C-X2 · From a pixel to the amplifier

CCD: Follow the Charge

Why does a bright CCD pixel leave a trail when charge transfer is imperfect? An imperfect clock leaves some electrons behind. Later clocks move them into following samples, spreading a sharp bright pixel into a tail. Permanently trapped charge lowers the total signal; amplifier noise adds fluctuations after the transfer.

Watch three clock phases move charge toward a readout amplifier. Compare the original exposure with the digitized stream, then separate delayed charge, trapping and read noise.

Recorded initial charge $0$

Recorded collected charge $0$

Recorded deferred charge $0$

Recorded trapped charge $0$

A clocked charge conveyor

Follow an exposure

Exposure strength

N_{\rm peak}/\mathrm{e}^{-}

1800

Transfer efficiency

\eta

0.985

Replay clock rate

f_{\rm replay}/\mathrm{Hz}

1.2

A default acquisition is ready.

Noise and material parameters

Permanent trapping per clock

\ell

0

Amplifier read noise

\sigma_r/\mathrm{e}^{-}

7

Sampling seed

s_0

41

Model, scale and sources

This synthetic sixteen-cell serial CCD starts with a fixed two-peak charge exposure. Each clock transfers a prescribed fraction toward the amplifier; deferred charge remains for later clocks, and an optional fraction is permanently trapped. Read noise is independent Gaussian amplifier noise in electrons. The replay uses the recorded cell states. Gate timing is schematic: no Poisson electrostatics, trap release kinetics, dark current, blooming, full-well saturation or photon shot noise is modeled. Poor transfer is deliberately exaggerated; scientific CCD transfer efficiencies can exceed 99.99 percent. Layer thickness and charge-cloud size are enlarged.

Hamamatsu · CCD image sensors Nikon · Introduction to CCDs

Synthetic acquisition

The amplifier’s readout stream

Default record

Saved amplifier samples

Complete-transfer reference

The dashed reference reads the initial charge in reverse cell order. The acquired stream includes transport delay, trapping and amplifier noise.

Start with the essentials

Focus question: Why does a bright CCD pixel leave a trail when charge transfer is imperfect?
One-sentence intuition: Deferred electrons arrive late; permanently trapped electrons never reach the amplifier during the readout.

Core mathematical model

Charge in a cell after one clock

q_j^{(k+1)}=(1-\ell)\left[(1-\eta)q_j^{(k)}+\eta q_{j-1}^{(k)}\right]

The cell on the left supplies the incoming charge. The first cell has no incoming packet. The last cell transfers charge into the amplifier.

Account for every electron

Q_{\rm initial}=Q_{\rm collected}+Q_{\rm deferred}+Q_{\rm trapped}

This equality applies before amplifier noise. The finite readout keeps the remaining tail explicitly.

Amplifier sample

y_k=q_{{\rm out},k}+\epsilon_k,\qquad \epsilon_k\sim\mathcal N(0,\sigma_r^2)

Independent electronic noise can make a faint digitized sample negative after baseline subtraction. It does not create or destroy the transported charge.

Common difficulties

A tail can conserve charge

Typical misconceptionEvery electron absent from the main peak has been destroyed.

Better mental modelDeferred charge moves into later samples or remains in the array when the finite readout ends. Only the explicitly trapped fraction is removed from mobile charge.

A teaching inefficiency is exaggerated

Typical misconceptionA transfer efficiency near eighty percent is typical of a scientific CCD.

Better mental modelReal scientific CCDs can exceed 99.99 percent per transfer. The degraded preset makes cumulative delay visible in a short sixteen-cell register.

Run the experiment

01
Follow a clean readout
Choose Clean transfer. Follow the bright packets to the amplifier and compare the two peaks with the saved output.
What to observe: The closest pixel is read first. With almost complete transfer, the stream preserves the reversed spatial order of the input profile.
02
Delay some of the charge
Choose A long tail and inspect the later readout clocks.
What to observe: Some electrons stay in each cell and arrive in later samples. The tail follows from those same recorded cell states.
03
Separate noise from missing charge
Compare Faint exposure with Charge trapped. Export their samples.
What to observe: Read noise fluctuates around the transported signal. Trapping reduces the collected charge and appears in the separate trapped-charge count.