  Microwave kinetic inductance detector (MKID) provides a way to build large
ground based sub-mm instruments such as NIKA and A-MKID. For such instruments,
therefore, it is important to understand and characterize the response to
ensure good linearity and calibration over wide dynamic range. We propose to
use the MKID readout frequency response to determine the MKID responsivity to
an input optical source power. A signal can be measured in a KID as a change in
the phase of the readout signal with respect to the KID resonant circle.
Fundamentally, this phase change is due to a shift in the KID resonance
frequency, in turn due to a radiation induced change in the quasiparticle
number in the superconducting resonator. We show that shift in resonant
frequency can be determined from the phase shift by using KID phase versus
frequency dependence using a previously measured resonant frequency. Working in
this calculated resonant frequency, we gain near linearity and constant
calibration to a constant optical signal applied in a wide range of operating
points on the resonance and readout powers. This calibration method has three
particular advantages: first, it is fast enough to be used to calibrate large
arrays, with pixel counts in the thousand of pixels; second, it is based on
data that are already necessary to determine KID positions; third, it can be
done without applying any optical source in front of the array.
