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In this paper, a method for the synthesis of phase-correcting mirrors for gyrotron output couplers is presented. A computer code for vector analysis of the electromagnetic fields in mirror systems has been developed in terms of the vector diffraction theory. Based on the vector analysis of the fields on mirror surfaces, a method for the synthesis of phase-correcting mirrors has been developed. As an example, the mirror system of a quasi-optical (QO) mode converter for a 94-GHz TE6,2-mode gyrotron has been designed. The QO mode converter consists of a simple, easily manufacturable Vlasov launcher, and two mirrors. Both are adapted phase-correcting mirrors and are optimized using the proposed synthesis method. The simulation results show that the conversion efficiency of the operating cavity mode to a fundamental Gaussian distribution at the window aperture is 87.19% (97.38% fundamental Gaussian mode content) including power transmission losses and depolarization.