Image Processing Reference
In-Depth Information
SN S
=
(3.12)
It should be noted that the signal charge quantity increases in proportion to the optical
intensity, but noise also increases in proportion to the square root of the signal. Thus, the
SNR increase is not in direct proportion, but is in proportion, to the square root of the
intensity in brighter scenes where the leading noise is optical shot noise.
Dark current shot noise, which is caused by the random generation of thermally excited
electrons, also obeys the Poisson distribution. The relationship between the expected
value and dispersion is the same as that with optical shot noise.
An example of the illuminance dependence of a signal and noise electron number of
a pixel is shown in Figure 3.8. The signal increases in proportion to the illuminance.
Dark noise is the summation of noise independent of the illuminance, such as read
noise. As shown, shot noise increases in proportion to the square root of illuminance.
Overall, noise is the summation of all noise, as shown in Equation 3.5. The SNR is
expressed as the logarithmic expression of the ratio of signal to noise in units of deci-
bels as follows:
(
)
SNR =
20 log
SN
(3.13)
The dynamic range is defined as the logarithmic expression of the ratio of the signal
to dark noise in units of decibels as well as the SNR. But this definition is inadequate for
nonlinear sensor systems, because the signal is not proportional to illuminance. In such
cases, a different expression such as a logarithmic expression of the ratio of the maximum
illuminance at saturation to the minimum illuminance at SNR = 1 in units of decibels as
well as the SNR is required.
Because the noise electron number of recent image sensors is a few at most, the leading
noise is optical shot noise, except at low illuminance, which assumes control of the SNR
in most cases. It is necessary to realize a highly dynamic range of sensors to achieve truly
high-SNR cameras.
1.E+05
Dynamic range (illuminance ratio)
Saturation level
1.E+04
Signal
Dynamic range
(electron number ratio)
1.E+03
Overall noise
1.E+02
SNR
1.E+01
Dark noise
Optical shot noise
1.E+00
1.E-02
1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
Illuminance (lux)
FIGURE 3.8
Illuminance dependence of a signal and noise electron number.
