We studied the relative accuracy of drifting gratings and noise stimuli for functionally characterizing neural populations using two-photon calcium imaging. Calcium imaging has the potential to distort measurements due to nonlinearity in the conversion from spikes to observed fluorescence. We demonstrate a dramatic impact of fluorescence saturation on functional measurements in ferret V1 by showing that responses to drifting gratings strongly violate contrast invariance of orientation tuning, a fundamental property of the spike rates. The observed relationship is consistent with saturation that clips the high-contrast tuning curve peaks by ∼40%. The nonlinearity was also apparent in mouse V1 responses to drifting gratings, but not as strong as in the ferret. Contrast invariance holds, however, for tuning curves measured with a randomized grating stimulus. This finding is consistent with prior work showing that the linear portion of a linear-nonlinear system can be recovered with reverse correlation. Furthermore, we demonstrate that a noise stimulus is more effective at keeping spike rates in the linear operating regime of a saturating nonlinearity, which both maximizes signal-to-noise ratios and simplifies the recovery of fast spike dynamics from slow calcium transients. Finally, we uncover spatiotemporal receptive fields by removing the nonlinearity and slow calcium transient from a model of fluorescence generation, which allowed us to observe dynamic sharpening of orientation tuning. We conclude that for two-photon recordings it is imperative that one considers the nonlinear distortion when designing stimuli and interpreting results, especially in sensory areas, species, or cell types with high firing rates.