A scheme is presented as an extension of the work by Burge and van Too
rn [Scanning Electron Microsc. I (1980) 81-91] that call reconstruct t
he phase of the specimen function to double the conventional bright fi
eld resolution. The technique uses images obtained from quadrant detec
tors in a scanning transmission electron microscope (STEM), for a thin
weak phase object with coherent illumination. The reconstruction meth
od assumes no knowledge of the state of the probe-forming lens. It is
shown that the reconstruction is not critically sensitive to noise or
to defocus and astigmatism in the probe forming lens, and that the val
idity of the assumptions made for the purposes of the reconstruction c
an be independently verified from the collected data.