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Microwave kinetic inductance detector (MKID) provides a way to build largeground based sub-mm instruments such as NIKA and A-MKID. For such instruments,therefore, it is important to understand and characterize the response toensure good linearity and calibration over wide dynamic range. We propose touse the MKID readout frequency response to determine the MKID responsivity toan input optical source power. A signal can be measured in a KID as a change inthe phase of the readout signal with respect to the KID resonant circle.Fundamentally, this phase change is due to a shift in the KID resonancefrequency, in turn due to a radiation induced change in the quasiparticlenumber in the superconducting resonator. We show that shift in resonantfrequency can be determined from the phase shift by using KID phase versusfrequency dependence using a previously measured resonant frequency. Working inthis calculated resonant frequency, we gain near linearity and constantcalibration to a constant optical signal applied in a wide range of operatingpoints on the resonance and readout powers. This calibration method has threeparticular advantages: first, it is fast enough to be used to calibrate largearrays, with pixel counts in the thousand of pixels; second, it is based ondata that are already necessary to determine KID positions; third, it can bedone without applying any optical source in front of the array.

Calibration scheme for large Kinetic Inductance Detector Arrays based on Readout Frequency Response