Exercise set

Photodiode and Optical Power Sensor Exercises

Solved photodiode and optical sensor exercises for responsivity, photon flux, quantum efficiency, shot noise, TIA range and calibration release.

Branch: Engineering Physics
Content: Exercise set
Updated: Jul 03, 2026
Revision: v1.1.0 · reviewed

These exercises focus on photodiodes and optical power sensors as calibrated electro-optical instruments. They connect optical power, wavelength, photon flux, responsivity, quantum efficiency, dark current, shot noise, transimpedance range, saturation, drift and release evidence.

Use the calculations as screening checks. A real optical measurement also needs aperture definition, alignment, spectral response, background light, detector area, amplifier headroom, calibration traceability and uncertainty tied to the installed geometry.

How to use these exercises

Use the set as an installed optical measurement review. Exercises 1 to 5 establish photocurrent, optical power, photon flux, quantum efficiency and dark-current correction. Exercises 6 to 10 check shot noise, SNR, transimpedance output, saturation and ambient-light headroom. Exercises 11 to 17 add neutral-density attenuation, responsivity drift, bandwidth, dynamic range, calibration factor, guard band and linearity. Exercise 18 combines these boundaries into a release decision.

Before calculating, state wavelength or spectrum, aperture, alignment, detector area, responsivity source, bias condition, installed background-light state, TIA gain, bandwidth and calibration reference. A photodiode current is not an optical power measurement until those boundaries are known. The engineering comment below each exercise identifies which optical, electronic or metrology assumption must be verified before release.

Release Evidence Notes

Optical sensor evidence should state wavelength or spectrum, optical path, aperture, detector area, responsivity basis, dark condition, background-light condition, amplifier gain, bandwidth, saturation limit and calibration date. A photodiode current is not optical power until those boundaries are known.

The evidence package should separate optical boundary, electronics boundary and metrology boundary. The optical boundary covers wavelength, aperture, alignment, coupling, beam profile and stray light. The electronics boundary covers dark current, TIA range, bandwidth, capacitance, stability and recovery. The metrology boundary covers reference instrument, calibration factor, traceability, uncertainty, drift and guard band.

Installed-background evidence is especially important. A bench dark measurement may not represent a sunlit installation, a dirty window, fiber misalignment, reflection, ambient flicker or temperature drift. Release records should therefore state whether the result is bench-calibrated, installed-calibrated or conditionally corrected.

Engineering Boundary Notes

The exercises use first-order responsivity and noise equations. They do not replace spectral calibration, beam profiling, TIA stability analysis, detector capacitance modeling, lock-in validation, temperature testing or stray-light assessment. Treat pass results as measurement screens, not as proof that the installed optical path is controlled.

The main boundary is spectral response. Responsivity, quantum efficiency, filter transmission and calibration factor are wavelength dependent. The second boundary is dynamic range: a sensor can have adequate noise at low light but saturate under ambient light or reflections.

Common Release Mistakes

applying a responsivity value at the wrong wavelength;
subtracting dark current without measuring installed background light;
ignoring TIA output swing, recovery time and input capacitance;
quoting optical power without aperture or coupling geometry;
using a clean bench calibration for a dirty, misaligned or sunlit installation;
omitting uncertainty and traceability from the release record.

Another common mistake is reporting a single optical power value without stating whether it is incident on the detector, transmitted through an aperture, coupled into a fiber or averaged over a beam. These are different measurement boundaries and can produce different release decisions.

Do not validate only at the nominal power. Linearity, saturation, drift and background headroom should be checked across the intended range, including the lowest claimed signal and the highest expected ambient or reflected light condition.

Scenario Map

The exercises progress from photocurrent and photon flux to quantum efficiency, dark correction, noise, bandwidth, transimpedance gain, saturation, drift, guard bands and calibration release.

Exercise 1: Photocurrent from Optical Power

A photodiode has responsivity $0.45\ \text{A/W}$ at the operating wavelength. Incident optical power is $2.0\ \text{mW}$ . Find photocurrent.

Solution

I=RP=0.45(0.0020)=9.0\times10^{-4}\ \text{A}

So the photocurrent is $0.90\ \text{mA}$ .

Engineering Comment

The interface must handle the current without saturating and the responsivity must match the wavelength and bias condition.

Plausibility Check

Milliwatts multiplied by amperes per watt should produce milliamperes.

Exercise 2: Optical Power from Current

A calibrated photodiode measures $120\ \mu\text{A}$ and has responsivity $0.40\ \text{A/W}$ . Estimate optical power.

Solution

P=\dfrac{I}{R}=\dfrac{120\times10^{-6}}{0.40}=3.0\times10^{-4}\ \text{W}

The optical power is $300\ \mu\text{W}$ .

Engineering Comment

This conversion is valid only for the same spectral and geometric boundary used during calibration.

Plausibility Check

A fractional ampere-per-watt detector converts hundreds of microamps into hundreds of microwatts.

Exercise 3: Photon Flux

Optical power is $1.0\ \text{mW}$ at photon energy $2.0\ \text{eV}$ . Use $1\ \text{eV}=1.602\times10^{-19}\ \text{J}$ . Find photon flux.

Solution

E=2.0(1.602\times10^{-19})=3.204\times10^{-19}\ \text{J}

\Phi=\dfrac{0.001}{3.204\times10^{-19}}=3.12\times10^{15}\ \text{photons/s}

Engineering Comment

Photon flux connects optical power to quantum efficiency, shot noise and detector saturation.

Plausibility Check

Visible photons have very small energy, so milliwatts imply very large photon rates.

Exercise 4: Quantum Efficiency from Responsivity

A photodiode responsivity is $0.50\ \text{A/W}$ at photon energy $2.0\ \text{eV}$ . Estimate quantum efficiency using $q=1.602\times10^{-19}\ \text{C}$ .

Solution

Responsivity satisfies

R=\eta\dfrac{q}{E}

\eta=\dfrac{RE}{q}=\dfrac{0.50(3.204\times10^{-19})}{1.602\times10^{-19}}=1.00

Engineering Comment

A result near unity is a physical upper-bound check. Values above one may indicate gain, wavelength mismatch or inconsistent units.

Plausibility Check

At 2 eV, one electron per photon gives about 0.5 A/W, matching the result.

Exercise 5: Dark-Current Correction

Measured current is $8.6\ \mu\text{A}$ and dark current is $0.9\ \mu\text{A}$ . Responsivity is $0.55\ \text{A/W}$ . Estimate corrected optical power.

Solution

I_\mathrm{photo}=8.6-0.9=7.7\ \mu\text{A}

P=\dfrac{7.7\times10^{-6}}{0.55}=14.0\ \mu\text{W}

Engineering Comment

Dark subtraction should use the installed thermal and bias state, not a datasheet typical value.

Plausibility Check

Subtracting about 10 percent of the measured current gives a power slightly below the uncorrected estimate.

Exercise 6: Shot-Noise Current

Photocurrent is $0.90\ \text{mA}$ and bandwidth is $10\ \text{kHz}$ . Estimate shot-noise RMS current with $q=1.602\times10^{-19}\ \text{C}$ .

Solution

i_n=\sqrt{2qIB} =\sqrt{2(1.602\times10^{-19})(0.00090)(10000)} =1.70\times10^{-9}\ \text{A}

Engineering Comment

Shot noise grows with current and bandwidth. Reducing bandwidth can improve measurement noise when response time allows it.

Plausibility Check

Nanoampere-scale noise is plausible for milliampere photocurrent over kilohertz bandwidth.

Exercise 7: Signal-to-Noise Ratio

Signal current is $30\ \mu\text{A}$ and RMS noise current is $0.60\ \mu\text{A}$ . Find SNR in dB.

Solution

\mathrm{SNR}_{dB}=20\log_{10}\left(\dfrac{30}{0.60}\right)=34.0\ \text{dB}

Engineering Comment

The SNR must be compared with the required optical-power resolution and with background-light variation.

Plausibility Check

A 50:1 amplitude ratio corresponds to about 34 dB.

Exercise 8: Transimpedance Output

A photodiode current of $14.7\ \mu\text{A}$ passes through a $68\ \text{kOhm}$ transimpedance resistor. Estimate output voltage.

Solution

V=IR=(14.7\times10^{-6})(68000)=1.00\ \text{V}

Engineering Comment

The resistor sets nominal gain, but stability, capacitance, input bias, leakage and output swing determine whether the circuit is releasable.

Plausibility Check

Ten microamps times tens of kilo-ohms gives a volt-scale output.

Exercise 9: Saturation Margin

A TIA saturates at $2.5\ \text{mA}$ input current. Expected maximum photodiode current is $0.90\ \text{mA}$ . Compute current margin.

Solution

\mathrm{margin}=\dfrac{2.5-0.90}{0.90}=1.78

The saturation margin is 178 percent relative to expected current.

Engineering Comment

This margin can disappear when ambient light or reflections add DC photocurrent.

Plausibility Check

The limit is almost three times the expected current, so the numerical margin is large but not infinite.

Exercise 10: Ambient-Light Headroom

Signal current is $0.25\ \text{mA}$ , ambient current is $1.7\ \text{mA}$ and the TIA saturates at $2.5\ \text{mA}$ . How much current headroom remains?

Solution

I_\mathrm{used}=0.25+1.7=1.95\ \text{mA}

I_\mathrm{headroom}=2.5-1.95=0.55\ \text{mA}

Engineering Comment

Ambient light is part of the measurement boundary. If it is not included in calibration, the release evidence is incomplete.

Plausibility Check

The circuit has some headroom, but only about half a milliampere remains for variation and overload.

Exercise 11: Neutral-Density Attenuation

An optical density filter has $OD=1.5$ . What fraction of incident power is transmitted?

Solution

T=10^{-OD}=10^{-1.5}=0.0316

The filter transmits about 3.16 percent of incident power.

Engineering Comment

Filter transmission should be validated at wavelength and angle. Nominal OD may not match the installed optical path.

Plausibility Check

One OD is 10 percent and two OD is 1 percent, so 1.5 OD should be between them.

Exercise 12: Responsivity Drift

A sensor responsivity drifts by $0.12$ percent per degree C. Temperature changes by $18^\circ\text{C}$ . Estimate gain error.

Solution

\epsilon=0.12(18)=2.16\ \text{percent}

Engineering Comment

Temperature drift should be included in the uncertainty budget or controlled by compensation and recalibration.

Plausibility Check

Several percent drift from tens of degrees is plausible for an uncompensated optical sensor.

Exercise 13: Bandwidth from Rise Time

An optical pulse measurement needs $5\ \mu\text{s}$ rise-time response. Estimate minimum bandwidth using $B\approx0.35/t_r$ .

Solution

B=\dfrac{0.35}{5\times10^{-6}}=70\ \text{kHz}

Engineering Comment

The detector, TIA and filters must all support this bandwidth without unacceptable noise or ringing.

Plausibility Check

Microsecond response requires tens of kilohertz bandwidth, not megahertz.

Exercise 14: Dynamic Range

Minimum resolvable optical power is $20\ \text{nW}$ and maximum linear optical power is $2.0\ \text{mW}$ . Find dynamic range in dB.

Solution

DR=20\log_{10}\left(\dfrac{2.0\times10^{-3}}{20\times10^{-9}}\right)=100\ \text{dB}

Engineering Comment

Dynamic range is only meaningful when the minimum and maximum are defined under the same bandwidth, geometry and linearity criteria.

Plausibility Check

A power ratio of $10^5$ gives 100 dB on an amplitude-style 20 log scale.

Exercise 15: Calibration Factor

A reference meter reports $1.25\ \text{mW}$ while the sensor output is $1.18\ \text{V}$ . Find calibration factor in mW/V.

Solution

K=\dfrac{1.25}{1.18}=1.06\ \text{mW/V}

Engineering Comment

The factor should be stored with wavelength, aperture, reference-meter traceability and calibration uncertainty.

Plausibility Check

The voltage is close to the milliwatt value, so a factor slightly above 1 mW/V is plausible.

Exercise 16: Guard-Banded Limit

An optical safety interlock limit is $4.0\ \text{mW}$ . Expanded uncertainty is $0.35\ \text{mW}$ . What maximum indicated value should be accepted with guard band?

Solution

P_\mathrm{ind,max}=4.0-0.35=3.65\ \text{mW}

Engineering Comment

Guard bands prevent a measurement near the limit from being accepted when uncertainty could put it out of specification.

Plausibility Check

The accepted indicated value is below the true limit by exactly the uncertainty allowance.

Exercise 17: Linearity Error

At a reference input of $800\ \mu\text{W}$ , ideal output is $0.848\ \text{V}$ from the calibration factor. Measured output is $0.826\ \text{V}$ . Estimate percent reading error.

Solution

\epsilon=\dfrac{0.826-0.848}{0.848}(100)=-2.59\ \text{percent}

Engineering Comment

Linearity should be checked across the intended range, not only at one convenient calibration point.

Plausibility Check

The voltage error is about 22 mV on 0.85 V, so a few percent error is reasonable.

Exercise 18: Optical Sensor Release Gate

A release checklist has 15 required optical-sensor evidence items. Thirteen are complete and two are missing: installed ambient-light test and calibration traceability. What is completion fraction and release decision?

Solution

\mathrm{completion}=\dfrac{13}{15}=0.867

The package is 86.7 percent complete. Release should not pass because both missing items are required evidence.

Engineering Comment

Optical release fails when the measurement boundary is unproven, even if the electrical conversion looks correct.

Plausibility Check

Two missing required items out of fifteen is visible release risk, not administrative noise.

Validation Package Checklist

Before accepting a photodiode or optical power sensor, collect:

wavelength or spectrum, aperture, alignment and optical path definition;
responsivity, calibration factor, reference instrument and traceability;
dark-current and installed background-light evidence;
TIA gain, output swing, bandwidth, stability and recovery evidence;
saturation margin, drift estimate, linearity check and guard band;
uncertainty budget tied to the exact installed geometry.
detector area, coupling condition, beam profile or fiber interface basis;
temperature condition, contamination state and recalibration interval;
release decision states accept, recalibrate, shield, realign, narrow range or hold.

A complete validation package should make the optical measurement reproducible. Another engineer should be able to see what light reached the detector, how current became power, what electronics limits applied and why the result was accepted or held.

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