  When using an electron microscope for imaging of particles embedded in
vitreous ice, the objective lens will inevitably corrupt the projection images.
This corruption manifests as a band-pass filter on the micrograph. In addition,
it causes the phase of several frequency bands to be flipped and distorts
frequency bands. As a precursor to compensating for this distortion, the
corrupting point spread function, which is termed the contrast transfer
function (CTF) in reciprocal space, must be estimated. In this paper, we will
present a novel method for CTF estimation. Our method is based on the
multi-taper method for power spectral density estimation, which aims to reduce
the bias and variance of the estimator. Furthermore, we use known properties of
the CTF and of the background of the power spectrum to increase the accuracy of
our estimation. We will show that the resulting estimates capture the
zero-crossings of the CTF in the low-mid frequency range.
