When referring to a computer monitor or other display, what do you mean by interlace or interlacing?
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On a CRT monitor (before LCD that is) the image on the screen is drawn as lines across the screen in a scanning pattern from top to bottom.
If HALF the lines are draw in one 'scan', then the other half in a second scan, it's known as interlacing.
It has the advantage that the electronics can run at a slower speed, and the user's eye/brain combines the two images to give a single image.
Interlacing is a display technique that enables a monitor to provide more resolution inexpensively. With interlacing monitors, the electron guns draw only half the horizontal lines with each pass (for example, all odd lines on one pass and all even lines on the next pass). Because an interlacing monitor refreshes only half the lines at one time, it can display twice as many lines per refresh cycle, giving it greater resolution. Therefore, Interlacing provides the same resolution as non-interlacing, but does it less expensively.
Interlace is a technique of improving the picture quality of a video signal primarily on CRT devices without consuming extra bandwidth. CRT production is declining and interlacing causes problems on certain display devices such as LCDs.
It is a somewhat old question but I have just found it and I think it needs some clarification.
(Update: Now it is a somewhat old answer - please note that it is specifically about HDTV and signals and resolutions that can be transferred with a standard HDMI cable. When I say "there is no 720i" I don't mean that it's impossible but that standard HD TV sets don't use it - or at least they didn't at the time of writing.)
PAL vs. NTSC
I will explain it on the example of the field rate of 50 fields per second that is used for PAL because the numbers are easier to reason about. For NTSC you have 60/1.001 fields per second which is roughly equal to 59.94 but not exactly - see below for more info. With PAL it's exactly 50 so this is what I will use below.
Frames: In frame-based or progressive-scan video you are dealing with frames. You have frame rate and it is expressed in frames per second.
Imagine that you are shooting 25 pictures per second and storing them as bitmaps. Every frame is a full picture from the given instant.
Fields: In field-based or interlaced or interleaved video you are dealing with fields. You have field rate and it is expressed in fields per second.
Imagine that you are shooting 50 pictures per second but storing only half of the bitmaps every time - sometimes you store the odd lines and sometimes the even lines. (Note that it is not the same as storing pictures with lower vertical resolution.)
PAL: 50 halves of pictures == 25 pictures? No.
Contrary to some comments here, 50Hz interlaced does not mean that 25 full pictures per second are shown. It means that 50 halves of pictures are shown but those are halves of 50 different pictures that were shot at 50 distinct moments of time in every second. You not only don't have 25 full pictures per second -- you don't have any full pictures at all!
NTSC: 60Hz or 59.94? None of the above.
For interlaced NTSC signal you have the field rate of 60/1.001 fields per second and for progressive signal you have the frame rate of 30/1.001 frames per second. You may find some info floating around (sadly including some of the Wikipedia articles that I refer to below - I'll try to correct them as soon as I have some time) that refers to those frequencies as 60 and 30 Hz or (more accurately but still incorrect) as 59.94 and 29.97 but all of those numbers are inaccurate and the actual values are exactly 60/1.001 and 30/1.001 Hz. Read about the NTSC color encoding on Wikipedia to know why is that.
Problems with interlaced video
Interlacing causes a lot of problems - for example you can't:
without doing some tricks and loosing quality. You don't get any of those problems with progressive video.
Problems with progressive video
The drawback is that usually progressive video of the same resolution has a frame rate that is only half of the field rate of interlaced video (like with 1080p vs. 1080i) so the motion is noticeably less fluid. You can see it on large flat TVs that deinterlace the video to be able to display it on their LCD screens (that, unlike CRT displays, are progressive in nature) which is the cause that they display picture of very high resolution but with jerky motion that I find extremely annoying.
Other way to have progressive video that is used is reducing the picture resolution like with 720p that has a frame rate of 50 or 60/1.001 full frames per second, but the resolution of only 1280 × 720 pixels (for a comparison, 1080p has a resolution of 1920 × 1080 pixels). The advantage is that it is twice as fluid as 1080p and has no problems that 1080i has. There is no 720i.
This is what I consider absolutely the best resource on the subject of field-based (aka interlaced or interleaved) and frame-based (aka progressive-scan) video and you should really read it to fully understand this subject:
See also the following articles on Wikipedia:
And my answer to this question, for a different view on the same subject:
Interlaced video is a complicated subject and most of the information that you find online has to be read with suspicion. Some texts are merely inaccurate, some texts are simply wrong. You have to be careful what you read - except with the material by Chris Pirazzi, where I found no errors and no even slight inaccuracies at all, which is quite amazing, I must say.