Table 1.

Mathematical formulae used to compute the distance measurement (d) and distance resolution (Δd) for the pulse-based and phase-difference TLS computational methods.

Parameter	Pulse-Based	Phase-Difference		Notation
distance (d)	$\mathrm{c}\cdot \frac{\mathrm{t}}{2}$	$\frac{\mathrm{c}}{2}\cdot \mathrm{T}\cdot \left[\mathrm{N}+\frac{\mathrm{\Delta }\phi }{2\pi }\right]$	t	flight time of light
			T	period of modulated signal
			c	speed of light in medium
resolution (Δd)	$\mathrm{c}\cdot \frac{\mathrm{\Delta }\mathrm{t}}{2}$	$\frac{1}{4\pi }\cdot \frac{\mathrm{c}}{\mathrm{f}}\cdot \mathrm{\Delta }\phi$	Δφ	phase difference between received and transmitted signal
			N	number of waves
			f	frequency of modulated signal
			Δt	time resolution