Dual-Comb Heterodyne Detection

• Dual-comb heterodyne detection is a frequency-domain downconversion method that uses two coherent optical combs to map optical spectra into RF beat notes.
• It achieves comb-tooth-resolved spectroscopy, ranging, and metrology by preserving both amplitude and phase information through linear optical-to-RF mapping.
• Implementations using electro-optic, QCL, and acousto-optic platforms showcase versatile, high-resolution performance with enhanced robustness against environmental changes.

Searching arXiv for the cited work to ground the article in the literature. arxiv_search.query({"^^^^^^^^2search_query2 interferometry via repetition-rate switching of a single frequency comb\"","start":^^^^2search_query2^^^^,"max_results":5}) Dual-comb heterodyne detection is a frequency-domain downconversion technique in which two mutually coherent optical frequency combs with slightly different repetition rates interfere on a fast detector, producing a radio-frequency comb whose tones map optical amplitude and phase line-by-line into the electronic domain. In its standard form, the method converts broadband optical spectra into evenly spaced RF beat notes that can be digitized and analyzed with high resolution, enabling comb-tooth-resolved spectroscopy, ranging, cavity metrology, phase retrieval, and coherent sensing; in time domain terms, it produces a sequence of interferograms whose periodicity is set by the repetition-rate difference rather than the optical repetition rate (&&&^^^^2search_query2^^^^&&&, &&&^^^^2all:\2^^^^&&&).

^^^^2all:\2^^^^. Optical-to-RF mapping and interferogram physics

For two combs with tooth frequencies

PRESERVED_PLACEHOLDER_^^^^2search_query2^^^^

heterodyne detection on a photodiode produces beat notes at frequency differences between optical modes. Under the usual one-to-one pairing PRESERVED_PLACEHOLDER_^^^^2all:\2^^^^, the RF comb is

$$f_{\mathrm{RF},n}=\Delta f_{\mathrm{ceo}}+n\,\Delta f_{\mathrm{rep}},$$

with $$\Delta f_{\mathrm{rep}}=f_{\mathrm{rep},2}-f_{\mathrm{rep},1}$$ and $$\Delta f_{\mathrm{ceo}}=f_{\mathrm{ceo},2}-f_{\mathrm{ceo},1}$$. This linear mapping is the central abstraction of dual-comb heterodyne detection: the optical line index is preserved in RF, so the complex RF spectrum directly encodes the complex optical spectrum (&&&^^^^2search_query2^^^^&&&, Kong et al., 2018, Dmitriev et al., 2021).

The time-domain interferogram repeats with period

$T=\frac{1}{\Delta f_{\mathrm{rep}}},$

so increasing $\Delta f_{\mathrm{rep}}$ shortens the acquisition period and increases update rate, while the optical bandwidth that can be mapped without ambiguity is constrained by detector bandwidth, digitizer Nyquist limits, and the need to prevent overlap between RF beat families. The practical conditions stated across reported implementations are therefore mutually consistent: RF tones must remain within the detection chain, the observation window must be long enough to resolve adjacent RF lines, and mutual coherence must be maintained over the acquisition time so that the RF tones remain narrow and phase-stable (&&&^^^^2search_query2^^^^&&&, Burghoff et al., 2016).

In the complex-field picture, if the $n$th signal and reference teeth have fields $E_K(n)=A_n^K e^{i\phi_n^K}$ and $E_E(n)=A_n^E e^{i\phi_n^E}$, then the corresponding RF line is proportional to

PRESERVED_PLACEHOLDER_^^^^2all:\2search_query2^^^^

The RF phase is therefore the optical phase difference, which is why dual-comb heterodyne detection can retrieve spectral phase, group delay, dispersive phase, and even sub-wavelength interferometric phase terms rather than only optical power (Kong et al., 2018).

2. Time-domain interpretations and one-comb variants

Although the RF mapping is usually presented in frequency-domain language, the method is equally an asynchronous time-sampling scheme. The relative emission times of the two pulse trains slip at a rate determined by PRESERVED_PLACEHOLDER_^^^^2all:\2all:\2^^^^, so the temporal overlap between successive pulses scans linearly and produces an interferogram that is a slowed representation of ultrafast optical dynamics. In the coherent time-domain reconstruction of frequency-modulated quantum cascade combs, the relevant stretch factor is

PRESERVED_PLACEHOLDER_^^^^2all:\22^^^^

and the slow frame period is PRESERVED_PLACEHOLDER_^^^^2all:\2^^^^3; with PRESERVED_PLACEHOLDER_^^^^2all:\2^^^^4 and PRESERVED_PLACEHOLDER_^^^^2all:\2^^^^5, the reported stretch factor is approximately PRESERVED_PLACEHOLDER_^^^^2all:\2^^^^6, allowing direct recovery of amplitude and phase quadratures from a mid-IR multi-heterodyne waveform (Chomet et al., 2024).

A notable reformulation is parallel heterodyne interferometry via rep-rate exchange, in which two physical combs are replaced by one comb whose repetition rate is rapidly switched between two values. In that architecture, a fixed delay line stores the previous repetition-rate state for half a modulation cycle, so the delayed branch interferes with the current branch and yields the same RF mapping as a conventional two-comb system. The delay is matched to the switching by

PRESERVED_PLACEHOLDER_^^^^2all:\2^^^^7

and the demonstrated configuration used an EOM comb with PRESERVED_PLACEHOLDER_^^^^2all:\2^^^^8, PRESERVED_PLACEHOLDER_^^^^2all:\2^^^^9, $$f_{\mathrm{RF},n}=\Delta f_{\mathrm{ceo}}+n\,\Delta f_{\mathrm{rep}},$$^^^^2search_query2^^^^, $$f_{\mathrm{RF},n}=\Delta f_{\mathrm{ceo}}+n\,\Delta f_{\mathrm{rep}},$$^^^^2all:\2^^^^, and an AOM offset $$f_{\mathrm{RF},n}=\Delta f_{\mathrm{ceo}}+n\,\Delta f_{\mathrm{rep}},$$2; the reported result was full dual-comb speed and comb-tooth resolution with one comb source rather than two (&&&^^^^2search_query2^^^^&&&).

The time-domain viewpoint also clarifies why the same formalism applies beyond pulsed mode-locked lasers. Electric-field cross-correlation of a single-soliton Kerr comb with a reference electro-optic comb retrieves a nearly flat soliton phase profile over a $$f_{\mathrm{RF},n}=\Delta f_{\mathrm{ceo}}+n\,\Delta f_{\mathrm{rep}},$$3 window, while direct time-domain analysis of multi-heterodyne signals reveals the linear chirp and near-constant amplitude of dense FM combs and the strong residual amplitude modulation of harmonic combs. This suggests that dual-comb heterodyne detection is best understood not as a particular laser architecture, but as a general interferometric sampling and phase-transfer mechanism (Kong et al., 2018, Chomet et al., 2024).

3. Physical implementations and detector architectures

The technique has been realized across a wide span of comb platforms. Electro-optic combs derived from a common CW laser are prominent because they provide natural mutual coherence and electronically controllable repetition rates. A representative integrated mid-IR implementation placed two QCL combs on one chip, used adjacent micro-heaters to tune $$f_{\mathrm{RF},n}=\Delta f_{\mathrm{ceo}}+n\,\Delta f_{\mathrm{rep}},$$4 and $$f_{\mathrm{RF},n}=\Delta f_{\mathrm{ceo}}+n\,\Delta f_{\mathrm{rep}},$$5, and reported 64 RF lines at $$f_{\mathrm{RF},n}=\Delta f_{\mathrm{ceo}}+n\,\Delta f_{\mathrm{rep}},$$6, corresponding to an optical bandwidth of $$f_{\mathrm{RF},n}=\Delta f_{\mathrm{ceo}}+n\,\Delta f_{\mathrm{rep}},$$7 centered at $$f_{\mathrm{RF},n}=\Delta f_{\mathrm{ceo}}+n\,\Delta f_{\mathrm{rep}},$$8 ($$f_{\mathrm{RF},n}=\Delta f_{\mathrm{ceo}}+n\,\Delta f_{\mathrm{rep}},$$9); the same work reported a relative frequency temperature dependence coefficient of $$\Delta f_{\mathrm{rep}}=f_{\mathrm{rep},2}-f_{\mathrm{rep},1}$$^^^^2search_query2^^^^ for the on-chip system versus $$\Delta f_{\mathrm{rep}}=f_{\mathrm{rep},2}-f_{\mathrm{rep},1}$$^^^^2all:\2^^^^ for a two-independent-comb system, i.e. approximately $$\Delta f_{\mathrm{rep}}=f_{\mathrm{rep},2}-f_{\mathrm{rep},1}$$2 improved robustness to temperature fluctuations (&&&^^^^2all:\22^^^^&&&).

At THz frequencies, QCLs also enable self-detected dual-comb configurations in which one comb acts as the detector for the other through photon-assisted transport in the active region. One on-chip realization around $$\Delta f_{\mathrm{rep}}=f_{\mathrm{rep},2}-f_{\mathrm{rep},1}$$3 detected up to 3^^^^2search_query2^^^^ modes over approximately $$\Delta f_{\mathrm{rep}}=f_{\mathrm{rep},2}-f_{\mathrm{rep},1}$$4 of optical bandwidth and used RF-domain frequency counting to verify comb equidistance with an accuracy of $$\Delta f_{\mathrm{rep}}=f_{\mathrm{rep},2}-f_{\mathrm{rep},1}$$5 at the carrier frequency. A second free-space self-detected THz system around $$\Delta f_{\mathrm{rep}}=f_{\mathrm{rep},2}-f_{\mathrm{rep},1}$$6 showed that approximately $$\Delta f_{\mathrm{rep}}=f_{\mathrm{rep},2}-f_{\mathrm{rep},1}$$7 of coupled power sufficed for robust self-detection, with $$\Delta f_{\mathrm{rep}}=f_{\mathrm{rep},2}-f_{\mathrm{rep},1}$$8, about $$\Delta f_{\mathrm{rep}}=f_{\mathrm{rep},2}-f_{\mathrm{rep},1}$$9 optical coverage, and real-time measurements of semiconductor samples and moist air (&&&^^^^2all:\2^^^^3&&&, &&&^^^^2all:\2^^^^4&&&).

Acousto-optic frequency-shifting loops define another family. Because the comb spacing is set electronically by the net per-roundtrip acousto-optic shift rather than a cavity free spectral range, the spacing is reconfigurable from the kHz region to tens of MHz. Reported acousto-optic combs contained more than ^^^^2all:\2^^^^5^^^^2search_query2search_query2^^^^ mutually coherent lines without nonlinear broadening; in dual-comb operation with approximately $$\Delta f_{\mathrm{ceo}}=f_{\mathrm{ceo},2}-f_{\mathrm{ceo},1}$$^^^^2search_query2^^^^ optical spacing and $$\Delta f_{\mathrm{ceo}}=f_{\mathrm{ceo},2}-f_{\mathrm{ceo},1}$$^^^^2all:\2^^^^, the compression factor was approximately ^^^^2all:\2start2search_query2search_query2^^^^, reducing multi-GHz optical bandwidths to MHz-scale RF spans (&&&^^^^2all:\2^^^^5&&&).

Detection need not occur in the native optical band. In upconversion mid-infrared dual-comb spectroscopy, mutually coherent mid-IR comb light around $$\Delta f_{\mathrm{ceo}}=f_{\mathrm{ceo},2}-f_{\mathrm{ceo},1}$$2 interrogates a sample and is then upconverted to the telecom band for balanced InGaAs detection. The reported implementation resolved approximately ^^^^2all:\2^^^^8,^^^^2search_query2search_query2search_query2^^^^ comb lines at approximately $$\Delta f_{\mathrm{ceo}}=f_{\mathrm{ceo},2}-f_{\mathrm{ceo},1}$$3 spacing over approximately $$\Delta f_{\mathrm{ceo}}=f_{\mathrm{ceo},2}-f_{\mathrm{ceo},1}$$4 bandwidth, with $$\Delta f_{\mathrm{ceo}}=f_{\mathrm{ceo},2}-f_{\mathrm{ceo},1}$$5, a ^^^^2all:\2^^^^–5 MHz RF comb, a 5 ms interferogram period, and figures of merit $$\Delta f_{\mathrm{ceo}}=f_{\mathrm{ceo},2}-f_{\mathrm{ceo},1}$$6 and $$\Delta f_{\mathrm{ceo}}=f_{\mathrm{ceo},2}-f_{\mathrm{ceo},1}$$7, near the shot-noise limit (&&&^^^^2all:\2^^^^6&&&).

Hybrid integrated microcomb sources push the same principle toward compact electrically driven operation. A fully integrated dual-microcomb source based on self-injection-locked laser diodes and Si$$\Delta f_{\mathrm{ceo}}=f_{\mathrm{ceo},2}-f_{\mathrm{ceo},1}$$8N$$\Delta f_{\mathrm{ceo}}=f_{\mathrm{ceo},2}-f_{\mathrm{ceo},1}$$9 resonators demonstrated down-conversion of the optical spectrum from ^^^^2all:\2max_results2search_query2search_query2^^^^ nm to ^^^^2all:\2^^^^7^^^^2search_query2search_query2^^^^ nm into RF, with reported RF spacings $T=\frac{1}{\Delta f_{\mathrm{rep}}},$^^^^2search_query2^^^^, central RF offsets $T=\frac{1}{\Delta f_{\mathrm{rep}}},$^^^^2all:\2^^^^, $T=\frac{1}{\Delta f_{\mathrm{rep}}},$2, and $T=\frac{1}{\Delta f_{\mathrm{rep}}},$3, and pump-to-comb sideband efficiency up to $T=\frac{1}{\Delta f_{\mathrm{rep}}},$4 at mW power levels (Dmitriev et al., 2021).

4. Signal processing, calibration, and phase recovery

The raw dual-comb observable is a broadband interferogram or RF comb, but most advanced use cases depend on post-detection phase handling. In repetition-rate-switched one-comb interferometry, oscilloscope sampling at $T=\frac{1}{\Delta f_{\mathrm{rep}}},$5, resampling to $T=\frac{1}{\Delta f_{\mathrm{rep}}},$6, segmentation into half-cycles, and processing in blocks containing an integer number of interferograms were used to preserve phase linearity and avoid spectral leakage; because interferograms reverse every half-cycle, the segments must be treated separately or their polarity must be corrected (&&&^^^^2search_query2^^^^&&&).

A more general framework treats the multi-heterodyne waveform itself as a state-estimation problem. In computational multiheterodyne spectroscopy, the measured signal is modeled as

$T=\frac{1}{\Delta f_{\mathrm{rep}}},$7

with $T=\frac{1}{\Delta f_{\mathrm{rep}}},$8 capturing offset fluctuations and $T=\frac{1}{\Delta f_{\mathrm{rep}}},$9 capturing repetition-rate fluctuations. A linearized extended Kalman filter, optionally refined with Rauch–Tung–Striebel smoothing, can estimate these quantities directly from the RF waveform without auxiliary optical references or CEO measurements. The reported method remained viable even when the relative linewidth exceeded the repetition-rate difference, with residual under $\Delta f_{\mathrm{rep}}$^^^^2search_query2^^^^ of signal power and corrected RF line widths near the uncertainty limit of approximately $\Delta f_{\mathrm{rep}}$^^^^2all:\2^^^^ for the integration used (Burghoff et al., 2016).

Phase recovery may also be extracted from the interferograms alone. In a free-running gigahertz dual-comb laser based on a Yb:CALGO cavity with an intracavity biprism, the phase fluctuations of all RF comb lines were inferred from the interferogram sequence without active stabilization, enabling coherent averaging of ^^^^2all:\2^^^^6,897 interferograms over ^^^^2search_query2^^^^.8 s for acetylene spectroscopy. The same source delivered more than 3 W average power per comb, 78 fs pulse duration, $\Delta f_{\mathrm{rep}}$2, and tunable $\Delta f_{\mathrm{rep}}$3 up to approximately $\Delta f_{\mathrm{rep}}$4; the uncorrelated timing jitter was approximately 3 fs when integrated down to ^^^^2all:\2^^^^ kHz, and the RF comb lines remained fully resolved in free-running operation (&&&2^^^^2search_query2^^^^&&&).

When the heterodyne signal probes a cavity response rather than a direct sample transmission, signal processing shifts from line extraction to cavity-mode estimation. In dual-comb cavity ring-down spectroscopy, Fourier-domain cavity modes are fit with an asymmetric Lorentzian plus linear background, so that widths map to ring-down times and absorption while positions map to dispersion. With $\Delta f_{\mathrm{rep}}$5, $\Delta f_{\mathrm{rep}}$6, cavity linewidths of $\Delta f_{\mathrm{rep}}$7, and 22 simultaneously resolved modes, the reported system retrieved methane absorption and dispersion with noise-equivalent absorption per spectral element down to $\Delta f_{\mathrm{rep}}$8 and $\Delta f_{\mathrm{rep}}$9 when widths and positions were jointly exploited (&&&^^^^2all:\2^^^^&&&).

5. Spectroscopy, metrology, and ranging

In spectroscopy, the principal advantage is parallel, high-resolution access to broad optical bandwidth. A line-by-line phase measurement of a single-soliton Kerr microresonator comb used dual-comb electric-field cross-correlation with a pre-characterized EO reference comb and a $n$^^^^2search_query2^^^^ acquisition window, yielding 23 RF lines over approximately $n$^^^^2all:\2^^^^ optical bandwidth. The retrieved phase was nearly flat across the soliton spectrum with standard deviation approximately $n$2, while the pump line showed a negative phase offset of approximately $n$3 at a representative operating point; at fixed pump power of 4^^^^2search_query2search_query2^^^^ mW, increasing detuning reduced the magnitude of that offset from about $n$4 to $n$5 (Kong et al., 2018).

The same heterodyne formalism supports absorption and dispersion spectroscopy in cavities. In the methane DC-CRDS implementation, cavity mode widths and positions over a $n$6 window near $n$7 were measured simultaneously, with per-mode sensitivities at 2 ms averaging of about $n$8 for both width and position and about $n$9 at ^^^^2all:\2^^^^ s. This separated absorption from dispersion without an instrumental line shape and without requiring exact probe–cavity frequency matching (&&&^^^^2all:\2^^^^&&&).

In absolute distance metrology, the spectral phase slope provides the time-of-flight. For reflective geometry,

$E_K(n)=A_n^K e^{i\phi_n^K}$^^^^2search_query2^^^^

while the basic non-ambiguity range is

$E_K(n)=A_n^K e^{i\phi_n^K}$^^^^2all:\2^^^^

For a $E_K(n)=A_n^K e^{i\phi_n^K}$2 comb this NAR is only about $E_K(n)=A_n^K e^{i\phi_n^K}$3 in air, but repetition-rate switching automatically yields an extended Vernier range

$E_K(n)=A_n^K e^{i\phi_n^K}$4

With $E_K(n)=A_n^K e^{i\phi_n^K}$5, the reported extended NAR was approximately $E_K(n)=A_n^K e^{i\phi_n^K}$6, together with time-of-flight precision of $E_K(n)=A_n^K e^{i\phi_n^K}$7 per half-period and $E_K(n)=A_n^K e^{i\phi_n^K}$8 after $E_K(n)=A_n^K e^{i\phi_n^K}$9 averaging; vibrometry segments were acquired at ^^^^2all:\2search_query2^^^^ kHz (&&&^^^^2search_query2^^^^&&&).

Dual-comb lidar adopts the same mapping but intentionally sparsifies the optical comb to maximize power per tooth. A multi-heterodyne DIAL system at $E_E(n)=A_n^E e^{i\phi_n^E}$^^^^2search_query2^^^^ used three transmit teeth at $E_E(n)=A_n^E e^{i\phi_n^E}$^^^^2all:\2^^^^ spacing, three LO teeth at $E_E(n)=A_n^E e^{i\phi_n^E}$2, a 4^^^^2search_query2^^^^ MHz AOM-defined RF offset, and $E_E(n)=A_n^E e^{i\phi_n^E}$3. With $E_E(n)=A_n^E e^{i\phi_n^E}$4 pulses of $E_E(n)=A_n^E e^{i\phi_n^E}$5 at 2^^^^2search_query2^^^^ kHz PRF, it measured path-average atmospheric CO$E_E(n)=A_n^E e^{i\phi_n^E}$6 over a $E_E(n)=A_n^E e^{i\phi_n^E}$7 optical path with approximately $E_E(n)=A_n^E e^{i\phi_n^E}$8 precision after a 6^^^^2search_query2^^^^ s moving average and simultaneously retrieved radial wind speed from aerosol backscatter; an RF Doppler shift of approximately $E_E(n)=A_n^E e^{i\phi_n^E}$9 corresponded to PRESERVED_PLACEHOLDER_^^^^2all:\2search_query2search_query2^^^^, and most wind estimates had standard deviation below PRESERVED_PLACEHOLDER_^^^^2all:\2search_query2all:\2^^^^ (Rosas et al., 2024).

6. Limitations, misconceptions, and emerging directions

A common misconception is that dual-comb heterodyne detection requires two independently stabilized modelocked lasers. Reported counterexamples include one-comb repetition-rate switching, single-cavity spatially multiplexed dual-comb oscillators, on-chip QCL pairs, and systems in which phase and timing are recovered computationally rather than by explicit hardware references (&&&^^^^2search_query2^^^^&&&, Burghoff et al., 2016, &&&2^^^^2search_query2^^^^&&&). A related misconception is terminological: single-comb heterodyne systems with a CW LO can perform parallel multiheterodyne spectroscopy, but they are not true dual-comb systems. A THz frequency-comb spectrometer with a single THz comb, a CW LO, and a fast Fourier spectrometer explicitly made this distinction while still acquiring more than 8^^^^2search_query2^^^^ comb modes over a PRESERVED_PLACEHOLDER_^^^^2all:\2search_query22^^^^ bandwidth with uniform PRESERVED_PLACEHOLDER_^^^^2all:\2search_query2^^^^3 resolution in under 2^^^^2search_query2^^^^ minutes (Hindle et al., 2024).

The method also has well-defined trade-offs. In dual-comb ranging, the reported precision scales linearly with non-ambiguity range through

PRESERVED_PLACEHOLDER_^^^^2all:\2search_query2^^^^4

where PRESERVED_PLACEHOLDER_^^^^2all:\2search_query2^^^^5 depends on the comb amplitude envelope and per-line SNR. The same study showed that different targets cannot be resolved when their RF combs overlap without distinct Doppler shifts; depending on relative amplitude and separation, the result is either a biased distance estimate or a breakdown of the linear phase-fit model (&&&3^^^^2search_query2^^^^&&&). More generally, long delays, switching transients, higher-order dispersion, detector bandwidth, and alias-free one-to-one mapping all place hard constraints on usable optical bandwidth and coherent averaging (&&&^^^^2search_query2^^^^&&&, Chomet et al., 2024).

Sensitivity limits are increasingly discussed at the fundamental level. Dual-comb correlation spectroscopy of thermal light derives a frequency-domain SNR per optical resolution element

PRESERVED_PLACEHOLDER_^^^^2all:\2search_query2^^^^6

making explicit the PRESERVED_PLACEHOLDER_^^^^2all:\2search_query2^^^^7 multiplexing penalty relative to channelized heterodyne radiometry. An experiment near ^^^^2all:\2^^^^547 nm reached spectral SNR PRESERVED_PLACEHOLDER_^^^^2all:\2search_query2^^^^8 after about ^^^^2all:\2^^^^ hour at the Solar Blackbody limit, with the measured scaling over three decades of optical PSD matching the theoretical model (Tsao et al., 2024).

Quantum proposals attempt to move beyond the shot-noise limit rather than merely approach it. In entanglement-enhanced dual-comb spectroscopy, side-band entanglement around each comb line reduces the heterodyne shot-noise floor. For representative parameters PRESERVED_PLACEHOLDER_^^^^2all:\2search_query2^^^^9, PRESERVED_PLACEHOLDER_^^^^2all:\2all:\2search_query2^^^^, PRESERVED_PLACEHOLDER_^^^^2all:\2all:\2all:\2^^^^, PRESERVED_PLACEHOLDER_^^^^2all:\2all:\22^^^^, PRESERVED_PLACEHOLDER_^^^^2all:\2all:\2^^^^3, and PRESERVED_PLACEHOLDER_^^^^2all:\2all:\2^^^^4, the reported analysis predicts that ^^^^2all:\2search_query2^^^^ dB squeezing yields approximately 4.9 dB SNR advantage over coherent states in the shot-noise-dominated region, with ultimate advantage up to approximately ^^^^2all:\2^^^^3.4 dB near PRESERVED_PLACEHOLDER_^^^^2all:\2all:\2^^^^5 under the specified NEP and RIN assumptions (Shi et al., 2023).

Across these variants, the unifying concept remains unchanged: dual-comb heterodyne detection is a linear, phase-sensitive mapping between discrete optical spectra and discrete RF spectra. What changes from platform to platform is how coherence is established, how timing and phase noise are corrected, how much optical bandwidth is compressed into the RF domain, and which observable—absorbance, dispersive shift, distance, velocity, cavity decay, or full electric field—is encoded in the heterodyne phase and amplitude.