118:. However, laser illumination is not the only way to produce spatially coherent light. In 1995, Guerra published results in which he used a "form of optical heterodyning" to detect and image a grating with frequency many times smaller than the illuminating wavelength, and therefore smaller than the resolution, or passband, of the microscope, by beating it against a local oscillator in the form of a similar but transparent grating. A form of super-resolution microscopy, this work continues to spawn a family and generation of microscopes of particular use in the life sciences, known as "structured illumination microscopy", Polaroid Corp. patented Guerra's invention in 1997.
220:
different energies are absorbed at a countable rate by a detector at different (random) times, the detector can still produce a difference frequency. Hence light seems to have wave-like properties not only as it propagates through space, but also when it interacts with matter. Progress with photon counting was such that by 2008 it was proposed that, even with larger signal strengths available, it could be advantageous to employ local oscillator power low enough to allow detection of the beat signal by photon counting. This was understood to have a main advantage of imaging with available and rapidly developing large-format multi-pixel counting photodetectors.
900:, 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 spatially scrambled-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
163:
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.
723:
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.
172:
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.
574:
805:
heterodyne array must usually 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.
755:, 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. Additionally, to a first approximation, absorption is perfectly quadratic, in contrast to RF detection by a diode non-linearity.
853:
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
849:
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
171:
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
873:
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
869:
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
722:
allows this phase to be detected. If the optical phase of the signal beam shifts by an angle phi, then the phase of the electronic difference frequency shifts by exactly the same angle phi. More properly, to discuss an optical phase shift one needs to have a common time base reference. Typically
825:
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. The multiplex disadvantage is that the shot noise from all the pixels combine since they are
741:
to image micrometer-sized features. Because of this, an electronic filter can define an effective optical frequency bandpass 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.
146:
Unlike 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.
865:
In RF detection, "diversity reception" is often used to mitigate low signals when the primary antenna is inadvertently 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
219:
After optical heterodyne became an established technique, consideration was given to the conceptual basis for operation at such low signal light levels that "only a few, or even fractions of, photons enter the receiver in a characteristic time interval". It was concluded that even when photons of
105:
with the invention in the 1990s of synthetic array heterodyne detection. The light reflected from a target scene is focussed on a relatively inexpensive photodetector consisting of a single large physical pixel, while a different LO frequency is also tightly focussed on each virtual pixel of this
762:
from the potential noises radiated during the process of generating either the signal or the LO signal, thus the spectral region near the difference frequency may be relatively quiet. Hence, narrow electronic filtering near the difference frequency is highly effective at removing the remaining,
210:
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
162:
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 inherent in the photon absorption process itself. Conventional light detectors—so
804:
by analogy to circuits), often at millions of cycles per second or more. At the typical frame rates for image sensors, which are much slower, each pixel would integrate the total light received over many oscillation cycles, and this time-integration would destroy the signal of interest. Thus a
579:
The first two terms are proportional to the average (DC) energy flux absorbed (or, equivalently, the average current in the case of photon counting). The third term is time varying and creates the sum and difference frequencies. In the optical regime the sum frequency will be too high to pass
820:
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
54:
light. The light signal is compared with standard or reference light from a "local oscillator" (LO) that would have a fixed offset in frequency and phase from the signal if the latter carried null information. "Heterodyne" signifies more than one frequency, in contrast to the single frequency
782:
only (i.e. there is no noise contribution from the powerful LO because it divided out of the ratio). 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; practical limits on the LO intensity matter in real
257:
736:
systems can discriminate wind velocities with a resolution better than 1 meter per second, which is less than a part in a billion
Doppler shift in the optical frequency. Likewise small coherent phase shifts can be measured even for nominally incoherent broadband light, allowing
731:
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
895:
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
750:
As with any small signal amplification, it is 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
838:. 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
1134:
U.S. Pat. No. 5,666,197; "Apparatus and methods employing phase control and analysis of evanescent illumination for imaging and metrology of subwavelength lateral surface topography"; John M. Guerra, inventor; Assigned to
Polaroid Corp.; Sept.
874:
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.
777:
Thus in practice one increases the LO level, until the gain on the signal raises it above all other additive noise sources, leaving only the shot noise. In this limit, the signal to noise ratio is affected by the shot noise of the
569:{\displaystyle I\propto \left^{2}\propto {\frac {1}{2}}E_{\mathrm {sig} }^{2}+{\frac {1}{2}}E_{\mathrm {LO} }^{2}+2E_{\mathrm {LO} }E_{\mathrm {sig} }\cos(\omega _{\mathrm {sig} }t+\varphi )\cos(\omega _{\mathrm {LO} }t)}
106:
detector, resulting in an electrical signal from the detector carrying a mixture of beat frequencies that can be electronically isolated and distributed spatially to present an image of the scene.
628:
1607:
Daher, Carlos; Torres, Jeremie; Iniguez-de-la-Torre, Ignacio; Nouvel, Philippe; Varani, Luca; Sangare, Paul; Ducournau, Guillaume; Gaquiere, Christophe; Mateos, Javier; Gonzalez, Tomas (2016).
247:
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
580:
through the subsequent electronics. In many applications the signal is weaker than the LO, thus it can be seen that gain occurs because the energy flux in the difference frequency
1396:
Liu, Lisheng; Zhang, Heyong; Guo, Jin; Zhao, Shuai; Wang, Tingfeng (2012). "Photon time-interval statistics applied to the analysis of laser heterodyne signal with photon counter".
716:
668:
251:
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.
977:
854:
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.
812:
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
1304:
Erkmen, Baris I.; Barber, Zeb W.; Dahl, Jason (2013). "Maximum-likelihood estimation for frequency-modulated continuous-wave laser ranging using photon-counting detectors".
774:
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.
766:
The primary remaining source of noise is photon shot noise from the nominally constant DC level, which is typically dominated by the Local
Oscillator (LO). Since the
179:, is an oversimplified model of optical heterodyne detection. Nevertheless, the intuitive pure-frequency heterodyne concept still holds perfectly for the
1145:
Hinkley, E.; Freed, Charles (1969). "Direct
Observation of the Lorentzian Line Shape as Limited by Quantum Phase Noise in a Laser above Threshold".
1538:
816:, which also has the multiplex advantage and also allows a single element detector to act like an imaging array. SAHD has been implemented as
1372:
1234:
870:
independently measured speckles. This improved signal-to-noise ratio makes absolute amplitude measurements feasible in heterodyne detection.
1671:
211:
frequencies. However, lasers of sufficiently narrow linewidth to allow the signal and LO to originate from different lasers do exist.
981:
1556:
1523:
1470:
Cooke, Bradly J.; Galbraith, Amy E.; Laubscher, Bryan E.; Strauss, Charlie E. M.; Olivas, Nicholas L.; Grubler, Andrew C. (1999).
866:
antenna signals. Simply adding the antennae coherently can produce destructive interference just as happens in the optical realm.
1056:
1355:
Erkmen, Baris; Dahl, Jason R.; Barber, Zeb W. (2013). "Performance
Analysis for FMCW Ranging Using Photon-Counting Detectors".
1224:
1180:
Winzer, Peter J.; Leeb, Walter R. (1998). "Coherent lidar at low signal powers: Basic considerations on optical heterodyning".
114:
Optical heterodyne detection began to be studied at least as early as 1962, within two years of the construction of the first
796:
Array detection of light, i.e. detecting light in a large number of independent detector pixels, is common in digital camera
813:
800:. However, it tends to be quite difficult in heterodyne detection, since the signal of interest is oscillating (also called
1515:
1672:
The
Syracuse University Library Radius Project: Development of a non-destructive playback system for cylinder recordings.
583:
1609:"Room Temperature Direct and Heterodyne Detection of 0.28–0.69-THz Waves Based on GaN 2-DEG Unipolar Nanochannels"
953:
948:
817:
738:
192:
808:
To solve this problem, synthetic array heterodyne detection (SAHD) was developed. In SAHD, large imaging arrays can be
862:
better than unity for phase, frequency or time-varying relative-amplitude measurements in a stationary speckle field.
90:
produced by the detector is in the radio or microwave band that can be conveniently processed by electronic means.
752:
43:
1526:
933:
681:
633:
187:. Crucially, one can obtain narrow-band interference from coherent broadband sources: this is the basis for
234:
were developed to optimize the statistical performance of the analysis of the data from photon counting.
151:
mixing is to down shift the signal from the optical band to an electronically tractable frequency range.
913:
859:
159:
154:
In RF band detection, typically, the electromagnetic field drives oscillatory motion of electrons in an
83:
1623:
1452:
1405:
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1021:
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One of the virtues of heterodyne detection is that the difference frequency is generally far removed
719:
224:
176:
39:
1608:
17:
801:
188:
175:
As a result, the mathematics of squaring the sum of two pure tones, normally invoked to explain RF
1692:
1657:
1537:"Multi-Pixel Synthetic Array Heterodyne Detection Report", 1995, Strauss, C.E.M. and Rehse, S.J.
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1602:
LANL Report LA-UR-99-1055 (1999) — Field
Imaging in Lidar via Fourier Transform Heterodyne
1253:
Jiang, Leaf A.; Luu, Jane X. (2008). "Heterodyne detection with a weak local oscillator".
958:
943:
856:
This upper bound signal-to-noise ratio of unity is only for absolute magnitude measurement
843:
227:
155:
131:
62:
The comparison of the two light signals is typically accomplished by combining them in a
1627:
1456:
1445:
Optical
Society of America, Proceedings of the 1995 Coherent Laser Radar Topical Meeting
1441:"Synthetic Array Heterodyne Detection: Developments within the Caliope CO2 DIAL Program"
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Mapping optical frequencies to electronic frequencies allows sensitive measurements
127:
86:. Typically, the two light frequencies are similar enough that their difference or
1010:"Synthetic-array heterodyne detection: a single-element detector acts as an array"
1596:
1417:
1364:
1089:
1567:
Gabriel
Lombardi, Jerry Butman, Torrey Lyons, David Terry, and Garrett Piech, "
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detectors and an impure LO might carry some noise at the difference frequency)
1201:
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63:
47:
31:
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1425:
1333:
1282:
1209:
1121:
1090:"Super-resolution through illumination by diffraction-born evanescent waves"
839:
79:
67:
1551:
Dainty C (Ed), Laser Speckle and Related Phenomena, 1984, Springer Verlag,
1341:
1290:
1041:
1062:(Report). Syosset, New York: Technical Research Group, Inc. Archived from
1325:
1274:
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923:
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detector. If the frequency comb is evenly spaced then, conveniently, the
718:, is DC and thus erases the phase associated with its optical frequency;
180:
98:
51:
1644:
200:
1518:" Lasers and Electro-Optics, 1996. CLEO Pub Date: 2–7 June 1996 (200)
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1113:
71:
1226:
The Feynman Lectures on Physics: The Definitive and Extended Edition
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842:
that are spatially incoherent. In laser scattering this is known as
206:
Consequently, optical heterodyne detection is usually performed as
1597:
US Patent 5689335 — Synthetic Array Heterodyne Detection invention
1223:
Feynman, Richard P.; Leighton, Robert B.; Sands, Matthew (2005) .
901:
733:
122:
Contrast to conventional radio frequency (RF) heterodyne detection
115:
102:
1057:
Technical Note on Heterodyne Detection in Optical Communications
882:
One can incoherently add the magnitudes of a time series of
1229:. Vol. 2 (2nd ed.). Addison Wesley. p. 111.
630:
is greater than the DC energy flux of the signal by itself
1472:"Laser field imaging through Fourier transform heterodyne"
978:"Optical detection techniques: homodyne versus heterodyne"
1480:. Proceedings of SPIE. Vol. 3707. pp. 390–408.
126:
It is instructive to contrast the practical aspects of
185:
provided that the signal and LO are mutually coherent
684:
636:
586:
260:
834:As discussed, the LO and signal must be temporally
623:{\displaystyle E_{\mathrm {LO} }E_{\mathrm {sig} }}
710:
662:
622:
568:
1474:. In Kamerman, Gary W; Werner, Christian (eds.).
167:Wideband local oscillators for coherent detection
30:is a method of extracting information encoded as
850:photo-generated electrons within the detector.
1547:
1545:
1248:
1246:
8:
1590:Encyclopedia of Laser Physics and Technology
1569:Multiple-pulse coherent laser radar waveform
93:This technique became widely applicable to
1477:Laser Radar Technology and Applications IV
678:By itself, the signal beam's energy flux,
195:. Mutual coherence permits the rainbow in
1670:Penn, William A., and Martha J. Hanson. "
1643:
980:. Renishaw plc (UK). 2002. Archived from
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66:detector, which has a response that is
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1001:
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814:Fourier transform heterodyne detection
711:{\displaystyle E_{\mathrm {sig} }^{2}}
663:{\displaystyle E_{\mathrm {sig} }^{2}}
142:Energy versus electric field detection
1616:IEEE Transactions on Electron Devices
7:
1055:Jacobs, Stephen (30 November 1962).
763:generally broadband, noise sources.
18:Synthetic array heterodyne detection
746:Noise reduction to shot noise limit
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1514:Strauss, C.E.M. and Rehse, S.J. "
223:Photon counting was applied with
1584:RĂĽdiger Paschotta (2011-04-29).
787:Key problems and their solutions
1439:Strauss, Charlie E. M. (1995).
1008:Strauss, Charlie E. M. (1994).
886:independent pulses to obtain a
830:Speckle and diversity reception
1586:"Optical Heterodyne Detection"
1088:Guerra, John M. (1995-06-26).
563:
542:
533:
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375:
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1:
674:Preservation of optical phase
147:Hence the primary purpose of
1516:Rainbow heterodyne detection
1418:10.1016/j.optcom.2012.05.019
1365:10.1364/CLEO_SI.2013.CTu1H.7
954:Rainbow heterodyne detection
949:Optical coherence tomography
818:Rainbow heterodyne detection
739:optical coherence tomography
193:optical coherence tomography
28:Optical heterodyne detection
878:Coherent temporal summation
792:Array detection and imaging
1709:
1167:10.1103/PhysRevLett.23.277
826:not physically separated.
189:white light interferometry
1202:10.1080/09500349808230651
44:electromagnetic radiation
1636:10.1109/TED.2015.2503987
1182:Journal of Modern Optics
934:Laser Doppler vibrometer
1147:Physical Review Letters
1094:Applied Physics Letters
712:
664:
624:
570:
201:supernumerary rainbows
1398:Optics Communications
914:Fibre-optic gyroscope
860:signal-to-noise ratio
753:Johnson–Nyquist noise
713:
665:
625:
571:
243:Gain in the detection
84:electromagnetic field
1359:. pp. CTu1H.7.
1326:10.1364/AO.52.002008
1275:10.1364/AO.47.001486
1069:on February 10, 2017
1034:10.1364/OL.19.001609
720:Heterodyne detection
682:
634:
584:
258:
232:Numerical algorithms
177:heterodyne detection
1628:2016ITED...63..353D
1457:1995STIN...9613278R
1410:2012OptCo.285.3820L
1318:2013ApOpt..52.2008E
1267:2008ApOpt..47.1486J
1194:1998JMOp...45.1549W
1159:1969PhRvL..23..277H
1106:1995ApPhL..66.3555G
1026:1994OptL...19.1609S
707:
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457:
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225:frequency-modulated
50:band of visible or
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685:
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637:
620:
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438:
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57:homodyne detection
1527:(See DOE archive)
1486:10.1117/12.351361
1404:(18): 3820–3826.
1374:978-1-55752-972-5
1236:978-0-8053-9045-2
1100:(26): 3555–3557.
823:Fourier transform
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230:(FMCW) lasers.
228:continuous wave
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215:Photon counting
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158:; the captured
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132:radio frequency
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988:15 February
810:multiplexed
138:detection.
101:-sensitive
42:or both of
1682:Categories
1357:Cleo: 2013
1153:(6): 277.
965:References
919:Heterodyne
840:wavefronts
768:shot noise
760:spectrally
249:amplitudes
149:heterodyne
136:heterodyne
134:(RF) band
64:photodiode
48:wavelength
32:modulation
1693:Metrology
1674:" (2003).
1654:0018-9383
1494:0277-786X
1451:: 13278.
1426:0030-4018
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52:infrared
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1688:Waves
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1498:S2CID
1379:S2CID
1135:1997.
1067:(PDF)
1060:(PDF)
902:LIDAR
734:lidar
183:case
116:laser
36:phase
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1553:ISBN
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