Adaptive optics

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A deformable mirror can be used to correct wavefront errors in an astronomical telescope.

 

Illustration of a (simplified) adaptive optics system. The light first hits a tip–tilt (TT) mirror and then a deformable mirror (DM) which corrects the wavefront. Part of the light is tapped off by a beamsplitter (BS) to the wavefront sensor and the control hardware which sends updated signals to the DM and TT mirrors.

 

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An artist's impression of adaptive optics.

Adaptive optics (AO) is a technology used to improve the performance of optical systems by reducing the effect of incoming wavefront distortions by deforming a mirror in order to compensate for the distortion. It is used in astronomical telescopes and laser communication systems to remove the effects of atmospheric distortion, in microscopy, optical fabrication and in retinal imaging systems to reduce optical aberrations. Adaptive optics works by measuring the distortions in a wavefront and compensating for them with a device that corrects those errors such as a deformable mirror or a liquid crystal array.

Adaptive optics should not be confused with active optics, which works on a longer timescale to correct the primary mirror geometry.

Other methods can achieve resolving power exceeding the limit imposed by atmospheric distortion, such as speckle imaging, aperture synthesis, and lucky imaging, or by moving outside the atmosphere with space telescopes, such as the Hubble Space Telescope.

History

Adaptive thin shell mirror.

Adaptive optics was first envisioned by Horace W. Babcock in 1953, and was also considered in science fiction, as in Poul Anderson's novel Tau Zero (1970), but it did not come into common usage until advances in computer technology during the 1990s made the technique practical.

Some of the initial development work on adaptive optics was done by the US military during the Cold War and was intended for use in tracking Soviet satellites.

Microelectromechanical systems (MEMS) deformable mirrors and magnetics concept deformable mirrors are currently the most widely used technology in wavefront shaping applications for adaptive optics given their versatility, stroke, maturity of technology and the high resolution wavefront correction that they afford.

Tip–tilt correction

The simplest form of adaptive optics is tip-tilt correction, which corresponds to correction of the tilts of the wavefront in two dimensions (equivalent to correction of the position offsets for the image). This is performed using a rapidly moving tip–tilt mirror that makes small rotations around two of its axes. A significant fraction of the aberration introduced by the atmosphere can be removed in this way.

Tip–tilt mirrors are effectively segmented mirrors having only one segment which can tip and tilt, rather than having an array of multiple segments that can tip and tilt independently. Due to the relative simplicity of such mirrors and having a large stroke, meaning they have large correcting power, most AO systems use these, first, to correct low order aberrations. Higher order aberrations may then be corrected with deformable mirrors.

In astronomy

Astronomers at the Very Large Telescope site in Chile use adaptive optics.

 

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Laser being launched into the night sky from the VLT Adaptive Optics Facility.

Atmospheric seeing

When light from a star passes through the Earth's atmosphere, the wavefront is perturbed.

 

The Shack-Hartmann sensor is one type of wavefront sensor used for adaptive optics.

 

Negative images of a star through a telescope. The left-hand panel shows the slow-motion movie of a star when the adaptive optics system is switched off. The right-hand panel shows the slow motion movie of the same star when the AO system is switched on.

When light from a star or another astronomical object enters the Earth's atmosphere, atmospheric turbulence (introduced, for example, by different temperature layers and different wind speeds interacting) can distort and move the image in various ways. Visual images produced by any telescope larger than approximately 20 centimeters are blurred by these distortions.

Wavefront sensing and correction

An adaptive optics system tries to correct these distortions, using a wavefront sensor which takes some of the astronomical light, a deformable mirror that lies in the optical path, and a computer that receives input from the detector. The wavefront sensor measures the distortions the atmosphere has introduced on the timescale of a few milliseconds; the computer calculates the optimal mirror shape to correct the distortions and the surface of the deformable mirror is reshaped accordingly. For example, an 8–10 m telescope (like the VLT or Keck) can produce AO-corrected images with an angular resolution of 30–60 milliarcsecond (mas) resolution at infrared wavelengths, while the resolution without correction is of the order of 1 arcsecond.

In order to perform adaptive optics correction, the shape of the incoming wavefronts must be measured as a function of position in the telescope aperture plane. Typically the circular telescope aperture is split up into an array of pixels in a wavefront sensor, either using an array of small lenslets (a Shack–Hartmann sensor), or using a curvature or pyramid sensor which operates on images of the telescope aperture. The mean wavefront perturbation in each pixel is calculated. This pixelated map of the wavefronts is fed into the deformable mirror and used to correct the wavefront errors introduced by the atmosphere. It is not necessary for the shape or size of the astronomical object to be known – even Solar System objects which are not point-like can be used in a Shack–Hartmann wavefront sensor, and time-varying structure on the surface of the Sun is commonly used for adaptive optics at solar telescopes. The deformable mirror corrects incoming light so that the images appear sharp.

Using guide stars

Natural guide stars

Because a science target is often too faint to be used as a reference star for measuring the shape of the optical wavefronts, a nearby brighter guide star can be used instead. The light from the science target has passed through approximately the same atmospheric turbulence as the reference star's light and so its image is also corrected, although generally to a lower accuracy.

A laser beam directed toward the centre of the Milky Way. This laser beam can then be used as a guide star for the AO.

The necessity of a reference star means that an adaptive optics system cannot work everywhere on the sky, but only where a guide star of sufficient luminosity (for current systems, about magnitude 12–15) can be found very near to the object of the observation. This severely limits the application of the technique for astronomical observations. Another major limitation is the small field of view over which the adaptive optics correction is good. As the angular distance from the guide star increases, the image quality degrades. A technique known as "multiconjugate adaptive optics" uses several deformable mirrors to achieve a greater field of view.

Artificial guide stars

An alternative is the use of a laser beam to generate a reference light source (a laser guide star, LGS) in the atmosphere. LGSs come in two flavors: Rayleigh guide stars and sodium guide stars. Rayleigh guide stars work by propagating a laser, usually at near ultraviolet wavelengths, and detecting the backscatter from air at altitudes between 15–25 km. Sodium guide stars use laser light at 589 nm to excite sodium atoms higher in the mesosphere and thermosphere, which then appear to "glow". The LGS can then be used as a wavefront reference in the same way as a natural guide star – except that (much fainter) natural reference stars are still required for image position (tip/tilt) information. The lasers are often pulsed, with measurement of the atmosphere being limited to a window occurring a few microseconds after the pulse has been launched. This allows the system to ignore most scattered light at ground level; only light which has travelled for several microseconds high up into the atmosphere and back is actually detected.

In retinal imaging

Artist's impression of the European Extremely Large Telescope deploying lasers for adaptive optics

Ocular aberrations are distortions in the wavefront passing through the pupil of the eye. These optical aberrations diminish the quality of the image formed on the retina, sometimes necessitating the wearing of spectacles or contact lenses. In the case of retinal imaging, light passing out of the eye carries similar wavefront distortions, leading to an inability to resolve the microscopic structure (cells and capillaries) of the retina. Spectacles and contact lenses correct "low-order aberrations", such as defocus and astigmatism, which tend to be stable in humans for long periods of time (months or years). While correction of these is sufficient for normal visual functioning, it is generally insufficient to achieve microscopic resolution. Additionally, "high-order aberrations", such as coma, spherical aberration, and trefoil, must also be corrected in order to achieve microscopic resolution. High-order aberrations, unlike low-order, are not stable over time, and may change over time scales of 0.1s to 0.01s. The correction of these aberrations requires continuous, high-frequency measurement and compensation.

Measurement of ocular aberrations

Ocular aberrations are generally measured using a wavefront sensor, and the most commonly used type of wavefront sensor is the Shack-Hartmann. Ocular aberrations are caused by spatial phase nonuniformities in the wavefront exiting the eye. In a Shack-Hartmann wavefront sensor, these are measured by placing a two-dimensional array of small lenses (lenslets) in a pupil plane conjugate to the eye's pupil, and a CCD chip at the back focal plane of the lenslets. The lenslets cause spots to be focused onto the CCD chip, and the positions of these spots are calculated using a centroiding algorithm. The positions of these spots are compared with the positions of reference spots, and the displacements between the two are used to determine the local curvature of the wavefront allowing one to numerically reconstruct the wavefront information—an estimate of the phase nonuniformities causing aberration.

Correction of ocular aberrations

Once the local phase errors in the wavefront are known, they can be corrected by placing a phase modulator such as a deformable mirror at yet another plane in the system conjugate to the eye's pupil. The phase errors can be used to reconstruct the wavefront, which can then be used to control the deformable mirror. Alternatively, the local phase errors can be used directly to calculate the deformable mirror instructions.

Open loop vs. closed loop operation

If the wavefront error is measured before it has been corrected by the wavefront corrector, then operation is said to be "open loop". If the wavefront error is measured after it has been corrected by the wavefront corrector, then operation is said to be "closed loop". In the latter case then the wavefront errors measured will be small, and errors in the measurement and correction are more likely to be removed. Closed loop correction is the norm.

Applications

Adaptive optics was first applied to flood-illumination retinal imaging to produce images of single cones in the living human eye. It has also been used in conjunction with scanning laser ophthalmoscopy to produce (also in living human eyes) the first images of retinal microvasculature and associated blood flow and retinal pigment epithelium cells in addition to single cones. Combined with optical coherence tomography, adaptive optics has allowed the first three-dimensional images of living cone photoreceptors to be collected.

In microscopy

In microscopy, adaptive optics is used to correct for sample-induced aberrations. The required wavefront correction is either measured directly using wavefront sensor or estimated by using sensorless AO techniques.

Other uses

GRAAL is a ground layer adaptive optics instrument assisted by lasers.

Besides its use for improving nighttime astronomical imaging and retinal imaging, adaptive optics technology has also been used in other settings. Adaptive optics is used for solar astronomy at observatories such as the Swedish 1-m Solar Telescope and Big Bear Solar Observatory. It is also expected to play a military role by allowing ground-based and airborne laser weapons to reach and destroy targets at a distance including satellites in orbit. The Missile Defense Agency Airborne Laser program is the principal example of this.

Adaptive optics has been used to enhance the performance of free space optical communication systems and to control the spatial output of optical fibers.

Medical applications include imaging of the retina, where it has been combined with optical coherence tomography. Also the development of Adaptive Optics Scanning Laser Opthalmoscope (AOSLO) has enabled correcting for the aberrations of the wavefront that is reflected from the human retina and to take diffraction limited images of the human rods and cones. Development of an Adaptive Scanning Optical Microscope (ASOM) was announced by Thorlabs in April 2007. Adaptive and active optics are also being developed for use in glasses to achieve better than 20/20 vision, initially for military applications.

After propagation of a wavefront, parts of it may overlap leading to interference and preventing adaptive optics from correcting it. Propagation of a curved wavefront always leads to amplitude variation. This needs to be considered if a good beam profile is to be achieved in laser applications.

Adaptive optics, especially wavefront-coding spatial light modulators, are frequently used in optical trapping applications to multiplex and dynamically reconfigure laser foci that are used to micro-manipulate biological specimens.

Beam stabilization

A rather simple example is the stabilization of the position and direction of laser beam between modules in a large free space optical communication system. Fourier optics is used to control both direction and position. The actual beam is measured by photo diodes. This signal is fed into some Analog-to-digital converters and a microcontroller runs a PID controller algorithm. The controller drives some digital-to-analog converters which drive stepper motors attached to mirror mounts.

If the beam is to be centered onto 4-quadrant diodes, no Analog-to-digital converter is needed. Operational amplifiers are sufficient.

Thirty Meter Telescope

From Wikipedia, the free encyclopedia

Thirty Meter Telescope

Artist's rendering of proposed telescope
Alternative names	California Extremely Large Telescope
Location(s)	(proposed) Mauna Kea Observatory in Hawaii, United States
Coordinates	19.8327°N 155.4816°WCoordinates: 19.8327°N 155.4816°W
Organization	TMT International Observatory
Altitude	4,050 m or 13,290 ft
Wavelength	Near UV, visible, and Mid-IR (0.31–28 μm)
Built	mid-2020
First light	est. 2027
Telescope style	Segmented Ritchey–Chrétien telescope
Diameter	30 m or 98 ft
Secondary diameter	3.1 m or 10 ft
Tertiary diameter	2.5 m × 3.5 m or 8.2 ft × 11.5 ft
Collecting area	655 m2 or 7,050 sq ft
Focal length	f/15 (450 m)
Mounting	Altazimuth mount
Enclosure	Spherical calotte
Website	TMT.org
Location of Thirty Meter Telescope

The Thirty Meter Telescope (TMT) is a proposed astronomical observatory with an extremely large telescope (ELT) that has become the source of controversy over its planned location on Mauna Kea on the island of Hawaii in the US state of Hawaii. Construction of the TMT on land which is sacred to Native Hawaiian culture and religion attracted press coverage after October 2014, when construction was temporarily halted due to protests. While construction of the telescope was set to resume on April 2 and later on June 24, 2015, it was blocked by further protests each time. The Board of Land and Natural Resources approved the TMT project, but the Supreme Court of Hawaii invalidated the building permits in December 2015, ruling that the board had not followed due process. On October 30, 2018, the Court approved the resumption of construction. The TMT would become the last area on Mauna Kea on which any telescope will ever be built.

Scientists have been considering ELTs since the mid 1980s. In 2000, astronomers considered the possibility of a telescope with a light-gathering mirror larger than 20 meters in diameter. The technology to build a mirror larger than 8.4 meters does not exist; instead scientists considered using either small segments that create one large mirror, or a grouping of larger 8-meter mirrors working as one unit. The US National Academy of Sciences recommended a 30-meter telescope be the focus of U.S. interests, seeking to see it built within the decade. Scientists at the University of California and Caltech began development of a design that would eventually become the TMT, consisting of 492 segmented mirrors with nine times the power of the Keck telescope. Due to its immense light-gathering power and the optimal observing conditions which exist atop Mauna Kea, the TMT would enable astronomers to conduct research which is infeasible with current instruments. The TMT is designed for near-ultraviolet to mid-infrared (0.31 to 28 μm wavelengths) observations, featuring adaptive optics to assist in correcting image blur. The TMT will be at the highest altitude of all the proposed ELTs. The telescope has government-level support from several nations.

Background

In 2000, astronomers began considering the potential of telescopes larger than 20 meters in diameter. Two technologies were considered; segmented mirrors like that of the Keck Observatory and the use of a group of 8-meter mirrors mounted to form a single unit. The US National Academy of Sciences made a suggestion that a 30-meter telescope should be the focus of US astronomy interests and recommended it to be built within the decade. The University of California, along with Caltech began development of a 30-meter telescope that same year. The California Extremely Large Telescope (CELT) began development along with the Giant Magellan Telescope, the Giant Segmented Mirror Telescope (GSMT) and the Very Large Optical Telescope (VLOT). These studies would eventually become the Thirty Meter Telescope. The TMT would have nine times the collecting area of the older Keck telescope using slightly smaller mirror segments in a vastly larger group. Another telescope of a large diameter in the works is the European Extremely Large Telescope (E-ELT) being built in northern Chile.

The telescope is designed for observations from near-ultraviolet to mid-infrared (0.31 to 28 μm wavelengths). In addition, its adaptive optics system will help correct for image blur caused by the atmosphere of the Earth, helping it to reach the potential of such a large mirror. Among existing and planned ELTs, the TMT will have the highest altitude and will be the second-largest telescope once the E-ELT is built. Both use segments of small 1.44 m hexagonal mirrors—a design vastly different from the large mirrors of the Large Binocular Telescope (LBT) or the Giant Magellan Telescope (GMT). The TMT has government-level support from the following countries: Canada, China, Japan and India. The United States is also contributing some funding, but less than the formal partnership.

Proposed locations

In cooperation with AURA, the TMT project completed a multi-year evaluation of five sites:

• Roque de los Muchachos Observatory, La Palma, Canary Islands, Spain
• Cerro Armazones, Antofagasta Region, Republic of Chile
• Cerro Tolanchar, Antofagasta Region, Republic of Chile
• Cerro Tolar, Antofagasta Region, Republic of Chile
• Mauna Kea, Hawaii, United States (This site was chosen and approval granted in April 2013)
• San Pedro Mártir, Baja California, Mexico
• Hanle, Jammu and Kashmir, India

The TMT Observatory Corporation board of directors narrowed the list to two sites, one in each hemisphere, for further consideration: Cerro Armazones in Chile's Atacama Desert, and Mauna Kea on Hawaii Island. On July 21, 2009 the TMT board announced Mauna Kea as the preferred site. The final TMT site selection decision was based on a combination of scientific, financial, and political criteria. Chile is also where the European Southern Observatory is building the E-ELT. If both next-generation telescopes were in the same hemisphere, there would be many astronomical objects that neither could observe. The telescope was given approval by the state Board of Land and Natural Resources in April 2013. There has been opposition to the building of the telescope, based on potential disruption to the fragile alpine environment of Mauna Kea due to construction, traffic and noise, which is a concern for the habitat of several species, and that Mauna Kea is a sacred site for the Native Hawaiian culture. The Hawaii Board of Land and Natural Resources conditionally approved the Mauna Kea site for the TMT in February 2011. The approval has been challenged; however, the Board officially approved the site following a hearing on February 12, 2013.

Partnerships and funding

The Gordon and Betty Moore Foundation has committed US$200 million for construction. Caltech and the University of California have committed an additional US$50 million each. Japan, which has its own large telescope at Mauna Kea, the 8.3-metre Subaru, is also a partner.

In 2008, the National Astronomical Observatory of Japan (NAOJ) joined TMT as a Collaborating Institution. The following year, the telescope cost was estimated to be $970 million to $1.4 billion. That same year, the National Astronomical Observatories of the Chinese Academy of Sciences (NAOC) joined TMT as an Observer.

In 2010, a consortium of Indian Astronomy Research Institutes (IIA, IUCAA and ARIES) joined TMT project as an observer. The observer status is the first step in becoming a full partner in the construction of the TMT and participating in the engineering development and scientific use of the observatory (Subject to approval of funding from Indian Government). Two years later, India and China became partners with representatives on the TMT board. Both countries agreed to share the telescope construction costs, expected to top $1 billion.

The continued financial commitment from the Canadian government had been in doubt due to economic pressures. Nevertheless, on April 6, 2015, Prime Minister Stephen Harper announced that Canada would commit $243.5 million over a period of 10 years. The structure will be built by Dynamic Structures Ltd. in British Columbia, and then shipped to Mauna Kea.

Approval process

In 2008, the TMT corporation selected two semi-finalists for further study, Mauna Kea and Cerro Amazones. In July 2009, Mauna Kea was selected. Once TMT selected Mauna Kea, the project began a regulatory and community process for approval. Mauna Kea is ranked as one of the best sites on Earth for telescope viewing and is home to 13 other telescopes built at the summit of the mountain, within the Mauna Kea Observatories grounds. Telescopes generate money for the big island, with millions of dollars in jobs and subsidies gained by the state. The TMT would be one of the most expensive telescopes ever created.

• In 2010 the Governor of Hawaii signed off on an environmental study after 14 community meetings.
• The BLNR held hearings on December 2 and December 3, 2010 on the application for a permit.
• On February 25, 2011 the board granted the permits after multiple public hearings. This approval had conditions, in particular that a hearing about contesting the approval be heard.
• A contested case hearing was held in August 2011, which led to a judgment by the hearing officer for approval in November 2012. The telescope was given approval by the state Board of Land and Natural Resources in April 2013. This process was challenged in court with a lower court ruling in May 2014. The Intermediate Court of Appeals of the State of Hawaii declined to hear an appeal regarding the permit until the Hawaii Department of Land and Natural Resources first issued a decision from the contested case hearing that could then be appealed to the court.
• The dedication and ground-breaking ceremony was held, but interrupted by protesters on October 7, 2014. The project became the focal point of escalating political conflict, police arrests and continued litigation over the proper use of conservation lands. Native Hawaiian cultural practice and religious rights became central to the opposition, with concerns over the lack of meaningful dialogue during the permitting process.
• On December 2, 2015, the Hawaii State Supreme Court ruled the 2011 permit from the Hawaii Board of Land and Natural Resources was invalid. The high court stated: "BLNR put the cart before the horse when it approved the permit before the contested case hearing". and "Once the permit was granted, Appellants were denied the most basic element of procedural due process – an opportunity to be heard at a meaningful time and in a meaningful manner. Our Constitution demands more". In March 2017, the Board’s hearing officer, retired judge Riki May Amano, finished six months of hearings in Hilo, Hawaii, taking 44 days of testimony from 71 witnesses. On July 26, 2017, Amano filed her recommendation that the Land Board grant the construction permit.
• On September 28, 2017, the State of Hawaii Board of Land and Natural Resources (BLNR), acting on Amano's report, approved, by a vote of 5-2, a Conservation District Use Permit (CDUP) for the TMT. Numerous conditions, including the removal of three existing telescopes and an assertion that the TMT is to be the last telescope on the mountain, were attached to the permit.
• On October 30, 2018, the Supreme Court of Hawaii ruled the CDUP was valid, allowing construction to proceed.

Observatory design

The TMT would be a general-purpose observatory capable of investigating a broad range of astrophysical problems. Total diameter of the dome will be 217 feet with the total dome height at 180 feet (comparable in height to an eighteen-story building). Total area of the structure is projected to be 1.44 acres within a 5-acre complex.

Telescope

Thirty Meter Telescope design (late 2007).

The centerpiece of the TMT Observatory is to be a Ritchey-Chrétien telescope with a 30-metre (98 ft) diameter primary mirror. This mirror is to be segmented and consist of 492 smaller (1.4 m), individual hexagonal mirrors. The shape of each segment, as well as its position relative to neighboring segments, will be controlled actively.

A 3.6-metre (12 ft) secondary mirror is to produce an unobstructed field-of-view of 20 arcminutes in diameter with a focal ratio of 15. A flat tertiary mirror is to direct the light path to science instruments mounted on large Nasmyth platforms. The telescope is to have an alt-azimuth mount. Target acquisition and system configuration capabilities need to be achieved within 5 minutes, or ten minutes if relocating to a newer device. To achieve these time limitations the TMT will use a software architecture linked by a service based communications system. The moving mass of the telescope, optics, and instruments will be 1430 tons. The design of the facility descends from the W. M. Keck Observatory.

Adaptive optics

Integral to the observatory is a Multi-Conjugate Adaptive Optics (MCAO) system. This MCAO system will measure atmospheric turbulence by observing a combination of natural (real) stars and artificial laser guide stars. Based on these measurements, a pair of deformable mirrors will be adjusted many times per second to correct optical wave-front distortions caused by the intervening turbulence.

This system will produce diffraction-limited images over a 30-arc-second diameter field-of-view, which means that the core of the point spread function will have a size of 0.015 arc-second at a wavelength of 2.2 micrometers, almost ten times better than the Hubble Space Telescope.

Scientific instrumentation

Mirror sizes of existing and proposed telescopes. The two other new ELT the E-ELT and GMT are being built in the southern hemisphere

Early-light capabilities

Three instruments are planned to be available for scientific observations:

• Wide Field Optical Spectrometer (WFOS)' providing near-ultraviolet and optical (0.3–1.0 μm wavelength) imaging and spectroscopy over a more than 40-square arc-minute field-of-view. Using precision cut focal plane masks, WFOS would enable long-slit observations of single objects as well as short-slit observations of hundreds of objects simultaneously. WFOS would use natural (uncorrected) seeing images.
• Infrared Imaging Spectrometer (IRIS) mounted on the observatory MCAO system, capable of diffraction-limited imaging and integral-field spectroscopy at near-infrared wavelengths (0.8–2.5 μm). Principal investigators are James Larkin of UCLA and Anna Moore of Caltech. Project scientist is Shelley Wright of UC San Diego.
• Infrared Multi-object Spectrometer (IRMS) allowing close to diffraction-limited imaging and slit spectroscopy over a 2 arc-minute diameter field-of-view at near-infrared wavelengths (0.8–2.5 μm).

Protests

Cultural practitioner Joshua Lanakila Mangauil, along with Kahoʻokahi Kanuha and Hawaiian sovereignty supporters block the access road to Mauna Kea in October 2014, demonstrating against the building of the Thirty Meter Telescope.

The proposed construction of the TMT on Mauna Kea sparked protests and demonstrations across the state of Hawaii. Mauna Kea is the most sacred mountain in Hawaiian culture. The mountain is also conservation land held in trust by the state of Hawaii.

On October 7, 2014, the groundbreaking for the TMT was interrupted by demonstrators causing a postponement of construction In late March 2015, demonstrators again halted the construction crews. On April 2, 2015, about 300 protesters gathered on Mauna Kea, some of them trying to block the access road to the summit; 23 arrests were made. Once the access road to the summit was cleared by the police, about 40 to 50 protesters began following the heavily laden and slow-moving construction trucks to the summit construction site.

On April 7, 2015, the construction was halted for one week at the request of Hawaii state governor David Ige, after the protest on Mauna Kea continued. Project manager Gary Sanders stated that TMT agreed to the one-week stop for continued dialogue; Kealoha Pisciotta, president of Mauna Kea Anaina Hou, one of the organizations that have challenged the TMT in court, viewed the development as positive but said opposition to the project would continue. On April 8, 2015, Governor Ige announced that the project was being temporarily postponed until at least April 20, 2015. Construction was set to begin again on June 24, though hundreds of protesters gathered on that day, blocking access to the construction site for the TMT. Some protesters camped on the access road to the site, while others rolled large rocks onto the road. The actions resulted in 11 arrests.

On December 2, 2015, the Supreme Court of Hawaii invalidated the TMT's building permits, ruling that due process was not followed when the Board of Land and Natural Resources approved the permit before the contested case hearing. The TMT company chairman stated: "T.M.T. will follow the process set forth by the state." A revised permit was approved on September 28, 2017 by the Hawaii Board of Land and Natural Resources. On October 30, 2018, the Supreme Court of Hawaii ruled, 4-1, that the revised permit was acceptable and construction may proceed.

Babylonian astronomy

From Wikipedia, the free encyclopedia

A Babylonian tablet recording Halley's comet in 164 BC.

Babylonian astronomy was the study or recording of celestial objects during early history Mesopotamia. These records can be found on Sumerian clay tablets, inscribed in cuneiform, dated approximately to 3500–3200 BC.

In conjunction with their mythology, the Sumerians developed a form of astronomy/astrology that had an influence on Babylonian culture. Therein Planetary gods played an important role.

Babylonian astronomy seemed to have focused on a select group of stars and constellations known as Ziqpu stars. These constellations may have been collected from various earlier sources. The earliest catalogue, Three Stars Each, mentions stars of the Akkadian Empire, of Amurru, of Elam and others.

A numbering system based on sixty was used, a sexagesimal system. This system simplified the calculating and recording of unusually great and small numbers. The modern practices of dividing a circle into 360 degrees, of 60 minutes each, began with the Sumerians.

During the 8th and 7th centuries BC, Babylonian astronomers developed a new empirical approach to astronomy. They began studying and recording their belief system and philosophies dealing with an ideal nature of the universe and began employing an internal logic within their predictive planetary systems. This was an important contribution to astronomy and the philosophy of science, and some modern scholars have thus referred to this novel approach as the first scientific revolution. This approach to astronomy was adopted and further developed in Greek and Hellenistic astrology. Classical Greek and Latin sources frequently use the term Chaldeans for the astronomers of Mesopotamia, who were considered as priest-scribes specializing in astrology and other forms of divination.

Only fragments of Babylonian astronomy have survived, consisting largely of contemporary clay tablets containing astronomical diaries, ephemerides and procedure texts, hence current knowledge of Babylonian planetary theory is in a fragmentary state. Nevertheless, the surviving fragments show that Babylonian astronomy was the first "successful attempt at giving a refined mathematical description of astronomical phenomena" and that "all subsequent varieties of scientific astronomy, in the Hellenistic world, in India, in Islam, and in the West … depend upon Babylonian astronomy in decisive and fundamental ways."

The origins of Western astronomy can be found in Mesopotamia, and all Western efforts in the exact sciences are descendants in direct line from the work of the late Babylonian astronomers. Modern knowledge of Sumerian astronomy is indirect, via the earliest Babylonian star catalogues dating from about 1200 BC. The fact that many star names appear in Sumerian suggests a continuity reaching into the Early Bronze Age.

Old Babylonian astronomy

"Old" Babylonian astronomy was practiced during and after the First Babylonian Dynasty (ca. 1830 BC) and before the Neo-Babylonian Empire (ca. 626 BC).
The Babylonians were the first to recognize that astronomical phenomena are periodic and apply mathematics to their predictions. Tablets dating back to the Old Babylonian period document the application of mathematics to the variation in the length of daylight over a solar year. Centuries of Babylonian observations of celestial phenomena were recorded in the series of cuneiform tablets known as the Enûma Anu Enlil—the oldest significant astronomical text that we possess is Tablet 63 of the Enûma Anu Enlil, the Venus tablet of Ammisaduqa, which lists the first and last visible risings of Venus over a period of about 21 years. It is the earliest evidence that planetary phenomena were recognized as periodic.

An object labelled the ivory prism was recovered from the ruins of Nineveh. First presumed to be describing rules to a game, its use was later deciphered to be a unit converter for calculating the movement of celestial bodies and constellations.

Babylonian astronomers developed zodiacal signs. they are made up of the division of the sky into three sets of thirty degrees and the constellations that inhabit each sector.

The MUL.APIN contains catalogues of stars and constellations as well as schemes for predicting heliacal risings and settings of the planets, and lengths of daylight as measured by a water clock, gnomon, shadows, and intercalations. The Babylonian GU text arranges stars in 'strings' that lie along declination circles and thus measure right-ascensions or time intervals, and also employs the stars of the zenith, which are also separated by given right-ascensional differences. There are dozens of cuneiform Mesopotamian texts with real observations of eclipses, mainly from Babylonia.

Planetary theory

The Babylonians were the first civilization known to possess a functional theory of the planets. The oldest surviving planetary astronomical text is the Babylonian Venus tablet of Ammisaduqa, a 7th-century BC copy of a list of observations of the motions of the planet Venus that probably dates as early as the second millennium BC. The Babylonian astrologers also laid the foundations of what would eventually become Western astrology. The Enuma anu enlil, written during the Neo-Assyrian period in the 7th century BC, comprises a list of omens and their relationships with various celestial phenomena including the motions of the planets.

Cosmology

In contrast to the world view presented in Mesopotamian and Assyro-Babylonian literature, particularly in Mesopotamian and Babylonian mythology, very little is known about the cosmology and world view of the ancient Babylonian astrologers and astronomers. This is largely due to the current fragmentary state of Babylonian planetary theory, and also due to Babylonian astronomy being independent from cosmology at the time. Nevertheless, traces of cosmology can be found in Babylonian literature and mythology.

In Babylonian cosmology, the Earth and the heavens were depicted as a "spatial whole, even one of round shape" with references to "the circumference of heaven and earth" and "the totality of heaven and earth". Their worldview was not exactly geocentric either. The idea of geocentrism, where the center of the Earth is the exact center of the universe, did not yet exist in Babylonian cosmology, but was established later by the Greek philosopher Aristotle's On the Heavens. In contrast, Babylonian cosmology suggested that the cosmos revolved around circularly with the heavens and the earth being equal and joined as a whole. The Babylonians and their predecessors, the Sumerians, also believed in a plurality of heavens and earths. This idea dates back to Sumerian incantations of the 2nd millennium BC, which refers to there being seven heavens and seven earths, linked possibly chronologically to the creation by seven generations of gods.

Omens

It was a common Mesopotamian belief that gods could and did indicate future events to mankind. This indication of future events were considered to be omens. The Mesopotamian belief in omens pertains to astronomy and its predecessor astrology because it was a common practice at the time to look to the sky for omens. The other way to receive omens at the time was to look at animal entrails. This method of recovering omens is classified as a producible omen, meaning it can be produced by humans, but sky omens are produced without human action and therefore seen as much more powerful. Both producible and unproducable omens however, were seen as messages from the gods. Just because gods sent the signs didn’t mean that Mesopotamians believed their fate was sealed either, the belief during this time was that omens were avoidable. In mathematical terms, the Mesopotamians viewed omens as “if x, then y”, where “X” is the protasis and “Y” is the apodosis. The relationship Mesopotamians had with omens can be seen in the Omen Compendia, a Babylonian text composed starting from the beginning of the second millennium on-wards. It is the primary source text that tells us that ancient Mesopotamians saw omens as preventable. The text also contains information on Sumerian rites to avert evil, or “nam-bur-bi”. A term later adopted by the Akkadians as “namburbu”, roughly, “[the evil] loosening”. The god Ea was the one believed to send the omens. Concerning the severity of omens, eclipses were seen as the most dangerous.

The Enuma Anu Enlil is a series of cuneiform tablets that gives insight on different sky omens Babylonian astronomers observed. Celestial bodies such as the sun and moon were given significant power as omens. Reports from Nineveh and Babylon, circa 2500-670 B.C.E., show lunar omens observed by the Mesopotamians. "When the moon disappears, evil will befall the land. When the moon disappears out of its reckoning, an eclipse will take place".

The Astrolabes

The astrolabes are one of the earliest documented cuneiform tablets that discuss astronomy and date back to the Old Babylonian Kingdom (not to be mistaken for the later astronomical measurement device of the same name). They are a list of thirty-six stars connected with the months in a year. Generally considered to be written between 1800-1100 B.C.E.. No complete texts have been found, but there is a modern compilation by Pinches, assembled from texts housed in the British Museum that is considered excellent by other historians who specialize in Babylonian astronomy. Two other texts concerning the astrolabes that should be mentioned are the Brussels and Berlin compilations. They offer similar information to the Pinches anthology, but do contain some differing information from each other.

The thirty-six stars that make up the astrolabes are believed to be derived from the astronomical traditions from three Mesopotamian city-states, Elam, Akkad, and Amurru. The stars followed and possibly charted by these city-states are identical stars to the ones in the astrolabes. Each region had a set of twelve stars it followed, which combined equals the thirty-six stars in the astrolabes. The twelve stars of each region also correspond to the months of the year. The two cuneiform texts that provide the information for this claim are the large star list “K 250” and “K 8067”. Both of these tablets were translated and transcribed by Weidner. During the reign of Hammurabi these three separate traditions were combined. This combining also ushered in a more scientific approach to astronomy as connections to the original three traditions weakened. The increased use of science in astronomy is evidenced by the traditions from these three regions being arranged in accordance to the paths of the stars of Ea, Anu, and Enlil, an astronomical system contained and discussed in the Mul.apin.

MUL.APIN

Mul.apin cuneiform tablet

MUL.APIN is a collection of two cuneiform tablets (Tablet 1 and Tablet 2) that document aspects of Babylonian astronomy such as the movement of celestial bodies and records of solstices and eclipses. Each tablet is also split into smaller sections called Lists. It was comprised in the general time frame of the astrolabes and Enuma Anu Enlil, evidenced by similar themes, mathematical principles, and occurrences.

Tablet 1 houses information that closely parallels information contained in astrolabe B. The similarities between Tablet 1 and astrolabe B show that the authors were inspired by the same source for at least some of the information. There are six lists of stars on this tablet that relate to sixty constellations in charted paths of the three groups of Babylonian star paths, Ea, Anu, and Enlil. there are also additions to the paths of both Anu and Enlil that are not found in astrolabe B.

The Connection Between a Calendar, Mathematics, and Astronomy

The exploration of the sun, moon, and other celestial bodies affected the development of Mesopotamian culture. The study of the sky led to the development of a calendar and advanced mathematics in these societies. The Babylonians were not the first complex society to develop a calendar globally and in nearby North Africa, The Egyptians developed a calendar of their own. The Egyptian calendar was solar based, while the Babylonian calendar was lunar based. A potential blend between the two that has been noted by some historians is the adoption of a crude leap year by the Babylonians after the Egyptians developed one. The Babylonian leap year shares no similarities with the leap year practiced today. it involved the addition of a thirteenth month as a means to re-calibrate the calendar to better match the growing season.

Babylonian priests were the ones responsible for developing new forms of mathematics and did so to better calculate the movements of celestial bodies. One such priest, Nabu-rimanni, is the first documented Babylonian astronomer. He was a priest for the moon god and is credited with writing lunar and eclipse computation tables as well as other elaborate mathematical calculations. The computation tables are organized in seventeen or eighteen tables that document the orbiting speeds of planets and the moon. His work was later recounted by astronomers during the Seleucid dynasty.

Neo-Babylonian astronomy

Neo-Babylonian astronomy refers to the astronomy developed by Chaldean astronomers during the Neo-Babylonian, Achaemenid, Seleucid, and Parthian periods of Mesopotamian history. A significant increase in the quality and frequency of Babylonian observations appeared during the reign of Nabonassar (747–734 BC). The systematic records of ominous phenomena in Babylonian astronomical diaries that began at this time allowed for the discovery of a repeating 18-year Saros cycle of lunar eclipses, for example. The Greco-Egyptian astronomer Ptolemy later used Nabonassar's reign to fix the beginning of an era, since he felt that the earliest usable observations began at this time.

The last stages in the development of Babylonian astronomy took place during the time of the Seleucid Empire (323–60 BC). In the 3rd century BC, astronomers began to use "goal-year texts" to predict the motions of the planets. These texts compiled records of past observations to find repeating occurrences of ominous phenomena for each planet. About the same time, or shortly afterwards, astronomers created mathematical models that allowed them to predict these phenomena directly, without consulting past records.

Arithmetical and geometrical methods

Though there is a lack of surviving material on Babylonian planetary theory, it appears most of the Chaldean astronomers were concerned mainly with ephemerides and not with theory. It had been thought that most of the predictive Babylonian planetary models that have survived were usually strictly empirical and arithmetical, and usually did not involve geometry, cosmology, or speculative philosophy like that of the later Hellenistic models, though the Babylonian astronomers were concerned with the philosophy dealing with the ideal nature of the early universe. Babylonian procedure texts describe, and ephemerides employ, arithmetical procedures to compute the time and place of significant astronomical events. More recent analysis of previously unpublished cuneiform tablets in the British Museum, dated between 350 and 50 BC, demonstrates that Babylonian astronomers sometimes used geometrical methods, prefiguring the methods of the Oxford Calculators, to describe the motion of Jupiter over time in an abstract mathematical space.

In contrast to Greek astronomy which was dependent upon cosmology, Babylonian astronomy was independent from cosmology. Whereas Greek astronomers expressed "prejudice in favor of circles or spheres rotating with uniform motion", such a preference did not exist for Babylonian astronomers, for whom uniform circular motion was never a requirement for planetary orbits. There is no evidence that the celestial bodies moved in uniform circular motion, or along celestial spheres, in Babylonian astronomy.

Contributions made by the Chaldean astronomers during this period include the discovery of eclipse cycles and saros cycles, and many accurate astronomical observations. For example, they observed that the Sun's motion along the ecliptic was not uniform, though they were unaware of why this was; it is today known that this is due to the Earth moving in an elliptic orbit around the Sun, with the Earth moving swifter when it is nearer to the Sun at perihelion and moving slower when it is farther away at aphelion.

Chaldean astronomers known to have followed this model include Naburimannu (fl. 6th–3rd century BC), Kidinnu (d. 330 BC), Berossus (3rd century BCE), and Sudines (fl. 240 BCE). They are known to have had a significant influence on the Greek astronomer Hipparchus and the Egyptian astronomer Ptolemy, as well as other Hellenistic astronomers.

Heliocentric astronomy

The only surviving planetary model from among the Chaldean astronomers is that of the Hellenistic Seleucus of Seleucia (b. 190 BC), who supported the Greek Aristarchus of Samos' heliocentric model. Seleucus is known from the writings of Plutarch, Aetius, Strabo, and Muhammad ibn Zakariya al-Razi. The Greek geographer Strabo lists Seleucus as one of the four most influential astronomers, who came from Hellenistic Seleuceia on the Tigris, alongside Kidenas (Kidinnu), Naburianos (Naburimannu), and Sudines. Their works were originally written in the Akkadian language and later translated into Greek. Seleucus, however, was unique among them in that he was the only one known to have supported the heliocentric theory of planetary motion proposed by Aristarchus, where the Earth rotated around its own axis which in turn revolved around the Sun. According to Plutarch, Seleucus even proved the heliocentric system through reasoning, though it is not known what arguments he used.

According to Lucio Russo, his arguments were probably related to the phenomenon of tides. Seleucus correctly theorized that tides were caused by the Moon, although he believed that the interaction was mediated by the Earth's atmosphere. He noted that the tides varied in time and strength in different parts of the world. According to Strabo (1.1.9), Seleucus was the first to state that the tides are due to the attraction of the Moon, and that the height of the tides depends on the Moon's position relative to the Sun.

According to Bartel Leendert van der Waerden, Seleucus may have proved the heliocentric theory by determining the constants of a geometric model for the heliocentric theory and by developing methods to compute planetary positions using this model. He may have used trigonometric methods that were available in his time, as he was a contemporary of Hipparchus.

None of his original writings or Greek translations have survived, though a fragment of his work has survived only in Arabic translation, which was later referred to by the Persian philosopher Muhammad ibn Zakariya al-Razi (865-925).

Babylonian influence on Hellenistic astronomy

Many of the works of ancient Greek and Hellenistic writers (including mathematicians, astronomers, and geographers) have been preserved up to the present time, or some aspects of their work and thought are still known through later references. However, achievements in these fields by earlier ancient Near Eastern civilizations, notably those in Babylonia, were forgotten for a long time. Since the discovery of key archaeological sites in the 19th century, many cuneiform writings on clay tablets have been found, some of them related to astronomy. Most known astronomical tablets have been described by Abraham Sachs and later published by Otto Neugebauer in the Astronomical Cuneiform Texts (ACT). Herodotus writes that the Greeks learned such aspects of astronomy as the gnomon and the idea of the day being split into two halves of twelve from the Babylonians. Other sources point to Greek pardegms, a stone with 365-366 holes carved into it to represent the days in a year, from the Babylonians as well.

Since the rediscovery of the Babylonian civilization, it has been theorized that there was significant information exchange between classical and Hellenistic astronomy and Chaldean. The best documented borrowings are those of Hipparchus (2nd century BCE) and Claudius Ptolemy (2nd century CE).

Early influence

Some scholars support that the Metonic cycle may have been learned by the Greeks from Babylonian scribes. Meton of Athens, a Greek astronomer of the 5th century BCE, developed a lunisolar calendar based on the fact that 19 solar years is about equal to 235 lunar months, a period relation that perhaps was also known to the Babylonians.

In the 4th century BCE, Eudoxus of Cnidus wrote a book on the fixed stars. His descriptions of many constellations, especially the twelve signs of the zodiac show similarities to Babylonian. The following century Aristarchus of Samos used an eclipse cycle called the Saros cycle to determine the year length. However, the position that there was an early information exchange between Greeks and Chaldeans are weak inferences; possibly, there had been a stronger information exchange between the two after Alexander the Great established his empire over Persia in the latter part of the 4th century BCE.

Influence on Hipparchus and Ptolemy

In 1900, Franz Xaver Kugler demonstrated that Ptolemy had stated in his Almagest IV.2 that Hipparchus improved the values for the Moon's periods known to him from "even more ancient astronomers" by comparing eclipse observations made earlier by "the Chaldeans", and by himself. However Kugler found that the periods that Ptolemy attributes to Hipparchus had already been used in Babylonian ephemerides, specifically the collection of texts nowadays called "System B" (sometimes attributed to Kidinnu). Apparently Hipparchus only confirmed the validity of the periods he learned from the Chaldeans by his newer observations. Later Greek knowledge of this specific Babylonian theory is confirmed by 2nd-century papyrus, which contains 32 lines of a single column of calculations for the Moon using this same "System B", but written in Greek on papyrus rather than in cuneiform on clay tablets.

It is clear that Hipparchus (and Ptolemy after him) had an essentially complete list of eclipse observations covering many centuries. Most likely these had been compiled from the "diary" tablets: these are clay tablets recording all relevant observations that the Chaldeans routinely made. Preserved examples date from 652 BC to AD 130, but probably the records went back as far as the reign of the Babylonian king Nabonassar: Ptolemy starts his chronology with the first day in the Egyptian calendar of the first year of Nabonassar; i.e., 26 February 747 BC.

This raw material by itself must have been tough to use, and no doubt the Chaldeans themselves compiled extracts of e.g., all observed eclipses (some tablets with a list of all eclipses in a period of time covering a saros have been found). This allowed them to recognise periodic recurrences of events. Among others they used in System B (cf. Almagest IV.2):

• 223 (synodic) months = 239 returns in anomaly (anomalistic month) = 242 returns in latitude (draconic month). This is now known as the saros period which is very useful for predicting eclipses.
• 251 (synodic) months = 269 returns in anomaly
• 5458 (synodic) months = 5923 returns in latitude
• 1 synodic month = 29;31:50:08:20 days (sexagesimal; 29.53059413 ... days in decimals = 29 days 12 hours 44 min 3⅓ s)

The Babylonians expressed all periods in synodic months, probably because they used a lunisolar calendar. Various relations with yearly phenomena led to different values for the length of the year.
Similarly various relations between the periods of the planets were known. The relations that Ptolemy attributes to Hipparchus in Almagest IX.3 had all already been used in predictions found on Babylonian clay tablets.

Other traces of Babylonian practice in Hipparchus' work are

• first Greek known to divide the circle in 360 degrees of 60 arc minutes.
• first consistent use of the sexagesimal number system.
• the use of the unit pechus ("cubit") of about 2° or 2½°.
• use of a short period of 248 days = 9 anomalistic months.

Means of transmission

All this knowledge was transferred to the Greeks probably shortly after the conquest by Alexander the Great (331 BC). According to the late classical philosopher Simplicius (early 6th century), Alexander ordered the translation of the historical astronomical records under supervision of his chronicler Callisthenes of Olynthus, who sent it to his uncle Aristotle. It is worth mentioning here that although Simplicius is a very late source, his account may be reliable. He spent some time in exile at the Sassanid (Persian) court, and may have accessed sources otherwise lost in the West. It is striking that he mentions the title tèresis (Greek: guard) which is an odd name for a historical work, but is in fact an adequate translation of the Babylonian title massartu meaning "guarding" but also "observing". Anyway, Aristotle's pupil Callippus of Cyzicus introduced his 76-year cycle, which improved upon the 19-year Metonic cycle, about that time. He had the first year of his first cycle start at the summer solstice of 28 June 330 BC (Julian proleptic date), but later he seems to have counted lunar months from the first month after Alexander's decisive battle at Gaugamela in fall 331 BC. So Callippus may have obtained his data from Babylonian sources and his calendar may have been anticipated by Kidinnu. Also it is known that the Babylonian priest known as Berossus wrote around 281 BC a book in Greek on the (rather mythological) history of Babylonia, the Babyloniaca, for the new ruler Antiochus I; it is said that later he founded a school of astrology on the Greek island of Kos. Another candidate for teaching the Greeks about Babylonian astronomy/astrology was Sudines who was at the court of Attalus I Soter late in the 3rd century BC.

Historians have also found evidence that Athens during the late 5th century may have been aware of Babylonian astronomy. astronomers, or astronomical concepts and practices through the documentation by Xenophon of Socrates telling his students to study astronomy to the extent of being able to tell the time of night from the stars. This skill is referenced in the poem of Aratos, which discusses telling the time of night from the zodiacal signs.

In any case, the translation of the astronomical records required profound knowledge of the cuneiform script, the language, and the procedures, so it seems likely that it was done by some unidentified Chaldeans. Now, the Babylonians dated their observations in their lunisolar calendar, in which months and years have varying lengths (29 or 30 days; 12 or 13 months respectively). At the time they did not use a regular calendar (such as based on the Metonic cycle like they did later), but started a new month based on observations of the New Moon. This made it very tedious to compute the time interval between events.

What Hipparchus may have done is transform these records to the Egyptian calendar, which uses a fixed year of always 365 days (consisting of 12 months of 30 days and 5 extra days): this makes computing time intervals much easier. Ptolemy dated all observations in this calendar. He also writes that "All that he (=Hipparchus) did was to make a compilation of the planetary observations arranged in a more useful way" (Almagest IX.2). Pliny states (Naturalis Historia II.IX(53)) on eclipse predictions: "After their time (=Thales) the courses of both stars (=Sun and Moon) for 600 years were prophesied by Hipparchus, ...". This seems to imply that Hipparchus predicted eclipses for a period of 600 years, but considering the enormous amount of computation required, this is very unlikely. Rather, Hipparchus would have made a list of all eclipses from Nabonasser's time to his own.