here to go to our three pages on radar cross-section reduction
and absorbing materials
here to go to our main page on antennas
A proposed Microwaves101
rule of thumb:
The side dimension of a cube corner reflector is ideally greater
than 10 wavelengths of the signal you are trying to reflect. Any
comments are appreciated!
What's a corner reflector? It's
a structure that is used as a radar target, often in calibrating
test equipment such as in an anechoic chamber. Corner reflectors
are used for many reasons: they have very high radar-cross-section
(RSC) for a small size, the high RCS is maintained over a wide incidence
angle, and an exact solution is known for their RCS. Corner reflectors
are easy to make from sheet metal such as aluminum, but care must
be used to be sure that the surfaces join at exactly at 90 degrees,
and they are robust enough to maintain good flatness after your
"range boy" comes back from a martini lunch and drops
them on a hard floor a couple of times!
There are two main types of corner
reflectors, dihedral and trihedral. The dihedral has two surfaces
that are on orthogonal planes, the trihedral has three. Sketches
of the two are shown below, along with generally used coordinate
systems. The conventions of using phi for elevation and theta for
azimuth angle are used here, as in most antenna work. Note that
the spherical coordinate systems are such that angles of zero for
both azimuth and elevation give the maximum, (often called specular)
Where might you
encounter a corner reflector in "real life?" Notice that
red taillights on vehicles "light up" when they are illuminated
by your headlamps, even when they are on parked cars that are switched
off. This is because they are constructed to have hundreds or even
thousands of tiny optical corner reflectors built in. Optical
corner reflectors work exactly as RF corner reflectors, even if
the materials and dimensions are slightly different.
For the equations on this page
we reference "Radar Cross Section" by Knott, Shaeffer
and Tuley. Lower-case Greek letter sigma
is used to denote radar cross section. Here's the equations for
maximum cross-section of both types of corner reflector, along their
Note that for the trihedral case,
the formula is accurate for reflectors with square sides. If you
cut them into triangles or arcs (like the photo at the top of the
page), the constant "12" will be reduced (sorry, we don't
have those exact expressions).
While we're at it let's provide
the equation for a flat-plate reflector's specular return:
Notice the RCS goes up as the
fourth power of the side dimension "a" for trihedral.
If you double the lengths of the edges, the RCS goes up by a factor
of 16. Yikes! The trihedral corner reflector has the strongest return
for its size of any object.
When we are discussing RCS here,
we mean the maximum RCS at the most favorable angle, which in the
case of a corner reflector is 45 degrees from each plane surface.
The trihedral corner reflector has a good return over a wide look
angle, perhaps a 10 degree displacement you won't even notice a
reduction in returned signal. Many times in practice the trihedral
is used as a dihedral, because of the convenience of just setting
it on a horizontal surface in the range. The cross-section is only
reduced about -1.8 dB (in this case 10xlog(2/3) is the exact solution).
The RCS is also a function of
the frequency squared. It is customary to write the equation using
the wavelength in the denominator. Be sure to use the same units
for "a" as you do for lambda (λ).
Below we have plotted the RCS
for a trihedral corner reflector, with side dimension 10, 15 and
20 centimeters. At X-band the RCS of the 20 cm reflector is already
almost 100 square meters.
Further information on RCS and corner reflectors
The Navy's publicly-released Electronic Warfare and Radar Systems Engineering Handbook has information on RCS, we have it here:
Or skip to the chapter on radar cross section:
And don't forget to visit our pages on reducing radar cross section.
Thanks to James for pointing out another broken link which is now fixed!