CACOFONI: Cosine Amplitude Calibration Organized in Frequency for On-sky Nimble Interaction-matrix. A Novel Method for Calibrating Adaptive Optics Systems II

Abstract The increasing use of adaptive secondary mirrors (ASMs) require robust on-sky calibration approaches in the presence of optical turbulence. One critical calibration is the interaction matrix that calibrates the wave front sensor response to the movement of the ASM actuators. While parametrically adjusted theoretical interaction matrices is a common practice, a fully empirical, model-free method is robust to errors in the model assumptions and the parameter estimation. Our previous random-pattern method (DO-CRIME) assumed the system response was faster than the noise injection rate—which is not always true in AO systems. To overcome this, we developed the Cosine Amplitude Calibration Organized in Frequency for On-sky Nimble Interaction-matrix (CACOFONI), a novel method that utilizes the system’s frequency response function. CACOFONI applies sinusoidal modulations with unique frequencies to each actuator and demodulates the wave front sensor response from the AO telemetry stream. This technique builds the full interaction matrix in a temporal frequency comb and can be applied in either open or closed loop operation. The minimum step between modulation frequencies is determined by the telemetry sample length; for a system with a wave front sensor sampling rate of 1 kHz, a 30 s long telemetry stream yields a 0.1 Hz separation between actuators or modes. The empirically measured CACOFONI matrix showed excellent agreement with our simple synthetic matrices, and we successfully demonstrated closed-loop AO operation with an adaptive secondary mirror using both the heuristic matrix and a parametrically adjusted simulated matrix. We also show how manipulating the frequency range and spacing allow the method to scale to ASMs with several thousands of actuators.