= Symmetric-overlap normalization drift
\b[Symmetric-overlap normalization drift] is a time-dependent change in the multiplicative scale of two overlap readings. The <symmetric log-overlap ratio> cancels one shared scale, but sequential settings need not experience that same scale.
Let the stable optical contributions at the two radius settings be $F_+$ and $F_-$, and let
$$
\log V_s(t)=F_s+a(t),\qquad s\in\{+,-\},
$$
where $a(t)=\log A(t)$. The ideal log-ratio is $D_0=F_+-F_-$. A positive-setting reading at time 0 followed by a negative-setting reading at time $\Delta$ instead gives $D_{\rm obs}=D_0+a(0)-a(\Delta)$. A drift in normalization can therefore mimic a signed radius mismatch.
An original four-reading design uses settings $+,-,-,+$ at equally spaced times $0,\Delta,2\Delta,3\Delta$. Form
$$
\widehat D=\frac{\log V_+(0)+\log V_+(3\Delta)-\log V_-(\Delta)-\log V_-(2\Delta)}2.
$$
The scale contribution vanishes exactly when $a(t)$ is linear in time: both settings have the same mean observation time. This cancels linear drift in logarithmic scale, not arbitrary drift in every measured quantity.
If $a(t)=a_0+bt+ct^2$, the remaining drift contribution is $2c\Delta^2$. For stipulated $D_0=0.05$, $b=0.02$ per time unit and $\Delta=1$, a simple two-reading comparison gives 0.03 under purely linear log-drift, while the four-reading design gives 0.05. Adding $c=0.003$ per squared time unit changes the latter to 0.056. These are analytical timing examples, not measurements from a beam experiment.
With independent equal log-readout variance $\sigma^2$, the four-reading estimator has variance $\sigma^2$, because it combines four coefficients of magnitude one half. A single two-reading difference has variance $2\sigma^2$ at half the acquisition count. Correlated noise and longer acquisition time can change the practical tradeoff.
<State-dependent gain in symmetric overlap measurements> does not cancel through this ordering. If the scale changes systematically with the radius-setting state, it remains confounded with $F_+-F_-$. The optical mismatch must also remain stable over the sequence; a changing beam is not merely an electronic scale drift.
NIST controlled mode and polarization matching while calibrating the receiver's electrical response.<Frequency response metrology for high-speed optical receivers by Paul D. Hale and others>[PDF pp. 1–2, Heterodyne measurements]{ref} The ordering above is an original drift-control calculation, not an attributed NIST procedure. Test its assumptions with timing records, repeated sequences and independent monitoring before feeding the resulting ratio into the radius inversion.
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