science

Kell factor

Kell factor is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Kell factor rather than just read about it. In short: The Kell factor, named after RCA engineer Raymond D. Kell, is a parameter used to limit the bandwidth of a sampled image signal to avoid the appearance of beat frequency patterns when displaying the image in a distinct display device, usually taken to be 0.7.

Key takeaways

Kell factor belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Kell factor to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Kell factor from memory before moving on to harder problems.

Reference excerpt

The Kell factor, named after RCA engineer Raymond D. Kell, is a parameter used to limit the bandwidth of a sampled image signal to avoid the appearance of beat frequency patterns when displaying the image in a distinct display device, 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 dependent of the type of display. It was later revised to 0.85 but can go higher than 0.9, when fixed pixel scanning (e.g., CCD or CMOS) and fixed pixel displays (e.g., LCD or plasma) are used, or as low as 0.7 for electron gun scanning. From a different perspective, the Kell factor defines the effective resolution of a distinct 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 charged coupled devices, the distribution is somewhat rectangular, and is also affected by the sampling grid and inter-pixel spacing. 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 (i.e., blurred) in the vertical dimension to avoid spatio-temporal aliasing (i.e., flickering effects), the Kell factor of interlaced video is said to be about 70% that of progressive video with the same scan line resolution.

The beat frequency problem To understand how the distortion comes about, 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 factor is the reduction necessary in signal bandwidth such that no beat frequency is perceived by the viewer.

Examples A 625-line analog (e.g., 50 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 0.7×576 = 403.2 lines of resolution. 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 576i at 50 Hz, 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 pixels per line. Taken further, since 537.6 pixels is equal to a maximum of 268.8 cycles for an alternating pixel pattern, and given 576i 50 Hz has an active line period of 52 μs, its luminance signal requires a bandwidth of 268.8/52 = 5.17 MHz. Kell factor applies equally to digital devices. Using a Kell factor of 0.9, a 1080p HDTV video system using a CCD camera and an LCD or plasma display will only have 1728×972 lines of resolution.

History

See also Aliasing Moiré pattern Optical resolution Resel

References

M. Robin, "Revisiting Kell", Broadcast Engineering, May 2003. S. Mullen, "Just What is 1080?", HDV@Work, Feb. 2006. J. Amanatides, "Antialiasing of Interlaced Video Animation", SIGGRAPH 90. G. Tonge, "The Television Scanning Process", SMPTE Journal, July 1984 pg 657 Kell factor explained in simple terms

Illustrations

Kell factor: At 0.5 cycles/pixel, the Nyquist limit, signal amplitude depends on phase, as visible by the three medium-gray curves where the signal goes 90° out of phase with the pixels. — At 0.5 cycles/pixel, the Nyquist limit, signal amplitude depends on phase, as visible by the three medium-gray curves where the signal goes 90° out of phase with the pixels.

Kell factor: At 0.33 cycles/pixel, 0.66 times the Nyquist limit, amplitude can largely be maintained regardless of phase. Some artifacts are still visible, but minor. — At 0.33 cycles/pixel, 0.66 times the Nyquist limit, amplitude can largely be maintained regardless of phase. Some artifacts are still visible, but minor.

Worked examples

Example 1 — a first encounter with Kell factor

Start with the simplest possible case. Write down what Kell factor claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Kell factor before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Kell factor ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Kell factor

In research: Kell factor appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Kell factor in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Kell factor is common in secondary-school and first-year university syllabi. It links to neighbouring topics Television technology, so understanding it makes those chapters shorter.
In everyday life: Look for Kell factor outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Kell factor in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Kell factor means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Kell factor out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Kell factor in simple terms?

Why does Kell factor matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Kell factor?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Kell factor.