title: Manny Villar

text: In 2019, "Forbes" magazine named Villar as the new richest individual in the Philippines, with an estimated net worth of $5.5 billion, surpassing Henry Sy Sr. In 2021, his net worth surged to approximately $6.7 billion despite being overtaken by the Sy siblings in "Forbes"' annual Philippines rich list.


title: Manny Villar

text: Villar entered politics when he was elected as the representative of Las Piñas-Muntinlupa's at-large district in 1992. At 42 years old, he was one of the youngest members of the House of Representatives. Early in his congressional career, Villar was a prolific filer of House bills; in the first 100 days of the Ninth Congress, Villar filed the most number of local bills in the House of Representatives. Due to congressional redistricting, he later represented the district of Las Piñas.


title: Manny Villar

text: Villar became the speaker of the House of Representatives in 1998, during his third term in congress. As speaker, he presided over the impeachment of President Joseph Estrada over corruption allegations in November 2000. Along with a large group of lawmakers which include the Senate president, Villar defected from Estrada's Laban ng Makabayang Masang Pilipino (LAMMP) coalition in order to hasten the process of impeachment. However, he was ousted as speaker by Estrada's allies, replacing him with Camarines Sur representative Arnulfo Fuentebella.


title: Manny Villar

text: Villar ran and won a seat as a senator in the 2001 elections. He ran as an independent candidate, but campaigned as a member of the People Power Coalition. He was later reelected in 2007, running as a member of the Genuine Opposition coalition.


title: Manny Villar

text: In July 2006, Villar became the Senate president, making him the first post-World War II public official to head both the House of Representatives and the Senate.


title: Manny Villar

text: In November 2008, due to issues regarding the construction of a road extension in C5, Villar lost support and resigned as president of the Senate. His successor, Juan Ponce Enrile, launched an inquiry regarding the project.


title: Manny Villar

text: Villar ran in the 2010 presidential election under the Nacionalista Party, with Senator Loren Legarda as his running mate.


title: Manny Villar

text: During the campaign, columnist William Esposo claimed that Villar lied in his television commercials and could not have been poor because his younger brother was admitted to FEU Hospital, which he claims was a top hospital at the time and, in 1962, there was no bone marrow transplantation and chemotherapy in the country yet. Villar clarified that his brother was admitted as a charity patient because the family was unable to afford treatment.


title: Manny Villar

text: As a junior at the University of the Philippines Diliman, Villar became friends with Cynthia Aguilar, his classmate at the UP College of Business Administration. They married at age 25. They have three children: Manuel Paolo, Mark, and Camille.


title: Geelong Football Club

text: The Geelong Football Club, nicknamed the Cats, is a professional Australian rules football club based in Geelong, Victoria, Australia. The club competes in the Australian Football League (AFL), the sport's premier competition, and are the 2022 reigning premiers.


title: Geelong Football Club

text: The club formed in 1859, making it the second oldest club in the AFL after Melbourne and one of the oldest football clubs in the world.


title: Geelong Football Club

text: In the 1860s, Geelong participated in a series of Challenge Cup competitions, and was a foundation member of both the Victorian Football Association (VFA) in 1877 and the Victorian Football League (VFL) in 1897, now the national AFL. The club won the Western District Challenge Cup in 1875, a then-record seven VFA premierships between 1878 and 1886, and six VFL premierships by 1963, after which it experienced a 44-year waiting period until it won its next premiership, a Grand Final-record 119-point victory in 2007. Geelong won a further three premierships in 2009, 2011 and 2022.


title: Geelong Football Club

text: Geelong play most of their home games at Kardinia Park (known for sponsorship reasons as GMHBA Stadium) and play the remainder at the Melbourne Cricket Ground. Geelong's traditional guernsey colours are white with navy blue hoops. The club's nickname was first used in 1923 after a run of losses prompted a local cartoonist to suggest that the club needed a black cat to bring it good luck. Geelong also field teams in other competitions; a reserves men's team in the Victorian Football League (VFL), a senior women's team in the AFL Women's (AFLW) and a reserves women's team in the VFL Women's (VFLW) competitions. The club's official team song and anthem is "We Are Geelong".


title: Geelong Football Club

text: The history of the Geelong Football Club, began in 1859 in the city of Geelong, Australia, is significant as the club is the second oldest AFL club, is believed to be the fourth oldest football club in Australia and one of the oldest in the world and one of the most successful. Initially playing under its own rules, some of which, notably, were permanently introduced into Australian Football. It adopted the Laws of Australian Football in the early 1860s after a series of compromises with the Melbourne Football Club.


title: Geelong Football Club

text: Geelong went on to play for most of its existence in the premier competitions, the first competition, the Caledonian Society Cup, a foundation club of both the Victorian Football Association (VFA) in 1877 and the Victorian Football League (VFL) in 1897., VFL and continues in the elite Australian Football League (AFL). The Cats have been the VFL/AFL premiers ten times, with four in the AFL era (since 1990) in 2007, 2009, 2011, and most recently, 2022, to be the most successful club over that period (sharing that title with Hawthorn). They have also won ten McClelland Trophies, the most of any AFL/VFL club.


title: Geelong Football Club

text: Geelong's traditional navy blue and white hooped guernsey has been worn since the club's inception in the mid-1800s. The design is said to represent the white seagulls and blue water of Corio Bay.


title: Geelong Football Club

text: The team has worn various away guernseys since 1998, all featuring the club's logo and traditional colours.


title: Geelong Football Club

text: Geelong has been nicknamed the 'Cats' since 1923. A run of losses prompted a local cartoonist to suggest that the club needed a black cat to bring it good luck.


title: Geelong Football Club

text: "We Are Geelong" is the song sung after a game won by the Geelong Football Club. It is sung to the tune of "Toreador" from "Carmen". The lyrics were written by former premiership player John Watts. Only the first verse is used at matches and by the team after a victory. The song currently used by the club was recorded by the Fable Singers in April 1972.


title: Geelong Football Club

text: Geelong's administrative headquarters is its home stadium, GMHBA Stadium or also known as Kardinia Park. The club trains here during the season, however it also trains at its alternate training venue, Deakin University's Elite Sport Precinct. The latter features an MCG-sized oval and is used often by the club in the pre-season, when Kardinia Park is being used for other events.


title: Geelong Football Club

text: The rivalry between Hawthorn and Geelong is defined by two Grand Finals: those of 1989 and 2008. In the 1989 Grand Final, Geelong played the man, resulting in major injuries for several Hawks players, Mark Yeates knocking out Dermott Brereton at the opening bounce; Hawthorn controlled the game, leading by approximately 40 points for most of the match; in the last quarter, Geelong almost managed to come from behind to win, but fell short by six points. In the 2008 Grand Final, Geelong was the heavily backed favourite and had lost only one match for the season, but lost by 26 points; Geelong then won its next eleven matches against Hawthorn over the following five years, under a curse, which was dubbed the "Kennett curse" which was attributed to disrespectful comments made by Hawthorn president Jeff Kennett following the 2008 Grand Final. It was later revealed that after the 2008 grand final, Paul Chapman initiated a pact between other Geelong players to never lose to Hawthorn again. The curse was broken in a preliminary final in 2013, after Paul Chapman played his final match for Geelong the previous week. Hawthorn went on to win the next three premierships. In 2016 Geelong again defeated Hawthorn in the qualifying final. In twenty matches between the two sides between 2008 and 2017, twelve were decided by less than ten points, with Geelong victorious in eleven of those twelve matches.


title: Geelong Football Club

text: In 1925, Geelong won their first flag over Collingwood. In 1930, Collingwood defeated Geelong in the grand final making it four flags in-a-row for the Pies. Geelong would later deny Collingwood three successive premierships in 1937, winning a famous grand final by 32 points.


title: Geelong Football Club

text: The two sides played against each other in 6 finals between 1951 and 1955, including the 1952 Grand Final when Geelong easily beat Collingwood by 46 points. In 1953, Collingwood ended Geelong's record 23-game winning streak in the home and away season, and later defeated them by 12 points in the grand final, denying the Cats a third successive premiership.


title: Geelong Football Club

text: Since 2007, the clubs have again both been at the top of the ladder and have met regularly in finals. Geelong won a memorable preliminary final by five points on their way to their first flag in 44 years. In 2008, Collingwood inflicted Geelong's only home-and-away loss, by a massive 86 points, but the teams did not meet in the finals. They would meet in preliminary finals in 2009 and 2010, each winning one "en route" to a premiership. They finally met again in a Grand Final in 2011, which Geelong won by 38 points; Geelong inflicted Collingwood's only three losses for the 2011 season.


title: Geelong Football Club

text: The Geelong reserves team began competing in the VFL Reserves competition with the league's other reserves teams from 1919. From 1919 to 1991 the VFL/AFL operated a reserves competition, and from 1992 to 1999 a "de facto" AFL reserves competition was run by the Victorian State Football League. The Geelong Football Club fielded a reserves team in both of these competitions, allowing players who were not selected for the senior team to play for Geelong in the lower grade. During that time, the Geelong reserves team won thirteen premierships (1923, 1924, 1930, 1937, 1938, 1948, 1960, 1963, 1964, 1975, 1980, 1981, 1982), the most of any club.


title: Geelong Football Club

text: Since the demise of the AFL reserves competition, the Geelong reserves team has competed in the new Victorian Football League, having won three premierships in that time. Unlike all other Victorian AFL clubs, Geelong has never operated in a reserves affiliation with an existing VFL club, having instead operated its stand-alone reserves team continuously. The team is composed of both reserves players from the club's primary and rookie AFL lists, and a separately maintained list of players eligible only for VFL matches. Home games are played at GMHBA Stadium, with some played as curtain-raisers to senior AFL matches.


title: Geelong Football Club

text: In 2017, following the inaugural AFL Women's (AFLW) season, Geelong was among eight clubs that applied for licenses to enter the competition from 2019 onwards. In September 2017, the club was announced as one of two clubs, along with , to receive a license to join the competition in 2019. The club has also had a team in the second-tier VFL Women's league since 2017.


title: Diamond cut

text: A diamond cut is a style or design guide used when shaping a diamond for polishing such as the brilliant cut. Cut does not refer to shape (pear, oval), but the symmetry, proportioning and polish of a diamond. The cut of a diamond greatly affects a diamond's brilliance; this means if it is cut poorly, it will be less luminous.


title: Diamond cut

text: In order to best use a diamond gemstone's material properties, a number of different diamond cuts have been developed. A diamond cut constitutes a more or less symmetrical arrangement of facets, which together modify the shape and appearance of a diamond crystal. Diamond cutters must consider several factors, such as the shape and size of the crystal, when choosing a cut. The practical history of diamond cuts can be traced back to the Middle Ages, while their theoretical basis was not developed until the turn of the 20th century. Design, creation and innovation continue to the present day: new technology—notably laser cutting and computer-aided design—has enabled the development of cuts whose complexity, optical performance, and waste reduction were hitherto unthinkable.


title: Diamond cut

text: The most popular of diamond cuts is the modern round brilliant, whose facet arrangements and proportions have been perfected by both mathematical and empirical analysis. Also popular are the fancy cuts, which come in a variety of shapes, many of which were derived from the round brilliant. A diamond's cut is evaluated by trained graders, with higher grades given to stones whose symmetry and proportions most closely match the particular "ideal" used as a benchmark. The strictest standards are applied to the round brilliant; although its facet count is invariable, its proportions are not. Different countries base their cut grading on different ideals: one may speak of the "American Standard" or the "Scandinavian Standard" ("Scan. D.N."), to give but two examples.


title: Diamond cut

text: The process of diamond cutting has been known in the Indian subcontinent as early as the sixth century AD. A sixth-century treatise Ratnapariksa, or "Appreciation of Gems", states that the best form in which to have the diamond is in its perfect natural octahedral crystal form, and not as a cut stone, indicating that diamond cutting was widespread practice. Al Beruni also describes the process of diamond grinding using lead plate in the 11th century AD Agastimata written before 10th century states:


title: Diamond cut

text: A 12th- or early 13th-century diamond ring attributed to Muhammad Ghauri contains two diamonds whose crude octahedral natural states are maintained, but they are in limpid condition, exhibiting diamond polishing and shaping predating Europe, where the first diamond processing dates back to the mid-14th century AD.


title: Diamond cut

text: The history of diamond cuts in Europe can be traced to the late Middle Ages, before which time diamonds were employed in their natural octahedral state—anhedral (poorly formed) diamonds simply were not used in jewelry. The first "improvements" on nature's design involved a simple polishing of the octahedral crystal faces to create even and unblemished facets, or to fashion the desired octahedral shape out of an otherwise unappealing piece of rough. This was called the "point cut" and dates from the mid 14th century; by 1375 there was a guild of diamond polishers at Nürnberg. By the mid 15th century, the point cut began to be improved upon: the top of the octahedron would be polished or ground off, creating the "table cut". The importance of a culet was also realised, and some table-cut stones may possess one. The addition of four corner facets created the "old single cut" (or old eight cut). Neither of these early cuts would reveal what diamond is prized for today; its strong dispersion or "fire". At the time, diamond was valued chiefly for its adamantine lustre and superlative hardness; a table-cut diamond would appear black to the eye, as they do in paintings of the era. For this reason, colored gemstones such as ruby and sapphire were far more popular in jewelry of the era.


title: Diamond cut

text: In or around 1476, Lodewyk (Louis) van Berquem, a Flemish polisher of Bruges, introduced the technique of absolute symmetry in the disposition of facets using a device of his own invention, the scaif. He cut stones in the shape known as "pendeloque" or "briolette"; these were pear-shaped with triangular facets on both sides. About the middle of the 16th century, the "rose" or "rosette" was introduced in Antwerp: it also consisted of triangular facets arranged in a symmetrical radiating pattern, but with the bottom of the stone left flat—essentially a crown without a pavilion. Many large, famous Indian diamonds of old (such as the Orloff and Sancy) also feature a rose-like cut; there is some suggestion that Western cutters were influenced by Indian stones, because some of these diamonds may predate the Western adoption of the rose cut. However, Indian "rose cuts" were far less symmetrical as their cutters had the primary interest of conserving carat weight, due to the divine status of diamond in India. In either event, the rose cut continued to evolve, with its depth, number and arrangements of facets being tweaked.


title: Diamond cut

text: The first brilliant cuts were introduced in the middle of the 17th century. Known as "Mazarins", they had 17 facets on the crown (upper half). They are also called "double-cut" brilliants as they are seen as a step up from old single cuts. Vincent Peruzzi, a Venetian polisher, later increased the number of crown facets from 17 to 33 ("triple-cut" or "Peruzzi" brilliants), thereby significantly increasing the fire and brilliance of the cut gem, properties that in the Mazarin were already incomparably better than in the rose. Yet Peruzzi-cut diamonds, when seen nowadays, seem exceedingly dull compared to modern-cut brilliants. Because the practice of bruting had not yet been developed, these early brilliants were all rounded squares or rectangles in cross-section (rather than circular). Given the general name of "cushion"—what are known today as "old mine cuts"—these were common by the early 18th century. Sometime later the "old European cut" was developed, which had a shallower pavilion, more rounded shape, and different arrangement of facets. The old European cut was the forerunner of modern brilliants and was the most advanced in use during the 19th century.


title: Diamond cut

text: Around 1900, the development of diamond saws and good jewelry lathes enabled the development of modern diamond cutting and diamond cuts, chief among them the "round brilliant" cut. In 1919, Marcel Tolkowsky analyzed this cut: his calculations took both "brilliance" (the amount of white light reflected) and fire into consideration, creating a delicate balance between the two. Tolkowsky's calculations would serve as the basis for all future brilliant cut modifications and standards.


title: Diamond cut

text: Tolkowsky's model of the "ideal" cut is not perfect. The original model served as a general guideline, and did not explore or account for several aspects of diamond cut:


title: Diamond cut

text: Because every facet has the potential to change a light ray's plane of travel, "every facet must be considered in any complete calculation of light paths".


title: Diamond cut

text: Just as a two-dimensional slice of a diamond provides incomplete information about the three-dimensional nature of light behavior inside a diamond, this two-dimensional slice also provides incomplete information about light behavior "outside" the diamond. A diamond's panorama is three-dimensional. Although diamonds are highly symmetrical, light can enter a diamond from many directions and many angles. This factor further highlights the need to reevaluate Tolkowsky's results, and to recalculate the effects of a diamond's proportions on its appearance aspects. ...


title: Diamond cut

text: Another important point to consider is that Tolkowsky did not follow the path of a ray that was reflected more than twice in the diamond. However, we now know that a diamond's appearance is composed of many light paths that reflect considerably more than two times within that diamond. Once again, we can see that Tolkowsky's predictions are helpful in explaining optimal diamond performance, but they are incomplete by today's technological standards.


title: Diamond cut

text: Tolkowsky's guidelines, while revolutionary in their day, are not a definitive solution to the problem of finding the optimum proportions of a round brilliant cut diamond.


title: Diamond cut

text: The world's top diamond cutting and polishing center is India. It processes 11 out of 12 diamonds in jewelry worldwide. The sector employs 1.3 million people and accounts for 14% of India's $80 billion of annual exports. Its share in the world polished diamond market is 92% by pieces and 55% by value.


title: Diamond cut

text: In its rough state, a diamond is fairly unremarkable in appearance. Most gem diamonds are recovered from secondary or alluvial deposits, and such diamonds have dull, battered external surfaces often covered by a gummy, opaque skin—a comparison to "lumps of washing soda" is apt. The act of polishing a diamond and creating flat facets in symmetrical arrangement brings out the diamond's hidden beauty in dramatic fashion.


title: Diamond cut

text: When designing a diamond cut, two primary factors are considered. Foremost is the refractive index (RI) of a diamond, which, at 2.417 (as measured by sodium light, 589.3 nm), is fairly high compared with that of most other gems. Diamond's RI is responsible for its "brilliance"—the amount of incident light reflected back to the viewer. Also important is a diamond's dispersive power—the ability of the material to split white light into its component spectral colors—which is also relatively high, at 0.044 (as measured from the B-G interval). The flashes of spectral colors—known as "fire"—are a function of this dispersion, but are, like brilliance, only apparent after cutting.


title: Diamond cut

text: Brilliance can be divided into the definitions "external brilliance" and "internal brilliance". The former is the light reflected from the surface of the stone—its "luster". Diamond's "adamantine" ("diamond-like") luster is second only to "metallic" (i.e., that of metals); while it is directly related to RI, the quality of a finished gem's polish will determine how well a diamond's luster is borne out.


title: Diamond cut

text: Internal brilliance—the percentage of incident light reflected back to the viewer from the rear (pavilion) facets—relies on careful consideration of a cut's interfacial angles as they relate to diamond's RI. The goal is to attain total internal reflection (TIR) by choosing the "crown angle" and "pavilion angle" (the angle formed by the pavilion facets and girdle plane) such that the reflected light's angle of incidence (when reaching the pavilion facets) falls outside diamond's "critical angle", or minimum angle for TIR, of 24.4°. Two observations can be made: if the pavilion is too shallow, light meets the pavilion facets within the critical angle, and is refracted (i.e., lost) through the pavilion bottom into the air. If the pavilion is too deep, light is initially reflected outside the critical angle on one side of the pavilion, but meets the opposite side within the critical angle and is then refracted out the side of the stone.


title: Diamond cut

text: The term "scintillation brilliance" is applied to the number and arrangement of light reflections from the internal facets; that is, the degree of "sparkle" seen when the stone or observer moves. Scintillation is dependent on the size, number, and symmetry of facets, as well as on quality of polish. Very small stones will appear milky if their scintillation is too great (due to the limitations of the human eye), whereas larger stones will appear lifeless if their facets are too large or too few.


title: Diamond cut

text: A diamond's fire is determined by the cut's "crown height" and "crown angle" (the "crown" being the top half of the stone, above the girdle), and the size and number of facets that compose it. The crown acts as a prism: light exiting the stone (after reflection from the pavilion facets) should meet the crown facets at as great an angle of incidence from the normal as possible (without exceeding the critical angle) in order to achieve the greatest fanning out or spread of spectral colors. The crown height is related to the crown angle, the crown facet size, and the "table size" (the largest central facet of the crown): a happy medium is sought in a table that is not too small (which would result in larger crown facets and greater fire at the expense of brilliance) or too large (which would result in smaller crown facets and little to no fire).


title: Diamond cut

text: Polish and symmetry are two important aspects of the cut. The polish describes the smoothness of the diamond's facets, and the symmetry refers to alignment of the facets. With poor polish, the surface of a facet may be scratched or dulled, and may cause a blurred or dulled sparkle. While most polish defects are a result of the cutting process, some surface flaws are a result of defects in the natural stone. One example is grain lines (produced when irregular crystallization occurs as a diamond is formed) running across the facet. Severe polish defects may cause the diamond to constantly look like it needs to be cleaned. With poor symmetry, light can be misdirected as it enters and exits the diamond.


title: Diamond cut

text: The choice of diamond cut is often decided by the original shape of the rough stone, location of internal flaws or "inclusions", the preservation of carat weight, and popularity of certain shapes among consumers. The cutter must consider each of these variables before proceeding.


title: Diamond cut

text: Most gem-quality diamond crystals are octahedra in their rough state (see material properties of diamond). These crystals are usually cut into "round brilliants" because it is possible to cut two such stones out of one octahedron with minimal loss of weight. If the crystal is malformed or twinned, or if inclusions are present at inopportune locations, the diamond is more likely to receive a "fancy cut" (a cut other than a round brilliant). This is especially true in the case of macle, which are flattened twin octahedron crystals. Round brilliants have certain requisite proportions that would result in high weight loss, whereas fancy cuts are typically much more flexible in this regard. Sometimes the cutters compromise and accept lesser proportions and symmetry in order to avoid inclusions or to preserve carat weight, since the per-carat price of diamond is much higher when the stone is over one carat (200 mg).


title: Diamond cut

text: While the round brilliant cut is considered standard for diamond, with its shape and proportions nearly constant, the choice of fancy cut is influenced heavily by fashion. For example, the step cut "baguette"—which accentuates a diamond's luster, whiteness, and clarity but downplays its fire—was all the rage during the Art Deco period, whereas the mixed "Princess cut"—which accentuates a diamond's fire and brilliance rather than its luster—is currently gaining popularity. The princess cut is also popular among diamond cutters because, of all the cuts, it wastes the least of the original crystal. Older diamonds cut before ca. 1900 were cut in "primitive" versions of the modern round brilliant, such as the "rose cut" and "old mine cut" (see History section). Although there is a market for antique stones, many are recut into modern brilliants to increase their marketability. There is also increasing demand for diamonds to be cut in older styles for the purpose of repairing or reproducing antique jewelry.


title: Diamond cut

text: The size of a diamond may also be a factor. Very small (< 0.02 carats [4 mg]) diamonds—known as "melée"—are usually given simplified cuts (i.e., with fewer facets). This is because a full-cut brilliant of such small size would appear milky to the human eye, owing to its inability to resolve the stone's dispersive fire. Conversely, very large diamonds are usually given fancy cuts with many extra facets. Conventional round brilliant or fancy cuts do not scale up satisfactorily, so the extra facets are needed to ensure there are no "dead spots". Because large diamonds are less likely to be set in jewelry, their cuts are considered for how well they display the diamonds' properties from a wide range of viewing directions; in the case of more moderate-sized diamonds, the cuts are considered primarily for their face-up appeal.


title: Diamond cut

text: The dominating round brilliant diamonds are not as trendy as they used to be since the market was overcrowded in the last decades of the century. Simultaneously, giving a fancy diamond cut as a precious jewel on specific celebrations became a part of tradition. A "Heart cut" diamond has romantic symbolism so it is a common gift for Valentine's Day or wedding anniversary. The "pear-shaped" diamonds look like a drop of water and the shape is suitable for diamond earrings. The most famous shapes are: "Princess, Cushion, Heart, Pear, Marquise, Radiant, Asscher cut, Emerald, Oval."


title: Diamond cut

text: Developed ca. 1900, the "round brilliant" is the most popular cut given to diamond. It is usually the best choice in terms of saleability, insurability (due to its relatively "safe" shape), and desired optics.


title: Diamond cut

text: The modern round brilliant (Figure 1 and 2) consists of 58 facets (or 57 if the culet is excluded); 33 on the "crown" (the top half above the middle or "girdle" of the stone) and 25 on the "pavilion" (the lower half below the girdle). The girdle may be frosted, polished smooth, or faceted. In recent decades, most girdles are faceted; many have 32, 64, 80, or 96 facets; these facets are excluded from the total facet count. Likewise, some diamonds may have small extra facets on the crown or pavilion that were created to remove surface imperfections during the diamond cutting process. Depending on their size and location, they may hurt the symmetry of the cut and are therefore considered during cut grading.


title: Diamond cut

text: Figure 1 assumes that the "thick part of the girdle" is the same thickness at all 16 "thick parts". It does not consider the effects of indexed upper girdle facets. Figure 2 is adapted from the Tolkowsky book, which was originally published in 1919. Since 1919, the lower girdle facets have become longer. As a result, the pavilion main facets have become narrower.


title: Diamond cut

text: While the facet count is standard, the actual proportions—"crown height" and "crown angle", "pavilion depth" and "pavilion angle", and "table size"—are not universally agreed upon. There are at least six "ideal cuts" that have been devised over the years, but only three are in common use as a means of benchmarking. Developed by Marcel Tolkowsky in 1919, the "American Standard" (also known as the "American Ideal" and "Tolkowsky Brilliant") is the benchmark in North America. It was derived from mathematical calculations that considered both brilliance and fire. The benchmark in Germany and other European countries is the "Practical Fine Cut" (, also known as the "Eppler Cut"), introduced in 1939. It was developed in Germany by empirical observations and differs only slightly from the American Standard. Introduced as part of the Scandinavian Diamond Nomenclature ("Scan. D. N.") in 1969, the "Scandinavian Standard" also differs very little.


title: Diamond cut

text: Other benchmarks include: the "Ideal Brilliant" (developed in 1929 by Johnson and Roesch), the "Parker Brilliant" (1951), and the "Eulitz Brilliant" (1968) The Ideal and Parker brilliants are disused because their proportions result in (by contemporary standards) an unacceptably low brilliance. The Eulitz cut is the only other mathematically derived benchmark; it is also historically the only benchmark to consider girdle thickness. A more modern benchmark is that set by Accredited Gem Appraisers (AGA). Although their standard generally makes a modern ideal cut it has been criticised for being overly strict. A summary of the different benchmarks is given below:


title: Diamond cut

text: Crown height, pavilion depth, and table diameter are percentages of the total girdle diameter. Because the pavilion angle (and consequently pavilion depth) is so closely tied to total internal reflection, it varies the least between the different standards.


title: Diamond cut

text: The term Hearts and Arrows is used to describe the visual effect achieved in a round brilliant cut diamond with perfect symmetry and angles that exhibit a crisp and complete pattern of Hearts & Arrows. When viewed under a special magnifying viewer, a complete and precise visual pattern of 8 hearts is seen while looking down through the pavilion, and 8 arrows can be seen when viewing the stone in the table up position.


title: Diamond cut

text: Another modification of the round Ideal Cut that maintains the basic proportions of its angles is the Passion Cut. This cut's design can be considered the opposite of the Hearts and Arrows, as it eliminates the arrows in order to capture a different light return from the center of the diamond. The cut splits the eight pavilion mains and increases the specifically-placed total facets from 57 to 81. The cut was designed to enhance brilliance and mask inclusions.


title: Diamond cut

text: Even with modern techniques, the cutting and polishing of a diamond crystal always results in a dramatic loss of weight; rarely is it less than 50%. The round brilliant cut is preferred when the crystal is an octahedron, as often two stones may be cut from one such crystal. Oddly-shaped crystals such as macles are more likely to be cut in a "fancy cut" (that is, a cut other than the round brilliant), which the particular crystal shape lends itself to. The prevalence and choice of a particular fancy cut is also influenced by fashion; generally speaking, these cuts are not held to the same strict standards as Tolkowsky-derived round brilliants. Most fancy cuts can be grouped into four categories: "modified brilliants", "step cuts", "mixed cuts", and "rose cuts".


title: Diamond cut

text: This is the most populous category of fancy cut, because the standard round brilliant can be effectively modified into a wide range of shapes. Because their facet counts and facet arrangements are the same, modified brilliants also look (in terms of brilliance and fire interplay) the most like round brilliants.


title: Diamond cut

text: Modified brilliants include the "marquise" (a prolate lemon-shape, also called "navette" which is French for "little boat", because it resembles the hull of a sailboat), "heart", triangular "trillion" (also "trillian" or "trilliant"), "oval", and the "pear" or "drop" cuts. These are the most commonly encountered modified brilliants;


title: Diamond cut

text: "Oval-shaped diamonds" have been created and introduced by Lazare Kaplan way back in the 1960s. Usually noted to have 56 facets, the weight of such diamonds is estimated by measuring the length and width of the stone. A ratio of 1.33 to 1.66 provides a good traditional range of oval-shaped diamonds.


title: Diamond cut

text: "Pear-shaped diamonds" are also known as the teardrop shape owing to their resemblance and is considered as a hybrid between the marquise cut and the round brilliant diamond. The stone has one end rounded while the other end is pointed. Pear shape diamonds can opt between varying length and width ratios for the ideal looking pear-shaped diamond. Length to width ratios between 1.45 and 1.75 are most common.


title: Diamond cut

text: Modern cutting technology has allowed the development of increasingly complex and hitherto unthinkable shapes, such as stars and butterflies. Their proportions are mostly a matter of personal preference; however, due to their sharp terminations and diamond's relative fragility, these cuts are more vulnerable to accidental breakage and may therefore be more difficult to insure.


title: Diamond cut

text: There are several older modified brilliant cuts of uncertain age that, while no longer widely used, are notable for history's sake. They are all round in outline and modify the standard round brilliant by adding facets and changing symmetry, either by dividing the standard facets or by placing new ones in different arrangements. These cuts include: the "King" and "Magna" cuts, both developed by New York City firms, with the former possessing 86 facets and 12-fold symmetry and the latter with 102 facets and 10-fold symmetry; the "High-Light" cut, developed by Belgian cutter M. Westreich, with 16 additional facets divided equally between the crown and pavilion; and the "Princess 144", introduced in the 1960s, with 144 facets and 8-fold symmetry. Not to be confused with the mixed "Princess" cut, the Princess 144 cut makes for a lively stone with good scintillation; the extra facets are cut under the girdle rather than subdivided. The extra care required for these sub-girdle facets benefits the finished stone by mitigating girdle irregularity and bearding (hairline fracturing).


title: Diamond cut

text: Today, with the increased understanding of light dynamics and diamond cutting, many companies have developed new, modified round brilliant cut diamonds. If designed correctly, these extra facets of the modified round brilliant could benefit the overall beauty of a diamond, such as in 91 facet diamonds.


title: Diamond cut

text: Stones whose outlines are either square or rectangular and whose facets are rectilinear and arranged parallel to the girdle are known as "step-" or "trap-cut" stones. These stones often have their corners truncated, creating an "emerald cut" (after its most common application to emerald gemstones) with an octagonal outline. This is done because sharp corners are points of weakness where a diamond may cleave or fracture. Instead of a culet, step-cut stones have a "keel" running the length of the pavilion terminus. Like other fancy shaped diamonds, emerald cut diamonds can come in a variety of length to width ratios. The most popular and classic outline of emerald cut diamonds are close a value of 1.5.


title: Diamond cut

text: Because both the pavilion and crown are comparatively shallow, step cut stones are generally not as bright and never as fiery as brilliant cut stones, but rather accentuate a diamond's clarity (as even the slightest flaw would be highly visible), whiteness, and lustre (and therefore good polish).


title: Diamond cut

text: Due to the current vogue for brilliant and brilliant-like cuts, step cut diamonds may suffer somewhat in value; stones that are deep enough may be re-cut into more popular shapes. However, the step cut's rectilinear form was very popular in the Art Deco period. Antique jewelry of the period features step-cut stones prominently, and there is a market in producing new step-cut stones to repair antique jewelry or to reproduce it. The slender, rectangular "baguette" (from the French, resembling a loaf of bread) was and is the most common form of the step cut: today, it is most often used as an accent stone to flank a ring's larger central (and usually brilliant-cut) stone.


title: Diamond cut

text: Square step cuts whose corners are not truncated are known as "carré"; they are also characteristic of antique jewelry. They may resemble the square-shaped "Princess cut" in passing, but a carré's lack of fire and simpler facets are distinctive. They may or may not have a culet. In Western jewelry dating to before the advent of brilliant-type cuts, very shallow step-cut stones were used as lustrous covers for miniature paintings: these are known in the antique trade as "portrait stones". Characteristic of Indian jewelry are "lasque" diamonds, which may be the earliest form of step cut. They are flat stones with large tables and asymmetric outlines.


title: Diamond cut

text: Other forms of the step cut include "triangle" (or "Trilliant cut"), "kite", "lozenge", "trapeze" (or "trapezoid"), and "obus" shapes.


title: Diamond cut

text: "Mixed cuts" share aspects of both (modified) brilliant and step cuts: they are meant to combine the weight preservation and dimensions of step cuts with the optical effects of brilliants. Typically the crown is brilliant cut and the pavilion step-cut. Mixed cuts are all relatively new, with the oldest dating back to the 1960s. They have been extremely successful commercially and continue to gain popularity, loosening the foothold of the "de facto" standard round brilliant.


title: Diamond cut

text: Among the first mixed cuts was the "Barion cut", introduced in 1971. Invented by South African diamond cutter Basil Watermeyer and named after himself and his wife Marion, the basic Barion cut is an octagonal square or rectangle, with a polished and faceted girdle. The total facet count is 62 (excluding the culet): 25 on the crown; 29 on the pavilion; and 8 on the girdle. This cut can be easily identified by the characteristic central cross pattern (as seen through the table) created by the pavilion facets, as well as by the crescent-shaped facets on the pavilion. A similar cut is the "Radiant cut": It differs in having a total of 70 facets. Both it and the Barion cut exist in a large number of modified forms, with slightly different facet arrangements and combinations.


title: Diamond cut

text: The most successful mixed cut is the "Princess cut", first introduced in 1960 by A. Nagy of London. It was originally intended for flat rough (macles), but has since become popular enough that some gemological labs, such as that of the American Gem Society (AGS), have developed Princess cut grading standards with stringency akin to standards applied to round brilliants. Its higher fire and brilliance compared to other mixed cuts is one reason for the Princess cut's popularity, but more importantly is the fact that, of all the diamond cuts, it wastes the least of the original crystal. Another beautiful cut is the Flanders cut, a modified square with cut corners, brilliant facets and is currently being cut by cutters at Russian Star.


title: Diamond cut

text: Various forms of the "rose cut" have been in use since the mid-16th century. Like the step cuts, they were derived from older types of cuts. The basic rose cut has a flat base—that is, it lacks a pavilion—and has a crown composed of triangular facets (usually 12 or 24) rising to form a point (there is no table facet) in an arrangement with sixfold rotational symmetry. The so-called "double rose cut" is a variation that adds six kite facets at the margin of the base. The classic rose cut is circular in outline; non-circular variations on the rose cut include the "briolette" (oval), "Antwerp rose" (hexagonal), and "double Dutch rose" (resembling two rose cuts united back-to-back). Rose-cut diamonds are seldom seen nowadays, except in antique jewelry. Like the older style brilliants and step cuts, there is a growing demand for the purpose of repairing or reproducing antique pieces.


title: Diamond cut

text: Related to the rose cut, and of similar antiquity, is the "mogul cut", named after the Great Mogul diamond that was the most famous example of its type. Like the classic rose cut, the mogul cut also lacks a pavilion and a table facet, and its crown is also composed of triangular facets rising to form a point. But in mogul-cut diamonds the rotational symmetry is normally fourfold or eightfold, and the eight apical facets are girded by two or more additional rings of facets. The modern mogul cut evolved from earlier faceting techniques originally used to disguise internal flaws in very large stones; in the modern day this cut has also become rare, but still finds occasional use where it is less important to showcase a stone's internal clarity, as with the black and internally opaque Spirit of de Grisogono Diamond.


title: Diamond cut

text: The "Cut" of the "4 Cs" is the most difficult part for a consumer to judge when selecting a good diamond. This is because some certificates will not show the important measurements influencing cut (such as the pavilion angle and crown angle) and will not provide a subjective ranking of how good the cut was. The other 3 Cs can be ranked simply by the rating in each category. It requires a trained eye to judge the quality of a diamond cut, and the task is complicated by the fact that different standards are used in different countries (see proportions of the round brilliant).


title: Diamond cut

text: The relationship between the crown angle and the pavilion angle has the greatest effect on the look of the diamond. A slightly steep pavilion angle can be complemented by a shallower crown angle, and "vice versa". This trade-off has been quantified by independent authors, using various approaches.


title: Diamond cut

text: Several groups have developed diamond cut grading standards. They all disagree somewhat on which proportions make the best cut. There are certain proportions that are considered best by two or more groups however.


title: Diamond cut

text: During the diamond cutting process, the diamond cutter wants to get the heaviest diamond out of a rough stone. However, this can come at the cost of lowering cut grade. If a diamond is too deep, the carat weight will increase but result in a loss of brilliance due to light leakage. Diamond cutters have to contend with working a stone to its best finished form with the least amount of waste. This strategy depends on the quality of the stone and its final proportions. If two diamonds of equal weight are inspected there can be a noticeable difference in size when viewed from above; arguably the most important view. A well cut 0.90ct diamond for example could have the same width as a poorly cut 1.00ct diamond. This phenomenon is known as spread.


title: Diamond cut

text: Cut also affects the color of a diamond. This is especially important when considering fancy colored diamonds, where the slightest shift in color could vastly affect the price of the diamond. Most fancy colored diamonds are not cut in to round brilliants, because whereas the round brilliant is prized for its ability to reflect white light, the most important characteristic in a fancy colored diamond is its color, not its ability to reflect white light.


title: Dianne Buswell

text: Dianne Claire Buswell (born 6 May 1989) is an Australian professional dancer. She is best known for her appearances on the British television show "Strictly Come Dancing". After competing on "Dancing with the Stars" in Australia, she joined the British series in 2017, reaching the final in 2018 with her partner Joe Sugg.


title: Dianne Buswell

text: Buswell is a former Australian Open champion and four-time Amateur Australian Open finalist. She and her brother Andrew Buswell were WA Open Adult New Vogue champions for 2008 and 2010. She also appeared on "So You Think You Can Dance Australia".


title: Dianne Buswell

text: Buswell turned professional at the age of 21 when she joined the touring dance company "Burn the Floor" in January 2011. In 2015, she was a professional dancer on the fifteenth season of Australia's "Dancing with the Stars", paired with AFL star Jude Bolton; they were the fifth couple eliminated.


title: Dianne Buswell

text: Buswell joined the BBC's "Strictly Come Dancing" in 2017. Her celebrity partner for the 2017 series was the Reverend Richard Coles. They were the second couple eliminated in the series, losing the dance-off to Simon Rimmer and Karen Hauer in a unanimous decision. Buswell was paired with television presenter Tim Vincent for the 2017 Children in Need special.


title: Dianne Buswell

text: For the sixteenth series of the show in 2018, she was partnered with YouTuber Joe Sugg. They were runners-up, alongside Faye Tozer and Giovanni Pernice and Ashley Roberts and Pasha Kovalev, behind Stacey Dooley and Kevin Clifton. In early 2019, the couple performed in the "Strictly Come Dancing Live!" tour, winning 28 of the 29 shows.


title: Dianne Buswell

text: Buswell returned for her third series in 2019, paired with radio DJ Dev Griffin. They were the third couple to leave the show, after losing a dance-off to Emma Weymouth and Aljaž Skorjanec.


title: Dianne Buswell

text: For series 18 in 2020, she was partnered with The Wanted singer, Max George. They were the third couple to be eliminated, after losing a dance-off to Maisie Smith and Gorka Marquez.


title: Dianne Buswell

text: Buswell returned for series 19 in 2021, partnered with Robert Webb, a comedian, actor and writer. Webb withdrew from the competition after three weeks, due to ill health.


title: Dianne Buswell

text: In 2022, she was paired with radio and television presenter Tyler West for series 20. They were the eighth couple to be eliminated after losing a dance-off to Molly Rainford and Carlos Gu.


title: Dianne Buswell

text: In 2017, Buswell danced with football player and pundit Robbie Savage for the show's Christmas special. In 2019, Buswell partnered Joe Sugg in the Christmas special. In 2021, she was paired with maître d'hôtel and television personality Fred Sirieix for the Christmas special.


title: Dianne Buswell

text: Buswell started a YouTube channel in March 2019, and in December of that year, she was named as the UK's most-subscribed new YouTuber of 2019, having gained almost 230,000 subscribers. In August 2020, Buswell launched a lifestyle channel, 'Buswellness', where she posts workouts and healthy recipes.


title: Dianne Buswell

text: Before becoming a professional dancer, Buswell was a hairdresser, and in January 2021, she began a podcast with BBC Sounds called 'Di's Salon', in which she chats to guests as they look back at the hairstyles they have had over the years.


title: Dianne Buswell

text: Buswell was born in Bunbury, Western Australia. She began dancing at age 5, and went on to compete from an early age in State, National and International Ballroom and Latin events.


title: Dianne Buswell

text: In late 2018, Buswell began dating Joe Sugg, her celebrity partner from "Strictly Come Dancing". The couple confirmed that they were living together in August 2019. In February 2021, they revealed that they had bought a house together.


title: Interferometry

text: Interferometry is a technique which uses the "interference" of superimposed waves to extract information. Interferometry typically uses electromagnetic waves and is an important investigative technique in the fields of astronomy, fiber optics, engineering metrology, optical metrology, oceanography, seismology, spectroscopy (and its applications to chemistry), quantum mechanics, nuclear and particle physics, plasma physics, remote sensing, biomolecular interactions, surface profiling, microfluidics, mechanical stress/strain measurement, velocimetry, optometry, and making holograms.


title: Interferometry

text: Interferometers are devices that extract information from interference. They are widely used in science and industry for the measurement of microscopic displacements, refractive index changes and surface irregularities. In the case with most interferometers, light from a single source is split into two beams that travel in different optical paths, which are then combined again to produce interference; two incoherent sources can also be made to interfere under some circumstances though. The resulting interference fringes give information about the difference in optical path lengths. In analytical science, interferometers are used to measure lengths and the shape of optical components with nanometer precision; they are the highest precision length measuring instruments in existence. In Fourier transform spectroscopy they are used to analyze light containing features of absorption or emission associated with a substance or mixture. An astronomical interferometer consists of two or more separate telescopes that combine their signals, offering a resolution equivalent to that of a telescope of diameter equal to the largest separation between its individual elements.


title: Interferometry

text: Interferometry makes use of the principle of superposition to combine waves in a way that will cause the result of their combination to have some meaningful property that is diagnostic of the original state of the waves. This works because when two waves with the same frequency combine, the resulting intensity pattern is determined by the phase difference between the two waves—waves that are in phase will undergo constructive interference while waves that are out of phase will undergo destructive interference. Waves which are not completely in phase nor completely out of phase will have an intermediate intensity pattern, which can be used to determine their relative phase difference. Most interferometers use light or some other form of electromagnetic wave.


title: Interferometry

text: Typically (see Fig. 1, the well-known Michelson configuration) a single incoming beam of coherent light will be split into two identical beams by a beam splitter (a partially reflecting mirror). Each of these beams travels a different route, called a path, and they are recombined before arriving at a detector. The path difference, the difference in the distance traveled by each beam, creates a phase difference between them. It is this introduced phase difference that creates the interference pattern between the initially identical waves. If a single beam has been split along two paths, then the phase difference is diagnostic of anything that changes the phase along the paths. This could be a physical change in the path length itself or a change in the refractive index along the path.


title: Interferometry

text: As seen in Fig. 2a and 2b, the observer has a direct view of mirror "M" seen through the beam splitter, and sees a reflected image "M"′ of mirror "M". The fringes can be interpreted as the result of interference between light coming from the two virtual images "S"′ and "S"′ of the original source "S". The characteristics of the interference pattern depend on the nature of the light source and the precise orientation of the mirrors and beam splitter. In Fig. 2a, the optical elements are oriented so that "S"′ and "S"′ are in line with the observer, and the resulting interference pattern consists of circles centered on the normal to "M" and "M'". If, as in Fig. 2b, "M" and "M"′ are tilted with respect to each other, the interference fringes will generally take the shape of conic sections (hyperbolas), but if "M"′ and "M"′ overlap, the fringes near the axis will be straight, parallel, and equally spaced. If S is an extended source rather than a point source as illustrated, the fringes of Fig. 2a must be observed with a telescope set at infinity, while the fringes of Fig. 2b will be localized on the mirrors.


title: Interferometry

text: Use of white light will result in a pattern of colored fringes (see Fig. 3). The central fringe representing equal path length may be light or dark depending on the number of phase inversions experienced by the two beams as they traverse the optical system. (See Michelson interferometer for a discussion of this.)


title: Interferometry

text: In homodyne detection, the interference occurs between two beams at the same wavelength (or carrier frequency). The phase difference between the two beams results in a change in the intensity of the light on the detector. The resulting intensity of the light after mixing of these two beams is measured, or the pattern of interference fringes is viewed or recorded. Most of the interferometers discussed in this article fall into this category.


title: Interferometry

text: The heterodyne technique is used for (1) shifting an input signal into a new frequency range as well as (2) amplifying a weak input signal (assuming use of an active mixer). A weak input signal of frequency f is mixed with a strong reference frequency f from a local oscillator (LO). The nonlinear combination of the input signals creates two new signals, one at the sum f + f of the two frequencies, and the other at the difference f − f. These new frequencies are called heterodynes. Typically only one of the new frequencies is desired, and the other signal is filtered out of the output of the mixer. The output signal will have an intensity proportional to the product of the amplitudes of the input signals.


title: Interferometry

text: The most important and widely used application of the heterodyne technique is in the superheterodyne receiver (superhet), invented in 1917-18 by U.S. engineer Edwin Howard Armstrong and French engineer Lucien Lévy. In this circuit, the incoming radio frequency signal from the antenna is mixed with a signal from a local oscillator (LO) and converted by the heterodyne technique to a lower fixed frequency signal called the intermediate frequency (IF). This IF is amplified and filtered, before being applied to a detector which extracts the audio signal, which is sent to the loudspeaker.


title: Interferometry

text: While optical heterodyne interferometry is usually done at a single point it is also possible to perform this widefield.


title: Interferometry

text: A double-path interferometer is one in which the reference beam and sample beam travel along divergent paths. Examples include the Michelson interferometer, the Twyman–Green interferometer, and the Mach–Zehnder interferometer. After being perturbed by interaction with the sample under test, the sample beam is recombined with the reference beam to create an interference pattern which can then be interpreted.


title: Interferometry

text: A "common-path interferometer" is a class of interferometer in which the reference beam and sample beam travel along the same path. Fig. 4 illustrates the Sagnac interferometer, the fibre optic gyroscope, the point diffraction interferometer, and the lateral shearing interferometer. Other examples of common path interferometer include the Zernike phase-contrast microscope, Fresnel's biprism, the zero-area Sagnac, and the scatterplate interferometer.


title: Interferometry

text: A wavefront splitting interferometer divides a light wavefront emerging from a point or a narrow slit ("i.e." spatially coherent light) and, after allowing the two parts of the wavefront to travel through different paths, allows them to recombine. Fig. 5 illustrates Young's interference experiment and Lloyd's mirror. Other examples of wavefront splitting interferometer include the Fresnel biprism, the Billet Bi-Lens, and the Rayleigh interferometer.


title: Interferometry

text: In 1803, Young's interference experiment played a major role in the general acceptance of the wave theory of light. If white light is used in Young's experiment, the result is a white central band of constructive interference corresponding to equal path length from the two slits, surrounded by a symmetrical pattern of colored fringes of diminishing intensity. In addition to continuous electromagnetic radiation, Young's experiment has been performed with individual photons, with electrons, and with buckyball molecules large enough to be seen under an electron microscope.


title: Interferometry

text: Lloyd's mirror generates interference fringes by combining direct light from a source (blue lines) and light from the source's reflected image (red lines) from a mirror held at grazing incidence. The result is an asymmetrical pattern of fringes. The band of equal path length, nearest the mirror, is dark rather than bright. In 1834, Humphrey Lloyd interpreted this effect as proof that the phase of a front-surface reflected beam is inverted.


title: Interferometry

text: An amplitude splitting interferometer uses a partial reflector to divide the amplitude of the incident wave into separate beams which are separated and recombined.


title: Interferometry

text: The Fizeau interferometer is shown as it might be set up to test an optical flat. A precisely figured reference flat is placed on top of the flat being tested, separated by narrow spacers. The reference flat is slightly beveled (only a fraction of a degree of beveling is necessary) to prevent the rear surface of the flat from producing interference fringes. Separating the test and reference flats allows the two flats to be tilted with respect to each other. By adjusting the tilt, which adds a controlled phase gradient to the fringe pattern, one can control the spacing and direction of the fringes, so that one may obtain an easily interpreted series of nearly parallel fringes rather than a complex swirl of contour lines. Separating the plates, however, necessitates that the illuminating light be collimated. Fig 6 shows a collimated beam of monochromatic light illuminating the two flats and a beam splitter allowing the fringes to be viewed on-axis.


title: Interferometry

text: The Mach–Zehnder interferometer is a more versatile instrument than the Michelson interferometer. Each of the well separated light paths is traversed only once, and the fringes can be adjusted so that they are localized in any desired plane. Typically, the fringes would be adjusted to lie in the same plane as the test object, so that fringes and test object can be photographed together. If it is decided to produce fringes in white light, then, since white light has a limited coherence length, on the order of micrometers, great care must be taken to equalize the optical paths or no fringes will be visible. As illustrated in Fig. 6, a compensating cell would be placed in the path of the reference beam to match the test cell. Note also the precise orientation of the beam splitters. The reflecting surfaces of the beam splitters would be oriented so that the test and reference beams pass through an equal amount of glass. In this orientation, the test and reference beams each experience two front-surface reflections, resulting in the same number of phase inversions. The result is that light traveling an equal optical path length in the test and reference beams produces a white light fringe of constructive interference.


title: Interferometry

text: The heart of the Fabry–Pérot interferometer is a pair of partially silvered glass optical flats spaced several millimeters to centimeters apart with the silvered surfaces facing each other. (Alternatively, a Fabry–Pérot "etalon" uses a transparent plate with two parallel reflecting surfaces.) As with the Fizeau interferometer, the flats are slightly beveled. In a typical system, illumination is provided by a diffuse source set at the focal plane of a collimating lens. A focusing lens produces what would be an inverted image of the source if the paired flats were not present, i.e., in the absence of the paired flats, all light emitted from point A passing through the optical system would be focused at point A'. In Fig. 6, only one ray emitted from point A on the source is traced. As the ray passes through the paired flats, it is multiply reflected to produce multiple transmitted rays which are collected by the focusing lens and brought to point A' on the screen. The complete interference pattern takes the appearance of a set of concentric rings. The sharpness of the rings depends on the reflectivity of the flats. If the reflectivity is high, resulting in a high Q factor (i.e., high finesse), monochromatic light produces a set of narrow bright rings against a dark background. In Fig. 6, the low-finesse image corresponds to a reflectivity of 0.04 (i.e., unsilvered surfaces) "versus" a reflectivity of 0.95 for the high-finesse image.


title: Interferometry

text: Fig. 6 illustrates the Fizeau, Mach–Zehnder, and Fabry–Pérot interferometers. Other examples of amplitude splitting interferometer include the Michelson, Twyman–Green, Laser Unequal Path, and Linnik interferometer.


title: Interferometry

text: Michelson and Morley (1887) and other early experimentalists using interferometric techniques in an attempt to measure the properties of the luminiferous aether, used monochromatic light only for initially setting up their equipment, always switching to white light for the actual measurements. The reason is that measurements were recorded visually. Monochromatic light would result in a uniform fringe pattern. Lacking modern means of environmental temperature control, experimentalists struggled with continual fringe drift even though the interferometer might be set up in a basement. Since the fringes would occasionally disappear due to vibrations by passing horse traffic, distant thunderstorms and the like, it would be easy for an observer to "get lost" when the fringes returned to visibility. The advantages of white light, which produced a distinctive colored fringe pattern, far outweighed the difficulties of aligning the apparatus due to its low coherence length. This was an early example of the use of white light to resolve the "2 pi ambiguity".


title: Interferometry

text: In physics, one of the most important experiments of the late 19th century was the famous "failed experiment" of Michelson and Morley which provided evidence for special relativity. Recent repetitions of the Michelson–Morley experiment perform heterodyne measurements of beat frequencies of crossed cryogenic optical resonators. Fig 7 illustrates a resonator experiment performed by Müller et al. in 2003. Two optical resonators constructed from crystalline sapphire, controlling the frequencies of two lasers, were set at right angles within a helium cryostat. A frequency comparator measured the beat frequency of the combined outputs of the two resonators. , the precision by which anisotropy of the speed of light can be excluded in resonator experiments is at the 10 level.


title: Interferometry

text: Michelson interferometers are used in tunable narrow band optical filters and as the core hardware component of Fourier transform spectrometers.


title: Interferometry

text: When used as a tunable narrow band filter, Michelson interferometers exhibit a number of advantages and disadvantages when compared with competing technologies such as Fabry–Pérot interferometers or Lyot filters. Michelson interferometers have the largest field of view for a specified wavelength, and are relatively simple in operation, since tuning is via mechanical rotation of waveplates rather than via high voltage control of piezoelectric crystals or lithium niobate optical modulators as used in a Fabry–Pérot system. Compared with Lyot filters, which use birefringent elements, Michelson interferometers have a relatively low temperature sensitivity. On the negative side, Michelson interferometers have a relatively restricted wavelength range and require use of prefilters which restrict transmittance.


title: Interferometry

text: Fig. 8 illustrates the operation of a Fourier transform spectrometer, which is essentially a Michelson interferometer with one mirror movable. (A practical Fourier transform spectrometer would substitute corner cube reflectors for the flat mirrors of the conventional Michelson interferometer, but for simplicity, the illustration does not show this.) An interferogram is generated by making measurements of the signal at many discrete positions of the moving mirror. A Fourier transform converts the interferogram into an actual spectrum.


title: Interferometry

text: Fig. 9 shows a doppler image of the solar corona made using a tunable Fabry-Pérot interferometer to recover scans of the solar corona at a number of wavelengths near the FeXIV green line. The picture is a color-coded image of the doppler shift of the line, which may be associated with the coronal plasma velocity towards or away from the satellite camera.


title: Interferometry

text: Fabry–Pérot thin-film etalons are used in narrow bandpass filters capable of selecting a single spectral line for imaging; for example, the H-alpha line or the Ca-K line of the Sun or stars. Fig. 10 shows an Extreme ultraviolet Imaging Telescope (EIT) image of the Sun at 195 Ångströms (19.5 nm), corresponding to a spectral line of multiply-ionized iron atoms. EIT used multilayer coated reflective mirrors that were coated with alternate layers of a light "spacer" element (such as silicon), and a heavy "scatterer" element (such as molybdenum). Approximately 100 layers of each type were placed on each mirror, with a thickness of around 10 nm each. The layer thicknesses were tightly controlled so that at the desired wavelength, reflected photons from each layer interfered constructively.


title: Interferometry

text: The Laser Interferometer Gravitational-Wave Observatory (LIGO) uses two 4-km Michelson–Fabry–Pérot interferometers for the detection of gravitational waves. In this application, the Fabry–Pérot cavity is used to store photons for almost a millisecond while they bounce up and down between the mirrors. This increases the time a gravitational wave can interact with the light, which results in a better sensitivity at low frequencies. Smaller cavities, usually called mode cleaners, are used for spatial filtering and frequency stabilization of the main laser. The first observation of gravitational waves occurred on September 14, 2015.


title: Interferometry

text: The Mach–Zehnder interferometer's relatively large and freely accessible working space, and its flexibility in locating the fringes has made it the interferometer of choice for visualizing flow in wind tunnels, and for flow visualization studies in general. It is frequently used in the fields of aerodynamics, plasma physics and heat transfer to measure pressure, density, and temperature changes in gases.


title: Interferometry

text: Mach–Zehnder interferometers are also used to study one of the most counterintuitive predictions of quantum mechanics, the phenomenon known as quantum entanglement.


title: Interferometry

text: An astronomical interferometer achieves high-resolution observations using the technique of aperture synthesis, mixing signals from a cluster of comparatively small telescopes rather than a single very expensive monolithic telescope.


title: Interferometry

text: Early radio telescope interferometers used a single baseline for measurement. Later astronomical interferometers, such as the Very Large Array illustrated in Fig 11, used arrays of telescopes arranged in a pattern on the ground. A limited number of baselines will result in insufficient coverage. This was alleviated by using the rotation of the Earth to rotate the array relative to the sky. Thus, a single baseline could measure information in multiple orientations by taking repeated measurements, a technique called "Earth-rotation synthesis". Baselines thousands of kilometers long were achieved using very long baseline interferometry.


title: Interferometry

text: Astronomical optical interferometry has had to overcome a number of technical issues not shared by radio telescope interferometry. The short wavelengths of light necessitate extreme precision and stability of construction. For example, spatial resolution of 1 milliarcsecond requires 0.5 µm stability in a 100 m baseline. Optical interferometric measurements require high sensitivity, low noise detectors that did not become available until the late 1990s. Astronomical "seeing", the turbulence that causes stars to twinkle, introduces rapid, random phase changes in the incoming light, requiring data collection rates to be faster than the rate of turbulence. Despite these technical difficulties, three major facilities are now in operation offering resolutions down to the fractional milliarcsecond range. shows a movie assembled from aperture synthesis images of the Beta Lyrae system, a binary star system approximately 960 light-years (290 parsecs) away in the constellation Lyra, as observed by the CHARA array with the MIRC instrument. The brighter component is the primary star, or the mass donor. The fainter component is the thick disk surrounding the secondary star, or the mass gainer. The two components are separated by 1 milli-arcsecond. Tidal distortions of the mass donor and the mass gainer are both clearly visible.


title: Interferometry

text: The wave character of matter can be exploited to build interferometers. The first examples of matter interferometers were electron interferometers, later followed by neutron interferometers. Around 1990 the first atom interferometers were demonstrated, later followed by interferometers employing molecules.


title: Interferometry

text: Electron holography is an imaging technique that photographically records the electron interference pattern of an object, which is then reconstructed to yield a greatly magnified image of the original object. This technique was developed to enable greater resolution in electron microscopy than is possible using conventional imaging techniques. The resolution of conventional electron microscopy is not limited by electron wavelength, but by the large aberrations of electron lenses.


title: Interferometry

text: Neutron interferometry has been used to investigate the Aharonov–Bohm effect, to examine the effects of gravity acting on an elementary particle, and to demonstrate a strange behavior of fermions that is at the basis of the Pauli exclusion principle: Unlike macroscopic objects, when fermions are rotated by 360° about any axis, they do not return to their original state, but develop a minus sign in their wave function. In other words, a fermion needs to be rotated 720° before returning to its original state.


title: Interferometry

text: Atom interferometry techniques are reaching sufficient precision to allow laboratory-scale tests of general relativity.


title: Interferometry

text: Interferometers are used in atmospheric physics for high-precision measurements of trace gases via remote sounding of the atmosphere. There are several examples of interferometers that utilize either absorption or emission features of trace gases. A typical use would be in continual monitoring of the column concentration of trace gases such as ozone and carbon monoxide above the instrument.


title: Interferometry

text: Newton (test plate) interferometry is frequently used in the optical industry for testing the quality of surfaces as they are being shaped and figured. Fig. 13 shows photos of reference flats being used to check two test flats at different stages of completion, showing the different patterns of interference fringes. The reference flats are resting with their bottom surfaces in contact with the test flats, and they are illuminated by a monochromatic light source. The light waves reflected from both surfaces interfere, resulting in a pattern of bright and dark bands. The surface in the left photo is nearly flat, indicated by a pattern of straight parallel interference fringes at equal intervals. The surface in the right photo is uneven, resulting in a pattern of curved fringes. Each pair of adjacent fringes represents a difference in surface elevation of half a wavelength of the light used, so differences in elevation can be measured by counting the fringes. The flatness of the surfaces can be measured to millionths of an inch by this method. To determine whether the surface being tested is concave or convex with respect to the reference optical flat, any of several procedures may be adopted. One can observe how the fringes are displaced when one presses gently on the top flat. If one observes the fringes in white light, the sequence of colors becomes familiar with experience and aids in interpretation. Finally one may compare the appearance of the fringes as one moves ones head from a normal to an oblique viewing position. These sorts of maneuvers, while common in the optical shop, are not suitable in a formal testing environment. When the flats are ready for sale, they will typically be mounted in a Fizeau interferometer for formal testing and certification.


title: Interferometry

text: Fabry-Pérot etalons are widely used in telecommunications, lasers and spectroscopy to control and measure the wavelengths of light. Dichroic filters are multiple layer thin-film etalons. In telecommunications, wavelength-division multiplexing, the technology that enables the use of multiple wavelengths of light through a single optical fiber, depends on filtering devices that are thin-film etalons. Single-mode lasers employ etalons to suppress all optical cavity modes except the single one of interest.


title: Interferometry

text: The Twyman–Green interferometer, invented by Twyman and Green in 1916, is a variant of the Michelson interferometer widely used to test optical components. The basic characteristics distinguishing it from the Michelson configuration are the use of a monochromatic point light source and a collimator. Michelson (1918) criticized the Twyman–Green configuration as being unsuitable for the testing of large optical components, since the light sources available at the time had limited coherence length. Michelson pointed out that constraints on geometry forced by limited coherence length required the use of a reference mirror of equal size to the test mirror, making the Twyman–Green impractical for many purposes. Decades later, the advent of laser light sources answered Michelson's objections. (A Twyman–Green interferometer using a laser light source and unequal path length is known as a Laser Unequal Path Interferometer, or LUPI.) Fig. 14 illustrates a Twyman–Green interferometer set up to test a lens. Light from a monochromatic point source is expanded by a diverging lens (not shown), then is collimated into a parallel beam. A convex spherical mirror is positioned so that its center of curvature coincides with the focus of the lens being tested. The emergent beam is recorded by an imaging system for analysis.


title: Interferometry

text: Mach–Zehnder interferometers are being used in integrated optical circuits, in which light interferes between two branches of a waveguide that are externally modulated to vary their relative phase. A slight tilt of one of the beam splitters will result in a path difference and a change in the interference pattern. Mach–Zehnder interferometers are the basis of a wide variety of devices, from RF modulators to sensors to optical switches.


title: Interferometry

text: The latest proposed extremely large astronomical telescopes, such as the Thirty Meter Telescope and the Extremely Large Telescope, will be of segmented design. Their primary mirrors will be built from hundreds of hexagonal mirror segments. Polishing and figuring these highly aspheric and non-rotationally symmetric mirror segments presents a major challenge. Traditional means of optical testing compares a surface against a spherical reference with the aid of a null corrector. In recent years, computer-generated holograms (CGHs) have begun to supplement null correctors in test setups for complex aspheric surfaces. Fig. 15 illustrates how this is done. Unlike the figure, actual CGHs have line spacing on the order of 1 to 10 µm. When laser light is passed through the CGH, the zero-order diffracted beam experiences no wavefront modification. The wavefront of the first-order diffracted beam, however, is modified to match the desired shape of the test surface. In the illustrated Fizeau interferometer test setup, the zero-order diffracted beam is directed towards the spherical reference surface, and the first-order diffracted beam is directed towards the test surface in such a way that the two reflected beams combine to form interference fringes. The same test setup can be used for the innermost mirrors as for the outermost, with only the CGH needing to be exchanged.


title: Interferometry

text: Ring laser gyroscopes (RLGs) and fibre optic gyroscopes (FOGs) are interferometers used in navigation systems. They operate on the principle of the Sagnac effect. The distinction between RLGs and FOGs is that in a RLG, the entire ring is part of the laser while in a FOG, an external laser injects counter-propagating beams into an optical fiber ring, and rotation of the system then causes a relative phase shift between those beams. In a RLG, the observed phase shift is proportional to the accumulated rotation, while in a FOG, the observed phase shift is proportional to the angular velocity.


title: Interferometry

text: In telecommunication networks, heterodyning is used to move frequencies of individual signals to different channels which may share a single physical transmission line. This is called frequency division multiplexing (FDM). For example, a coaxial cable used by a cable television system can carry 500 television channels at the same time because each one is given a different frequency, so they don't interfere with one another. Continuous wave (CW) doppler radar detectors are basically heterodyne detection devices that compare transmitted and reflected beams.


title: Interferometry

text: Optical heterodyne detection is used for coherent Doppler lidar measurements capable of detecting very weak light scattered in the atmosphere and monitoring wind speeds with high accuracy. It has application in optical fiber communications, in various high resolution spectroscopic techniques, and the self-heterodyne method can be used to measure the linewidth of a laser.


title: Interferometry

text: Optical heterodyne detection is an essential technique used in high-accuracy measurements of the frequencies of optical sources, as well as in the stabilization of their frequencies. Until a relatively few years ago, lengthy frequency chains were needed to connect the microwave frequency of a cesium or other atomic time source to optical frequencies. At each step of the chain, a frequency multiplier would be used to produce a harmonic of the frequency of that step, which would be compared by heterodyne detection with the next step (the output of a microwave source, far infrared laser, infrared laser, or visible laser). Each measurement of a single spectral line required several years of effort in the construction of a custom frequency chain. Currently, optical frequency combs have provided a much simpler method of measuring optical frequencies. If a mode-locked laser is modulated to form a train of pulses, its spectrum is seen to consist of the carrier frequency surrounded by a closely spaced comb of optical sideband frequencies with a spacing equal to the pulse repetition frequency (Fig. 16). The pulse repetition frequency is locked to that of the frequency standard, and the frequencies of the comb elements at the red end of the spectrum are doubled and heterodyned with the frequencies of the comb elements at the blue end of the spectrum, thus allowing the comb to serve as its own reference. In this manner, locking of the frequency comb output to an atomic standard can be performed in a single step. To measure an unknown frequency, the frequency comb output is dispersed into a spectrum. The unknown frequency is overlapped with the appropriate spectral segment of the comb and the frequency of the resultant heterodyne beats is measured.


title: Interferometry

text: One of the most common industrial applications of optical interferometry is as a versatile measurement tool for the high precision examination of surface topography. Popular interferometric measurement techniques include Phase Shifting Interferometry (PSI), and Vertical Scanning Interferometry(VSI), also known as scanning white light interferometry (SWLI) or by the ISO term Coherence Scanning Interferometry (CSI), CSI exploits coherence to extend the range of capabilities for interference microscopy. These techniques are widely used in micro-electronic and micro-optic fabrication. PSI uses monochromatic light and provides very precise measurements; however it is only usable for surfaces that are very smooth. CSI often uses white light and high numerical apertures, and rather than looking at the phase of the fringes, as does PSI, looks for best position of maximum fringe contrast or some other feature of the overall fringe pattern. In its simplest form, CSI provides less precise measurements than PSI but can be used on rough surfaces. Some configurations of CSI, variously known as Enhanced VSI (EVSI), high-resolution SWLI or Frequency Domain Analysis (FDA), use coherence effects in combination with interference phase to enhance precision.


title: Interferometry

text: Phase Shifting Interferometry addresses several issues associated with the classical analysis of static interferograms. Classically, one measures the positions of the fringe centers. As seen in Fig. 13, fringe deviations from straightness and equal spacing provide a measure of the aberration. Errors in determining the location of the fringe centers provide the inherent limit to precision of the classical analysis, and any intensity variations across the interferogram will also introduce error. There is a trade-off between precision and number of data points: closely spaced fringes provide many data points of low precision, while widely spaced fringes provide a low number of high precision data points. Since fringe center data is all that one uses in the classical analysis, all of the other information that might theoretically be obtained by detailed analysis of the intensity variations in an interferogram is thrown away. Finally, with static interferograms, additional information is needed to determine the polarity of the wavefront: In Fig. 13, one can see that the tested surface on the right deviates from flatness, but one cannot tell from this single image whether this deviation from flatness is concave or convex. Traditionally, this information would be obtained using non-automated means, such as by observing the direction that the fringes move when the reference surface is pushed.


title: Interferometry

text: Phase shifting interferometry overcomes these limitations by not relying on finding fringe centers, but rather by collecting intensity data from every point of the CCD image sensor. As seen in Fig. 17, multiple interferograms (at least three) are analyzed with the reference optical surface shifted by a precise fraction of a wavelength between each exposure using a piezoelectric transducer (PZT). Alternatively, precise phase shifts can be introduced by modulating the laser frequency. The captured images are processed by a computer to calculate the optical wavefront errors. The precision and reproducibility of PSI is far greater than possible in static interferogram analysis, with measurement repeatabilities of a hundredth of a wavelength being routine. Phase shifting technology has been adapted to a variety of interferometer types such as Twyman–Green, Mach–Zehnder, laser Fizeau, and even common path configurations such as point diffraction and lateral shearing interferometers. More generally, phase shifting techniques can be adapted to almost any system that uses fringes for measurement, such as holographic and speckle interferometry.


title: Interferometry

text: In coherence scanning interferometry, interference is only achieved when the path length delays of the interferometer are matched within the coherence time of the light source. CSI monitors the fringe contrast rather than the phase of the fringes. Fig. 17 illustrates a CSI microscope using a Mirau interferometer in the objective; other forms of interferometer used with white light include the Michelson interferometer (for low magnification objectives, where the reference mirror in a Mirau objective would interrupt too much of the aperture) and the Linnik interferometer (for high magnification objectives with limited working distance). The sample (or alternatively, the objective) is moved vertically over the full height range of the sample, and the position of maximum fringe contrast is found for each pixel. The chief benefit of coherence scanning interferometry is that systems can be designed that do not suffer from the 2 pi ambiguity of coherent interferometry, and as seen in Fig. 18, which scans a 180μm x 140μm x 10μm volume, it is well suited to profiling steps and rough surfaces. The axial resolution of the system is determined in part by the coherence length of the light source. Industrial applications include in-process surface metrology, roughness measurement, 3D surface metrology in hard-to-reach spaces and in hostile environments, profilometry of surfaces with high aspect ratio features (grooves, channels, holes), and film thickness measurement (semi-conductor and optical industries, etc.).


title: Interferometry

text: Fig. 19 illustrates a Twyman–Green interferometer set up for white light scanning of a macroscopic object.


title: Interferometry

text: Holographic interferometry is a technique which uses holography to monitor small deformations in single wavelength implementations. In multi-wavelength implementations, it is used to perform dimensional metrology of large parts and assemblies and to detect larger surface defects.


title: Interferometry

text: Holographic interferometry was discovered by accident as a result of mistakes committed during the making of holograms. Early lasers were relatively weak and photographic plates were insensitive, necessitating long exposures during which vibrations or minute shifts might occur in the optical system. The resultant holograms, which showed the holographic subject covered with fringes, were considered ruined.


title: Interferometry

text: Eventually, several independent groups of experimenters in the mid-60s realized that the fringes encoded important information about dimensional changes occurring in the subject, and began intentionally producing holographic double exposures. The main Holographic interferometry article covers the disputes over priority of discovery that occurred during the issuance of the patent for this method.


title: Interferometry

text: Double- and multi- exposure holography is one of three methods used to create holographic interferograms. A first exposure records the object in an unstressed state. Subsequent exposures on the same photographic plate are made while the object is subjected to some stress. The composite image depicts the difference between the stressed and unstressed states.


title: Interferometry

text: Real-time holography is a second method of creating holographic interferograms. A holograph of the unstressed object is created. This holograph is illuminated with a reference beam to generate a hologram image of the object directly superimposed over the original object itself while the object is being subjected to some stress. The object waves from this hologram image will interfere with new waves coming from the object. This technique allows real time monitoring of shape changes.


title: Interferometry

text: The third method, time-average holography, involves creating a holograph while the object is subjected to a periodic stress or vibration. This yields a visual image of the vibration pattern.


title: Interferometry

text: Interferometric synthetic aperture radar (InSAR) is a radar technique used in geodesy and remote sensing. Satellite synthetic aperture radar images of a geographic feature are taken on separate days, and changes that have taken place between radar images taken on the separate days are recorded as fringes similar to those obtained in holographic interferometry. The technique can monitor centimeter- to millimeter-scale deformation resulting from earthquakes, volcanoes and landslides, and also has uses in structural engineering, in particular for the monitoring of subsidence and structural stability. Fig 20 shows Kilauea, an active volcano in Hawaii. Data acquired using the space shuttle Endeavour's X-band Synthetic Aperture Radar on April 13, 1994 and October 4, 1994 were used to generate interferometric fringes, which were overlaid on the X-SAR image of Kilauea.


title: Interferometry

text: Electronic speckle pattern interferometry (ESPI), also known as TV holography, uses video detection and recording to produce an image of the object upon which is superimposed a fringe pattern which represents the displacement of the object between recordings. (see Fig. 21) The fringes are similar to those obtained in holographic interferometry.


title: Interferometry

text: When lasers were first invented, laser speckle was considered to be a severe drawback in using lasers to illuminate objects, particularly in holographic imaging because of the grainy image produced. It was later realized that speckle patterns could carry information about the object's surface deformations. Butters and Leendertz developed the technique of speckle pattern interferometry in 1970, and since then, speckle has been exploited in a variety of other applications. A photograph is made of the speckle pattern before deformation, and a second photograph is made of the speckle pattern after deformation. Digital subtraction of the two images results in a correlation fringe pattern, where the fringes represent lines of equal deformation. Short laser pulses in the nanosecond range can be used to capture very fast transient events. A phase problem exists: In the absence of other information, one cannot tell the difference between contour lines indicating a peak "versus" contour lines indicating a trough. To resolve the issue of phase ambiguity, ESPI may be combined with phase shifting methods.


title: Interferometry

text: A method of establishing precise geodetic baselines, invented by Yrjö Väisälä, exploited the low coherence length of white light. Initially, white light was split in two, with the reference beam "folded", bouncing back-and-forth six times between a mirror pair spaced precisely 1 m apart. Only if the test path was precisely 6 times the reference path would fringes be seen. Repeated applications of this procedure allowed precise measurement of distances up to 864 meters. Baselines thus established were used to calibrate geodetic distance measurement equipment, leading to a metrologically traceable scale for geodetic networks measured by these instruments. (This method has been superseded by GPS.)


title: Interferometry

text: Other uses of interferometers have been to study dispersion of materials, measurement of complex indices of refraction, and thermal properties. They are also used for three-dimensional motion mapping including mapping vibrational patterns of structures.


title: Interferometry

text: Optical interferometry, applied to biology and medicine, provides sensitive metrology capabilities for the measurement of biomolecules, subcellular components, cells and tissues. Many forms of label-free biosensors rely on interferometry because the direct interaction of electromagnetic fields with local molecular polarizability eliminates the need for fluorescent tags or nanoparticle markers. At a larger scale, cellular interferometry shares aspects with phase-contrast microscopy, but comprises a much larger class of phase-sensitive optical configurations that rely on optical interference among cellular constituents through refraction and diffraction. At the tissue scale, partially-coherent forward-scattered light propagation through the micro aberrations and heterogeneity of tissue structure provides opportunities to use phase-sensitive gating (optical coherence tomography) as well as phase-sensitive fluctuation spectroscopy to image subtle structural and dynamical properties.


title: Interferometry

text: Optical coherence tomography (OCT) is a medical imaging technique using low-coherence interferometry to provide tomographic visualization of internal tissue microstructures. As seen in Fig. 22, the core of a typical OCT system is a Michelson interferometer. One interferometer arm is focused onto the tissue sample and scans the sample in an X-Y longitudinal raster pattern. The other interferometer arm is bounced off a reference mirror. Reflected light from the tissue sample is combined with reflected light from the reference. Because of the low coherence of the light source, interferometric signal is observed only over a limited depth of sample. X-Y scanning therefore records one thin optical slice of the sample at a time. By performing multiple scans, moving the reference mirror between each scan, an entire three-dimensional image of the tissue can be reconstructed. Recent advances have striven to combine the nanometer phase retrieval of coherent interferometry with the ranging capability of low-coherence interferometry.


title: Interferometry

text: Phase contrast and differential interference contrast (DIC) microscopy are important tools in biology and medicine. Most animal cells and single-celled organisms have very little color, and their intracellular organelles are almost totally invisible under simple bright field illumination. These structures can be made visible by staining the specimens, but staining procedures are time-consuming and kill the cells. As seen in Figs. 24 and 25, phase contrast and DIC microscopes allow unstained, living cells to be studied. DIC also has non-biological applications, for example in the analysis of planar silicon semiconductor processing.


title: Interferometry

text: Angle-resolved low-coherence interferometry (a/LCI) uses scattered light to measure the sizes of subcellular objects, including cell nuclei. This allows interferometry depth measurements to be combined with density measurements. Various correlations have been found between the state of tissue health and the measurements of subcellular objects. For example, it has been found that as tissue changes from normal to cancerous, the average cell nuclei size increases.


title: Interferometry

text: Phase-contrast X-ray imaging (Fig. 26) refers to a variety of techniques that use phase information of a coherent x-ray beam to image soft tissues. (For an elementary discussion, see Phase-contrast x-ray imaging (introduction). For a more in-depth review, see Phase-contrast X-ray imaging.) It has become an important method for visualizing cellular and histological structures in a wide range of biological and medical studies. There are several technologies being used for x-ray phase-contrast imaging, all utilizing different principles to convert phase variations in the x-rays emerging from an object into intensity variations. These include propagation-based phase contrast, Talbot interferometry, Moiré-based far-field interferometry, refraction-enhanced imaging, and x-ray interferometry. These methods provide higher contrast compared to normal absorption-contrast x-ray imaging, making it possible to see smaller details. A disadvantage is that these methods require more sophisticated equipment, such as synchrotron or microfocus x-ray sources, x-ray optics, or high resolution x-ray detectors.


title: Currency of Germany

text: This is a list of current and historical currency of Germany. The sole currency of Germany has been the Euro since 2002.