I guess this builds on what others have said, but here goes anyway:
- there are two independent circuits controlling beam position, one controlling its horizontal position and one its vertical;
- they are genuinely independent, neither influences the other;
- the CRT will lengthen or shorten the period each one takes to sweep the entire display to match the pattern of incoming syncs (up to a point, but if your syncs are within that screen's tolerance of the specification, don't worry about it).
Suppose (0, 0) is the top left of the display, and (1, 1) is the bottom right. In that case the pattern the beam follows on the surface of the screen during a frame might be:
- the diagonal from (0, 0) to (1, just less than 1/525); then
- the diagonal from (0, 1/525) to (1, just less than 2/525); then
- the diagonal from (0, 2/525) to (1, just less than 3/525); etc.
If you want progressive scan, your job is easy — make sure that vertical retrace completes at the same time as horizontal retrace. So each new frame starts at (0, 0).
If you want a two-field interlaced scan, you can ensure your vertical retrace ends when horizontal deflection is halfway across the screen. So your next frame will include:
- the diagonal from (0.5, 0) to (1, just less than 0.5/525);
- the diagonal from (0, 0.5/525) to (1, just less than 1.5/525);
- the diagonal from (0, 1.5/525) to (1, just less than 2.5/525); etc.
Alternate between those two and you've got interlaced video. The two sets of diagonals have the same slope as each other, but one is 0.5 lines above the other.
Two misconceptions tend to arise:
- that interlaced video at 60Hz is just a way of describing 30Hz motion in a different order; and
- that there must be gaps between the lines in a single field.
On a real, analogue video camera, the brightness captured at location (x, y) is the brightness at that location at the exact moment the raster passed it. So each field is in total a representation of its subset of the image 1/60th of a second later than the previous. Each line is a representation of its subset of the image 1/15750th of a second later than the previous. Etc. It's not an instantaneous snapshot that is serialised, it's a continuous capture.
There's then no actual benefit whatsoever to putting gaps between the lines. There's no original static 535-line picture that the TV is seeking to reproduce. The primary concerns are (i) make the raster too fat and consecutive lines will overlap, causing blur; but (ii) make it too thin and you'll reduce screen brightness, which was a significant problem, especially so after colour introduced a shadow mask.
So you'd normally aim for the raster to be almost large enough for scanlines that are consecutive in time to meet, but not so large that your engineering tolerances (on beam focus and guidance) meant the two might often overlap.
As per Raffzahn's comments to another answer, the idea of thick blank in-between lines is fairly modern and primarily a fiction created by trying to rationalise analogue behaviour into a digital sampling.