I was reading the paper SISAR Imaging for Space Debris based on Nanosatellites, in which the Fresnel-Kirchoff diffraction formula is applied for a scenario in which the receiver, transmitter and target are moving. The author arrives to the following equation, defined as the complex profile function (CPF):
$$ H(x') = \int_{m(x') - \frac{h(x')}{2}}^{m(x') + \frac{h(x')}{2}} e^{j k z'^2 \left( \frac{1}{2 r_{c1}} + \frac{1}{2 r_{c2}} \right)} e^{j k z' \left( \frac{Z_p(t) - Z_T(t)}{r_{c1}} + \frac{Z_p(t) - Z_R(t)}{r_{c2}} \right)} dz' $$
Then, the author says: "by ignoring the second order variation of z' and carrying out the integral, the CPF can be approximated as:
$$ H(x') \approx h(x') \mathrm{sinc} \left[k h(x') \left( \frac{Z_p(t) - Z_T(t)}{2r_{c1}} + \frac{Z_p(t) - Z_R(t)}{2r_{c2}}\right) \right] e^{jkm(x')\left( \frac{Z_p(t) - Z_T(t)}{r_{c1}} + \frac{Z_p(t) - Z_R(t)}{r_{c2}}\right)} $$
What does the author mean by second order variation of z'? How does the author go from the first to the second equation?
