  When it comes to long-wavelength gravitational waves (GWs), diffraction
effect becomes significant when these waves are lensed by celestial bodies.
Typically, the traditional diffraction integral formula neglects large-angle
diffraction, which is often adequate for most of cases. Nonetheless, there are
specific scenarios, such as when a GW source is lensed by a supermassive black
hole in a binary system, where the lens and source are in close proximity,
where large-angle diffraction can play a crucial role. In our prior research,
we have introduced an exact, general diffraction integral formula that accounts
for large-angle diffraction as well. This paper explores the disparities
between this exact diffraction formula and the traditional, approximate one
under various special conditions. Our findings indicate that, under specific
parameters, such as a lens-source distance of $D_{\rm LS}=0.1$\,AU and a lens
mass of $M_{\rm L}=4\times10^{6}M_\odot$, the amplification factor for the
exact diffraction formula is notably smaller than that of the approximate
formula, differing by a factor of approximately $r_F\simeq0.806$. This
difference is substantial enough to be detectable. Furthermore, our study
reveals that the proportionality factor $r_F$ gradually increases from 0.5 to 1
as $D_{\rm LS}$ increases, and decreases as $M_{\rm L}$ increases. Significant
differences between the exact and approximate formulas are observable when
$D_{\rm LS}\lesssim0.2$ AU (assuming $M_{\rm L}=4\times10^{6}M_\odot$) or when
$M_{\rm L}\gtrsim2\times10^6M_\odot$ (assuming $D_{\rm LS}=0.1$ AU). These
findings suggest that there is potential to validate our general diffraction
formula through future GW detections.
