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A monochrome monitor is a type of CRT computer display which was very common in the early days of computing, from the 1960s through the 1980s, before color monitors became popular. They are still widely used in applications such as computerized cash register systems. Green screen was the common name for a monochrome monitor using a green "P1" phosphor screen.
Unlike color monitors, which display text and graphics in multiple colors through the use of alternating-intensity red, green, and blue phosphors, monochrome monitors have only one color of phosphor (mono means "one", and chrome means "color"). All text and graphics are displayed in that color. Some monitors have the ability to vary the brightness of individual pixels, thereby creating the illusion of depth and color, exactly like a black-and-white television.
Monochrome monitors are commonly available in three colors: if the P1 phosphor is used, the screen is green monochrome. If the P3 phosphor is used, the screen is amber monochrome. If the P4 phosphor is used, the screen is white monochrome (known as "page white"); this is the same phosphor as used in early television sets. An amber screen was claimed to give improved ergonomics, specifically by reducing eye strain; this claim appears to have little scientific basis.
Well-known examples of early monochrome monitors are the VT100 from Digital Equipment Corporation, released in 1978, and the IBM 5151, which accompanied the IBM PC model 5150 upon its 1981 release. The 5151 was designed to work with the PC's Monochrome Display Adapter (MDA) text-only graphics card, but the third-party Hercules Graphics Card became a popular companion to the 5151 screen because of the Hercules' high-resolution bitmapped monochrome graphics capability, much used for business presentation graphics generated from spreadsheets like Lotus 1-2-3.
Pixel for pixel, monochrome monitors produce sharper text and images than color CRT monitors. This is because each pixel on a monochrome monitor is made up of one phosphor dot, located in the center of the pixel; whereas on a color monitor, each pixel is made up of three phosphor dots (one red, one blue, one green), none of which are in the center of the pixel. Monochrome monitors were used in almost all dumb terminals and are still widely used in text-based applications such as computerized cash registers and point of sale systems because of their superior sharpness and enhanced readability.
Some green screen displays were furnished with a particularly full/intense phosphor coating, making the characters very clear and sharply defined (thus easy to read), but generating a somewhat disturbing afterglow-effect (sometimes called a "ghost image") when the text scrolled down the screen or when a screenful of information was quickly replaced with another as in word processing page up/down operations. Other green screens avoided the heavy afterglow-effects, but at the cost of much more pixelated character images. The 5151, amongst others, had brightness and contrast controls to allow the user to set their own compromise.
The ghosting effects of the now-obsolete green screens have become an eye-catching visual shorthand for computer-generated text, frequently (and ironically) in "futuristic" settings. The opening titles of the first Ghost in the Shell film and the Matrix source code of the Matrix trilogy science fiction films prominently feature computer displays with ghosting green text. Green text is also featured in the Swan's computer in Lost series.
Screen burn 
Monochrome monitors are particularly susceptible to screen burn (hence the advent, and name, of the screensaver), because the phosphors used are very high intensity. Another effect of the high-intensity phosphors is an effect known as "ghosting", wherein a dim afterglow of the screen's contents is briefly visible after the screen has been blanked. This has a certain place in pop culture, as evidenced in movies such as The Matrix.
This ghosting effect is deliberate on some monitors, known as "long persistence" monitors. These use the relatively long decay period of the phosphor glow to reduce flickering (and, therefore, eye-strain).