Method: porbits

The frequency shift $\Delta f$ between the master and slave range data spectra equals

$$\Delta f = -\frac{c}{\lambda} \frac{{B_{\perp}}}{r_1\tan(\theta-\... ...ta-\alpha)} \approx -\frac{c}{\lambda} \frac{\Delta\theta}{\tan(\theta-\alpha)}$$ (V1)

Where:
$\Delta\theta = \theta_1-\theta_2$, $\alpha$ is the local terrain slope w.r.t. the ellipsoid, $c$ is the speed of light, $\theta$ is the local incidence angle (!), $\lambda$ is the radar wavelength, $r_1$ is the slant range ground to master. The approximation is used in Doris. Of course, the sign of ${B_{\perp}}$, or $\Delta\theta$ is important to filter the correct side of the spectra. Note that

$$\alpha \rightarrow 23\ensuremath{^\circ}\Leftrightarrow \Delta f \rightarrow \infty$$ (V2)

The local incidence angle is computed with the dot product of vectors P, and P-M. See also [5].

The algorithm in Doris works as

• While there is a line in the overlap, get next line for master and slave.
• Get block of FFT_LENGTH pixels.
• Compute viewing angle, perpendicular baseline, delta theta for middle pixel of block.
• Compute frequency shift by equation 22.1, and compose filter of rect and hamming.
• Filter master and slave.
• Write block back (for last block only partially).