Started with an incentive to learn on LiDAR (Light Detection And Ranging) technology, this project has been a very complete involving many interesting aspects of analog and system design.
The aim of this project is to understand the working principles and constraints involved in such a front end and have fun along the way !
Laser ToF sensors extracts the distance between itself and a target by counting the elapsed time between the emission and reception of a traveling light wave pulse. The system may extract the time value either directly (i.e Counting time) or indirectly (i.e Measuring a phase shift).
Direct time of flight systems generally use a Time to Digital Converter (TDC) to get a digital representation of the elapsed time between the emission and reception of the wave. As a light wave travels at a speed very close to its one in vaccuum (\(C-0.03\%\)), a distance of 1m will correspond to :
\[Speed = \frac{Distance}{Time} \leftrightarrow Time = \frac{1m}{C-0.03\%} = 3.336\text{ ns}\]
An indirect ToF system will constantly shine a laser at the object, modulating its intensity as a sinewave. On the receiver side, a mixer combines the TX and RX signals to extract their phase difference (\(\delta_{\Phi} = \Phi_{LO} - \Phi_{MOD}\)).
When the TX and RX frequencies are matched, the mixer output voltage (With LP filter) may be expressed as :
\[\text{TBC } V_{\delta\phi}=A_{RX} \cdot \frac{2}{\pi}\cdot \sin(\Phi_{LO} - \Phi_{MOD}) \quad \text{(iToF1)}\]
The phase shift between two identical periodic signals of frequency \(f_0\) represents a time delay between this signals expressed as :
\[\delta_{\Phi_{Rad}} = \frac{\text{Time delay}}{\text{Signal period}}\cdot 2\pi \quad \text{(iToF2)}\]
Remember, this is only valid for the phase shift between signals of identical period and spectrum ! For two single harmonic signals of different frequencies, the phase shift cannot be related to their time delay and will change over time.
Using equations iToF1 and iToF2, time delay Vs mixer voltage can be expressed as :
\[\tau = \frac{T}{2\pi}\cdot \arcsin{\frac{\pi\cdot V\delta_{\Phi}}{2\cdot A_{RX}}}\]
KW : Single mode lasers Beam deviation Optics, collimation Power, lambert model