Laser Microphone

A laser spot illuminating a vibrating surface should move along with it, and tracking the motion of the spot should theoretically allow us to retrieve some of the information regarding the vibrations of the surface. If a loud enough sound causes the surface to vibrate, this should theoretically be enough for the transmission of audio information through visual means.

Team Members

A0166927N | Marcus Low Zuo Wu

A0171267A | Nicholas Chong Jia Le

Methods and Requirements

Using a photodiode / array of photodiodes, we attempt to record audio by measuring the signal from a laser reflecting off a surface near the sound.

Due to the nature of the setup mentioned, we require a decently dim environment to minimise noise, a visible light laser (does not need to be high powered but needs to be decently collimated), an optical bench, a set of photodiodes that can detect the laser light and produce a signal, and an electronic setup that allows us to capture and export the signal from the photodiodes.

Background

Level (logarithmic quantity)

A power level is a logarithmic quantity used to measure power, power density or sometimes energy, with commonly used unit decibel (dB).

Power level

Level of a power quantity, denoted L_P, is defined by

$L_{P}={\frac {1}{2}}\log _{\mathrm {e} }\!\left({\frac {P}{P_{0}}}\right)\!~\mathrm {Np} =\log _{10}\!\left({\frac {P}{P_{0}}}\right)\!~\mathrm {B} =10\log _{10}\!\left({\frac {P}{P_{0}}}\right)\!~\mathrm {dB} .$

where

• P is the power quantity;
• P₀ is the reference value of P.

Field (or root-power) level

The level of a root-power quantity (also known as a field quantity), denoted L_F, is defined by

$L_{F}=\log _{\mathrm {e} }\!\left({\frac {F}{F_{0}}}\right)\!~\mathrm {Np} =2\log _{10}\!\left({\frac {F}{F_{0}}}\right)\!~\mathrm {B} =20\log _{10}\!\left({\frac {F}{F_{0}}}\right)\!~\mathrm {dB} .$

where

• F is the root-power quantity, proportional to the square root of power quantity;
• F₀ is the reference value of F.

Low-pass filter

First order passive low-pass filter (top) and second order passive low-pass filter (bottom) demonstrating how higher order filters can be obtained by chaining together lower order filters.

A low-pass filter is a filter that passes frequencies lower than a selected cutoff frequency and attenuates signals with frequencies higher than the cutoff. Low-pass filters provide a smoother form of a signal, removing the short-term fluctuations and leaving the longer-term trend.

RC filter

The cutoff frequency of a passive first order low-pass filter is given by

$F={1 \over 2\pi RC}$

where $R$ is the value of the resistance and $C$ is the value of the capacitance.

The top circuit on the right shows a configuration that forms such a low-pass filter. As seen on the bottom circuit on the right, higher order passive filters can be made simply by chaining together lower order filters.

Butterworth Filter

The Butterworth filter is a signal processing filter that is designed to have a uniform sensitivity in the passband ("desired" frequencies), while having a sufficient rejection in the stopband ("unwanted" frequencies).

The (power) gain $G(f)$ of such a filter, with a cutoff frequency $f_{c}$ and filter order $n$ is given by:

$$G(f)={\frac {1}{1+\left({\frac {if}{if_{c}}}\right)^{2n}}}$$

The gain curves for various orders of low-pass Butterworth filters are shown in the plot below, showing a roll-off of $-20n$ dB/decade of frequency. The roll-off at the cutoff frequency also gets sharper (roll-off starts closer to the cutoff frequency $f_{c}$ as opposed to slightly before $f_{c}$) as the order of the filter increases, as can be seen in the zoomed in plot below.

• 
  Plot of the (power) gain $G(f)$ of low-pass Butterworth filters of different orders with cutoff frequency $f=1$, showing the increasing rate of frequency rejection as the order of the filters increase.
• 
  Plot of the different order low-pass Butterworth filters with the cutoff point magnified, showing increasing sharpness and precision in the cutoff behaviour as the order of the filters increase.