= Heterodyne RF-to-DC gain transfer check
A \b[heterodyne RF-to-DC gain transfer check] tests whether the calibration converting a beat-frequency measurement into current amplitude is compatible with the calibration of the separate arm currents. The <gain-matching condition for heterodyne normalization> involves amplitude gains, so an RF power gain cannot be substituted without conversion.
For corrected peak beat current $B$ and arm currents $I_1,I_2$, the normalized overlap is $\gamma=B/(2\sqrt{I_1I_2})$. Suppose an electrical model gives sinusoidal peak current $B$ through a known resistive load $Z$. Its average beat power is
$$
P_{\rm RF}=\frac{B^2Z}{2},\qquad B=\sqrt{\frac{2P_{\rm RF}}Z}.
$$
Source/load division and impedance corrections must already be included when relating that load current to the detector-current convention. A factor converting power is therefore square-rooted when converting amplitude.
Let measured RF power carry multiplicative factor $g_P$, while the arm currents carry factors $g_1,g_2$. Under this model,
$$
\frac{\widehat\gamma_{\rm obs}}\gamma=\sqrt{\frac{g_P}{g_1g_2}}.
$$
Cancellation requires $g_P=g_1g_2$. With one common DC current factor $g_{\rm DC}$, the condition is $g_P=g_{\rm DC}^2$, not $g_P=g_{\rm DC}$.
An original example takes $g_{\rm DC}=1.10$. An RF power factor 1.21 produces amplitude factor 1.10 and cancels in the normalized overlap. Applying RF power factor 1.10 instead leaves multiplier $1/\sqrt{1.10}\approx0.95346$, despite using the same numerical gain label in both paths. The example isolates <heterodyne amplitude-versus-power gain conversion>, rather than a change of optical overlap.
NIST's receiver experiment measured microwave power and separately corrected sensor calibration, electrical loss and <impedance matching>. Its two-laser optical source used polarization and spatial matching to establish calculable modulation.<Frequency response metrology for high-speed optical receivers by Paul D. Hale and others>[PDF pp. 1–2, Heterodyne measurements and Eqs. 1–4]{ref} Those separate operations make the RF-to-DC comparison a physical calibration problem.
Record peak versus RMS conventions, frequency response, load model and arm-current calibration. Test a known or independently characterized modulation while varying power within the linear range. Changed polarization, aperture clipping or optical alignment can alter the true overlap and imitate a gain-transfer defect, so one unexplained normalized ratio does not uniquely diagnose the electrical path.
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