The fundamental concepts of image evaluation were established for film-based systems in the 1940s. In the 1970s, the introduction of discrete element detector arrays and the advent of digital computers capable of performing complex Fourier computations improved upon these concepts and popularized the field of digital image processing. Despite the widespread use charge-coupled-devices (CCDs) and of digital signal processing (DSP), knowledge of the underlying factors contributing to image quality from the CCD detector array is lacking. Despite the wide spread use of the terms MTF, CTF, limiting resolution, minimum resolvable target, and contrast to describe CCD image system quality, the terms are often misused and their relations are little understood. In fact, the concepts of image evaluation, indispensable for system implementation and signal analysis, seem to be slipping away from engineers and scientist practicing in the field. The following paper, discusses the concepts relating to image quality, and relates the commonly used parameters for image system characterization.

The term line spread function (LSF) is used to describe the size and intensity distribution of a distant slit source.

The modulation transfer function (MTF) is a Fourier transform of the line spread function i.e. its equivalent as an integral sum of sine waves taken over the whole range of spatial frequencies. MTF by its Fourier nature can only be used to operate on sinusoidal frequencies. Fourier mathematical analysis assumes that any function, representing an intensity profile of a target, can be analyzed into a series of component sine waves of different frequencies and into different phase relationships. Use of the MTF in the characterization of an imaging system, requires first a Fourier transform of the object into its spectrum then multiplication of the object spectrum by the system MTF, followed by an inverse Fourier transform to obtain the modified profile of the image.

Although the simplicity of the sine-wave representation used in MTF analysis makes it attractive for image characterization, there are relatively few examples of sinusoids in natural image scenes. Due to its more complex characteristics, a square wave response (CTF) is more popular as it better resembles complex target images.

The analysis is one dimensional, i.e. the variation is occurring at right angels to the bars. For the purposes of analysis it is assumed that the bar pattern continues infinitely in both directions. If the period of the square wave is 1/k, it can be synthesized from as series of sine waves having frequencies k, 3k, 5k, 7k, 9k, etc. the corresponding amplitudes being 1, 1/3, 1/5, 1/7, 1/9, etc. respectively. In principle the series is continued infinitely. The fundamental has a relative amplitude 4/p when the amplitude of the complete square wave is unity.

Figure 3 shows that the frequency spectrum of the single bar turns out to be the familiar function sin(p ax/p ax) . If we designate the frequency rage out to the first zero as the bandwidth, we see that the bandwidth in the frequency domain is inversely proportional to the bandwidth in the spatial domain.

In the limit, the single bar turns into an infinitesimally narrow single pulse, a delta function, whose spectrum extends at a uniform level over all frequencies. It is interesting that because the impulse function has no fundamental frequency there is no fundamental frequency band that must be reproduced if the bar is to be recognized.

The wide spectral bandwidth of the delta function provides an explanation for the appearance of objects whose spatial length is shorter than the resolution limit. Any MTF, which allows for a significant fraction of the total energy in the bandwidth to pass, will permit an image to be recorded.

The edge spread function (ESF), the point spread function (PSF), and the line spread functions (LSF) define the performance of the imaging system in terms if an isolated patch of luminance of negligible size. The spatial and frequency domain representations of an edge function are shown in Figure 3a. The luminance is constant, e.g. zero, over a finite distance, suddenly rises to a finite value for a very small distance, then as suddenly collapses again to the original level. In the limit the luminance rises to an infinite value of an infinitely short distance. If the luminance does not collapse but continues indefinitely at the new level , we have a step function or ideal edge object (Figure 3b). The image is thus the edge spread function The relationship between the line spread function and the edge spread function can be visualized from the graphical reconstruction shown in Figure 2. The discontinuities of the ideal edge or step function occurs at a distance x₀. To the left of x₀ there is zero intensity to the right finite uniform intensity. We imagine the area of spatially finite luminance to be made up of an infinite number of elementary lines at right angels to the paper. The images of these form a series of line spread functions. The first line spread function is centered at xo, the intensities from all of the spread function add up to the same total at any value of x. .

Considering the spectrum of a single bar shows that care should be used in mentally equating size to frequency. A small size is not a high frequency, even though the period corresponding to a high frequency is a small distance. As was shown in the case of the delta function of Figure 3a, a small object certainly has a wide bandwidth, and its adequate reproduction calls for an MTF extending to high frequencies, but good frequency response at the expense of low frequency response is valueless; the full frequency response is necessary for proper reproduction. As this is not possible, the low frequencies should not be sacrificed as they carry the contrast by which the object is seen.

Another consideration that must be taken into account when analyzing high frequency images, is that the negative lobes of the square wave spectrum can account for the phase reversal that can be seen in high contrast images and can lead to improper characterization.