Libration fading and the
scattering properties of the lunar surface

The following discussion about libration fading and the scattering properties of the lunar surface took place in the Moon-Net reflector. I found the subject so interesting that I decided to put together all the messages in this page.

On 13-Nov-2002 VK2KU wrote:
Libration Fading is something we all know and tolerate; indeed with some patience the libration peaks often make otherwise marginal EME QSOs just possible.

I have read a number of "explanations" of this effect from well-known EMEers. Typical among these might be: "Libration Fading ... this is caused by the irregular surface of the moon, which rocks back and forth slightly as viewed from the earth." - N1BUG

I hesitate to disagree with those more knowledgable about EME than I, but ....... I do not find any of these explanations very satisfying.

Anyone with some background in Coherent Optics knows that when you shine a laser beam on a rough surface and look at the back-scattered light on a sheet of paper (in a dark room), you see a random "speckle pattern" of bright and dark regions. This pattern arises because of the random phases of the radiation scattered from the different parts of the rough surface. If the rough surface is moved, the speckle pattern moves. The approximate size of the bright speckles (the coherence area) can easily be calculated. If you move a detection aperture (antenna) through the speckle pattern, the magnitude of the detected signal of course varies too.

The coherent radiation source is the transmitting antenna, the rough surface is the moon, and the detector is the receiving antenna. The source and detector are both moving with respect to the moon (and maybe the moon is rocking too), so of course we see a fluctuating signal. Surely the so-called "libration fading" is simply the radio equivalent of the moving optical speckle pattern, and would much better be called "Coherence Fading", or even "Speckle Fading".

Will anyone agree with me?

On 13-Nov-2002 S57UUU wrote:
Yes, libration fading is a speckle phenomenon, but if the Moon was smooth (in terms of wavelength) there would be no speckle, just a single bright spot (1st Fresnel zone) and no libration fading.

So

> "Libration Fading ... this is caused by the irregular surface of the moon, which rocks back and forth 
> slightly as viewed from the earth." - N1BUG

is perfectly true - the 'rocking' meaning the sum of all movement.

On 13-Nov-2002 VK3AUU wrote:
IMHO the only rocking back and forward is either in an arm chair or the orbit as the moon travelles from apogee to perigee.

Looking at the physical nature of the beast and the way that it is moving with respect to the earth. i.e. it is coming or going, I would expect that the signal reflected from various parts of the moon are arriving at all sorts of phases with respect to one another and these phases will vary perhaps in a somewhat cyclic pattern as the relative length of the path changes. I personally thing that this rocking back and forth idea is "bullshit". It is a physical impossibility. The moon has too much inertia to be rocking back and forward in the comparatively short period that is involved.

I wonder if anyone has done a long term plot of the strength of a constant reflected signal. If my theory is correct, libration fading should be at a minimum amplitude and frequency at both perigee and apogee and will increase both in amplitude and frequency somewhere in between.

On 13-Nov-2002 K1JT wrote:
Libration is real. The moon's rotation and orbital motion are syncronized so that approximately the same face is always toward Earth. But the orbit is eccentric and therefore the orbital speed varies; since the rotation rate does not vary in that way, there is an effective "rocking" evident to an observer on Earth. As a consequence, the total fraction of the moon's surface that can be seen and photographed is considerably more than half of a sphere.

Since received EME signals are the coherent vector sums of reflections from many different regions on the rough lunar surface, having different distances from Earth, they may sometimes add in phase and sometimes not. Changes in the apparent orientation -- libration induced changes -- cause the phase relations to shift, and thereby cause QSB.

It's perfectly acceptable to consider this type of fading in the same category as the "speckle" phenomena mentioned by Guy, VK2KU.

On 13-Nov-2002 GM4JJJ wrote:
A nice demo is on http://www.customcpu.com/al7ob/libration.htm

On 14-Nov-2002 K2TXB wrote:
Yes, it is a nice demo. But it appears to be showing about a month of motion every second. Clearly that would generate a lot of signal change (if the moon were really moving that fast)!

I don't doubt that what you are others are saying about this 'rocking' effect causing libration fading is correct - but I still have a little trouble with the concept. I have heard libration fading on 432 take what should be a morse code dash sent at 15 WPM and turn it onto three dots (or 2 dots and a space). To do this, it seems to me, requires a very fast position change. The reflecting surface has to move fast enough to cause cancellation 3 times in the course of a few hundred milliseconds. The motion shown by the demo, if slowed down by 2.6 million times to it's actual rate, is not intuitively fast enough to cause this rapid signal change.

Does anyone have any figures in distance/seconds as to the actual rate of motion produced by this rocking effect?

On 14-Nov-2002 DF5AI wrote:
Thank you very much indeed for this brilliant discussion which gives me a lot. However, there is one aspect which baffles me:

Reflections from different regions of the rough lunar surface cause QSB, of course. However, the visible disk of the Moon is not equivalent to the scattering region causing moon echoes. Comparing the delay of signals scattered at the center of the Moon with those scattered at the limb would result in a delay spread of approx. 12 milliseconds (center-limb-center = additional path length equivalent to the radius of the Moon). However, short radar pulses transmitted at high peak power revealed that about 50 percent of the reflected power was returned within the first 50 microseconds from the leading edge of the moon. Thus, most of the power is returned from a small region of just a few hundred kilometers near the center.

There is no question that even in this situation we will experience fading as described above. But does it still explain the burst-like behaviour of the echo power? Years ago I heard W7HAH on 50 MHz and his moon-echoes were the hell, just like meteor-pings. I would expect that this fading characteristic is more severe on higher frequencies, e.g. 23 cm, but this is not the case.

Perhaps, this is a consequence of different lunar roughness as a function of the probing wavelength. On the other hand, the ionosphere could also play a major role in this scenario. Below 10 degree elevation, the radio waves travel more than 1000 km between the height of 90 km and 400 km. Thus, the full scenario of vertical and horizontal structures in the ionosphere affect the signal on its way to moon - and on its way back.

It's no statement, it's a question.

On 14-Nov-2002 K1JT wrote:
One easy way to understand libration fading and estimate the QSB rate at a particular frequency is to model the patch of lunar surface that is reflecting most of the signal as a big antenna. In effect this region is a phased array with reflecting "elements" scattered all over the patch.

If the patch has diameter d and the wavelength is lambda, the array produces a beamwidth lambda/d (in radians). A large distance D, say the distance from moon to earth, that beam would illuminate a spot of diameter (D*lambda)/d.

But, you say, this "phased array" isn't really phased! The phases of all those reflecting elements are surely random!

Yes! And that means that the reflected power is really not beamed very well. It's scattered over an angle much wider than lambda/d. However, within the wider angle there will be many bright spots ("speckles") in which many randomly phased rays happen to arrive in phase. The speckles will be sized as described above.

The rotation of the earth moves our receiving stations from west to east at approximate velocity v=300 m/s. We therefore move through the speckle pattern, alternately seeing bright and dark regions. The time to move through one speckle is the spot diameter divided by the velocity,

t = (D*lambda)/(d*v)

Equivalently, the QSB frequency in Hz is

f = 1/t = (d*v)/(D*lambda)

For d = 500 km, v = 300 m/s, D = 400,000 km, lambda = 0.7 m, this gives approximately

f = 0.5 Hz

and shows why Morse dashes can get chopped up into dots on 432 MHz.

Is it really motion of the moon or motion of the earth that is responsible for the fading? Both, of course: in this picture it's the relative geometry that matters. And of course we know that there is no absolute standard of rest.

On 14-Nov-2002 VK3AUU wrote:
Leif SM5BSZ wrote

"It happens very seldomly but sometimes the libration fading nearly disappears. I have experienced it once only. Really an extremely unusual feeling. Strong solid qsb-free copy of 144 MHz EME during 15 seconds or more, then the signal was absent for a very long time. Absolutely different from every other EME signal I have heard! It was in a qso with VE3ASO during an ARRL contest. If someone takes the trouble to write a program to calculate libration fading I would be most interested. The rare occasions when it is very low should make microwave EME very much easier if frequency stable rigs were used."

This supports my contention that at perigee and apogee there should be very little libration, because the distance of the moon from an observer on the earth is almost constant. I agree with K1JT that we can see more of the moon than just half of it, but the period over which that happens is a complete lunar cycle, not a fraction of a second, which is the period of libration fading.

Also, if my theory is correct, then the frequency of the fading should be proportional to the frequency being observed. i.e. 432 mhz should show 3 times the rate of fading as 144 mhz. Has anyone observed this?

On 14-Nov-2002 K1JT wrote:
David --

I assume that by now you will have read the message I sent to Russ, K2TXB, and posted to Moon-Net earlier today. In that message I developed described a model with equations to specify the time scale for libration fading as a function of frequency. As you say, the QSB rate is proportional to the observing frequency.

It is correct that the changes in lunar aspect take place over a monthly cycle, and that the changes over a second or so are very small. However, there are over 500 million wavelengths at 432 MHz between earth and moon. As a consequence, changing the reflection geometry by even a nano-radian (1E-9 radians) is enough to change constructive interference into destructive interference, and therefore to cause deep QSB.

Speckle phenomena are stochastic. Some statistical properties are stable and predictable, such as the mean rate of fading and its dependence on hour angle of the moon. However, as with most stochastic phenomena, there can be large variations even of those quantities that have a well defined statistical mean.

As a familiar example, consider the twinkling of a star -- a phenomenon having many features in common with libration fading. Occasionally the twinkling appears to stop for a few seconds, and then it will pick up again.

On 15-Nov-2002 WA6PY wrote:
As we know libration fading is a result of multipath propagation and among other variables is a function of the wavelength. Libration fading is different on each band. On 1296 even strong signals can be distorted causing difficulty to read. On 2304 one of the strongest stations on that band OE9XXI and OE9ERC can be chopped so badly that although signals peaks more then 20 dB over the noise I could have sometimes difficulties to recognize if it was XXI or ERC. On 10 GHz signals sounds like aurora, but are not badly chopped any more.

On 15-Nov-2002 SM2BYA wrote:
So far no one has mentioned polarisation effects, but they are in there:

If the lunar surface was rough in the statistical sense at the wavelength in question, waves of arbitrary plane polarisation would scatter equally and "speckles" would form in specific directions regardless of the polarisation of the incident wave. The factors that would matter would be the reflectivities, orientations and relative positions of individual scatterers (Joe's "phased array elements").

However, at scales corresponding to VHF/UHF wavelengths the Moon's surface is not really rough. There are patches of ordered structures all over the place. These behave like partially polarised phased array elements and each of them responds differently to incident waves of different polarisations. And so the scattered field at any particular spot in space will look different depending on the wavelength and polarisation of the incident field. In the general case, assuming you illuminate the Moon with a circularly polarised wave, you get an elliptically polarised wave back. The obliquity and tilt of the polarisation ellipse will vary with time and the directions where the partial waves will add constructively are also polarisation dependent.

(In a different context, the de-polarisation effect is actually used to advantage by advanced meteorological L and S band radars to deduce precipitation type and droplet shape from comparing LHC and RHC radar returns.)

So, we should be very careful when comparing libration observations on 144/432 (linear polarisation) to observations made at 1296 and 2304 (circular) - they are a bit like apples and oranges. At first sight one might expect circular to be intrinsically less prone to total cancellation than linear, but that depends on what the surface really looks like. The scientifically inclined may want to look up some of the old Arecibo work on depolarisation by Tor Hagfors (who was my first boss at EISCAT in 1980-81):

Hagfors, T., Remote probing of the Moon by infrared and microwave emissions and by radar, Radio Science, 5, 189-227, 1970.

Hagfors, T., A study of the depolarization of lunar radar echoes, Radio Science, 2, 445-465, 1967.

Unfortunately I don't have the papers handy, but could dig them out of the basement storage room if there is interest - or maybe Joe can find them for us ?

On 15-Nov-2002 S57UUU wrote:
David Tanner wrote: >

> This supports my contention that at perigee and apogee there should be very 
> little libration, because the distance of the moon from an observer on the earth is almost constant

I don't think Earth-Moon distance has any significant effect on libration fading. It's the rotation of the earth, which contributes the biggest part of the apparent 'moon rocking' angular speed, that causes most libration fading. Therefore, the fading might change depending on whether the moon is rising/setting or transiting and not on preigee/apogee. The 'rocking' component due to the Moons elliptic orbit will only shift this apparent 'stillstand' of the moon for maybe an hour or so.

ugw wrote:

>However, at scales corresponding to VHF/UHF wavelengths the Moon's surface is 
>not really rough. There are patches of ordered structures all over the place. 
>These behave like partially polarised phased array elements and each of them 
>responds differently to incident waves of different polarisations. And so the 
>scattered field at any particular spot in space will look different depending on 
>the wavelength and polarisation of the incident field. In the general case, 
>assuming you illuminate the Moon with a circularly polarised wave, you get an 
>elliptically polarised wave back. The obliquity and tilt of the polarisation 
>ellipse will vary with time and the directions where the partial waves will add 
>constructively are also polarisation dependent.

There is no preferred orientation of the rocks on the Moon (in contrast to raindrops in wind) so the returned wave is just depolarized (= part of the energy comes back with random polarization) and not elliptical. Even if small parts of the Moon surface have orientation (crater 'rays'), our beams cover the whole Moon and this cancels out. On lower frequencies, most energy stays polarized, so receiving the other polarization will not improve libration fading much, because there isn't much energy in the cross polarized speckle pattern.

Dual polarization RX will of course help a lot against ionospheric effects on the lower bands, but that's another story.

On 15-Nov-2002 SM5BSZ wrote:
At 144MHz the moon surface is not very rough at all. Take a look at http://ham.te.hik.se/~sm5bsz/sm5frh/sm5frh.htm Here you can see that most of the received power comes from a very small region at the center of the moon. The polarisation of this signal is conserved and would be conserved equally well for a circularly polarised wave.

When observing the received signal at orthogonal polarisation the level is about 20dB lower and the signal coms from the entire surface of the moon as one can see from the much larger spectral width. If the two components are combined to a polarisation vector one finds that it does not oscillate much, only about +/- 5 degrees (unless the ionosphere is strongly perturbed).

It seems to me that the moon is rough at 10 GHz because the bandwidth corresponds to the orthogonal component at 144 MHz. As a consequence I expect depolarisation to be more or less complete at 10GHz. A dual polarisation receiver would therefore receive twice as much signal power. Unfortunately it would receive twice as much noise as well but with twice the bandwidth (effectively) one should gain 1.5dB.

On 15-Nov-2002 VK2KU wrote:
Thanks Joe. You have elegantly quantified what I was trying to say. I hesitated to do that!

One point I was making didn't come over very clearly. Suppose the distance between Earth and Moon did NOT vary at all through the month, so that there would be no apparent rocking motion. We would still see signal fluctuations due to the earth's rotation carrying the receiving antenna through the speckle pattern of the scattered radiation.

I think this is really why I don't like the term "Libration Fading". These are all coherence effects, and "Coherence Fading" would describe the phenomenon much more clearly.

On 15-Nov-2002 SM5BSZ wrote:
Long term measurements could of course be done, but I do not think it will be necessary. Check http://ham.te.hik.se/~sm5bsz/arrl2001/index.htm You will see power vs time for KB8RQ. You may download the raw data and extract similar curves for a large number of stations.

I think one would have to make a guess about the phase before trying an fft on the data. With more stable equipment one could exteact the carrier as a complex amplitude and transform it directly. This kind of data is easily obtained any time but I do not think one can get very much information out of it. I think one could get something like the most common frequency (the average qsb peak length) and it would surely be most interesting to correlate it to the computed libration fading rate if someone cares to make the appropriate computer program. I think the recordings over several hours of more than 100 EME stations would show some correlation between calculated "rocking rate" and qsb rate. The expected fading must be very dependant on the location of the two stations since earth rotation is an important factor.

At 50 MHz the ionosphere is probably causing more qsb than the libration.

During strong aurora, the qsb pattern as well as the polarisation becomes very different from normal even on 144 MHz.

If someone can calculate the times for zero libration fading for various transmission paths it would be very interesting to monitor the qsb one really observes. What remains when the libration fading is eliminated should be the ionospheric scintillation. I guess it would be strongly frequency dependant - and in opposite direction to the libration fading.

On 16-Nov-2002 S57UUU wrote:
Hello Leif,

you're right here. And it will probably happen even less often, since it depends on the relative tilts of the Earth's axis of rotation, axis of the Moon orbit and axis of the Moon rotation. The Moon's ascending node has a precession period of cca 18 years, and the perigee precesses in about 9 years - it could be quite a long wait for a prefect apparent standstill of the libration - and moreover, it will hapen at different times for different places on Earth.

Even with a circular Moon orbit there would still be libration (apparent 'rocking' of the Moon) because of our changing viewpoint from a rotating Earth.

And there's more to libration fading than just us traveling through the speckle: the phase also changes on 'uplink', so the elemets of the 'phased array' on the Moon are fed with changing phases, and the speckle pattern itself moves and changes with about the same modulation rate.

I think 'libration fading' is more apropriate, since for example the ionospheric multipath fading on shortwaves also depends on coherence and could be called "coherence fading". 'Libration' is the word that reminds us this is a Moon-related phenomenon. (and it would not exist with a fixed EME geometry = no libration)

On 16-Nov-2002 DF5AI  wrote:
Hi Leif,

the dynamic frequency spectrum of the 90 kHz segment is superb. One of the best EME measurements I ever saw.

Did you notice any fading (periods in the order of seconds or minutes) in this recordings which simultaneously affects all the moon-echoes?

On 16-Nov-2002 SM5BSZ wrote:
Hi Volker,

> the dynamic frequency spectrum of the 90 kHz segment is superb. One 
> of the best EME measurements I ever saw. 

Well, it is the SM5FRH X-yagi antenna.....

> Did you notice any fading (periods in the order of seconds or 
> minutes) in this recordings which simultaneously affects all the 
> moon-echoes? 

NO. Such a thing happens never ever in a time scale of 30 seconds or more. I am sure I would have noticed. It could have happened during a few seconds because I usually do not run the waterfall graph fast enough to observe in a 1 second timescale.

For theoretical reasons one can say the QSB must contain one component that is common to all signals, that is the ionospheric scintillation at the rx side. It is never visible. Just looking at waterfall diagrams always gives the impression that the qsb is completely uncorrelated. Now, since the moon is so big so even though the reflections originate from a small area near the center of the moon, the signal source may be large enough to effectively suppress ionospheric scintillation. As far as I know one can tell the difference between stars and planets by the fact that planets do not twinkle because they are not point like sources. Maybe the same is valid for the moon? I think this must be well known among astronomers.

On 18-Dec-2010 EA6VQ wrote:

K1JT's paper on libration fading presented in the 14th International EME conference is now available

On 23-Mar-2013 EA6VQ wrote:

"A millimeter wave lunar radar" article, by J.J.G. McCue and E.A. Crocker (MIT Lincon laboratory) / November 1968


(Note: I'm not showing any E-Mail address here in order to avoid them from being collected by SpamBots. You can possibly find the E-Mail addresses of the above OM at QRZ.COM.)

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