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Probe penetration should be set to a minimum; the position depends upon signal power, detected output voltage and type of measurement.
A slotted waveguide is mostly used for single-frequency standing-wave tests. To minimize probe depth (and its effect on measurement), signal source is chopped (e.g. at 1 kHz) and detector output easily amplified as 1 kHz AC signal for measurement of VSWR. Using a DC only output is not recommended as only a sensitive galvanometer can be used to read detector output; this can lead to errors.
As Jiri said, penetration should be minimum. You may try your same measurement with two (or more) different settings and note the difference. If acceptable, you can use the penetration for all measurements that have VSWR not exceeding the value you measured during your penetration depth influence measurement.
If in a new measurement the VSWR turns out to be higher, you should again evaluate the penetration.
I hope you have some calibrated loads to compare the measurements with the published values for the loads.
Are you using a diode probe or a passive probe that goes to a spectrum analyzer (just a nice to know issue for me).