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Dylan F. Williams is a metrology researcher identified with NIST in a 2001 paper coauthored with Paul D. Hale and Tracy S. Clement. Their work connects measurement calibration of an optical receiver with corrections for electrical loss and electrical impedance mismatch.^[ref]

Why does the electrical connection matter when the original signal is light? A photodiode produces a photocurrent, but the measured signal also passes through cables, connectors and an electrical load. A simple original model writes the measured transfer function asFor this scalar model, if the connection has amplitude gain $0.8$ and the measured amplitude gain is $0.4$ at one frequency, the inferred receiver amplitude gain is $0.4/0.8=0.5$. Treating $0.4$ as the receiver result would incorrectly include the connection's attenuation. A real mismatched connection requires a fuller model than this product.

The distinction between amplitude and power also matters. At the same real electrical impedance, an amplitude ratio $1/2$ corresponds to a power ratio $1/4$. Both give the same change in decibels when the appropriate definitions are used:Using $10{\log }_{10}$ on the amplitude ratio would instead give about $-3.01$ and describe a different quantity. These are illustrative calculations, rather than measurements attributed to Williams; the documented contribution is his coauthorship of the shared receiver-metrology work.

Paul D. Hale is a metrology researcher named with Tracy S. Clement and Dylan F. Williams on a 2001 NIST paper about optical receiver frequency response. It compares frequency-domain optical heterodyne detection with time-domain measurements using an oscilloscope, including corrections for the electrical connection and finite optical stimulus.^[ref]

An oscilloscope trace need not be the receiver's isolated impulse response. In an original idealized model of linear time-invariant systems, let $r(t)$ be the receiver impulse response, $p(t)$ the optical pulse envelope and $o(t)$ the readout impulse response. Ignoring mismatch for this illustration, the measured waveform is the convolutionA broader measured pulse can therefore reflect the receiver, the stimulus or the readout. If all three envelopes are normalized Gaussian functions, with independent convolution widths, their variances add:For illustrative widths ${\sigma }_y=5\mathrm{ps}$, ${\sigma }_p=3\mathrm{ps}$ and ${\sigma }_o=\sqrt{7}\mathrm{ps}$, the inferred receiver width is ${\sigma }_r=3\mathrm{ps}$, rather than $5\mathrm{ps}$. These are chosen model values, not results reported by Hale.

The example motivates characterizing the stimulus and readout as well as the specimen. Dividing by $P(f)O(f)$ where that product is nearly zero also amplifies measurement noise, so a formal Fourier transform inversion does not guarantee a reliable corrected response. This is why measurement uncertainty belongs alongside the quoted frequency response.