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302 DIGITAL IMAGE PROCESSING
• For microscope images where the visibility of an extended object is of interest, the
S/N ratio can be calculated based on dozens or even hundreds of pixels and not on
a per pixel basis. In this case, an object covering a large patch of pixels can have an
S/N value that is hundreds of times larger than the S/N of an individual pixel. For-
mulas for determining the S/N of extended objects are given in this chapter.
The fundamental principles are described in a series of excellent articles by New-
berry (1991, 1994a,b, 1995a,b,c) and at the Web sites of CCD camera manufacturers.
S/N and the Precision of Numeric Values
One valuable benefit of S/N analysis is that you can state the confidence limits (in units
of standard deviations) that a signal stands out from the noise of the background. This
calculation is possible because S/N is the ratio of the object signal to the standard devi-
ation of the background signal, and because standard deviations are directly related to
-values and percent confidence. Consider an image with an object signal of 100 elec-
trons and a noise of 100 10 e , giving an S/N ratio of 10. The inverse of this value,
N/S 0.1, is called the relative error—that is, the fractional component of the signal
that is noise. For our example, we would say that noise is 0.1 or 10% of the signal. Since
photon noise is the same as the standard deviation (SD) of the photon signal, we can say
that fluctuations in the signal greater than 10% can be detected at a confidence level of
68% (1 SD). Extending this further, by multiplying by 2 for 2 standard deviations, we
would say that fluctuations in the signal 20% are detected at the 95% confidence level
(2 SD), and so on. Another way of interpreting this is to say that given a relative error of
0.1, we can say we detect a signal at 10% precision, or that our ability to measure the
signal precisely is no better than 10%. The ability to set confidence limits has profound
implications, because it allows the investigator to calculate in advance how many elec-
trons (and therefore how many ADUs and what exposure time) are required to visualize
fluctuations of a certain percent at a specified confidence level.
In summary, given S/N 10, taking (1/S/N) 2 SD 100 20%, we say that
fluctuations 20% are detected at the 95% confidence level.
Correlation of S/N with Image Quality
The relationships between S/N, % fluctuations detected at 95% confidence, and image
quality are given in Table 15-1. An object image with S/N 10–20 is poor and grainy-
looking, whereas the appearance of the same object at S/N 100 is good to excellent.
Effect of the Background Signal on S/N
In microscopy, the background signal can be large, sometimes 90% of the total signal
representing an object. Figure 11-10 demonstrates the significance of the background
signal in an immunofluorescence image. In most cases, photon noise from the back-
ground is the major source of noise, not the read noise of the camera. Thus, the S/N
equation includes a term for the background noise as will be recognized in the follow-
ing sections. As seen in Table 15-2, a high background signal reduces S/N considerably.