Piston Sensing for Golay-6 Sparse Aperture System with Double-Defocused Sharpness Metrics via ResNet-34.

In pursuit of high imaging quality, optical sparse aperture systems must correct piston errors quickly within a small range. In this paper, we modified the existing deep-learning piston detection method for the Golay-6 array, by using a more powerful single convolutional neural network based on ResNet-34 for feature extraction; another fully connected layer was added, on the basis of this network, to obtain the best results. The Double-defocused Sharpness Metric (DSM) was selected first, as a feature vector to enhance the model performance; the average RMSE of the five sub-apertures for valid detection in our study was only 0.015λ (9 nm). This modified method has higher detecting precision, and requires fewer training datasets with less training time. Compared to the conventional approach, this technique is more suitable for the piston sensing of complex configurations.

Cramér-Rao lower bound analysis of phase diversity for sparse aperture optical systems.

Aberration detection of subapertures is critical to the resolution of a sparse aperture optical system. In this work, the Cramér-Rao lower bound (CRLB) expression of aberrations was first derived for the subapertures of a sparse aperture optical system. The aberrations were estimated by phase diversity, assuming that the photons follow the Poisson distribution. The derived formula has been applied to the Golay3 sparse aperture system to calculate the CRLB of the subapertures' aberrations with different defocus distances, fill factors, and ratios of photon numbers between the focal and defocal images. According to the CRLB criterion, the results indicate that the accuracy of aberration estimation increases as the fill factor of the sparse aperture system increases. The results also demonstrate that the optimal defocus distance of phase diversity is achieved when the CRLB reaches its minimum. The optimal ratio of photon numbers between the focal and defocal images is around 3∶7. However, for the piston error, more photons in the defocal image yield more accurate estimation results. This method can also be applied to the sparse aperture optical systems with other different configurations.

Error analysis of the Golay3 optical imaging system.

We use aberration theory to derive a generalized pupil function of the Golay3 imaging system when astigmatisms exist in its submirrors. Theoretical analysis and numerical simulation using ZEMAX show that the point spread function (PSF) and the modulation transfer function (MTF) of the Golay3 sparse aperture system have a periodic change when there are piston errors. When the peak-valley value of the wavefront (PV(tilt)) due to the tilt error increases from zero to λ, the PSF and the MTF change significantly, and the change direction is determined by the location of the submirror with the tilt error. When PV(tilt) becomes larger than λ, the PSF and the MTF remain unvaried. We calculate the peaks of the signal-to-noise ratio (PSNR) resulting from the piston and tilt errors according to the Strehl ratio, and show that the PSNR decreases when the errors increase.