Real-world CMB lensing quadratic estimator power spectrum response

I describe a method to estimate response matrices of Cosmic Microwave Background (CMB) lensing power spectra estimators to the true sky power under realistic conditions. Applicable to all lensing reconstruction pipelines based on quadratic estimators (QE), it uses a small number of Gaussian CMB Monte-Carlos and specially designed QE's in order to obtain sufficiently accurate matrices with little computational effort. This method may be used to improve the modelling of CMB lensing band-powers by incorporating at least some of the non-idealities encountered in CMB lensing reconstruction. These non-idealities always include masking, and often inhomogeneous filtering, either in the harmonic domain or pixel space. I obtain these matrices for Planck latest lensing reconstructions, and then show that the residual couplings induced by masking explain very well the residual multiplicative bias seen on the Planck simulations, removing the need for an empirical correction.