 Operating-point transfer of an overlap reference

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.