Kell factor: Difference between revisions

{{Citations missingRefimprove|date=March 2007}}

The '''Kell Factorfactor''', named after [[RCA]] engineer [[Raymond D. Kell]],<ref name=":0">{{Cite journal |last1=Kell |last2=Bedford |last3=Fredendall |date=July 1940 |title=A Determination Of Optimum Number Of Lines In A Television System |journal=RCA Review |volume=5 |issue=1 |pages=8–30}}</ref> is a parameter used to limit the bandwidth of a sampled image signal as to avoid the appearance of [[beat frequency]] patterns to appear when displaying the image in a discrete display devicesdevice, usually taken to be 0.7. The number was first measured in 1934 by Raymond D. Kell and his associates as 0.64 but has suffered several revisions given that it is based on image perception, hence subjective, and is not independent of the type of display.<ref name=":1">{{Cite journal |last1=Kell |first1=R. D. |last2=Bedford |first2=A.V. |last3=Trainer |first3=M. A. |date=November 1934 |title=An Experimental Television System |url= |journal=Proceedings of the Institute of Radio Engineers |volume=22 |issue=11 |pages=1246}}</ref> It was later revised to 0.85 but can go higher than 0.9, when fixed pixel scanning (e.g., [[charge-coupled device|CCD]] or [[Active pixel sensor|CMOS]]) and [[fixed pixel display]]s (e.g., [[liquid crystal display|LCD]] or [[plasma display|plasma]]) are used, or as low as 0.7 for [[electron gun]] scanning.

From a different perspective, the Kell Factorfactor defines the effective [[image resolution|resolution]] of a discrete display device since the full resolution cannot be used without viewing experience degradation. The actual sampled resolution will depend on the spot size and intensity distribution. For [[electron gun]] scanning systems, the spot usually has a Gaussian intensity distribution. For CCDs, the distribution is somewhat rectangular, and is also affected by the sampling grid and inter-pixel spacing.

To understand how the distortion comes about, let us consider an ideal linear process from sampling to display. When a signal is sampled at a frequency that is at least double the [[Nyquist frequency]], it can be fully reconstructed by low-pass filtering since the first repeat spectra does not overlap the original baseband spectra. In discrete displays the image signal is not low-pass filtered since the display takes discrete values as input, i.e. the signal displayed contains all the repeat spectra. The proximity of the highest frequency of the baseband signal to the lowest frequency of the first repeat spectra induces the [[beat frequency]] pattern. The pattern seen on screen can at times be similar to a [[Moiré pattern]]. The Kell Factorfactor is the reduction necessary in signal bandwidth so that the distance between both frequencies is sosuch that no beat frequency is perceived by the viewer.

* A 625-line analogueanalog (e.g., 50Hz50&nbsp;Hz [[PAL]]) television picture is divided into 576 visible lines from top to bottom. Suppose a card featuring horizontal black and white stripes is placed in front of the camera. The effective vertical resolution of the TV system is equal to the largest number of stripes that can be within the picture height and appear as individual stripes. Since it is unlikely the stripes will line up perfectly with the lines on the camera's sensor, the number is slightly less than 576. Using a Kell factor of 0.7, the number can be determined to be 0.7&times;5767×576 = 403.2 lines of resolution.