Kell factor

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Kell factor is a parameter used to determine the effective resolution of a discrete display device. The number was first measured in 1934 by RCA engineer Raymond D. Kell and his associates. It has no fixed value, but is usually taken to be about 0.7, for electron gun scanning. Kell originally defined this as 0.64, and then later revised it to about 0.85. The number can be higher than 0.9, when fixed pixel scanning (e.g. CCD or CMOS) and fixed pixel displays (e.g. LCD or plasma) are used.

For example, a 625-line analogue (e.g., 50Hz 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 0.7×576 = 403.2 lines of resolution.

In addition, 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.

Kell factor can be used to determine the horizontal resolution that is required to match the vertical resolution attained by a given number of scan lines. For 576i50, given its 4:3 aspect ratio, the required horizontal resolution must be 4/3 times the effective vertical resolution, or (4/3)×0.7×576 = 537.6 lines of resolution. Taken further, since 537.6 lines is equal to 268.8 cycles, and given 576i50 has an active line period of 52µs, its luminance signal requires a bandwidth of 268.8/52 = 5.17 MHz.

Kell factor also applies to digital display devices. Using a Kell factor of 0.9, a 1080i HDTV using an LCD or plasma display will only have 1728×972 lines of resolution.

Kell factor is sometimes incorrectly stated to exist to account for the effects of interlacing. Interlacing itself does not affect Kell factor, but because interlaced video must be low-pass filtered in the vertical dimension to avoid spatio-temporal aliasing, the Kell factor of interlaced video is said to be about 70% that of progressive video with the same scan line resolution.