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 a 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 the 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 thousands 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.
