As it is known, the EOT's have a time C-shaped distortion resulting in a band of equal time lines
on the EOT screen. This distortion may be compensated for by an external optical system  or
eliminated with the aid of a spherical cathode and (or) accelerating grid [2, 3]. The designs of refs
[2, 3] were calculated by exhaustion ofdifferent cathode and grid radii ofcurvature and a subsequent
numerical calculation of the time-of-flight values for central and peripheral electrons (it is the
difference in these time-of-flight values that results in the time distortion).
However, for practical purposes it is more convenient to calculate the radii of curvature, required
for elimination of the time distortion, by using analytical formulae. These formulae are obtained in
the first part of the present talk.
The accelerating diaphragm (AD) used instead of the fine-structure grid  has a number of
advantages over the latter: the simplicity of its manufacturing, the possibility for operating the EOT
without the external optical system, the decrease of the photocathode reverse illumination and, as
it has been shown above, the improvement ofthe spatialresolution along the slit. The EOT luminosity
rises with increasing slit width in the AD of 2h; it is mentioned in ref.  that the image width of
the EOT screen does not depend on h (if an imaginary cross-over of the beam is displayed, which
arises due to the electron scattering by the AD). Hence, it follows that a broad (equal to hundreds
ofji) slit is more efficient than a narrow one (oftens ofp), the more so that it is easier to manufacture
a broad slit.
However, with rising width of the slit the spread of transverse velocities of electrons scattered from
the slit also increases, as well as the lens aberration, which causes blurringofthe imaginary cross-over
image and deterioration ofthe time resolution. The second part ofthe talk deals with the examination
of the above-mentioned phenomena. Restrictions imposed by the latter on the slit width of 2h are