High-performance industrial camera

I. Definition of Signal-to-Noise Ratio

In the imaging process of a camera, in addition to the real signal, a series of uncertainties will be introduced (such as the uncertainty of the optical signal itself, the thermal movement of materials, etc.), which are called noise. The signal-to-noise ratio refers to the ratio of the signal to the noise.

The signal-to-noise ratio of a camera can be calculated by the following formula:

$S N R = \frac{N \cdot Q E \cdot t}{\sqrt{N \cdot Q E \cdot t + I_{D} \cdot t + R^{2}}}$

Wherein:

The numerator in the formula is the "signal", and N is the number of incident photons per unit time;

t is the exposure time;

QE is the quantum efficiency (the ratio of photons converted into electric charges);

The denominator in the formula is the "noise", $\sqrt{N \cdot Q E \cdot t}$ ,It is the shot noise from the "real signal", namely photon shot noise (which is related to the intensity of the measured signal). $\sqrt{I_{D} \cdot t}$ ,It is the shot noise from dark current, namely dark shot noise (a thermal phenomenon caused by the spontaneous generation of charges in the silicon wafer, which is related to the temperature of the sensor).

R is the read noise.

Under specific shooting conditions, dark current and read noise are fixed. The stronger the signal, the greater its shot noise, which becomes the main source of noise; if the signal is very weak, the shot noise from the signal is small, and at this time, the influence of dark current and read noise cannot be ignored.

II. Factors Affecting Signal-to-Noise Ratio

Exposure Time

It can be seen from the signal-to-noise ratio formula that the longer the exposure time (t), the higher the signal-to-noise ratio. However, if the exposure time is too long, the frame rate cannot be guaranteed.

Pixel Size

Pixel size affects "N" in the signal-to-noise ratio formula. The larger the pixel size, the more photons fall on a single pixel. All other parameters being equal, the signal-to-noise ratio will be higher. However, excessively large pixel sizes can result in a loss of camera resolution.

Dark Current

Dark current (" $I_{D}$ " in the signal-to-noise ratio formula) stems from the thermal motion of electrons in the material. Therefore, the higher the temperature of the chip, the greater the dark current. Since dark current accumulates over exposure time, cooling becomes increasingly important in applications requiring longer exposure times.

Quantum Efficiency

Quantum efficiency ("QE" in the signal-to-noise ratio formula) is the proportion of photons that are converted into electrons at the camera's pixels. For example, if 100 photons fall on a pixel, a quantum efficiency of 80% means the camera can convert them into 80 electrons. The higher the quantum efficiency, the higher the signal-to-noise ratio of the camera.

Read Noise

When it comes to weak signal detection, the shot noise from the signal is relatively small. Moreover, in high-end scientific research cameras, dark shot noise can usually be ignored, so the read noise of the camera needs to be taken into account. For the same chip, the magnitude of read noise is related to the readout speed: the faster the readout speed, the higher the read noise.