7.2 Noise and Uncertainty in CCD and CMOS
81
The read process cannot be 100%, efficient and some loss during the transfer
process can be expected. The rate of loss is known as the charge transfer efficiency
(CTE). It affects the pixel diagonally opposite the read pixel the most and the read
pixel the least. Consequently, the CTE results in a gradient appearing across the
frame increasing outwards from the read pixel. For example, in a 512 by 512 array,
the last pixel will go through 1,024 read cycles during a full-frame transfer. If the
CTE is 0.999999, then the last pixel read will have lost about 0.1% of its electrons
to CTE. The design of CMOS chips prevents them from being affected by CTE loss
to the same extent as a CCD-based camera.
The process of reading the frame itself introduces errors. Using the read electronics
in the system will have a tendency to add electrons to the system. This problem is
exacerbated if you increase the transfer rate and also due to errors within the ADU
itself. These errors, known as readout noise, are largely, but not entirely, dealt with
by the subtraction of the bias calibration frame discussed in Sect. 7.5. Because CCDs
use only one ADU, in contrast to CMOS chips, which use multiple ADUs, the read
noise associated with the ADU is higher in CMOS-based cameras than in CCD-based
ones because of variation in performance between the individual ADU processors
in the CMOS. However, in general, ADU noise in both CCD- and CMOS-based
cameras is low.
When we apply the gain to the electron count, we will in most cases get a noninteger number. However, as previously mentioned, the ADU is integer-only, so fractions
are lost, either by a rounder processor or by just being truncated, so that at best, the
ADU will report the count with an uncertainty of ±1, unless of course, the gain
is one. This is known as digitisation noise. Compared to other sources of noise,
digitisation noise is not that significant. However, both the pixels and the ADU tend
to have a nonlinear response as they approach their limit, just as photographic film
becomes nonlinear. Nonlinearity is a major problem in imaging, as a pixel whose
count is in the nonlinear range is effectively useless for most scientific uses. Nor
is it immediately apparent whether a pixel is in the nonlinear range without first
identifying the nonlinear range and determining whether the pixel lies within it. In
Sect. 7.6 you will go through the process of identifying the nonlinear range for your
CCD or CMOS. When exposing the CCD or CMOS to light, a number of thermal
electrons leak into the pixels. These cannot be distinguished from those liberated by
the interaction with a photon and can become a considerable component of the noise.
This dark current is both temperature- and exposure-time-dependent and takes the
form of a Poisson distribution, which we discuss in more detail in Chap. 5. The dark
current should increase linearly with exposure time; hence if you are undertaking
a long exposure of a faint object, the dark current may become very significant if
left unaddressed. Likewise, an uncooled camera will have a significantly larger dark
current than a cooled one. One of the most common reasons for bad image quality is
either the failure to run the cooler or failing to deal with the dark current by applying
a calibration frame, as discussed in detail in Sect. 7.5.
The last source of noise we will discuss that is directly, although not wholly,
associated with the CCD or CMOS is flat field noise. In an ideal setup, the amount of
light falling on the CCD or CMOS and the response to that light should be uniform,
81
The read process cannot be 100%, efficient and some loss during the transfer
process can be expected. The rate of loss is known as the charge transfer efficiency
(CTE). It affects the pixel diagonally opposite the read pixel the most and the read
pixel the least. Consequently, the CTE results in a gradient appearing across the
frame increasing outwards from the read pixel. For example, in a 512 by 512 array,
the last pixel will go through 1,024 read cycles during a full-frame transfer. If the
CTE is 0.999999, then the last pixel read will have lost about 0.1% of its electrons
to CTE. The design of CMOS chips prevents them from being affected by CTE loss
to the same extent as a CCD-based camera.
The process of reading the frame itself introduces errors. Using the read electronics
in the system will have a tendency to add electrons to the system. This problem is
exacerbated if you increase the transfer rate and also due to errors within the ADU
itself. These errors, known as readout noise, are largely, but not entirely, dealt with
by the subtraction of the bias calibration frame discussed in Sect. 7.5. Because CCDs
use only one ADU, in contrast to CMOS chips, which use multiple ADUs, the read
noise associated with the ADU is higher in CMOS-based cameras than in CCD-based
ones because of variation in performance between the individual ADU processors
in the CMOS. However, in general, ADU noise in both CCD- and CMOS-based
cameras is low.
When we apply the gain to the electron count, we will in most cases get a noninteger number. However, as previously mentioned, the ADU is integer-only, so fractions
are lost, either by a rounder processor or by just being truncated, so that at best, the
ADU will report the count with an uncertainty of ±1, unless of course, the gain
is one. This is known as digitisation noise. Compared to other sources of noise,
digitisation noise is not that significant. However, both the pixels and the ADU tend
to have a nonlinear response as they approach their limit, just as photographic film
becomes nonlinear. Nonlinearity is a major problem in imaging, as a pixel whose
count is in the nonlinear range is effectively useless for most scientific uses. Nor
is it immediately apparent whether a pixel is in the nonlinear range without first
identifying the nonlinear range and determining whether the pixel lies within it. In
Sect. 7.6 you will go through the process of identifying the nonlinear range for your
CCD or CMOS. When exposing the CCD or CMOS to light, a number of thermal
electrons leak into the pixels. These cannot be distinguished from those liberated by
the interaction with a photon and can become a considerable component of the noise.
This dark current is both temperature- and exposure-time-dependent and takes the
form of a Poisson distribution, which we discuss in more detail in Chap. 5. The dark
current should increase linearly with exposure time; hence if you are undertaking
a long exposure of a faint object, the dark current may become very significant if
left unaddressed. Likewise, an uncooled camera will have a significantly larger dark
current than a cooled one. One of the most common reasons for bad image quality is
either the failure to run the cooler or failing to deal with the dark current by applying
a calibration frame, as discussed in detail in Sect. 7.5.
The last source of noise we will discuss that is directly, although not wholly,
associated with the CCD or CMOS is flat field noise. In an ideal setup, the amount of
light falling on the CCD or CMOS and the response to that light should be uniform,