Abstract: An integrated optical spectrometer includes an optical bus configured to accept a light to be measured. Each ring resonator of an array of integrated ring resonators and detectors is optically coupled to the optical bus and to at least one detector. A matrix multiplication process is operatively coupled to each detector. The matrix multiplication process determines based on data from the array of integrated ring resonators and detectors and a calibration matrix of the array of integrated ring resonators and detectors, a spectral content of the light to be measured. A method of calibrating and operating an integrated optical spectrometer, a method to generate a calibration matrix for a ring array of a photonic integrated circuit (PIC) spectrometer, and a method for spectrum reconstruction for a photonic integrated circuit (PIC) spectrometer are also described.