The essential answer
A lock-in detector multiplies a measured waveform by a reference and low-pass filters the product to estimate components at the reference frequency. In-phase and quadrature outputs retain amplitude and phase information that simple averaging loses. Noise outside the effective bandwidth is strongly reduced, but disturbances synchronized with the reference are not rejected merely because they are unwanted. Electrical pickup, vibration, and thermal modulation can all appear in the selected channel. Interpret a lock-in output as a frequency-specific measurement requiring a calibrated response model.
How to reason about it
For a sinusoid, multiplication creates a difference-frequency component near zero and a sum-frequency component that filtering removes. The remaining value depends on relative phase and instrument amplitude convention. Dual-phase readout supplies X and Y, allowing amplitude and phase reconstruction, but magnitude estimates near the noise floor can have a positive bias. Longer time constants reduce bandwidth while increasing settling time and correlation between successive outputs. Record filter order, time constant, reference source, input range, and overload status. Phase can discriminate mechanisms only when their expected transfer functions are known; a cable delay or mechanical response can rotate a genuine signal. Perform dark or disconnected-input controls with the modulation electronics still running to reveal synchronous pickup. Frequency sweeps provide more diagnostic information than a single reference frequency because different mechanisms often have different response times.
ILLUSTRATIVE · NOT A REPORTED RESULT
An example to work through
Assume a calibrated dual-phase readout uses RMS conventions and returns X = 3 µV and Y = 4 µV for a hypothetical sinusoidal signal. Its amplitude is sqrt(3²+4²) = 5 µV RMS and phase is arctan(4/3) = 53.1 degrees. At a sensitivity of 2 µV/nN RMS, the inferred force amplitude is 2.5 nN RMS. If a dark control gives the same vector, the apparent signal is not attributable to illumination. Subtract vectors only when the background is stable; subtracting magnitudes would discard essential phase information.
Where interpretation fails
A clean sinusoid at the drive frequency is not evidence of the intended mechanism. The drive may create a parasitic force with exactly the same timing. Likewise, taking only the in-phase channel can conceal a changing phase response and produce an artificial amplitude change when the reference setting drifts.
The next decision
Choose a modulation frequency where the intended response is calibrated, competing responses are distinguishable, and settling remains practical. Retain X and Y, compare control vectors, and check more than one frequency. A narrow noise bandwidth is useful only after synchronous artifacts and detector overload have been excluded or bounded.
Sources & context
These sources support the concepts noted below. Our synthetic examples and research framing are educational interpretation; they are not findings from these organizations or validation of our ventures.
- SRS: About Lock-In Amplifiers ↗
Phase-sensitive detection; PDF text inspected.
Source check: Relevant excerpt or resource metadata checked; see support note. Original illustrative calculation, not source data.
Educational research context, not a validated device specification or clinical protocol. Read our editorial and correction policy.