= Photodiode responsivity measurement
Thorlabs' <silicon> FDS100 experiment sends a collimated, fibre-coupled <laser> beam through a <beam splitter> to the <photodiode> and a reference <optical power meter>. Varying reverse bias and <electrical load> tests linearity. The measured readout approaches saturation when its <electric potential difference> consumes the bias.<Photodiodes by Thorlabs>[Photodiodes, Lab Facts, Photodiode Saturation Limit and Noise Floor, opening experiment description and Figs. 1–3: reference power sensor, bias/load comparisons and saturation]{ref} A separate low-signal setup uses a $637\,\mathrm{nm}$ <laser>, <polarizers>, an <optical chopper>, <optical attenuators> and a <lock-in amplifier> inside a light-tight enclosure. These are actual apparatus choices, not the parameters of the constructed example above.<Photodiode Saturation and Noise Floor by Thorlabs>[Photodiode Saturation and Noise Floor, p. 7 of 12, Experimental Design — Noise Floor: 637 nm source, polarizers, chopper, attenuation filters, lock-in readout and light-tight enclosure]{ref}
For an independent <dark current> check, Thorlabs enclosed a <photodiode> in nested metal boxes to exclude <light> and suppress interference, used a Keithley 6487 <ammeter> supplying reverse bias, and monitored <temperature>. Only one specimen per type was tested; the nearby temperature sensor did not directly contact the <semiconductor>. Such a dark control measures the baseline but cannot certify <spectral responsivity>.<Photodiodes by Thorlabs>[Photodiodes, Lab Facts, Dark Current as a Function of Temperature, Experimental Setup and Experimental Limitations: nested enclosure, ammeter and specimen/temperature limitations]{ref}
To infer <spectral responsivity> at a selected <wavelength>, measure the <radiant flux> actually reaching the test <photodiode>, rather than just the reference arm. A reference-arm <measurement calibration> must include the <beam splitter> ratio and path losses. With signed readouts in one fixed orientation, subtract a beam-blocked baseline and use
$$
R(\lambda)=\frac{|I_{\rm light}-I_{\rm blocked}|}{P_{\rm test}},\qquad
R(\lambda)=\frac{|V_{\rm light}-V_{\rm blocked}|}{R_fP_{\rm test}}
$$
for direct <electric current> readout or a calibrated linear <transimpedance amplifier>, respectively. Repeating at several incident <powers> tests whether this ratio is constant. Blocking only the source estimates ambient <light> plus electronic baseline; covering the detector excludes ambient <light> too. Their difference distinguishes optical background from <dark current> and readout offset. For a broad <optical spectrum>, the ratio is a spectrum-weighted response, not generally $R$ at one <wavelength>.
For independent <Poisson distribution> collection, the <root mean square> shot <noise> in a one-sided rectangular <frequency> band of <signal bandwidth> $B>0$ is
$$
i_{\rm shot}=\sqrt{2q(I_{\rm ph}+I_d)B},
$$
Here $I_d$ is reverse <dark current>; <thermal electrical noise> and amplifier <noise> also contribute.<Si photodiodes by Hamamatsu Photonics K.K.>[Si photodiodes, p. 6, §2-4, equations (2-4)–(2-7): independent thermal, dark-current and photocurrent noise terms]{ref}
Subtracting a mean <dark current> removes its offset, not its fluctuations: subtracting a constant leaves the <variance> unchanged. Consequently $I_{\rm ph}\gg I_d$ makes <dark current> shot <noise> small relative to signal shot <noise>; it does not by itself establish high <signal-to-noise ratio>. With an independently measured baseline, the <variance> of that estimate must also be propagated. Increasing the measurement <signal bandwidth> raises the admitted <noise>. Calibration of <wavelength>, reference <radiant flux>, readout gain and collection geometry, together with drift and linearity, determines what <measurement uncertainty> can be claimed.
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