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Operating-point transfer of an overlap reference asks whether a state-dependent normalization correction measured under reference conditions remains valid at the specimen's optical and electrical settings. Detector bias, optical power, beat frequency, amplifier range and illumination can all define the operating point. Repeated readings at one setting establish repeatability there, rather than transfer over an untested range.

Let the true optical log-ratio be $D_h(u)$ and the instrumental state offset at power $P$ be $\delta (P)$. A reference measurement estimates $\delta (P_R)$. Applying it to a specimen at $P_S$ leavesThis follows directly from reference-state transfer in overlap normalization. The difference between operating points is a measurement-model input, not extra independent readout noise.

An original local model writes $\delta (P)=a+bP$. References at two powers $P_1<P_2$ support linear interpolation at an intermediate $P$:The weights sum to one. A specimen outside the tested range requires extrapolation, which is more sensitive to model error.

Curvature error in overlap-reference transfer is visible in an exactly solvable example. If the true offset is linear plus $c{P}^2$, its difference from endpoint interpolation is $c(P-P_1)(P-P_2)$. For powers 1 and 3 mW, suppose the measured endpoint offsets are 0.02 and 0.06. The interpolated offset at 2 mW is 0.04. A quadratic term $0.01(P-1)(P-3)$, with powers expressed in mW, leaves both endpoints unchanged but makes the actual midpoint offset 0.03. Correcting by 0.04 then leaves a log-ratio error of $-0.01$. These are stipulated response values, not observations.

Reference uncertainty also transfers. At a fixed, known interpolation power,Here $u_1,u_2$ are standard uncertainties; uncertainty in $P$ requires additional terms. A shared calibration can correlate the endpoints, so their covariance should not be dropped merely because they were measured at different powers.^[ref]

A useful proposed experiment brackets specimen acquisitions in time, samples several operating powers and repeats at the intended bias and frequency. Check for optical changes as well as electronic response: NIST's primary heterodyne apparatus controls spatial mode and polarization before electrical calibration.^[ref] The interpolation calculation above diagnoses a transfer assumption; it is not an attributed NIST procedure.

State-dependent gain in symmetric overlap measurements is a multiplicative response that changes with the optical radius-setting state. It can imitate the radius mismatch inferred from a symmetric log-overlap ratio. An acquisition order that cancels time drift does not remove a scale change tied to the state itself.

For positive overlap readings, supposewhere $u=\log \rho$ is the true logarithmic radius ratio, $A_s$ is a fixed state-specific gain and $a(t)$ is shared logarithmic drift. Even after perfectly removing $a(t)$, the measured log-ratio isHere $h=\log q>0$ describes the known symmetric radius settings. The two unknowns $u$ and $\delta$ cannot be determined from this one ratio without further information. This is an identifiability problem, not merely a larger readout variance.

For an original matched-beam example, $\rho =1$ gives $D_h=0$. A state-gain ratio $A_{+}/A_{-}=1.04$ instead produces $D_{\mathrm{obs}}=\log 1.04\approx 0.03922$. With $q=2$, ignoring the gain difference givesapproximately 0.98379. The apparently small radius mismatch is entirely instrumental in this stipulated example. Repeating the same states more often reduces independent scatter without removing the state offset.

A reference-state transfer in overlap normalization can supply additional information. If a reference has known $u=0$ and the same state-gain ratio as the specimen measurement, its observed log-ratio estimates $\delta$. Subtracting that log-ratio is justified only if the state response transfers. Changing optical power, detector operating point or aperture illumination between reference and specimen can break that assumption.

Another explicit model uses a simultaneous monitor $M_s=K{A}_s{e}^{a(t)}$ with the same constant $K$ in both states. Then $\log V_s-\log M_s=F_s(u)-\log K$, and the state difference cancels the monitored gain. A separate optical-power monitor does not automatically satisfy this equation for an RF-amplifier gain change: verify which part of the measurement chain the monitor actually samples.

NIST's primary receiver apparatus uses variable attenuators, a beam splitter, a polarizer and single-mode-fibre coupling to match the incident modes, followed by electrical calibration.^[ref] Those controls motivate distinguishing an electronic gain change from an optical change in polarization, clipping or beam shape. The reference and monitor designs above are original diagnostic models, not procedures attributed to that paper.