Heterodyne detection

Heterodyne detection is a method of signal processing to detect waves of an unknown frequency by mixing them with waves of a reference frequency. It is used in optics , image processing , telecommunications and astronomy for the detection and analysis of signals. With radio waves one speaks of a heterodyne receiver , with light of interferometry .

principle

The reference wave is called the local oscillator . The signal and the local oscillator are processed by a mixer . The mixing is based on a non-linear product of the input signals, so that at least part of the output signal is proportional to the square of the input signals.

Be

${\displaystyle E_{\mathrm {sig} }(t)=E_{\mathrm {sig,0} }\cos(\omega _{\mathrm {\mathrm {sig} } }t+\varphi (t))\,}$

the electric field of the received signal and

${\displaystyle E_{\mathrm {LO} }(t)=E_{\mathrm {LO,0} }\cos(\omega _{\mathrm {LO} }t)\,}$

that of the local oscillator.

${\displaystyle E_{\mathrm {sig,0} },E_{\mathrm {LO,0} }}$ are the respective amplitudes.

For simplicity, let's assume that the detector output, I , is proportional to the square of the amplitude:

${\displaystyle I\propto \left(E_{\mathrm {sig,0} }\cos(\omega _{\mathrm {sig} }t+\varphi )+E_{\mathrm {LO,0} }\cos(\omega _{\mathrm {LO} }t)\right)^{2}}$

${\displaystyle =E_{\mathrm {sig,0} }^{2}(1/2)\left(1+\cos(2\omega _{\mathrm {sig} }t+2\varphi )\right)}$

${\displaystyle +E_{\mathrm {LO,0} }^{2}(1/2)(1+\cos(2\omega _{\mathrm {LO} }t))}$

${\displaystyle +E_{\mathrm {sig,0} }E_{\mathrm {LO,0} }\left[\cos((\omega _{\mathrm {sig} }+\omega _{\mathrm {LO} })t+\varphi )+\cos((\omega _{\mathrm {sig} }-\omega _{\mathrm {LO} })t+\varphi )\right].}$

The output signal has high-frequency ( and ) and constant components. In heterodyne detection, the high-frequency components and usually also the constant components are filtered out. Remain as mixing product, the intermediate sum and difference frequencies and . The amplitude of these components is proportional to the product of the amplitudes of the input signals. The phase of the signal can also be determined with suitable signal analysis . ${\displaystyle 2\omega _{\mathrm {sig} }}$ ${\displaystyle 2\omega _{\mathrm {LO} }}$ ${\displaystyle \omega _{\mathrm {sig} }+\omega _{\mathrm {LO} }}$ ${\displaystyle \omega _{\mathrm {sig} }-\omega _{\mathrm {LO} }}$

literature

• Christian Heipke: photogrammetry and remote sensing. 1st edition, Springer Verlag, Berlin / Heidelberg 2017, ISBN 978-3-662-47093-0 .
• Reiner Thiele: Optical communication systems and sensor networks. A system-theoretical approach, Friedrich Vieweg & Sohn Verlagsgesellschaft, Braunschweig 2002, ISBN 978-3-322-89925-5 .
• Karl J. Ebeling: Integrated Optoelectronics. Waveguide optics - photonics - semiconductors, Springer Verlag, Berlin / Heidelberg 1989, ISBN 978-3-540-51300-1 .
• Yun-Shik Lee: Principles of Terahertz Science and Technology. Springer Science + Business Media LLC, New York 2009, ISBN 978-0-387-09539-4 .

See also

• Homodyne detection

Web links

• Innovative Technologies for THz Heterodyne Detection (accessed September 4, 2017)
• Optical Heterodyne Detection of Phase-Shifted Signals (accessed September 4, 2017)