"You are right. But frankly speaking I do not understand why the spurious do not influence the test results. I am lacking the theory behind."
If the system is linear, the harmonics can be separated and filtered out. Usually with DSP processing.
But if the harmonics start to enter nonlinear region of component, mixer for example, filtering does not work completely.
One of your countrymen, Michael Knitter has an English-language presentation where he describes, in detail, how the harmonics are handled internally by the FA-VA5 antenna analyzer that he designed. It should answer you questions. He also wrote a article for QEX magazine, July, 2015, where more of the math is shown.
