Mathematics of television technology
The mathematics of television technology encompasses the principles and calculations behind capturing, transmitting, and displaying visual and auditory information through electronic systems. Television, a relatively recent innovation, has evolved from initial electromechanical systems, like the Nipkow disk, to contemporary electronic technologies such as cathode ray tubes (CRT), liquid crystal displays (LCD), and plasma screens. The process of converting images involves disassembling them into discrete parts that are transmitted separately and then reassembled at the receiver, where they create the illusion of continuous motion.
Aspect ratios, which define the width-to-height relationship of images, have mathematical roots; the 16:9 aspect ratio, established by Kerns H. Powers in 1980, serves as today's standard for high-definition television. Additionally, capturing images effectively on film has led to the development of various anamorphic lenses that correct geometric distortions through mathematical designs. The transition to high-definition systems brought about a shift from CRT technology, where images were produced by controlling electron beams, to LCD and plasma technologies, which rely on manipulating light through pixels. Each of these advancements illustrates the critical role that mathematical principles play in the ongoing development of television technology, influencing how images and sounds are recorded and experienced by audiences.
Mathematics of television technology
Summary: Innovations in television technology rely upon a sophisticated use of mathematics, physics, and engineering.
Humans process reality by initially recording light and sound waves through the eyes and ears and then transmitting these data to the brain where they are transformed and synthesized into intelligible matter. In a similar manner, the engineering challenge of television from its conception has been to record data, transmit them (via electricity), and then reconstitute them at a physical distance from its origin. Television is a relatively recent invention. The first appearance of the word (a combination of Greek and Latin words, meaning “far-seeing”) occurred in 1900 at the International Electricity Congress at the Paris Exhibition. It was not one single person who invented television, but a number of scientists, engineers, and visionaries working independently in different countries who devised the necessary technology and mathematics. Television has changed dramatically from its first appearance as an electromechanical system to electronic systems, including cathode ray tube (CRT), liquid crystal display (LCD), plasma, and three-dimensional (3D) television.
Image Scanning and Aspect Ratio
Scanning the image required it to be disassembled into discrete pieces of picture that could then be transmitted separately and reassembled as a sequence of images on a screen, with each image recomposed from those smaller pieces of the picture. If the sequence of images could be displayed on the receiver’s end rapidly enough, they would appear to the human eye as a continuous whole of moving images. This approach makes use of the fact that the human eye can distinguish two parallel lines only if they are about one-thirtieth of a degree apart and will blend 12 images per second into a moving whole. In the 1920s, the transmission of images went from an unacceptably choppy five per second to 12.5 and more.
The earliest scanning mechanism is known as the “Nipkow disk,” named for the German physicist Paul Nipkow, and versions and refinements of this were used as late as the 1930s. It consisted of a disk with a spiral of small holes in it and a photosensitive cell made of selenium on the other side of the plate from the image. One revolution of the disk corresponded to one complete image, with the holes as they rotated capturing the image in a series of lines. The number of such lines depended on the number of holes, which thus determined the degree of resolution of the image. A second disk was then rotated at the receiving end, playing back the captured image. One drawback of the Nipkow disk was that the scanned lines were not linear, which changed the geometry.
Historians debate why Thomas Edison chose to represent the geometry of television using the rectangular 4:3 aspect ratio, which indicates the ratio of the width to the height of the image. Some hypothesize that Edison chose this because the ratio approximates the golden mean while others assert that his motivation was to save money by cutting 70 mm film stock in half. The Society of Motion Picture Engineers adopted this ratio in 1917 and it was standard for many years. The international standard for high-definition television was devised mathematically in 1980 by electrical engineer Kerns H. Powers. Powers analyzed the common aspect ratios in use at the time and normalized them to a constant area to fit them in a rectangle. When overlapped via their centers, they shared a common inner rectangle. He computed the geometric mean to obtain the 16:9 aspect ratio that continues to be the standard for televisions in the twenty-first century.
A uniform aspect ratio for television created another problem of how to capture the ratio on 35 mm film. Mathematical principles were used to develop lenses that were “anamorphic,” which stemmed from the Greek words meaning “formed again.” Ultra Panavision used counter-rotated prisms, Technirama used curved mirrors and reflection principles, and CinemaScope used a cylindrical lens. However, the lenses created distortion problems as compared to spherical lenses. In the twenty-first century, mathematics continues to play a role in anamorphic widescreen processes.
CRT Television
While electromechanical televisions such as the Nipkow disk were being developed, an electronic alternative that used a CRT rather than mechanical parts was also being explored. Philo Farnsworth and Vladimir Zworykin, among others, worked independently on this technology in the United States in the late 1920s. The diameter of the round picture tube, which was also the diagonal of the rectangular cover, was the critical parameter. Televisions are still measured on the diagonal in the twenty-first century.
The innovation involved harnessing electrical properties of matter. At the receiving end is a CRT—a glass vacuum tube, which receives the incoming transmitted signal that represents the picture, known as the “video signal” (audio and visual components are transmitted separately). At one end of the CRT is a cathode, which is heated so that it will radiate electrons (negatively charged particles) that are then attracted along the circuit to the other end of the tube (called the “anode end”), which is at positive electric potential for this purpose. This beam of electrons is focused electrically by charged plates and can be delicately manipulated by interactions with a magnetic field produced by electric current passing through coils.
At this end of the tube is a photosensitive phosphor-coated screen, which has the property of responding to the beam of electrons by emitting light that is proportional in intensity, point for point, to the beam that is moved across it. The video signal is synchronized with the electron beam so that the variations in the beam relay image information. The beam moves line-by-line, lighting the phosphor that illuminates the screen on which the image is viewed. Color images necessitate a more complicated technology than black-and-white images: three signals, one for each of the primary colors (red, green, and blue) and three electron beams are exploited to produce color images.
LCD and Plasma
CRT television was standard through the 1980s but the line-by-line sweeping of the electron beam across the screen takes time and faster technology is available on high-definition television (HDTV), which depends on either an LCD or a plasma screen. The image received via these newer technologies is still comprised of small units, called “pixels” (an abbreviation of “picture elements”), but these operate differently. In an LCD system, each pixel is deployed by an electrically stimulated liquid crystal, which undergoes internal molecular rearrangement in such a way as to polarize (filter) light that is shone from the back. Intensity of light is adjusted by a blocking procedure similar to sunglasses. In a plasma screen, however, each pixel functions like a miniature fluorescent light, since it contains a mixture of gases and mercury that respond to electric charge by radiating energy that in turn causes phosphor on a screen to emit light.
Bibliography
Abramson, Albert. The History of Television, 1880–1941. Jefferson, NC: McFarland & Company, 1987.
———. The History of Television, 1942–2000. Jefferson, NC: McFarland & Company, 2003.
Noll, A. Michael. Television Technology: Fundamentals and Future Prospects. Norwood, MA: Artech House, 1988.
Todorovic, Aleksandar Louis. Television Technology Demystified: A Non-Technical Guide. Philadelphia: Elsevier, 2006.