Most Recent Update: 1st August 2026
Feedback is welcome at the email
address "dan.meehan@ddhfradar.com ".
The aim of this site is to inform/educate in the
context of HF radars, though I also include notes on
some areas of physics I find interesting but not
necessarily related to HF radars.
Of course, none of the information here is guaranteed
in any way to be fit for any purpose.
Lissajous/Bowditch Figures
The figure below is a Lissajous Figure.
Why are these figures important--the interested reader is
encouraged
to do some research.
There are eight controls given...The X and Y frequencies, X and Y tiny extra frequencies,
the X and Y amplitudes, and the X and Y extra phases.
The X and Y extra phases can be reduced to a single phase
control because it is the phase difference that matters.
The X and Y frequencies will produce a figure which depends on
their lowest common integer multiple. For example, the following pairs of frequencies
produce the same figures....2:3, 4:6, 6:9, and so on.
To be "complete" there must be a whole number of cycles in the X direction
in the same time as a whole number of cycles in the Y direction.
When the lowest common integer multiple is large, the figure is very complex.
For example, a pair of frequencies 2.2:3 has a lowest integer common
multiple of 11:15.
You can test this using the interactive display.
Originally (before they became known as Lissajous Figures)
these might have been drawn by suspended bags of sand leaking their
contents as they swung back and forth.
A French chap Jules Lissajous, in the mid 1800's, used pairs of
tuning forks with mirrors stuck on their prongs to draw
thee figures on a screen. Before him, an American,
Nathaniel Bowditch (1773-1838) studied these same curves.
The Australian Broadcasting Corporation (ABC) is
Australia's public broadcaster and
has a nice web page describing
why its logo is a 3:1 Lissajous Figure.
A university in America, MIT Lincoln Labs, has as its
emblem a Lissajous figure which is a ratio of 4 to 3 with a
phase added.
A Backscatter Ionogram
This is an example of a backscatter ionogram,
one of the fundamental real-time measurements of
ionospheric propagation crucial to the operation of
High Frequency Over The Horizon Radars.
What is measured and how does it show in this display?
What might this image look like if there had just been
a solar flare?
