Photonics Essentials: Detector Operating Modes and Camera Pixels

Source

Thomas P. Pearsall, Photonics Essentials: An Introduction with Experiments (McGraw-Hill, 2003), Chapter 3, Section 3.3, Photodiode Operation: The Photocurrent Mode and the Photovoltage Mode, printed pages 47–48.

The two modes in Section 3.3

Illumination shifts the diode current by the photocurrent:

\[I(V)=I_s \left[ \exp\left(\frac{qV}{nk_BT}\right)-1 \right] -I_{\mathrm{ph}}.\]

The external circuit selects the operating point on this current-voltage curve.

Operation

Electrical condition

Measured signal

Flux response

Photocurrent mode

Usually reverse bias; voltage is controlled

\(I_{\mathrm{ph}}\)

Approximately linear

Photovoltage mode

Open circuit; \(I=0\)

\(V_{\mathrm{OC}}\)

Logarithmic and therefore nonlinear

Camera integration

Reset, finite exposure, then readout

Stored charge followed by voltage

Approximately linear until saturation

In reverse bias, the ideal diode term is nearly constant:

\[I\approx-I_s-I_{\mathrm{ph}}.\]

The small current \(-I_s\) that remains without illumination is the ideal dark current. Real dark current is larger because thermal generation, defects, surfaces, and leakage paths also contribute. The Chapter 3 curve explorer shows this in Photodiode I–V family (Figs. 3.2–3.4) with four-quadrant axes.

Why photovoltage is nonlinear

At open circuit, set \(I=0\) and solve for voltage:

\[V_{\mathrm{OC}} = \frac{nk_BT}{q} \ln\left(1+\frac{I_{\mathrm{ph}}}{I_s}\right).\]

The logarithm compresses large changes in photon flux into smaller voltage changes. That is useful when circuit simplicity or wide dynamic range is more important than a faithful measurement of flux. It can distort a spectral line shape because relative optical intensities are not preserved.

What mode does a camera pixel use?

A conventional CMOS or CCD camera pixel is closest to photocurrent mode, but a more precise name is photocurrent integration or charge accumulation. It does not normally wait for the steady-state open-circuit photovoltage described above.

During an exposure of duration \(T_{\mathrm{exp}}\), the photodiode stores the charge generated by its photocurrent:

\[Q_{\mathrm{sig}} = \int_0^{T_{\mathrm{exp}}}I_{\mathrm{ph}}(t)\,dt.\]

For constant illumination,

\[Q_{\mathrm{sig}} = I_{\mathrm{ph}}T_{\mathrm{exp}} = \eta qN_\gamma,\]

where \(N_\gamma\) is the number of incident photons that contribute to the signal and \(\eta\) is the quantum efficiency. Readout electronics convert charge to a voltage on a sensing capacitance:

\[\left|\Delta V\right| = \frac{Q_{\mathrm{sig}}}{C_{\mathrm{sense}}}.\]

The voltage sign depends on the pixel circuit’s node convention. The important result is

\[\boxed{ \text{raw pixel signal} \mathrel{\propto} \text{photon flux} \times \text{exposure time} }.\]

CMOS and CCD readout

A common four-transistor CMOS pixel follows this sequence:

  1. Reset the sensing node and pinned photodiode.

  2. Accumulate photoelectrons in the pinned photodiode during the exposure.

  3. Open the transfer gate and move the stored charge to a floating diffusion.

  4. Measure the resulting voltage with the pixel source follower and column electronics.

Correlated double sampling subtracts a reset measurement from the signal measurement. A CCD also integrates a charge packet, but shifts that packet through the sensor to an output amplifier instead of placing an amplifier in each pixel.

Where camera response becomes nonlinear

The sensor RAW value is designed to remain approximately linear with collected photons, but not under every condition:

  • At full well, the pixel cannot store more charge and saturates.

  • Junction and sensing capacitances can vary with voltage.

  • Charge transfer, source-follower, column amplifier, and ADC errors can add nonlinearity.

  • Dark current adds charge even without light.

  • Gamma correction, tone mapping, and JPEG processing are deliberately nonlinear, even when the underlying RAW measurement is nearly linear.

There are also special-purpose exceptions. Logarithmic high-dynamic-range pixels deliberately use a response closer to photovoltage operation. SPAD pixels use Geiger-mode avalanche events and count photons rather than integrating ordinary photodiode current.

The concise classification is therefore

\[\boxed{ \text{ordinary camera pixel} = \text{photocurrent generation} + \text{finite-time charge integration} }.\]

Continue interactively

Use Photonics Essentials: Chapter 3 Interactive Physics Lab to compare the linear I–V photocurrent family, logarithmic open-circuit photovoltage, and the Chapter 3 absorption models.