Wave interference

When electromagnetic waves meet, they combine. This combination creates patterns of reinforcement and cancellation — an effect known as interference (Figure 1).

Wave interference is the phenomenon that occurs when two or more waves overlap in space, producing a new wave whose amplitude is the vector sum of the individual wave amplitudes — as indicated by the principle of superposition.

As mentioned in the corresponding Wikipedia article: "If a crest of a wave meets a crest of another wave of the same frequency at the same point, then the amplitude is the sum of the individual amplitudes—this is constructive interference. If a crest of one wave meets a trough of another wave, then the amplitude is equal to the difference in the individual amplitudes—this is known as destructive interference.

More generally (Wikipedia): "Constructive interference occurs when the phase difference between the waves is an even multiple of π (180°), whereas destructive interference occurs when the difference is an odd multiple of π. If the difference between the phases is intermediate between these two extremes, then the magnitude of the displacement of the summed waves lies between the minimum and maximum values."

Figure 1: The interference of two waves. In phase (left panel): the two lower waves combine, resulting in a wave of added amplitude (constructive interference). Out of phase — by 180 degrees (right panel): the two lower waves combine, resulting in a wave of zero amplitude (destructive interference). Source: Wikipedia

Interferometry 

Astronomical interferometry — Aperture synthesis — Radio frequency aperture synthesis interferometers*

*Please note that the term "Synthetic-aperture radar (SAR) interferometry" refers to a different context, where imaging results following illumination from different positions or time points are combined.

Interferometry is a technique which uses the interference of waves to extract information (Wikipedia). As mentioned in the Wikipedia article subsection "Radio interferometry": "In 1946, a technique called astronomical interferometry was developed. Astronomical radio interferometers usually consist either of arrays of parabolic dishes or two-dimensional arrays of omni-directional antennas. All of the telescopes in the array are widely separated and are usually connected together using coaxial cable, waveguide, optical fiber, or other type of transmission line. Interferometry increases the total signal collected, but its primary purpose is to vastly increase the resolution through a process called Aperture synthesis. This technique works by superposing (interfering) the signal waves from the different telescopes". "This creates a combined telescope that is equivalent in resolution (though not in sensitivity) to a single antenna whose diameter is equal to the spacing of the antennas farthest apart in the array."

As mentioned in the Wikipedia article "Astronomical interferometer": "An astronomical interferometer or telescope array is a set of separate telescopes, mirror segments, or radio telescope antennas that work together as a single telescope to provide higher resolution images of astronomical objects such as stars, nebulas and galaxies by means of interferometry. The advantage of this technique is that it can theoretically produce images with the angular resolution of a huge telescope with an aperture equal to the separation, called baseline, between the component telescopes."

"Interferometry is most widely used in radio astronomy, in which signals from separate radio telescopes are combined. A mathematical signal processing technique called aperture synthesis is used to combine the separate signals to create high-resolution images. In Very Long Baseline Interferometry (VLBI), radio telescopes separated by thousands of kilometers are combined to form a radio interferometer with a resolution which would be given by a hypothetical single dish with an aperture thousands of kilometers in diameter." As mentioned in the Wikipedia article Aperture synthesis: "Most aperture synthesis interferometers use the rotation of the Earth to increase the number of baseline orientations included in an observation."

Aperture masking interferometry (Wikipedia) is a technique which includes the use of masked apertures, where most of the aperture is blocked off and electromagnetic waves (cf. light) can only pass through a series of small holes (subapertures). This allows for the removal of atmospheric noise from the measurements. As  mentioned by Wikipedia: "This technique allows ground-based telescopes to reach the maximum possible resolution", while it also allows ground-based telescopes with large diameters to produce far greater resolution than the Hubble Space Telescope". It is noted that aperture masking interferometry was first made available in space on the James Webb Space Telescope (Wikipedia).

Figure 2: A large telescope with an aperture mask over it (labelled Mask), only allowing light through two small holes (Wikipedia —By Krishnavedala, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=23651217)

Very-long-baseline interferometry (VLBI) and polarimetry

What are the technological capabilities that allow the detection of magnetic fields from space objects located million light-years away? The example of the detection of the magnetic fields of M87's black hole.

A world-wide network of sensors is required to achieve high resolutions: the larger the distance between the sensors, the higher the resolution.

Event Horizon Telescope (EHT) Press Release (April 10, 2019): "Astronomers Capture First Image of a Black Hole"

https://eventhorizontelescope.org/press-release-april-10-2019-astronomers-capture-first-image-black-hole

The EHT used a technique called very-long-baseline interferometry (VLBI) which connected eight telescope facilities around the world, forming one huge, Earth-size telescope observing at a wavelength of 1.3 mm. 

VLBI allowed the EHT to achieve an increased resolution, one that is "enough to read a newspaper in New York from a sidewalk café in Paris [6]."

It is noted that the Earth rotation was also added computationally to increase resolution.

Presentation on Very-long-baseline interferometry (VLBI) and polarimetry entitled "VLBI Polarimetry Techniques I" — Notes and figures

• Origin of polarization: https://youtu.be/J_oXou6QGpI?t=483

  • Unlike scalar waves (such as sound), EM waves have polarization i.e. directionality of oscillations (Figure 3). By convention, we refer to polarization as the orientation of the electric field.

  • Ordinary light is made of photons with random E field orientations (Figure 4). 

  • Certain media may select specific orientations of the electric field (Figure 4). This is the case, for instance, for polarized glasses.

• Two polarization modes: 

  • Linear polarization: The electric field has a preferred direction of oscillations

  • Circular polarization: The electric field rotates around the direction of propagation (which is represented by the "Poynting vector")

• Description of polarization using the Stokes parameters

  • In order to fully describe polarization, the four Stokes parameters, I, Q, U and V, are needed. These describe how much polarized versus unpolarized light we have, how much circular polarization we have and what is the strength and orientation of the linear and circular polarization.

• Different analyses can be performed in space. 

  • For instance, electrons in very strong magnetic fields are rotating around magnetic field lines with acceleration, thereby emitting synchrotron light. This can be analyzed.

• Measuring Polarization: https://youtu.be/J_oXou6QGpI?t=1442

  • How polarizers register polarization.

• Polarization and interferometry/ https://youtu.be/J_oXou6QGpI?t=1684

• VLBI in a nutshell: https://youtu.be/J_oXou6QGpI?t=2024

  • We increase step-by-step the number of radiotelescopes on a map and we appreciate how a representation is reconstructed and enhanced in each step.

  • First, we place one radiotelescope and we get a poor image. Same for two. When we place three telescopes, we have three baselines, meaning three different combinations for a plane wave, or three plane waves. These will interfere and will be added coherently to offer a better reconstruction (Figure 5).

  • By using the Earth rotation and performing "Earth rotation synthesis" we obtain a high-fidelity image (Figure 5). 

Reference to very long baseline interferometry from Scientific American: https://twitter.com/sciam/status/1116071802944593920

The Very Long Baseline Array (VLBA): a 5000-mile-wide or 9000-Km-wide telescope.

"With an instrument this powerful, a person on the East Coast could read a newspaper on the West Coast." 

Excerpts from Wikipedia article: "The Very Long Baseline Array (VLBA) is a system of ten radio telescopes which are operated remotely from their Array Operations Center located in Socorro, New Mexico, as a part of the National Radio Astronomy Observatory (NRAO). These ten radio antennas work together as an array that forms the longest system in the world that uses very long baseline interferometry. The longest baseline available in this interferometer is about 8,611 kilometers (5,351 mi)." 

Excerpts from the article "Globe Spanning Telescope" by  Ray Nelson (from magazine "Popular Mechanics"):

"For decades, astronomers have patched together networks of radio telescopes to achieve the high resolution —ability to distinguish fine detail— of long baseline astronomy. But now they have a full-time dedicated tool, one with tremendous speed and flexibility and more resolving power than anything on Earth or in space. With an instrument this powerful, a person on the East Coast could read a newspaper on the West Coast. An astronomer using the array can peer deep into the core of a quasar some 12 billion light-years distant (...)."

"Closer to home, the array helps confirm satellite orbit locations for the Global Positioning System, or GPS, and aids in earthquake research. Using distant quasars as beacons, the antenna positions are triangulated for measurements within a centimeter, sometimes even within millimeters. This helps corroborate GPS satellite status and gives geodetic scientists a new way to gauge tectonic plate movement. All the antennas are controlled from headquarters at the Array Operations Center in Socorro, New Mexico."

"For some research, the Very Long Baseline Array can work with other radio observatories, such as the Very Large Array in New Mexico or the 330-foot-diameter dish now being built in Green Bank, West Virginia, a highly specialized instrument for close-up zooming. When Japan launches a 33-foot radio dish into orbit next year, the world's first space radio telescope will use the Very Long Baseline Array's correlator in Socorro as its "brain," and will tie in with the array for joint observations. Maybe they'll call it Very, Very Long Baseline astronomy."

It is noted that to obtain this order of resolution, a global infrastructure is required. Given that this global infrastructure exists, adequate safeguards against dual-use are required, to forbid the use for nefarious purposes of global scale.

Figure 4:  Image from the article "Globe Spanning Telescope" by  Ray Nelson (from magazine "Popular Mechanics").