Uhoh, I'll jump in the deep end and take a shot at this since you've been waiting 2 months for an answer, there certainly are people better qualified than I to answer this as I've limited my efforts to what I could come up with over several hours. Improving edits welcome.
The fabric is simply a means to hold something like CoBlasted Solarblack (they might use a different brand). It's a heatshielding compound that is transparent to radio waves (unlike carbon fiber); combined with the fabric it provides lightweight stiffening and thermal protection to the metal honeycomb dish reflector underneath.
Based on your comments your question is not so much "Why is TESS' high gain antenna made of undulating BLACK fabric rather than metal?" and more about why the surface is corrugated. They also make SolarWhite which is electrically conductive.
Solarblack (which you wrote in all caps) was chosen over Solarwhite because the corrugated surface must hold precise tolerances and the white coating is conductive, thus it would be the reflector rather than the precisely shaped metal underneath.
Q: Why isn't it smooth?
It's a Floquet corrugated surface: http://www.academia.edu/13976543/Periodic_Structures_and_Floquets_Theorem or http://www.chebfun.org/examples/ode-linear/Floquet.html
A really easy way to demonstrate this without complicated mathematics is to show a photo from a simple experiment.
You'll need a flashlight, a Fresnel lens (like a "Magnifying Sheet" used to enlarge small type), a mirror, and a wall.
The Foquet surface on a parabolic dish is like (not the same as) a first surface mirror on a Fresnel lens.
Interesting facts and other info: https://tess.gsfc.nasa.gov/overview.html
TESS Twitter: https://mobile.twitter.com/tessatmit
The mission is scheduled to last 2 years but the orbit was designed to remain stable for decades with minor course corrections: https://directory.eoportal.org/web/eoportal/satellite-missions/t/tess
TESS still needs to use it's hydrazine thrusters for unloading angular momentum build-up induced by solar radiation pressure but requires no propulsion for station-keeping.
The payload consists of four cameras of 20.4 cm^2, 16.8 Mpixel, low-noise, low-power, MIT/LL CCID-80 detectors.
The four CCDs (Charge Coupled Devices) arrays are attached to the spacecraft such that their FOVs are lined up to form a rectangle measuring 24º x 96º on the sky.
They capture the spectrum from 600 nm to 1000 nm through 4 lenses with seven 10.5 cm f/1.4 optical elements each.
With a payload like that you'll want a first rate means to transmit the data: https://directory.eoportal.org/web/eoportal/satellite-missions/t/tess#spacecraft
Answer:
Making a smooth carbon fiber Ka band satellite dish is not too difficult. Electromagneticly transparent composites are are available from companies like TenCate and are used in radomes. They wanted to squeeze better performance out of the relatively small dish.
The high gain antenna (HGA) is a Cassegrain (2 reflector, convex secondary) antenna https://en.m.wikipedia.org/wiki/Cassegrain_antenna with a Floquet on the primary surface.
The presence of a second reflecting surface in the signal path allows additional opportunities for tailoring the radiation pattern for maximum performance and permits placing a larger feed outside the path of the signal. They don't appear to do that, opting for a more conventional convex conical secondary.
The feed's sidelobes that miss the secondary can be placed out of phase with correctly reflected signals (cutting interference) and the Floquet corrugations reduce the sidelobes on the main dish (concentrating the beam).
It is also possible to use a modified electromagnetic-bandgap (M-EBG) structure in the feed to both allow ultrawide bandwidth with a center notch and orient the lobes of the feed to avoid the secondary's supports - since there are 3 supports rather than 4 one would presume that is not being done either.
In addition it's also possible to use a Curved-aperture Corrugated Conical Horn: http://www.antennamagus.com/newsletter.php to further narrow the beamwidth.
The dish appears that it could contain 14 corrugations in half it's diameter, it has fewer since the feedhorn occupies the central portion.
The diameter (0.7 meters) / (14*2) = 2.5 centimeters, peak to peak. A wavelength of 1.25 centimetres = 23.98339664 gigahertz, (1.00 cm = 29.98 GHz). So the peak to peak distance is a bit under 2.5 cm.
Floquet Theorem: https://en.wikipedia.org/wiki/Floquet_theory
Uhoh's question: "Are there Optical Magnetic Mirrors (OMMs) which actually reflect via interaction with the magnetic field?" https://physics.stackexchange.com/questions/273422/are-there-optical-magnetic-mirrors-omms-which-actually-reflect-via-interaction
Update January 19, 2018:
http://aip.scitation.org/doi/abs/10.1063/1.372241
In the paper: "The coupling of microwave radiation to surface plasmon polaritons and guided modes via dielectric gratings" by Hibbinsa, Sambles, and Lawrence they write:
"It is shown that an absorbing dielectric layer, sinusoidally modulated in height, on top of a planar metal substrate, may be used to provide coupling between both s-and p-polarized incident microwave photons and surface plasmon polaritons, which propagate along the metal-dielectric interface.".
http://ieeexplore.ieee.org/document/1548109/
In the paper "Mirror that does not change the phase of reflected waves" by Fedotov, Rogacheva, and Zheludeva 2006 they write:
"Wavelength sensitive transmission and reflection of a structured thin metal layers in the optical and microwave parts of the spectrum currently attract considerable attention.
Such selectivity results from patterning the interface on a subwavelength scale in a way that makes electromagnetic excitation couple with the structure in a resonant fashion.
In this letter, we report on the first experimental observation of the “magnetic wall” property of novel structured metallic surfaces. The magnetic wall is a mirror that imposes extremely unusual electromagnetic boundary conditions see Fig. 1b:
It does not change the phase of the electric field upon reflection, but reverses the phase of the magnetic field. This property is in sharp contrast to the reflection from a dielectric interface or metal mirror, which reverses the phase of the electric field of the reflected electromagnetic wave and preserves the phase of the magnetic field instead Fig. 1a.
What differs from the parabolic under discussion is the shape of the pattern. It provides proof that a sinusoidal pattern can affect the EM wave, though it's orientation is rotated in respect to what is used on the TESS' reflector.
http://iopscience.iop.org/article/10.1088/1674-1056/21/1/017301/meta
In the paper "Anomalous microwave reflection from a metal surface induced by spoof surface plasmon" by Liang, Jin-Xiang, Yin-Chang and Jian they write:
"... metallic subwavelength structures have become one of the main research branches, also in the studies of the microwave regime and THz frequencies.
In the wavelength range of microwave frequencies, the electromagnetic surface modes are referred to as spoof surface plasmons using language borrowed from optical technology.
As is known, metal surfaces are outstanding ref lectors for incident electromagnetic waves. However, if SPs are launched in a certain wavelength region at the metal–dielectric interface, the energy of the incident electromagnetic waves will convert into that of SPs, giving rise to the reflection minimum. In this study, the influence of spoof SPs on the microwave reflection from a metallic aluminum (Al) surface was examined.
The spoof SPs at the Al surface were excited by patterning the metal surface with periodic corrugated grooves, i.e., to form a surface grating coupler. Extraordinary attenuation of microwave reflection from the periodic corrugated Al surface was observed when spoof SPs are excited successfully. This grating coupling method of exciting SPs to decrease microwave reflection has also recently been employed in experiments performed with overdense plasma.
The groove gratings are clearly acting as resonators, and the experimental phenomenon is similar to the famous anomalies in diffraction from metal gratings (Wood’s anomaly) in the optical regime."
https://arxiv.org/abs/1610.04780
In the paper "Flat Engineered Multi-Channel Reflectors" by Asadchy, D´ıaz-Rubio, Tcvetkova, Kwon, Elsakka, Albooyeh, and Tretyakov they write:
"Here we introduce a concept of multi-channel functional metasurfaces, which are able to control incoming and outgoing waves in a number of propagation directions simultaneously. In particular, we reveal a possibility to engineer multi-channel reflectors.
Under the assumption of reciprocity and energy conservation, we find that there exist three basic functionalities of such reflectors: Specular, anomalous, and retro reflections. Multi-channel response of a general flat reflector can be described by a combination of these functionalities.
To demonstrate the potential of the introduced concept, we design and experimentally test three different multi-channel reflectors: Three-and five-channel retro-reflectors and a three-channel power splitter. Furthermore, by extending the concept to reflectors supporting higher-order Floquet harmonics, we forecast the emergence of other multiple-channel flat devices, such as isolating mirrors, complex splitters, and multi-functional gratings.".
This is demonstrated on a flat surface and would need to be rotated around the central point to create a round structure.
http://www.inatel.br/biblioteca/artigos-cientificos/2014/7536-design-of-a-high-gain-frequency-selective-surface-antenna-system/file
The paper: "Design of a High-Gain Frequency Selective Surface Antenna System" by Alves, Barros, Mologni, Juliano F.; da Silva, Siqueira, Cesareo , Cerqueira and Ribas has this abstract:
"An idealized planar infinite array of circle elements is evaluated using Floquet theory based on only a single unit cell to determine the reflection and transmission coefficients in the frequency band from 800MHz to 4GHz. The circle elements are then projected on the parabolic surface made of polyethylene and a complete hybrid full-wave simulation is carried out using a horn antenna as excitation. The proposed methodology results in a parabolic reflector made of circular frequency selective surface elements that provide high gain and is able to filter electromagnetic waves from a given frequency band. Numerical results demonstrate a 4.5 dB gain improvement compared to a parabolic reflector made of perfect electric conductor for the operational frequency of 3.1GHz.".
Update January 21st, 2018:
The TESS HGA was made by Vanguard Space Technologies Inc. which was acquired by SolAero Technologies Corp. and operates under the name of Alliance Space Systems.
"Vanguard was responsible for structural engineering, fabrication, assembly and test of the High Gain Antenna (HGA), and fabrication and assembly of the TESS Spacecraft Primary Bus Structure as well as the Camera Accommodation Structure (CAS).".
Unfortunately none of those websites explain the manufacturing of the antenna, the search engine on the Alliance site returns no hits for "TESS" (but it's clear that their search engine doesn't return as many hits as Google).
Their webpage says that they use Astroquartz® fabric and Kevlar.
See page 37: http://www.jpscm.com/jps/wp-content/uploads/2017/10/2017-Data-Book-Small-1.pdf for info on http://www.jpscm.com/astroquartz/ .
They use Bismaleimide Polyamide http://www.huntsman.com/advanced_materials/a/Our%20Technologies/High%20Performance%20Components/Imides%20and%20Benzoxazines/Bismaleimides%20%20%20Polyimides as the resin for Astroquartz. I see no reason that SolarBlack couldn't be used on the fabric since it's 99% silicon.
An very simple explanation of parabolic antenna design is provided at Wikipedia. It mentions 2 points relevant to the question(s):
- "Since a shiny metal parabolic reflector can also focus the sun's rays, and most dishes could concentrate enough solar energy on the feed structure to severely overheat it if they happened to be pointed at the sun, solid reflectors are always given a coat of flat paint.".
Black is a less reflective color than white.
"The reflector can be of sheet metal, metal screen, or wire grill construction, and it can be either a circular "dish" or various other shapes to create different beam shapes. A metal screen reflects radio waves as well as a solid metal surface as long as the holes are smaller than one-tenth of a wavelength, so screen reflectors are often used to reduce weight and wind loads on the dish. To achieve the maximum gain, it is necessary that the shape of the dish be accurate within a small fraction of a wavelength, to ensure the waves from different parts of the antenna arrive at the focus in phase. Large dishes often require a supporting truss structure behind them to provide the required stiffness.
A reflector made of a grill of parallel wires or bars oriented in one direction acts as a polarizing filter as well as a reflector. It only reflects linearly polarized radio waves, with the electric field parallel to the grill elements.
The reflector dish could have been made of wire spaced less than one-tenth of a wavelength
A solid dish was likely chosen to ensure that every portion of the dish was fully supported, wind loading is not a consideration in outer space and precise accuracy improves performance; a sinusoidal surface serves to increase the performance at one specific frequency.
A reflector made of wire or solid metal consisting of rings (rather than parallel wires) reflects circularly polarized radio waves (rather than linearly polarized waves).
Wikipedia describes the Ka band as: "frequencies in the range 26.5–40 gigahertz (GHz), i.e. wavelengths from slightly over one centimeter down to 7.5 millimeters".
26.5 gigahertz = a wavelength of 11.3129229434 millimetres.
40 gigahertz = a wavelength of 7.49481145 millimetres.
NASA's frequencies are given below.
NASA's Ka band webpage purports that 3rd generation technology is capable of delivering 2400 Mbps (2.4 Gbps), with a higher transmitted power option of 10 watts.
The solar arrays are rated at 500W (EoL). Material available from NASA (.PDF) explains that TESS will use a Ka-band with a 100 Mbps science downlink (some 24 times slower than is possible at such a high frequency).
In addition to the "science data" there is also commanding and telemetry data (which I presume would be less than the science data).
It is claimed that TESS has a 192 GB solid-state buffer that needs to be transferred every 13.7 days, (192 gigabytes) / (100 Mbps) = 4.26666667 hours, so science data alone will require 4 hours and 16 minutes to transmit (if the buffer is full, but the following video link, next paragraph, says that they expect most transmissions to last only 3 hours).
TESS's orbit and a bit about the mission is explained in the Video you linked to above (so I removed my duplicate link here) - the closeup animations show a smooth faced antenna.
- Information on the Relay Satellite:
NASA’s Tracking and Data Relay Satellite (TDRS) Ka-band Single Access (KaSA)
KaSA Service via large steerable antennas in auto-track mode:
–Return (from spacecraft) of mission data and spacecraft telemetry; G/T: 26.5 dB/K; 25.25-27.5 GHz
–Forward (toward) command and control EIRP: 63.0 dBW; 22.55-23.55 GHz – Field of View +76.8oE-W; +30.5oN-S
Transmitter: µKaTx-300 Ka-band Transmitter (.PDF)
Frequency: 25.25-27.5GHz (Frequency Agile) Occupied bandwidth up to 850 MHz at a maximum of 5 watts output (requires 68W @ 18-40 Vdc) with a data rate of 100kbps – 4.0Gbps.
29 gigahertz = a wavelength of 10.337671 millimetres.
It's far from the most advanced antenna technology.
While that's a simplified version, a fair bit more knowledge and effort is needed to design an aperture antenna suitable for reliable communication.
Acoustic noise dissipation:
Two examples explaining that tri-woven fabric is often used since it can be stretched over a parabolic mold (while 'traditionally woven' fabric usually only stretches in a single direction).
Patent US 20040113863 A1 "Microwave frequency antenna reflector" (Jun 17, 2004) http://www.google.com/patents/US20040113863 explains:
"The high levels of acoustic noise produced during launch of the spacecraft can result in high structural loading of lightweight antenna reflector structures, and has been a major problem in the past.
Holes in both the microwave reflective layer along with the holes in the tri-axial woven fabric second layer are desirable, because the acoustic noise that is produced during launch of the reflector on a spacecraft into space and during maneuvers in space are transmitted and dissipated through the holes in the two layers without causing structural damage or failure that would affect the ability of the reflector to reflect microwaves.
It will continue to be a problem with thin and lightweight space structures having large unstiffened surface areas, with this acoustic noise environment sometimes resulting in structural failures of the reflector and its materials. ".
Patent US 9685710 B1 "Reflective and permeable metalized laminate" (Jun 20, 2017) http://www.google.com/patents/US9685710 explains:
"TECHNICAL FIELD
This invention relates generally to a laminated material, and more particularly to an antenna reflector configured as a laminated structure where a first layer includes an acoustically permeable, nonwoven metallized fiber matte and a second layer includes an acoustically permeable, open weave fabric.
BACKGROUND OF THE INVENTION
The assignee of the present invention manufactures and deploys spacecraft for, inter alia, communications and broadcast services from geostationary orbit. During launch, such spacecraft experience environmental dynamic loads, particularly acoustic launch loads.
Spacecraft components, including particularly radio frequency (RF) antenna reflectors, are required to be compatible with such launch loads, but must also comply, subsequent to launch, with challenging performance specifications in the face of substantial temperature variations and solar radiation exposure, typical of a space environment. Furthermore, such structures must be designed in view of stringent mass and cost objectives.
...
In another implementation, the antenna reflector may include a honeycomb core. The honeycomb core may be sandwiched between the laminated structure and a rear skin, the laminated structure being disposed proximate to a first surface of the honeycomb core and the rear skin being disposed proximate to a second surface of the honeycomb core, the second surface being opposite to the first surface.
In a yet further implementation, the fiber matte may include one or more of carbon fibers, carbon composite fibers, polyamide fibers and glass fibers.
In another implementation, the second layer may include a triaxially woven open weave fiber. The triaxially woven open weave fiber may include one or more of carbon fibers, carbon composite fibers, polyamide fibers and glass fibers.".
Necessary Accuracy:
https://en.wikipedia.org/wiki/Ruze%27s_equation
http://adsbit.harvard.edu/cgi-bin/nph-iarticle_query?bibcode=2002ASPC..278...45G&db_key=AST&page_ind=20&plate_select=NO&data_type=GIF&type=SCREEN_GIF&classic=YES
The Ruze equation gives the often-cited result that the aperture efficiency is reduced by 3 dB (a factor of 2) for an rms surface error 'e' equal to 1/16.
http://www.cv.nrao.edu/course/astr534/2DApertures.html#SurfaceEfficiency
The surface efficiency \eta_{\rm s} declines rapidly as the rms error in wavelengths \sigma / \lambda exceeds 1/16 \approx 0.06.
27.5 GHz * 16 = 440 GHz
440 gigahertz = a tolerance for error of 0.6813464954545 millimetres (0.0268 inches).
So if the surface is off by ~ 0.7 mm (rms) the signal strength will be reduced 50%.
Offsetting the surface in a controlled manner would act like a Single-Frequency Mirror (https://physics.aps.org/articles/v8/20) except it would amplify one particular frequency while reflecting the others to a lesser extent.
Beam Width:
The angular half-power beam width (HPBW) of a parabolic reflector can be estimated from the diameter of the dish and the frequency of operation:
Angular beam width (degrees)=70 degrees/(D/lambda)
29 gigahertz = a wavelength of 10.337671 millimetres.
70 / (70 / 10.337671) = 10.337671 degrees HPBW.
Link Budget:
[I'll wisely leave this calculation to someone else.]
