  Spectrophotometric stability, which is crucial in the spectral
characterization of transiting exoplanets, is affected by photometric
variations arising from field-stop loss in space telescopes with pointing
jitter or primary mirror deformation. This paper focuses on a new method for
removing slit-loss or field-stop-loss photometric variation through the use of
a pupil mask. Two types of pupil function are introduced: the first uses
conventional (e.g., Gaussian or hyper-Gaussian) apodizing patterns; whereas the
second, which we call a block-shaped mask, employs a new type of pupil mask
designed for high photometric stability. A methodology for the optimization of
a pupil mask for transit observations is also developed. The block-shaped mask
can achieve a photometric stability of $10^{-5}$ for a nearly arbitrary
field-stop radius when the pointing jitter is smaller than approximately $0.7
\lambda/D $ and a photometric stability of $10^{-6}$ at a pointing jitter
smaller than approximately $0.5 \lambda/D $. The impact of optical aberrations
and mask imperfections upon mask performance is also discussed.
