Wiki / Detectors / Camera

Camera

Measures a pixel-integrated one-dimensional intensity profile and resolves supported interference from sized monochromatic CW lasers.

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In the real world

A consumer camera is built to produce a pleasing picture. A scientific camera is built to produce a number: one that is proportional to how many photons arrived at a given place, by a known factor, with a known uncertainty. Everything that distinguishes the sensors below follows from that one change of purpose.

The chain is short and every link loses something. Photons land on silicon and a fraction of them free an electron — that fraction is the quantum efficiency. The freed electrons accumulate in a potential well under each pixel for the duration of the exposure. At the end the accumulated charge is converted to a voltage, amplified, and digitised into an integer count. Read that integer back through the chain and you have an estimate of the photon flux, plus everything the chain added on the way.

S_{\text{ADU}} = \frac{\eta\, N_{\gamma} + D t}{g} + \text{offset}

What a pixel actually reports: incident photons N_γ scaled by quantum efficiency η, plus dark current D accumulated over exposure t, divided by the gain g in electrons per count.

\sigma_{\text{total}} = \sqrt{\underbrace{\eta N_{\gamma}}_{\text{shot}} + \underbrace{D t}_{\text{dark}} + \underbrace{\sigma_{\text{read}}^{2}}_{\text{read}}}

The three noise sources add in quadrature, in electrons. Shot noise is the photons themselves and cannot be engineered away; the other two are what a camera is designed to minimise.

Because shot noise grows as the square root of the signal, it dominates in bright light and read noise dominates in dim light. That single fact explains why scientific cameras are specified the way they are, and why the three architectures below divide the work between them.

CCD

A charge-coupled device shifts the charge packet from pixel to pixel across the chip to a single readout node, where one amplifier converts every pixel in turn^[1]. One amplifier for the whole sensor is what makes a CCD so uniform — there is no pixel-to-pixel variation in gain or offset to calibrate, because every pixel is measured by the same electronics. Back-thinned devices, illuminated from the rear so light does not cross the wiring layers, reach a quantum efficiency around 95% near 550 nm^[1]. The cost is speed: serialising millions of pixels through one amplifier is slow, and reading faster raises the read noise.

EMCCD

The electron-multiplying CCD, introduced around 2001, attacks read noise by amplifying the signal before it reaches the amplifier. Charge is clocked through a long multiplication register — 536 elements in the e2v CCD97 — where a high voltage gives each transfer a small probability of impact ionisation, so the packet grows geometrically^[1]. With 30 electrons of read noise and a gain of 100, the noise referred back to the input is 0.3 electrons.

The catch is that multiplication is itself stochastic. Each electron either does or does not multiply at each stage, and that randomness adds a noise contribution of its own — an excess noise factor of √2, conventionally handled by treating the camera as though its quantum efficiency were halved^[1]^[3]. A 95% QE back-illuminated EMCCD is therefore quoted with an effective QE near 0.48 when it is run at high gain^[3]. It buys the ability to count almost nothing at the price of counting everything else less well.

sCMOS

Scientific CMOS reverses the CCD's arrangement: each pixel carries its own amplifier, and each column its own analogue-to-digital converter, so millions of pixels are converted in parallel rather than in series^[1]. The technology arrived in 2009 from a consortium of Fairchild Imaging, Andor and PCO, combining properties that had not previously coexisted — read noise near one electron, quantum efficiency of 60–70% or more, high frame rate, high resolution and wide dynamic range at once^[2].

A current sensor reads about 5 megapixels at 100 frames per second with an effective read noise around one electron and a peak QE of 82%, linear across almost four orders of magnitude^[1]. Read noise is not even uniform: on a measured sCMOS sensor the median is around 0.9 electrons, and more than half the pixels contribute either one noise electron or none in a given frame^[2]. The price of per-pixel amplifiers is that every pixel has its own gain, offset and dark current, so a scientific camera ships with a per-pixel calibration applied in firmware — which is a large part of what separates a scientific sensor from the same silicon sold as an industrial one^[3].

Which one wins

Less obvious than the datasheets suggest. A controlled comparison that put an sCMOS, an EMCCD and an industry-grade CMOS camera on the two arms of one 50/50 beamsplitter — so all three saw the same photons frame by frame — found the sCMOS delivering 1.5× to 2.4× the signal-to-noise of the industrial CMOS, but the industrial CMOS slightly outperforming the EMCCD, by 1.2× to 1.4×, at the photon levels of fluorescence fluctuation imaging^[3]. The EMCCD's higher quantum efficiency could not compensate for the excess noise of its multiplication stage. EMCCDs remain the right answer where the photon count really is very low — spinning-disk confocal is the standard example^[1]^[3] — while sCMOS wins wherever field of view and speed matter, which is most of super-resolution and light-sheet imaging^[1].

The same comparison found one thing that no datasheet reports: the industrial camera introduced spurious correlations between neighbouring pixels, which the calibrated scientific sensors did not^[3]. For any method that reads correlations rather than intensities, that is disqualifying regardless of how good the SNR looks.

Full well capacity and bit depth

Two numbers set the range of a scientific camera, and they are routinely confused with each other.

The full well capacity is a property of the silicon: the maximum number of charge carriers a pixel can hold before it overflows^[2]. Fill it and the pixel saturates — further photons are simply not recorded, and on a CCD the excess charge can spill into neighbours as blooming. It scales with pixel area, which is one of the real reasons EMCCDs use large 16 µm pixels where sCMOS uses 6.5 µm^[1]^[3]. Typical sCMOS sensors hold around 30 000 electrons^[2].

Divide that ceiling by the smallest signal the camera can distinguish — its read noise — and you have the dynamic range, the ratio of the brightest to the faintest thing measurable in one exposure^[2].

\mathrm{DR} = \frac{N_{\text{well}}}{\sigma_{\text{read}}} \qquad\Longrightarrow\qquad N_{\text{bits}} \ge \log_{2}\mathrm{DR}

Intra-scene dynamic range, and the number of bits an ADC needs before it stops being the limiting element. Published sCMOS figures run from about 1:5000 to 1:33 000.

Bit depth is a property of the electronics, not the silicon: how many discrete levels the converter divides the signal into. It does not create dynamic range, it only decides whether the sensor's own range survives digitisation. The link between the two is the gain, in electrons per count.

Take a sensor holding 30 000 electrons with 1.1 electrons of read noise — a dynamic range near 27 000:1^[2]. Since log₂(27 000) ≈ 14.7, a 16-bit converter carries it comfortably, at about 0.46 electrons per count. A 12-bit converter has only 4096 levels, so each count is worth about 7.3 electrons: the quantisation step alone is now several times the read noise, and the low-light performance the sensor was built for has been discarded in the last stage of the chain. More bits than the dynamic range justifies is equally pointless — it digitises noise into finer and finer slices without adding information.

The engineering difficulty is that a fast converter with many bits is itself noisy. The solution now standard in sCMOS is to stop trying: each column carries two amplifier–converter pairs, one high-gain and low-noise for small signals, one low-gain and high-capacity for large ones, sampling every pixel simultaneously and reconstructing one image from both. Two 11-bit converters used this way contribute less noise than a single faster 16-bit converter would, while the combined output still spans a 16-bit range^[2].

One consequence catches people out, and it is a display problem rather than a camera one: 16-bit data has to be squeezed into the 8-bit range of an ordinary monitor before anyone can look at it, so choosing which part of the range to show is a decision the user has to make and can easily make badly^[2].

A related trap appears whenever two cameras are compared by swapping them onto the same port. If their pixel sizes differ, they are not seeing the same thing: a signal that filled one 12 µm pixel is divided among four 6 µm pixels, so the smaller-pixel camera reports a quarter of the signal per pixel and looks less sensitive than it is^[2]. A fair comparison matches the projected pixel size through the optics, which is exactly what the SOFI study did — it set each camera's tube lens so all three landed within 97–102 nm at the sample^[3].

Finally, most scientific cameras are monochrome by design, and deliberately so. A colour sensor puts a mosaic of filters over the pixels — the Bayer pattern gives half the pixels to green and a quarter each to red and blue — so each pixel measures only about a third of the spectrum and the missing values are interpolated, a step that introduces artefacts of its own and is usually accompanied by a deliberate blur filter to suppress them^[4]. For quantitative work, the wavelength is selected by a filter in front of an unfiltered sensor instead: every pixel then measures the same band, with no interpolation and no sampling artefacts. It is worth noting that this is also why silicon's response varies so strongly across the spectrum — short wavelengths are absorbed within a fraction of a micrometre of the surface while red and near-infrared light penetrates several micrometres before being absorbed, if it is absorbed at all^[4].

In OpticalSetup

The Camera measures a one-dimensional intensity profile across its sensor face. Its two geometric settings are the sensor height and the number of pixels that height is divided into; each ray that lands is deposited into the pixels its ray tube actually covers, rather than being counted at a single point, so a beam that falls between two pixel centres still contributes to both.

That is what makes the profile a measurement rather than a histogram of ray arrivals: the number under it is conserved, and a beam clipped by an aperture upstream reports exactly the fraction that survived. The reading is reported as Σw, a fraction of one source's emitted power, and a linked Detector screen draws the profile.

When the interference option is on, the camera resolves fringes formed by a sized monochromatic CW laser whose routes recombine with a modelled carrier phase — the two ports of an interferometer come out complementary, and a phase object in one arm writes a real pattern across the pixels. Where a route's phase cannot be reconstructed, the camera falls back to depositing intensity conservatively rather than inventing a fringe, and says so in its reading.

Profile height can track the reading absolutely, so a port carrying a tenth of the light draws a tenth as tall, or auto-fit to its own peak when only the shape matters.

Simplified vs. reality

This is a geometric intensity model, not a sensor model. Nothing above about noise, sensitivity or dynamic range is simulated: there is no quantum efficiency, so every ray is detected with equal weight at every wavelength; no read noise, dark current, or shot noise, so repeating an exposure gives an identical answer; and no full well capacity, so a pixel never saturates, never blooms, and responds linearly without limit. There is no bit depth either — readings are continuous numbers, never quantised into counts — which means none of the full-well-versus-gain reasoning above can be demonstrated here.

The sensor is one-dimensional, matching the tracer's 2D meridional plane, so there is no second transverse axis and no image in the ordinary sense: a “camera image” here is a line profile, not a picture. It is monochrome with no colour filter array, has no exposure time, no frame rate, and no shutter — global or rolling — so the rolling-shutter distortions and synchronisation problems that dominate real fast imaging cannot appear. Pixels are perfectly uniform, with no per-pixel gain or offset variation, no hot or blinking pixels, and no inter-pixel crosstalk, which is precisely the set of imperfections that separates camera technologies from one another in practice.