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Round mild-steel versus ribbed high-tensile

These bar types actually differ in two separate aspects, the effects of which are not easy to disentangle:

a) Material: mild steel or high-tensile;

This affects the conductivity and the permeability of the steel, and both properties should affect the signal strength received from a bar.
It is a fortuitous consequence of the pulse-induction technique that most ferrous metals give very similar signals, despite their differing electical properties; nevertheless, mild steel does tend to give a consistently stronger signal than high-tensile steel, and so the CM52 will tend to under-estimate the cover to mild steel bars.
Rather than tabulate a correction to be added to the indicated cover, a better result is usually achieved by instead setting the DIAM knob to one size larger than the actual diameter (which works by expecting a greater signal and thus compensating for the increase).

b) Cross-section: smooth round or ribbed;

Deformed bars are normally made to have the same cross-sectional area as that of a circle of diameter equal to the nominal size.
This means that the central core of the bar has a diameter marginally less than the nominal diameter, but a measurement over the crests of the ribs of significantly more; which poses some doubt as to where the "surface" of the bar is.

If you consider the physics of the detection process, the magnetic field radiated by the search head passes through the entire cross-section of the bar, ie approximately through the centre, and the eddy-currents induced flow in circular paths whose centre is the centre of the bar; hence the signal received from a given bar should theoretically depend on the distance to the centre of the bar as the primary variable, and if the measuring instument were expected to yield the vertical position of the bar, then that is what would be displayed.
However, if the instrument is called a cover meter, it will be expected to display the distance to the surface of the bar, and so will have been designed and internally calibrated to display that figure; which by requirement is taken to mean the distance to the nearest point of a deformed bar, ie a projecting rib.

So if a CM52 is used to measure two bars of the same size and at the same depth (to centre), but one is round and the other ribbed, the CM52 will display the same reading for each bar; and this reading will be the correct "cover" for the ribbed bar whereas it will be an underestimate of the cover to the round bar (by the height of the ribs above the notional surface).
In practice this effect is not large, and in many instances will be no more than the uncertainties due to the roughness of the concrete surface; however if the round bar is also of mild steel, this effect will combine with effect (a) above, to give a significantly low reading of cover.

CM52: Bar-sizing of Mild-steel

The first stage of the procedure should be carried out as normal (taking a spaced white-face then black-face reading of signal strength, calculating the ratio, and reading the distance-to-centre range from the graph).

Theoretical considerations suggest that the second stage should be modified as follows:
When investigating each possible bar size as a contender, the "indicated cover" should be read with the DIAM knob set to the next-size-larger bar, but the "radius" added should be half of the diameter of the bar-size actually being checked for:
Thus, when testing to see if the bar might be R16, the DIAM knob is set to 20, the indicated cover read, and then 8mm added. If that result is within the range expected, then it is a 16mm bar; if it is less, set DIAM to 25, and add 10mm to the indicated cover, and if that result is in range, it must be R20; and so on.

However, actual experiments suggest that better results are achieved by performing the second stage exactly as usual in order to deduce the probable bar size, but then taking the indicated cover for the next bar size up to deduce the probable cover.

(Of course, for round bars, there will still be a small residual error due to the allowance for the ribs which aren't there!)

Of course, no method will tell you for sure whether the bar is mild-steel or high-tensile.
What you will get is one estimate of size and cover on the assumption of a high-tensile bar and two estimates (which might be the same as each other) on the assumption of mild steel; typically all three results will be quite similar, which allows you to place upper and lower limits on both size and cover, ie determine the confidence level.

In practice, this does not require any more steps than the normal procedure; and even if you do not know whether it is mild-steel or high-tensile, you will get the two possible results out without having to duplicate any readings -- you simply "skew" the figures that have already been recorded on the work-sheet.

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