginald Fessenden where high frequency signals are converted to lower frequencies by combining two frequencies. Heterodyning is useful for frequency shifting information of interest into a useful...
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
EMF
- Music :* EMF , a British band** "EMF", a bonus track on EMF's album Schubert Dip* E.M.F. , a 1983 album by GG Allin* English Music Festival, a British music festival- Organizations :...
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 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 mixing, is an oversimplified model of optical heterodyne detection. Nevertheless, the intuitive pure-frequency heterodyne concept still holds perfectly for the wideband
Wideband
In communications, wideband is a relative term used to describe a wide range of frequencies in a spectrum. A system is typically described as wideband if the message bandwidth significantly exceeds the channel's coherence bandwidth....
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
White light scanner
A White Light Scanner is a device for measuring the physical geometrical characteristics of an object using White light interferometry. Frequency domain analysis is an alternate approach that uses all of the information available in the interferogram...
and optical coherence tomography
Optical coherence tomography
Optical coherence tomography is an optical signal acquisition and processing method. It captures micrometer-resolution, three-dimensional images from within optical scattering media . Optical coherence tomography is an interferometric technique, typically employing near-infrared light...
. Mutual coherence permits the rainbow in Newton's rings
Newton's rings
The phenomenon of Newton's rings, named after Isaac Newton who first studied them in 1717, is an interference pattern caused by the reflection of light between two surfaces - a spherical surface and an adjacent flat surface...
, and supernumerary rainbows.
Consequently, optical heterodyne detection is usually performed as interferometry
Interferometry
Interferometry refers to a family of techniques in which electromagnetic waves are superimposed in order to extract information about the waves. An instrument used to interfere waves is called an interferometer. Interferometry is an important investigative technique in the fields of astronomy,...
where the LO and signal share a common origin, rather than, as in radio, a transmitter sending to a remote receiver. That is to say, the remote receiver geometry is unusual because generating a local oscillator signal that is mutually 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.
Gain in the detection
The amplitude of the down-mixed difference frequency can be larger than the amplitude of the original signal itself. The difference frequency signal is proportional to the product of the amplitudes of the LO and signal electric fields. Thus the larger the LO amplitude, the larger the difference-frequency amplitude. Hence there is gain in the photon conversion process itself.Preservation of optical phase
If the optical phase of the signal beam shifts by an angle theta, then the phase of the electronic difference frequency shifts by exactly the same angle theta. More properly, to discuss an optical phase shift one needs to have a common time base reference. Typically the signal beam is derived from the same laser as the LO but shifted by some modulator in frequency. In other cases, the frequency shift may arise from reflection from a moving object. As long as the modulation source maintains a constant offset phase between the LO and signal source, any added optical phase shifts over time arising from external modification of the return signal are added to the phase of the difference frequency and thus are measurable.Mapping optical frequencies to electronic frequencies allows sensitive measurements
As noted above, the difference frequency linewidth can be much smaller than the optical linewidth of the signal and LO signal, provided the two are mutually coherent. Thus small shifts in optical signal center-frequency can be measured: For example, Doppler lidarLIDAR
LIDAR is an optical remote sensing technology that can measure the distance to, or other properties of a target by illuminating the target with light, often using pulses from a laser...
systems can discriminate wind velocities with a resolution better than 1 meter per second, which is less than a part in a billion shift in the optical frequency. Likewise small coherent phase shifts can be measured even for nominally incoherent light, allowing optical coherence tomography
Optical coherence tomography
Optical coherence tomography is an optical signal acquisition and processing method. It captures micrometer-resolution, three-dimensional images from within optical scattering media . Optical coherence tomography is an interferometric technique, typically employing near-infrared light...
to image micrometer-sized features. Moreover, an electronic filter can define an effective optical bandwidth that is narrower than any realizable wavelength filter operating on the light itself, and thereby enable background light rejection and hence the detection of weak signals.
Noise reduction to shot noise limit
As with any small signal amplification, it's most desirable to get gain as close as possible to the initial point of the signal interception: moving the gain ahead of any signal processing reduces the additive contributions of effects like resistor Johnson-Nyquist noise, or electrical noises in active circuits. In optical heterodyne detection, the mixing-gain happens directly in the physics of the initial photon absorption event, making this ideal.One of the virtues of heterodyne detection is that the difference frequency is generally far removed spectrally from the potential noises radiated during the process of generating either the signal or the LO signal, thus making the spectral region near the difference frequency relatively quiet. Hence, narrow electronic filtering near the difference frequency is highly effective at removing the remaining, generally broadband, noise sources.
The primary remaining source of noise is photon shot noise from the nominally constant level of the Local Oscillator (LO) on the optical detector. Since the Shot noise
Shot noise
Shot noise is a type of electronic noise that may be dominant when the finite number of particles that carry energy is sufficiently small so that uncertainties due to the Poisson distribution, which describes the occurrence of independent random events, are of significance...
scales as the amplitude of the LO electric field level, and the heterodyne gain also scales the same way, the ratio of the shot noise to the mixed signal is constant no matter how large the LO.
Thus in practice one increases the LO level, until the gain on the signal raises it above all other noise sources, leaving only the shot noise. At that point there is no change in the signal to noise as the gain is raised further. (Of course, this is a highly idealized description.)
AC detection and imaging
Array detection of light, for instance, as applied in digital cameras, is common place. However that is only possible because each pixel can integrate the light level prior to serially reading out the array. With heterodyne detection the signal at each pixel is oscillating with a zero average and is often multi-frequency, so a pixel cannot be integrated directly on the chip to a scalar value. Thus a heterodyne array must have parallel direct connections from every sensor pixel to separate electrical amplifiers, filters, and processing systems. This makes large, general purpose, heterodyne imaging systems prohibitively expensive. For example, simply attaching 1 million leads to a megapixel coherent array is a daunting challenge.To solve this problem, synthetic array heterodyne detection was developed. In SAHD, large imaging arrays can be multiplex
Multiplexing
The multiplexed signal is transmitted over a communication channel, which may be a physical transmission medium. The multiplexing divides the capacity of the low-level communication channel into several higher-level logical channels, one for each message signal or data stream to be transferred...
ed into virtual pixels on a single element detector with single readout lead, single electrical filter, and single recording system. The time domain conjugate of this approach is Fourier transform heterodyne detection, which also has the multiplex advantage and also allows a single element detector to act like an imaging array. SAHD has been implemented as Rainbow heterodyne detection in which instead of a single frequency LO, many narrowly-spaced frequencies are spread out across the detector element surface like a rainbow. The physical position where each photon arrived is encoded in the resulting difference frequency itself, making a virtual 1D array on a single element detector. If the frequency comb is evenly spaced then, conveniently, the Fourier transform
Fourier transform
In mathematics, Fourier analysis is a subject area which grew from the study of Fourier series. The subject began with the study of the way general functions may be represented by sums of simpler trigonometric functions...
of the output waveform is the image itself. Arrays in 2D can be created as well, and since the arrays are virtual, the number of pixels, their size, and their individual gains can be adapted dynamically. Because this technique uses more total LO power (spread over multiple pixels) it has more total shot noise than a single pixel detector at the same pixel power density.
Speckle and diversity reception
As discussed, the LO and signal must be temporally coherent. They also need to be spatially coherent across the face of the detector or they will destructively interfere. In many usage scenarios the signal is reflected from optically rough surfaces or passes through optically turbulent media leading to wavefrontWavefront
In physics, a wavefront is the locus of points having the same phase. Since infrared, optical, x-ray and gamma-ray frequencies are so high, the temporal component of electromagnetic waves is usually ignored at these wavelengths, and it is only the phase of the spatial oscillation that is described...
s that are spatially incoherent. In laser scattering this is known as speckle.
In RF detection the antenna is rarely larger than the wavelength so all excited electrons move coherently within the antenna, whereas in optics the detector is usually much larger than the wavelength and thus can intercept a distorted phase front, resulting in destructive interference by out-of-phase photo-generated electrons within the detector.
Interestingly, while destructive interference dramatically reduces the signal level, the summed amplitude of a spatially incoherent mixture does not approach zero but rather the mean amplitude of a single speckle. However, since the standard deviation of the coherent sum of the speckles is exactly equal to the mean speckle intensity, optical heterodyne detection of scrambled phase fronts can never measure the absolute light level with an error bar less than the size of the signal itself. This upper bound signal-to-noise ratio of unity is only for absolute magnitude measurement: it can have signal-to-noise ratio
Signal-to-noise ratio
Signal-to-noise ratio is a measure used in science and engineering that compares the level of a desired signal to the level of background noise. It is defined as the ratio of signal power to the noise power. A ratio higher than 1:1 indicates more signal than noise...
better than unity for phase, frequency or time-varying relative-amplitude measurements in a stationary speckle field.
In RF detection, "diversity reception" is often used when the primary antenna is coincidentally located at an interference null point: by having more than one antenna one can adaptively switch to whichever antenna has the strongest signal or even incoherently add all of the antenna signals. Simply adding the antenna coherently can produce destructive interference just as happens in the optical realm.
The analogous diversity reception for optical heterodyne has been demonstrated with arrays of photon-counting detectors. For incoherent addition of the multiple element detectors in a random speckle field, the ratio of the mean to the standard deviation will scale as the square root of the number of independently measured speckles. This improved signal-to-noise ratio makes absolute amplitude measurements feasible in heterodyne detection.
However, as noted above, scaling physical arrays to large element counts is challenging for heterodyne detection due to the oscillating or even multi-frequency nature of the output signal. Instead, a single-element optical detector can also act like diversity receiver via synthetic array heterodyne detection or Fourier transform heterodyne detection. With a virtual array one can then either adaptively select just one of the LO frequencies, track a slowly moving bright speckle, or add them all in post-processing by the electronics.
Coherent addition
One can incoherently add the magnitudes of N-independent pulses to obtain a √N improvement in the signal to noise on the amplitude, but at the expense of losing the phase information. Instead coherent addition (adding the complex magnitude and phase) of multiple pulse waveforms would improve the signal to noise by a factor of N, not its square root, and preserve the phase information. The practical limitation is adjacent pulses from typical lasers have a minute frequency drift that translates to a large random phase shift in any long distance return signal, and thus just like the case for adjacent mixed phase pixels, destructively interfere when added coherently. However, coherent addition of multiple pulses is possible with advanced laser systems that narrow the frequency drift far below the difference frequency (intermediate frequency). This technique has been demonstrated in multi-pulse coherent Doppler LIDARLIDAR
LIDAR is an optical remote sensing technology that can measure the distance to, or other properties of a target by illuminating the target with light, often using pulses from a laser...
.
See also
- InterferometryInterferometryInterferometry refers to a family of techniques in which electromagnetic waves are superimposed in order to extract information about the waves. An instrument used to interfere waves is called an interferometer. Interferometry is an important investigative technique in the fields of astronomy,...
- HeterodyneHeterodyneHeterodyning is a radio signal processing technique invented in 1901 by Canadian inventor-engineer Reginald Fessenden where high frequency signals are converted to lower frequencies by combining two frequencies. Heterodyning is useful for frequency shifting information of interest into a useful...
- Superheterodyne
- Homodyne
- Optical coherence tomographyOptical coherence tomographyOptical coherence tomography is an optical signal acquisition and processing method. It captures micrometer-resolution, three-dimensional images from within optical scattering media . Optical coherence tomography is an interferometric technique, typically employing near-infrared light...
- Optical hybridOptical hybridA 90° optical hybrid is a six-port device that is used for coherent signal demodulation for either homodyne or heterodyne detection. It would mix the incoming signal with the four quadratural states associated with the reference signal in the complex-field space...