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Separating power imbalance from mode mismatch in optical beating requires more information than a single modulation-depth reading. In the optical heterodyne modulation depth model, two effects multiply:The power ratio controls one term, while $\gamma$ describes the mode-overlap factor in optical heterodyne detection. A low beat depth can result from either effect or both.

Measure each arm separately with the same detector and collection geometry, subtracting dark current. For sufficiently close optical frequencies with the same detector responsivity, let the separate currents be $I_s$ and $I_{\mathrm{LO}}$. After correcting the receiver's beat-frequency response,This consistency bound for separately measured heterodyne arm powers requires $I_{\mathrm{beat},\mathrm{pk}}\le 2\sqrt{I_s{I}_{\mathrm{LO}}}$. An apparent value above unity indicates inconsistent calibration, background treatment, conditions or model assumptions.

For an original example, separate currents are $0.40$ and $0.10\mathrm{mA}$. Their power-imbalance limit is $m_{\max }=0.80$. A corrected beat depth $m=0.56$ means peak beat current $0.28\mathrm{mA}$ and overlap $|\gamma |=0.70$. If the electrical chain instead attenuates the beat amplitude by $0.75$ relative to DC and that effect is ignored, the apparent depth becomes $0.42$ and inferred overlap $0.525$.

NIST's physical receiver experiment matched the two optical modes and received photocurrent contributions; it separately corrected electrical loss and impedance mismatch when inferring receiver response and modulation.^[ref] Holding alignment fixed while changing one arm's power tests whether the corrected overlap remains constant. Source drift, changed polarization or aperture clipping during the separate-arm measurements can spoil that inference.

Tracy S. Clement is a metrology researcher and coauthor, with Paul D. Hale and Dylan F. Williams, of NIST work on optical receiver frequency response. The 2001 paper describes combining two tunable lasers, a beam splitter, a polarizer and a single-mode material fibre for optical heterodyne detection.^[ref]

The apparatus turns the difference between two optical frequencies into a measurable intensity oscillation. For beams in the same spatial mode and with matched polarization, an original derivation from interference givesHere $P_1$ and $P_2$ are the separate received powers and $\varphi$ is their relative optical phase. The optical heterodyne modulation depth is thereforeEqual powers give $m=1$. Powers in the ratio $9:1$ instead give $m=6/10=0.6$, even though a clear beat remains. Dividing the measured photocurrent amplitude by the wrong assumed $m$ would give the wrong receiver response. Matching the beams' polarization and spatial modes is thus part of establishing a known stimulus, rather than merely improving the visual appearance of an interference pattern.

The equations explain the measurement principle; they do not assign individual apparatus tasks to Clement or claim a separate invention. The paper documents a joint contribution to making an optical stimulus useful for quantitative measurement calibration.