  We develop a simple coordinate transformation which can be employed to
compensate for the nonlinearity introduced by a Microwave Kinetic Inductance
Detector's (MKID) homodyne readout scheme. This coordinate system is compared
to the canonically used polar coordinates and is shown to improve the
performance of the filtering method often used to estimate a photon's energy.
For a detector where the coordinate nonlinearity is primarily responsible for
limiting its resolving power, this technique leads to increased dynamic range,
which we show by applying the transformation to data from a hafnium MKID
designed to be sensitive to photons with wavelengths in the 800 to 1300 nm
range. The new coordinates allow the detector to resolve photons with
wavelengths down to 400 nm, raising the resolving power at that wavelength from
6.8 to 17.
