Last Updated on June 13, 2026 by John Berry
As I’ve noted on many pages, a wave launched as vertically polarised is best received by an antenna that is likewise vertically polarised. The same applies if horizontally polarised. Simply, the wave must maximally couple with the antenna. So, if something happens along the path and the wave has its polarisation distorted by some angle relative to that when launched, there will be a loss of signal.
There are two mechanisms for this in EME/moonbounce: Faraday rotation and geometric polarisation rotation. This page is about the latter. There’s calculator at the foot of this page to calculate loss.
Concept
The following diagram illustrates the concept. A station S1 at the North Pole transmits a signal vertically polarised with respect to its local horizon. That signal is reflected from the Moon. The polarisation is maintained. On arrival at a receiver at the Earth’s equator, the polarisation is still vertically polarised with respect to the local horizon at S1, but that is now horizontally polarised with respect to the local horizon at S2.
The figure above shows the extreme as an example. The loss will theoretically be total, or in practice the cross-polar discrimination offered by the two antennas. Typically that might be 20dB for Yagis.
Geometric polarisation rotation occurs between any two points on the Earth’s surface. For stations at the same location, the loss is 0dB. So someone testing their own echos experiences no loss. But for stations further apart (so called bistatic stations), loss rises. And its value depends on the geometry between S1, the Moon, and S2.
The loss as a result of geometric polarisation rotation can be calculated and used in a path budget to determine if a QSO will be possible. You can jump now directly to the calculator at the foot of this page, or read on to learn more.
Criticalities
There are two key points to remember:
1. Reflection from the Moon is semi-specular and polarisation sense is maintained on return from the Moon; and
2. Polarisation is always stated relative to the local horizon.
There are two key points in the following discussion:
the angles involved in constructing the geometric polarisation offset between the polarisation of the wave when launched from the transmitter and the expected polarisation at the receiver. I’ve developed a diagram that I hope explains this.
and…
the method of calculation of 𝚫P, using trigonometry to transform local topocentric coordinates into the global geocentric polar reference frame. I refer here to work by Rastislav Galuščák (OM6AA) and Pavel Hazdra at the Czech Technical University in Prague.
The inputs to the computation
The first station, labelled S1, and at latitude L1 points it’s antennas at azimuth A1 and elevation E1. As noted above, these angles are relative to the local horizon. The second station S2 at latitude L2 expects the wave to arrive off the Moon at a particular polarisation. It points its antennas at azimuth A2 and elevation E2 to optimally receive the signal.
When projected onto a common plane, a horizontally polarised wave (for example) launched from S1 may arrive experiencing a geometric polarisation rotation, such that horizontal from S1 is not horizontal as it advances towards S2. And the polarisation of the wave arriving will not be that expected.
Calculating geometric polarisation rotation
To compute the polarisation angle, we use the Earth’s polar axis as a common reference frame. The polarisation angle, P, of each station relative to this axis is given by the formula:
The total offset from geometric polarisation rotation is the difference between these individual station angles. The spatial offset is:
This spatial misalignment reduces the received signal power. This cross-polarisation loss is calculated by the equation:
This last formula is theoretical and does not consider the real cross-polar discrimination characteristics of the practical antennas at the stations.
Calculator
I’ve built a spreadsheet in Apple Sheets to model the loss using these formulae. I’ve given this to Gemini AI to produce the following online calculator for several cities. This allows the reader to play with the various scenarios to get a feel for geometric polarisation rotation in practice. It also allows station locations to be defined by their Maidenhead grids.
The instructions for using the calculator are given below.
Station 1 Location
Station 2 Location
To use the calculator, you need to select the name of the cities (if simply playing with the calculator to learn) or enter the Maidenhead locator grids of the stations (if using it for real). Then enter the UTC date and time and click calculate.
Both stations must be able to see the Moon. If one station can’t, the calculation will fail. If you are playing, use an application like Stellarium to find a good date and time at the locations. Alternatively, select a time and date when you intend operating. There are also amateur radio applications that compute when two stations will be able to see the Moon.
You do not need to accurately position the stations to get a good idea of the loss.
Unless you have a big station, a decibel loss of under 3dB is essential if a QSO is to be possible.
Once calculated, enter the value as variable E in the path budget calculator on the adjacent page and probe the resulting effect on the fade margin.