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Detector nonlinearity is an important factor limiting the maximal power and hence the signal-to-noise ratio (SNR) in dual-comb interferometry. To increase the SNR without overwhelming averaging time, specific experimental conditions must be met to ensure that photodetector nonlinearity is properly handled for high input power. Detectors exhibiting nonlinear behavior can produce linear dual-comb interferograms if the area of the detector's impulse response does not saturate and if the overlap between successive time-varying impulse responses is properly managed. Here, a high bandwidth non-amplified photodetector is characterized in terms of its impulse response to high intensity short pulses to exemplify the conditions. With 30 mW of continuous power on the detector, nonlinear spectral artifacts in dual-comb interferograms are at least 35 dB below the signal. A comparative spectroscopic measurement with a frequency swept laser shows that no systematic transmittance error can be attributed to nonlinearity.