The Gaussian diffraction pattern initially assumed in the diffraction inverse problem is further sharply defined by multiplying $e^{-q{omega}_0$mid${chi}$mid$}$</TEX>. The modified pupil function is obtained and the diffraction intensity distribution for the finite aperture ($-{omega}_0~{ imes}{omega}_0$ is obtained, and then the OTF is derived analytically. It is found the OTF is equal to or less than the $(OTF)_{q=0}$, namely the modulation is not useful. It is shown that the narrowing down the initial Gaussian diffraction pattern does not give the anticipated improvement in OTF and the reason is clarified.