My main "job" is the Internet Foundation, so I am constantly monitoring global issues, methods and activities on the Internet. But I have a heart for research groups and gravitational noise detector arrays.  A group of people started following me on ResearchGate.

Just so you can see what others are doing with gravitational sensors "for real", here is a link to my notes on ResearchGate titled 

Solar System Gravimetry and Gravitational Engineering

https://www.researchgate.net/project/Solar-System-Gravimetry-and-Gravitational-Engineering

I have not posted updates here for a while, but I work on this continually.  The latest possible technology that I will be trying to adapt is related to piezoelectric films and piezoelectric fibers.  I have seen several efforts to use piezo disks, but not these films.  As I am reading the history of these materials and devices, particularly polyvinyliden fluoride polymers -  https://en.wikipedia.org/wiki/Polyvinylidene_fluoride it goes back about 50 years.

There are many related topics that make this messy, and lots of people grabbing after money. Too much marketing and high priced things.

"piezo film", "piezoelectric film", "PVDF film", "PVDF energy harvesting", "piezoelectric energy harvesters", "piezoelectric nanogenerators", "piezoelectric polymers", and many more.

("piezoelectric film" OR "piezo film") ("gravimeter" OR "accelerometer") has close to 60,000 entry points.  Many of them false leads or hype.

These films, mounted along X Y Z axes with some fairly simple electronics for interface - plus some sophisticated algorithms for noise classification, management and reporting - should be able to beat the MEMS gravimeters (hyped up MEMS accelerometers sensitive enough to track the sun and moon, and - at high time of flight sampling rates - all kinds of imagine of masses.  My target is to map the interior of the moon, but lots of things found looking for how to do it.

The main reason I am excited about these films is they can support up to Gsps (samples per second)  or GHz data streams for time of flight.  The key issue I  realized many years ago is the need to use time of flight (gravity has exactly the same speed as light) for locating, characterizing and calibrating sources.  Once a source of gravitational (or electromagnetic) "noise" has been identified, it is no longer "noise" but a "signal" that can be used as a reference source. Since the natural thing it so find the strong noises first, that means many earth and solar system gravitational reference sources.  The strongest is NOT earthquakes. But rather atmospheric density fluctuations and flows. The reason they are "good" sources, is they can be independently verified by lidar and many 3D imaging methods now. Same with ocean waves and currents.  And subsurface imaging of seismic waves.

I have been learning how to design chips and PCBs.  How to order and manufacture test devices.  I have always known the data engineering and statistical side of the problem.

I measured the speed of gravity about 20 years ago.  I hope to get a device that any kid in high school or college or on their own, can build and use with readily available tools.  I have many of Arduino type processors, Raspberry Pi, Jetson, Ryzen and Intel devices for the data handling.  95 % of the problem is collecting and processing the data streams.

"It is not hard, just tedious".  I don't know how much 7312347343*434388234377234 might be, but it is not hard to get an exact answer - just tedious to work out by hand.  This problem is now "gravitational engineering".  Nothing really much unknown, just tedious working out of tedious details.

I have spent the last year going over possible technologies and methods.  My criteria for the gravitational imaging network is

Three axes : so that each sensor can determine direction. Each axis of the signal is very precise. Fitting a one dimensional signal is ambiguous.  Fitting three orthogonal axes signals at once is very precise.  A three axis gravimeter can be as precise or more precise than a GPS station.  And you can solve for the orientation of the sensor.  We are not to where someone walking around can use it like a gravitational compass, but I think in the future that will be possible.  I started out just trying to track the sun an moon precisely. But in the last 17 years I have learned a few things.

High Sampling Rate:  So that arrays of sensors can correlate and solve for direction of the source.  Higher data rates mean more samples and data to characterize and study the source.  Higher rates over time mean a wide range of single pixel and super-resolution and correlation techniques can be applied.

Arrays:  From the beginning, I knew that the  current sensors are crude, and the gravitational signals are mixed in with magnetic, thermal, seismic, acoustic, and many sources of noise. But even though the signals move at the speed of light and gravity at a million samples per second, each microsecond sample is 299.8 meters. At a Giga samples per second that is 0.2998 meters or 29.98 centimeters.  

I spent much of the last couple of decades trying to find sensors that are sensitive to gravity, to magnetic and electromagnetic fields. My intention is to then correlate to global "magnetic" and "electric" and "acoustic" and "gravitational" and "thermal" sensor networks and then use statistical methods to sort out and calibrate all the signals.  Most of the noise is a mixture of radiation field (particularly thermal radiation), low frequency magnetic and electric, and many many natural and man made sources of electromagnetic noise.  The movements of air (remember we are looking at things at Msps and Gsps so all the acoustic and ultrasonic events and air movements are there in principle.

An earthquake is not an instantaneous explosion. Rather it is the movement of mass in one area that causes movement to spread out in a pretty well known, and "model-able" way. The surface waves are fairly obvious. Cubic voxels that only held air get filled with soil and rock and water. Later they get filled with air again.  Those seismic surface waves and interior wave are tracked precisely by thousands of sensitive and daily more integrated sensor networks. So the gravitational potential changes with time can be calculated.  That travels out at the speed of light, and the signal gradient (the acceleration field) at sensor locations is reliable and can be used to learn more about the mass distributions, speeds and volumes and locations.

The electron is a wonderful tool. It has electric charge so it responds to electric fields, It has magnetic moment so that it responds to changing magnetic fields and gradients. It has mass, so it responds to change in the gravitational potential and its gradients.  I have come to treat the gravitational and electromagnetic fields as one field. And I can use the properties and behaviors of electrons to sort out and quantify the contributions from each field to motions and orientations of single electrons, and groups of electrons. The atoms and molecules and particles and gluons and states of matter and the vacuum are there as a backdrop. 

I am spending more and more time looking at and organizing information related to "single electron" and "single photon" devices. These seem rather wonderful that people are getting down to that level of precisions. But I finally understood where to put the "magnetic flux quantum".

If you ask, what is the energy of a photon whose frequency is 1 Hertz, in electron Volts, you get your answer by multiplying by Planck's Constant, then dividing by the elementary charge. That is 6.62607015 x 10^-34 Joules/Hertz time 1 Hertz divided by 1.602176634  x 10^-19 Joules/ElectronVolt to get 2 times 2.067833848  x 10^-15 ElectronVolts.  

I wrote it this way because h/e is the energy of a 1 Hertz photon. And that is twice the numeric value for the magnetic flux quantum. So you can think of a 1 Hertz photon as a pair of bound magnetic flux quantums at least in terms of the energy the photon carries. Now this is not perfect, but a good way for me to thing about the energy density and flows associated with the gravitational field and electromagnetic field.  I like the magnetic flux quantum as a unit of energy, because most of the sensors for gravity are down in the nano, pico, femto, atto and smaller scales.  nano meters per second squared for sun and moon signals on the earths surface.  Pico and femto meters per second squared for earthquakes and tracking planets. and find details of parcels of air or currents and waves in oceans.  

I am probably going to run out of space on Hackaday.io   It is hard for me to work where I control the colors and layouts. 

I am reviewing laser measurement techniques at nanometer resolution.  I need to go beyond that, but wanted to be sure I have a good foundation.  This article is helpful:

"A review of nanometer resolution position sensors: Operation and performance"
Andrew J. Fleming at

https://pdfs.semanticscholar.org/a4e5/72ca05d17881c875767f6fd848a222365390.pdf

It includes many low cost methods, and encourages the use of statistical measures that cannot be gamed or spun for marketing purposes.  My interest is on the "interferometer" and "encoder" categories, since the sensors need to be insensitive to magnet fields. When he wrote this in 2013, the sampling rate was in the kilosamples per second (ksps) range.  Now the same methods can use Msps and Gsps low cost solutions.

[ "capacitive positions sensors" "nanometer" ] and [ non contact "atomic force" "nanometer" ] yield many useful efforts, but much reported is heavy on potential markets and dreams, then practical low cost commodity sensors you and I can use.

I definitely need to look more at piezo devices and linear motors.  If my pendulum starts to swing I need to get out of the way, then track closer and closer as it settles down.

A LOT of these things are the end result of people pushing older amplifier and ADC technologies, and they are about a thousand times more expensive than the new ones. But I cannot ignore anything.  I wish there were a way to help all the older instrument makers to upgrade.  There are still a lot of older instruments that do not use embedded processors, data sharing, modeling or statistics at all.

This one at http://www.lionprecision.com/capacitive-sensors/ seems well reasoned and helpful, but one glance at the photos, and I know it is well beyond my meager budget.  They do mention "Simple capacitive sensors, such as those used in inexpensive proximity switches or elevator touch switches, are simple devices and in their most basic form could be designed in a high school electronics class. ", so I am going to be reading "Capacitive Sensor Operation and Optimization (How Capacitive Sensors Work and How to Use Them Effectively)" at http://www.lionprecision.com/tech-library/technotes/cap-0020-sensor-theory.html to learn from a master craftsman.

Go to run.  I am reading so much my sight keeps going out. Wish I had some help.

The mass of the object being monitored keeps shrinking.  The old seismometers had big masses on a spring, or supported by a wire and able to swing.  But as electronic techniques make the measurement of position faster, smaller and more precise, the big masses are stil useful.

That is why I am trying to instrument a simple pendulum with precise sensors.

But follow the thought all the way down.

The "atom interferometers" make use of the fact that the wavelength for a particle is h/mv, where h is Planck's constant , m is the mass of the particle, and v is the velocity of the particle. The larger the mass of the particle being used, the smaller the wavelength.  

h = 6.626070040E-34 Joules/Hertz

But other than some experiments with atom interferometer chips, the cost and complexity of the "atom" methods seems difficult to implement.  I will keep looking, but will it is hard to find something I can adapt during this short period of this contest.  Oh, most of the "quantum" experiments with Bose Einstein condensates, including some superconducting configurations can be treated as simple atom methods.

My note here goes to still smaller particles, the electrons.  These are used in large quantities in our current (pun intended) devices.  We store them in our capacitors, move them from place to place, modulate them, and find them generally fairly useful

But we have not (so far as I have found yet) used the fact they have mass that is sensitive to gravitational potential (time dilation effects), and gravitational potential gradients (acceleration and velocity effects).  The atom interferometers make use of well studied internal states of atoms and molecules to manipulate and monitor them for use in sensing.  But there are very very specific interactions of electrons that can as well.

I do not like the term "spin spin", because it doesn't tell me what is happening or what I can do with it.  I like the term "permanent magnetic dipole interaction".  I will put up with "hyperfine interaction" when it is applied to interactions of magnetic dipoles, magnetic quadupoles or any combination of Schrodinger states of atoms, molecules or particles.  If it can be represented as a "particle" whose field has multipoles, and these interact, I would say "multipole interactions".

So I am looking at all the electron magnetic dipole interactions to see which phenomena might be "hacked" to make a low cost, small, precise gravimeter.

One magnetic dipole interaction I have used for a long time is electron-electron magnetic dipole binding, where two electrons bind magnetically to form a stable pair.  I think that is the basis of supeconductivity generally, but I am trying to stay on track to solve this gravimeter problem in time. I am pretty sure the same thing is going on with proton-proton magnetic dipole binding in neutron stars and everyday nuclei here on earth.  I use magnetic dipole binding to estimate nuclear reactions where particles with permanent magnetic dipoles bind with nuclear energies. Sorry, just reminding myself of all the pathways I have investigated over the years.  I want one to help me here.

So in a radio receiver, the fluctuations in the voltage of the electrons in a capacitor are related to "kT".  But part of that signal is gravity, part is the earth's magnetic field, part seismic, part human noise, and part kinetic fluctuations and phonons in the parts.  We distinguish "kT" in resistors, but it is just the same mix of signals coming through the potentials affecting particular devices in our circuits called resistors.  I tried to use a "kT" sensor (Johnson noise) sensor recently, but so far inconclusive, because you have to measure "everything" to sort out the source of the noise. 

So, in parallel, I am gathering data from magnetometer arrays, seismometer arrays, gravimeter arrays, VLF ELF ULF and all frequencies of electromagnetic sources, power system noise --- any signal that is coming in from anywhere to affect the pendulum, and the electronics.

So, perhaps, my "pendulum" is any oscillator.  Maybe electrons in a capacitor, or the specific collection of electrons in a resistor.  Or electrons in a coil.  It has to be big and unique enough to track with current (pun intended) technology, but low cost and easy to adapt.

I am not forgetting photons in ring lasers either.  The Sagnac effect is very useful.  It is just so expensive still.  I will check if anyone has hacked the fiber ring laser interferometer for gravimetry.  Maybe I need to check rotation as well.  :)

Sorry for all the speciallized terms.  But that is how people keep track of the phenomena and capabilities of these kinds of devices and processes.

So sorting out all the possibilities and how things work, is helpful.  I just hope I can focus to get this particular device working soon.

Ben Krasnow has uncovered a simple method for laser measurement.  It will take some effort to convert it to a convenient tool, but he gave enough instructions to do that.  Here is his video:

https://www.youtube.com/watch?v=MUdro-6u2Zg - "Laser diode self-mixing: Range-finding and sub-micron vibration measurement."

He found some laser diodes that have an integrated "internal monitor photodiode" with feedback.  The feedback signal is what he is tracking.  You get "interference" because the reflected wave timing matches the timing of the outgoing wave.  So you should be able to get the same effect with an on purpose emitter and receiver pair. 

I checked just now, and I think this "Self-mixing laser diode vibrometer December 2002" at  https://www.researchgate.net/publication/228874101_Self-mixing_laser_diode_vibrometer is the same approach.  

Looking more deeply, this paper 2004 "Self-Mixing Laser Diode Velocimetry: Application to Vibration and Velocity Measurement" by Lorenzo Scalise, Yanguang Yu, Guido Giuliani at http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.474.4663&rep=rep1&type=pdf explains "

"Laser Doppler velocimetry  and laser Doppler vibrometry  are well-known measurement techniques widely used for the precise remote measurement of the velocity of fluids, and for accurate measurement of the displacement, velocity and acceleration of solid objects. With these types of instruments, it is possible to measure the velocity and displacement of the target surface, simply by using a light beam."

So there is a rich source of useful techniques - once you know to google "velocimetry" "laser" and "internal monitor photodiode".

Still further checking find "Microcantilever Displacement Measurement Using a Mechanically Modulated Optical Feedback Interferometer"  at https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4970047/  By 2016 they have broadened the concept from piezo to cantilever, and cleared up that it is an optical feedback loop. 

Finally, "Optical feedback interferometry" today has over 10,000 results for the exact phrase. 

https://www.google.com/search?q="Optical+feedback+interferometry"

Now to find one to adapt to my problem and move on.  I just need a data stream.

This project's immediate goal is low cost acceleration field measurement and imaging techniques. 

But the gravitational potential changes the rate of clocks, nuclear and chemical processes, at the surface of the earth - particularly, because of the changing distances and orientations of the sun, moon, earth and many things on earth.  These "direct potential" instruments derive from resonance measurement on the electronic and magnetic states of atoms - cesium and rubidum as a start - for use as precise atomic clocks.  As such they found the that clocks do change their rate at rest because of the absolute value of the gravitational potential (the acceleration is just the gradient of this potential), and can be "inverted" to report on the potential itself.

Mossbauer effect (very precise accounting for recoil energies during state changes in atoms and molecules with narrow linewidths) can be used to measure the gravitational redshift, which depends on an integral of the potential between two points.  His innovation was to find materials where the lattice surrounding the emitting (and absorbing) atoms (molecules) could absorb the recoil energy on the timescale in which the state change occurs.  That is difficult because finding and characterizing materials to have precise atomic and nuclear properties is hard for bulk materials.

With laser tools and fast ADCs and computing, it should be possible to use a wide variety of paired emissions and absorptions where the recoil can be tracked, accounted for, and compensated for.  There should be cyclotron versions and microwave plasma versions as well.  I am reviewing all those methods and possibilities, and will report later, or as I have updates.

The importance of the gravitational potential detectors, is there are broad classes of instruments and experiments being proposed, just started, or going on, sensitive enough that they need to account for (1) earth tides, (2) small variation in station location, (3) changes in the rates of atomic and molecular rates, frequencies, and energies due to the changing potential due to the sun and moon relative to the station. The earth itself is changing shape, and its potential changes are tracked by the International Center for Global Gravity Field Models (ICGEM), http://icgem.gfz-potsdam.de, along with its temporal variations.

This last affects many Bose Einstein condensate, quantum, superfluid, plasma and nuclear experiments.  I am trying to lay out the general rules, but my advice is that if you are saying "nano" and starting to whisper "pico" and "femto" and "atto", you need to check your local gravitational potential and acceleration field "weather report".  :)

Now it is a general rule of thumb, that any system that has to account for these types of changes, can invert their models for correction to become reporting nodes in a global network of sensors.  Sensor monitoring the positions of the sun and moon, and the shape and gravitational events on the surface of the earth and in the solar system.  So if someone's G experiment is giving them fairly wide variation from place to place, and time to time, it might well be they have not accounted for the sun, moon and earth portions of the potential and its gradient.

I do not know exactly how the signal is initated and travels from where the change is made, to "direct potential" or gradient sensors.  For a pendulum swinging nearby, used as a reference source, or just keeping video tracking and identification senors on poles of the nearby highway to identify them and correlate with gravity signals. Or using 3D video and imaging to get the shape of the ocean to calculate its gravity signal at your site.  All of these are quite complex.  Easy to do, but with noise and careful work required. The signals travel at the speed of (light and gravity) so you need to sample at rates appropriate to your needs.  If you want to use a gravity array to image ocean waves, it might need to be 1 cubic centimeter.  Is that possible?  Before all these new technologies, and the price of sophisticated measurement dropping, I might have said it will be decades.  But now maybe it will be much quicker.

This MEMS gravimeter at the University of Glasgow uses an interesting "optical shadow" detector.  And they have added tilt and temperature monitoring and compensation. They still have not calibrated all three axis, nor are they doing routine sun moon calibration, but seem to be making progress.

A High Stability Optical Shadow Sensor with Applications for Precision Accelerometers

https://arxiv.org/pdf/1711.01253.pdf

https://arxiv.org/abs/1711.01253

Field tests of a portable MEMS gravimeter

http://eprints.gla.ac.uk/151688/1/151688.pdf