Active Control of Microinterferometers for Low-Noise Parallel Operation

Active control of phase-sensitive interferometric metrology systems is necessary for low noise, high resolution, high bandwidth, and parallel operation. Conventional active control methods have several drawbacks like low SNR, high complexity, and low bandwidth. With the development of micromachined scanning grating interferometers ( $\mu$SGIs), high-bandwidth parallel active control of an array of interferometers is feasible. This paper introduces a novel “recurrent-calibration-based active control algorithm.” Utilizing the high-bandwidth integrated electrostatic actuator, this algorithm splits the calibration of the optics and the displacement measurement in time to achieve better noise reduction. The novel algorithm is implemented digitally using a field-programmable gate array on an array of $\mu$SGIs simultaneously. Nonlinearity and the limited range of actuation of the electrostatic actuator affect the performance of the active control. It is compensated by using a lookup table and a gain reversal algorithm. A system model is built to design and analyze the control algorithm. A $\mu$SGI interferometer setup validates the model and control approach. The control algorithm reduces the vibration noise by 40 dB at low frequencies with a cutoff frequency of 6.5 kHz. The resolution of the $\mu$SGI coupled with the control system is measured as $\hbox{1} \times \hbox{10}^{-4}\ \hbox{nm}_{\rm rms}/\surd \hbox{Hz}$ .