An airborne scanning laser profiler transmits pulses at a frequency f₀. Its field of view is scanned in a direction perpendicular to the aircraft€™s velocity through an angle ±Î¸ either side of the nadir direction, at a scanning frequency f_s. The aircraft€™s speed is v and its flying height is H over level ground. The spatial arrangement of samples on the surface is shown schematically in Figure 8.4. Show that the average along-track spacing s_aof the samples is v/2f_sand that the average across-track spacing s_cis 4Hθf_s/f₀.
The system has f₀= 33.3 kHz and is flown on an aircraft at v = 70 ms^-1. It is subject to the following constraints on its operation: 

150 m < H < 2000 m

θ < 0.35 radian
f_sθ < 14 Hz
f_s < 50 Hz

It is required to operate the system so that s_a < 1 m and s_c < 1 m, while at the same time maximizing the swath width w.
(i) Calculate the value of the scanning frequency f_s that satisfies these criteria, and the corresponding maximum swath width w.
(ii) Calculate the minimum flying height consistent with your results in (i) and all the constraints. Suggest why it it desirable to minimize the flying height.

Figure 8.4