Optimal tilt angle calculation algorithm

From the PSF we identify the weakest resolved directions in the map and determine tilt axes and angles, which can improve the resolution in these directions. By applying rotation matrices, we calculate how collecting data at tilt changes the apparent particle orientation angles, and, therefore, the Fourier space coverage and the real-space PSF shape and orientation. In practice, attainable tilt angles are limited by the quality loss in the resulting micrographs. We hypothesise that micrograph quality loss depends on the cosine of the tilt angle, i.e., the effective transverse thickness of the specimen. Due to this signal degradation, a tilt angle that improves the final resolution is not guaranteed to exist in all cases. We find the optimal tilt angle and axis (if these exist), which are expected to yield the most significant resolution improvement in the weakest direction.