Lowercase k for Kell factor is unrelated to K rating, sometimes called K factor, which I will describe on page 542; neither is related to 1000 or 1024.

Kell, Ray D., Alda V. Bedford, and

G.L. Fredendall (1940), “A determination of the optimum number of lines in a television system,” in RCA Review 5: 8–30 (July).

Hsu, Stephen C. (1986),“The Kell factor: past and present,” in SMPTE Journal 95 (2): 206–214 (Feb.).

Kell effect

Early television systems failed to deliver the maximum resolution that was to be expected from Nyquist’s work (which was introduced on page 78). In 1934, Kell published a paper quantifying the fraction of the maximum theoretical resolution achieved by RCA’s experimental television system. He called this fraction k; later – apparently without Kell’s consent! – it became known as the Kell factor (less desirably denoted K). Kell’s first paper gives a factor of 0.64, but he failed to completely describe his experimental method. A subsequent paper (in 1940) detailed the method, and gives a factor of 0.8, under somewhat different conditions.

Kell’s k factor was determined by subjective, not objective, criteria. If the system under test had a spot profile resembling a Gaussian, closely spaced lines on a test chart would cease to be resolved as their spacing diminished beyond a certain value. If a camera under test had an unusually small spot size, or a display had a sharp distribution (such as a box), then k was determined by the intrusion of objectionable artifacts as the spacing reduced – also a subjective criterion.

Kell and other authors published various theoretical derivations that justify various numerical factors; Hsu has published a comprehensive review. In my opinion, such numerical measures are so poorly defined and so unreliable that they are now useless. Hsu says:

Kell factor is defined so ambiguously that individual researchers have justifiably used different theoretical and experimental techniques to derive widely varying values of k.

Today I consider it poor science to quantify a numerical Kell factor. However, Ray Kell made an important contribution to television science, and I think it entirely fitting that we honour him with the Kell effect:

In a video system – including image capture, signal processing, transmission, and display – Kell effect refers to the loss of resolution, relative to the Nyquist limit, caused by the spatial dispersion of light power. Some dispersion is necessary to avoid aliasing upon capture; some dispersion is necessary to avoid objectionable scan line or pixel structure at a display.

Twitter is introduced on page 89.

Mitsuhashi, Tetsuo (1982), “Scanning specifications and picture quality,” in Fujio, Takashi, et al.,

High Definition Television, NHK Science and Technical Research Laboratories Tech. Monograph 32 (June).

Kell’s 1934 paper concerned only progressive scanning. With the emergence of interlaced systems, it became clear that twitter resulted from excessive vertical detail. To reduce twitter to tolerable levels, it was necessary to reduce vertical resolution to substantially below that of a well-designed progressive system having the same spot size – for a progressive system with a given k, an interlaced system having the same spot size had to have lower k. Many people have lumped this consideration into “Kell factor,” but researchers such as Mitsuhashi identify this reduction separately as an interlace factor or interlace coefficient.

Resolution

SD (at roughly 720× 480), HD at 1280× 720, and HD at 1920× 1080 all have different pixel counts. Image quality delivered by a particular number of pixels depends upon the nature of the image data (e.g., whether the data is raster-locked or Nyquist-filtered), and upon the nature of the display device (e.g., whether it has box or Gaussian reconstruction).

In computing, unfortunately, the term resolution has come to refer simply to the count of vertical and horizontal pixels in the pixel array, without regard for any overlap at capture, or overlap at display that may have reduced the amount of detail in the image. A system may be described as having “resolution” of 1152× 864 – this system has a total of about one million pixels (one megapixel, or 1 Mpx). Interpreted this way, “resolution” doesn’t depend upon whether individual pixels can be discerned (“resolved”) on the face of the display.

Resolution in a digital image system is bounded by the count of pixels across the image width and height. However, as picture detail increases in frequency, signal processing and optical effects cause response to diminish even within the bounds imposed by sampling. In video, we are concerned with resolution that is delivered to the viewer; we are also interested in limitations of frequency response (“bandwidth”) that may have been imposed in capture, recording, processing, and display. In video, resolution concerns the maximum number of line pairs (or cycles) that can be resolved on the display screen. This is a subjective criterion! Resolution is related to perceived sharpness.

MTF: Modulation transfer function

Lechner worked at RCA Labs in Princeton, New Jersey. Jackson worked at Philips Research Laboratories, Redhill, Surrey, U.K.; he is unrelated to my like-named colleague who worked at Grass Valley Group, now at AJA Video.

Closest viewing distance is constrained by pixel count; however, visibility of pixel or scan-line structure in an image depends upon many other factors such as camera MTF, spot profile (PSF), and frequency response. In principle, if any of these factors reduces the amount of detail in the image, the optimum viewing distance is pushed more distant. However, consumers have formed an expectation that SD is best viewed at about 7·PH; as people become familiar with HD they will form an expectation that it is best viewed at about 3·PH.

A countervailing argument is based upon the dimensions of consumers’ living rooms. In unpublished research, Bernie Lechner found that North American viewers tend to view SD receivers at about 9 ft. In similar experiments in England, Richard Jackson found a preference for 3 m. This viewing distance is sometimes called the Lechner distance – or in Europe, the Jackson distance! These numbers are consistent with Equation 9.2, on page 100 applied to an SD display with a 27-inch (70 cm) diagonal.

Rather than saying that improvements in bandwidth or spot profile enable decreased viewing distance, and therefore wider picture angle, we assume that viewing distance is fixed, and say that resolution is improved.

Interlace revisited

We can now revisit the parameters of interlaced scanning. With the luminance and surround conditions typical of consumer television receivers, a vertical scan rate of 50 or 60 Hz is sufficient to overcome flicker. As I mentioned on page 88, at practical vertical scan rates, it is possible to flash alternate image rows in alternate vertical scans without causing flicker. This is interlace. The scheme is possible owing to the fact that temporal sensitivity of the visual system decreases at high spatial frequencies.

Twitter is introduced, however, by vertical detail whose scale approaches the scan-line pitch. Twitter can be reduced to tolerable levels by reducing the vertical detail somewhat, to perhaps 0.7 times. On its own, this reduction in vertical detail would push the viewing distance back to 1.4 times that of progressive scanning.

However, to maintain the same sharpness as a progressive system at a given data capacity, all else being