Principal Investigator Karl Berggren
Recently, several electron-beam-based low-damage imaging schemes for radiation-sensitive samples (such as proteins and biomolecules) have been investigated. It is now possible to incorporate a Mach-Zehnder inter-ferometer (MZI) in a standard transmission electron microscope (TEM) to perform Elitzur-Vaidman Inter-action-free imaging (IFI). We are theoretically investigating the performance of an MZI-based IFI with a Poisson source. We combined IFI with a conditional re-illumination scheme that reduced the probability of imaging errors at low illumination doses.
As a first step, we considered imaging of purely black-and-white pixels. We considered two schemes: classical and IFI, with various imaging detectors. We quantified error as the probability of incorrectly inferring the transparency of a pixel (Perr), and damage as the mean number of electrons that scatter off a black pixel (ndamage), respectively. At the start of our calculations, we assumed a prior probability q of a given pixel being black. Then, we found expressions to update q based on the electron detection statistics, assuming a Poisson beam with mean λt. If the value of q was within a pre-defined minimum acceptable error threshold ∈, we made an inference on whether the pixel was black or white. If this condition was not met, we re-updated q using a second round of detection statistics. This process was repeated a maximum of Nmax times.
We show the results of imaging utilizing conditional re-illumination, for both classical and IFI. These results were calculated with Nmax=1 (circles with dotted line) and Nmax=50 (crosses with dashed lines) illuminations. For both schemes, conditional re-illumination offered a reduction in ndamage at 50 illuminations as compared to single-stage illumination. For classical imaging, Ndamage was reduced to 1, and for IFI, ndamage saturated to 0.67, at Nmax=50.
We are now working on extending these calculations to semi-transparent samples, as well as implementing this illumination scheme in a scanning TEM.