The Kell Factor

In
a practical scanning system, the maximum vertical resolution obtainable is less
than the active number of lines available for scanning. This is because of the
finite beam size and its alignment not coinciding with the elementary
resolution lines.

Consider a finite size of a beam spot scanning a series of
closely spaced horizontal black and white lines of minimum resolvable
thickness, when the beam spot is nearly as much in size as the thickness of the
line as shown in figure 1 below.

If
the beam is in perfect alignment, the output will be exactly the lines as black
or white levels as shown in figure 1 above. If however, the beam spot is
shifted slightly and happens to align on the junction of the black and white
lines, it actually senses both black and white areas simultaneously. Hence it
integrates the effects of both areas to give a resultant gray level output in
between the black and white levels. This happens for all scanning positions and
the output as well as the reproduced picture will be a continuous gray without
any vertical resolution at all. In positions of intermediate alignment of the
beam, it will be more on one line than on the adjacent one and the output lines
will be reproduced with diminished contrast.
This
indicates that there is degradation in vertical resolution due to finite beam
size. Statistical analysis as well as subjective tests based on a bar pattern
consisting of tapered wedges of almost horizontal, converging, alternate black
and white bars, have indicated that the average number of effective line is of
the order of 0.7 times the total active scan lines present. This factor
indicating the reduction in effective number of lines is called ‘Kell Factor’.
It is obviously not a precisely determine quantity, and values from 0.64 to
0.85 are ascribed to it.

What
the Kell factor indicates is that it is unrealistic to state that the vertical
resolution is equal to the number of active lines. In a picture, not all lines
or parts of lines are fully effective at all times. The number of active lines
multiplied by the Kell factor leads to a smaller figure used in the assessment
of available vertical resolution. In the 625-line system, the number of active
line left after deducting lines lost in vertical beam are (625-40) = 585 lines.
With a Kell factor of 0.7, the vertical resolution is (0.7 x 585) = 409.5
lines. The horizontal may not exceed this value multiplied by aspect ratio.

 

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