Photodetector

A photodiode is a semiconductor diode that converts absorbed photons into electrical carriers. A reverse-biased detector separates the carriers and collects charge; its quantum efficiency and dark current determine sensitivity.

Dark current is charge produced in a detector without illumination, often by thermally excited carriers. Cooling reduces it, although cooling requirements also depend on the wavelength range and thermal background.

Correlated double sampling differences a signal reading and its associated reset or baseline reading. It suppresses correlated offsets and reset noise, while the noise of the two measurements must still be propagated.

A hybrid infrared detector bonds a photosensitive semiconductor array to a separate silicon readout circuit. Each pixel has its own electrical connection; charge need not be transferred across the array as in a charge-coupled device.

A detector reference pixel has no illuminated photosensitive connection and samples readout offsets. Reference-pixel subtraction can suppress common electronic drifts but does not measure the sky background or all pixel-dependent errors.

A nondestructive read samples a pixel’s accumulated signal without resetting it. Repeated samples permit Fowler sampling and up-the-ramp sampling, and can help identify saturation and cosmic-ray charge steps.

Up-the-ramp sampling measures accumulated charge repeatedly through an exposure and estimates flux from its slope. Cosmic-ray steps, saturation and nonlinearity must be identified or modelled.

Fowler sampling averages several nondestructive reads near the start and end of an integration and differences the two averages. For independent equal read noise, averaging lowers the read-noise variance; correlated noise limits the improvement.

The HAWAII-2RG architecture has a $2048\times 2048$ grid with an 18-micrometre pitch. For infrared work its readout circuit is normally bonded to a mercury cadmium telluride absorber. Reference pixels track electronic offsets and an independently addressed guide window can be read alongside the science array.

Background subtraction estimates a source contribution by removing a sky or detector-background measurement. An independent background estimate adds photon shot noise; a mismatched background adds bias of an estimator.

Let $X\sim \mathrm{Poisson}(Q+B)$ and $Y\sim \mathrm{Poisson}(fB)$ be independent. Then $X-Y$ has source-estimation bias $(1-f)B$ and variance $Q+(1+f)B$. Its accuracy ratio $Q/\sqrt{\mathbb{E}[(X-Y-Q{)}^2]}$ tends to $R_Q/(|1-f|R_B)$ when $Q=R_{Q}T$, $B=R_{B}T$ and $T$ grows. This uses mean squared error, not variance alone, and assumes a fixed uncorrected mismatch.

Read noise is uncertainty added by measuring detector charge or voltage. It is often expressed as an equivalent number of input electrons per pixel per read.

Independent photon arrivals have a Poisson distribution: a mean count $\mu$ has variance $\mu$ and standard deviation $\sqrt{\mu }$. Subtraction of independent counting measurements adds their variances.

Quantum efficiency is the mean fraction of incident photons producing collected signal carriers. Noise-equivalent quantum efficiency can be lower when amplification adds fluctuations; this does not imply a corresponding loss of actual photon absorption.

A charge-coupled device stores photoelectrons in potential wells and transfers the charge through clocked stages to an output amplifier. The transfer differs from independently addressed pixels in a hybrid infrared detector.

An electron-multiplying CCD adds a high-field multiplication register before the output amplifier. Impact ionization generates a large mean gain, reducing input-referred read noise but adding multiplication excess noise.

Random multiplication increases the noise relative to deterministic gain. If the output from one input electron has mean $g$ and variance $g^2$, a Poisson distribution of input electrons with mean $\mu$ produces output variance $2g^2\mu$, by the law of total variance. The high-gain analog-mode excess-noise factor is $\sqrt{2}$.

An energetic charge carrier creates an additional electron–hole pair. In a multiplication register this is stochastic, so the output charge fluctuates even when the input electron number is fixed.

For source counts $S$ and independent background counts $B$ with Poisson distributions, the ideal counting standard deviation is $\sqrt{S+B}$, so the signal-to-noise ratio is $S/\sqrt{S+B}$. Detector noise and uncertainty in the estimated background add further variance. A larger sky aperture raises $B$, while better throughput raises $S$; both affect the faintness limit of a spectrograph.