The sensitivity of a camera is typically expressed in either the number of photons or in a measure of photon flux which can be related to human observations, called the Lux. A Lux is a measure of illumination which has a value of 1 lumen per square meter. The Lumen is a photometric equivalent of a watt which is weighted to match the eye response of the "standard observer".
The sensitivity of the human eye varies at different wavelengths and this has an implication of the number of photons equivalent to a given photometric quantity. The conversion to photons in the table above assumes the light is monochromatic yellowish green light with a wavelength of 555nm which is at the peak of the sensitivity of the human eye. For a given minimum sensitivity in lumens the number of photons varies, for example, see below a table showing the minimum light levels discernable by a typical human observer in the various measures.
Photons per second
Radiometric Measure Watts
Photometric Measure Lumens
The details of photometry (which takes in consideration the human perception of light intensity) versus radiometry which is the absolute measure of light intensity are covered in a later section.
If a given light signal induces a signal on the camera below the readout noise of the camera it cannot be detected so the total noise of the camera is a useful way to define the sensitivity of the camera.The noise measured by a digital camera comes from a number of sources which will be covered in detail in a later section.
Here we will concentrate predominately on the three main sources and they are: Sensor readout noise Thermal noise The noise from the signal itself: photon noise
The total camera noise is the sum, in quadrature, (i.e. the square root is taken of the sum of the various square of the noises) is calculated as shown here:
The readout noise is an inherent property of the sensor and except for EMCCD cameras, which will be covered in a later section, is usually the limit on sensitivity for most cameras. The readout noise is a combination of noise sources, which originate from the process of amplifying and converting the photoelectrons created into a voltage. Over the years readout noise has improved but fundamentally the faster the readout of the camera, the higher the noise due to the increasing bandwidth required. Low noise CCD’s in the past have typically employed very low readout speeds and hence they are often known as Slow Scan CCD's.
The second source of noise is the dark noise that arises from thermally generated charges in the silicon sensor. Recent improvements in CCD design have greatly diminished dark noise to negligible levels and reduced their contribution to total read-out noise to less than 10 electrons per pixel at room temperatures. For the ultimate sensitivity cooling the CCD to temperatures ~-100°C is still required.
Some room temperature cameras may have such a low dark signal that it can be ignored for integration periods of a second or less. Cooling further reduces the dark signal and permits much longer integration periods, up to several hours, without significant dark charge accumulation. The noise arising from the dark charge is given by Poisson statistics as the square root of the charge arising form the thermal effects, i.e.:
The incoming photons have an inherent noise ?signal known as photon Shot noise. If we consider the effects of a number of photons P which would generate in a pixel with QE DQE a signal of Ne electrons they will have a noise as defined by Poisson statistics shown here:
If we look at the chart above we can see the results of a practical example by calculating the sensitivity - and hence noise - of a DW436 camera for increasing exposure from 1 second to 1000 seconds when the camera is cooled to either –65°C or –25°C.
From Specification sheets we can see the Readout noise = 7.5e- @ 1MHz and the Dark Current at -65°C = 0.003 e-/pixel/second and at –25°C is 1e-/pixels/second.
As can be seen above the higher dark current at –25°C starts to increase the overall noise with exposures of 10 seconds or more. When cooled to –65°C the dark current has negligible effect for exposures less than 1,000 seconds.A note of caution: the noise calculated is an average and actual measurements will have peak-to-peak values typically 5 times higher than the average noise. In subsequent sections you will see that to detect a signal with a reasonably high level of confidence the signal must typically greater than the read noise squared!