Tests of limb-darkening equations (with optimal coefficients) compared with the method described in this paper. Red shows the inverse method approach described in this paper, including optimal filtering. Green shows the limb-darkening equation with optimal filtering. Blue shows the limb-darkening equation with no optimal filtering; instead, the data are binned over 50 neighboring points. The large jumps around 1.9 μm have their origin in telluric contamination. It is not seen in the other cases due to optimal filtering.