A fast algorithm for computing and correcting the CTF for tilted, thick specimens in TEM

► Different CTF models for tilted and thick specimens are related. ► Computation time for tilted CTF reduced more than 100 × by new algorithm. ► Loss of resolution due to specimen thickness predicted by analytic expression. ► Effect of specimen thickness on resolution is quantified using simulations. ► New approach for space-variant phase-flipping which increases resolution.