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Chris, that is one possible way to do a measurement if the detector response can be sufficiently linearized in post-ADC computation.

One downside is that the amplifier's output impedance and the load impedance are interdependent, and the filter's input impedance can vary depending on the frequency. So, the measurement is a good one for real-life output vs freq at any particular operating power, but it is not necessarily a fair measurement method for the LPF's frequency response. Measuring the latter in vivo is difficult, as Hans said.