crt magnetic deflection issues

The problem, basically, is; for an astigmatic free image the magnetic field
inside the deflection coil(s) needs to be linear, which is possible to come
by, by winding the coils in  some very special way (much more expensive to
produce). Well, geometry distortions weren't that much of a problem as screens
used to be curvy. But on a flats, under magnetic deflection, you get cushion
distortion (forget about the pin! xD). Now one can counter the cushion by
shaping the magnetic field within the coil's deflection space and/or by
manipulating the field between the coils and the screen, in which the
electrons are just drifting, by placing magnets around the tube. However, any
modification of the ideal field will produce spot astigmatism, unfortunately.
So a trade-off was being made here more towards a linear raster, because
people get more annoyed seeing a cured raster on a flat screen contrary to
some spot astigmatism. As an effect, cheap CRTs will have pretty bad
astigmatism towards the edges of the screen making the resolution go down.

But there is a third method to counter (theoretically) all these issues
without modifying the magnetic field, which sounds counter intuitive at first,
but isn't considering magnetic deflection more in detail. The insight is that
the rate of magnetic deflection increases away from the center. To counter
this rate one needs to modify the rate of change of the sweeping current --
making it non-linear in the process. The main issue here is that the new
current waveform won't be any simple function since it depends on the other
deflection direction as well (and on the coils). And since the function
describing magnetic deflection is a pretty complicated one in itself (esp.
when screens are considered with large diagonals), it becomes impossible to
produce the correct current waveform to counter the increasing rate of
magnetic deflection away from the center. Hence, there will be astigmatism as
well. However, approximations are used, known as S-corrections, where the
sweeping saw-tooth current gets modified to counter the otherwise resulting
geometric distortion. The better the correction, the better the picture gets,
but as more expensive the CRT becomes.

Combining all three methods, i.e.
(a) deflection current waveform manipulation,
(b) magnetic field manipulation within the coil, and
(c) magnetic field manipulation between the coil and the screen,
one can find a balance to make the picture look very good, but the cost/issues
will rise in order of magnitudes esp. considering CRTs with large diagonals.

(Btw; there is actually a fourth method by using multiple acceleration anodes
in the space between the coil and the screen.)

Good CRTs use all three methods to some extend. With respect to
(a) by using special S-corrections circuitry to shape the current waveform,
(b) the magnetic field insight the coils will be barrel distorted, and
(c) magnets are placed around the screen.

So when you see a large CRT having very good geometry and almost no spot
astigmatism towards the edges, it will be a very expensive one -- no question
about it -- like Sony's BVMs. Sony may have used all the knowledge on the
planet while doing their own research producing the best balance possible give
the technology at the time. However, standard TVs will produce all sorts of
issued coming along with magnetic deflection. As one can see, straighten out
the geometric distortions on such TVs will reduce the resolution towards the
edges. One basically trades on for the other.