Page 316 - Fundamentals of Light Microscopy and Electronic Imaging

SIGNAL-TO-NOISE RATIO 299

magnitudes (amplitudes) and the other of phases. The relation of the image to its Fourier
transform is analogous to the relation of images in the image plane and diffraction plane
(back aperture of the objective lens) of the microscope. To review these concepts, refer
to Chapter 5. The FFT operation is performed in a high-resolution data type such as
floating point. Usually only the amplitude (or magnitude) plot is used for display,
manipulation and filtering. Most programs display the amplitude or power spectrum
with a log rather than a linear scale, since the transform is otherwise too dark to see any-
thing. Depending on the program, histogram stretching and scaling can be applied to
improve visibility of the amplitude plot without affecting the data. In a Fourier trans-
form:

• Frequency information is represented at different distances from the central point in
the magnitude image such that information from large structural features (low spa-
tial frequencies) is found near the center of the image, and information from small
features (high spatial frequencies) is located at some distance away from the center.
• Amplitudes seen along one axis in the magnitude plot are represented in the image
on an axis shifted by 90°.
• The amplitude at each location in the magnitude plot is proportional to the amount
of information at that frequency and orientation in the image.

On the computer, perform an FFT transformation and obtain a pair of amplitude
and phase plots. Next, apply an occluding spatial frequency mask over one of the plots
(the amplitude plot) to select low, midrange, or high spatial frequencies to block out
unwanted frequencies. The masked plots are then used to produce an inverse transform:
an image that is re-created based on frequencies not occluded by the mask. Both the
magnitude and phase plots are required for this operation. Processing images in the fre-
quency domain is useful for:

• Removing noise that occurs at specific frequencies (electrical interference, raster
scan lines)
• Enhancing or removing periodic structural features of the object
• Identifying spatial frequencies of defined structures in an image
• Determining the periodicity and/or orientation of indistinct features that are diffi-
cult to see in the object image
• Detecting optical aberrations such as astigmatism
• Applying convolution kernels to the magnitude plot for sharpening or blurring

SIGNAL-TO-NOISE RATIO

S/N is the ratio of a signal to the noise of the surrounding background from which the
signal must be distinguished. It is the accepted parameter for describing image quality.
As we shall see, S/N also has statistical meaning because it describes the confidence
level ( -value) at which an object of a certain intensity can be distinguished from the
background. In qualitative terms, S/N values are used to describe the visibility of an
object in an image. For reference, Figure 15-12 shows a test pattern of gray squares