title: Ridin'

text: "Ridin'" is a song by American rapper Chamillionaire featuring fellow American rapper Krayzie Bone of Bone Thugs-n-Harmony, released on February 27, 2006, as the second single from his debut studio album "The Sound of Revenge" (2005). Produced by hip hop producer Play-N-Skillz, the song's lyrics discuss racial profiling and police brutality, in addition to the stereotyping of African-Americans driving a vehicle with drugs and other contraband on the inside.


title: Ridin'

text: The music video shows cops abusing their powers, though Chamillionaire does admit to various crimes of this being promoted, including DWI and prostitution. He juxtaposes police actions with wrestling scenes to show how the police allegedly treat suspects. The music video, filmed in Houston, features appearances from Tom Lister Jr., Wish Bone, Layzie Bone, Play-N-Skillz, Chingo Bling, OG Ron C, Big Tuck, and Chamillionaire's younger brother Rasaq.


title: Ridin'

text: The song topped the "Billboard" Hot 100 in the U.S. for two weeks and peaked at number two in the United Kingdom, behind Shakira when it was released. At the 49th Annual Grammy Awards, "Ridin'" won Best Rap Performance by a Duo or Group and received a nomination for Best Rap Song. It was awarded the last Best Rap Video at the MTV Video Music Awards in 2006. The song ranked number three on "Rolling Stone" 100 Best Songs of 2006 and number 6 on BET's Top 100 Music Videos Of 2006. It was the best-selling ringtone in 2006, with 3.2 million sales, certified by the RIAA as the first multi-platinum Mastertone artist in history.


title: Ridin'

text: "Ridin'" debuted on the "Billboard" Hot 100 at number 88 the week of February 25, 2006. Eight weeks later, it moved eight spots from number 12 to number 4 the week of April 29, 2006 and stayed there for two weeks. It peaked at number one and stayed there for two weeks. This gave both artists their first Hot 100 number-one hit in their career. It stayed on the chart for thirty-one weeks. In New Zealand, the song debuted at number 3, then moved to number 2 the next week where it peaked at and stayed for seven consecutive weeks.


title: BAFTA Award for Best Film

text: The BAFTA Award for Best Film is given annually by the British Academy of Film and Television Arts and presented at the British Academy Film Awards. It has been given since the 1st BAFTA Awards, representing the best films of 1947, but until 1969 it was called the BAFTA Award for Best Film From Any Source. It is possible for films from any country to be nominated, although British films are also recognised in the category BAFTA Award for Best British Film and (since 1983) foreign-language films in BAFTA Award for Best Film Not in the English Language. As such, there have been multiple occasions of a film being nominated in two of these categories.


title: BAFTA Award for Best Film

text: There has been one tie for the Best Film Award when, in 1962, "Ballad of a Soldier" tied with "The Hustler" for Best Film From Any Source. Throughout the history of the category, the award has been given to the director(s), the producer(s) or both.


title: BAFTA Award for Best Film

text: In the following lists, the titles and names in bold with a dark grey background are the winners and recipients respectively; those not in bold are the nominees. The years given are those in which the films under consideration were released, not the year of the ceremony, which always takes place the following year.


title: David Grutman

text: David Grutman is an owner and partner in several Miami-based restaurants and night clubs. "Rolling Stone" magazine has listed Grutman as one of the 50 most important people in electronic dance music.


title: David Grutman

text: David was born and raised in Naples, Florida to a Jewish family. He graduated from Barron G. Collier High School in 1993, and holds a degree in finance from the University of Florida. He married Isabela Rangel in 2016. They have two daughters, Kaia (born 2017), and Vida (born 2019).


title: David Grutman

text: Grutman opened the LIV nightclub at the Fontainebleau Miami Beach hotel in 2008, and it was the fifth highest grossing nightclub in the United States in 2014. Grutman subsequently opened the club Story in 2013, followed by the restaurant Komodo, the café OTL, the restaurant Planta South Beach, and the Swan and Bar Bevy, in which Pharrell is also a partner. His newest addition to his Groot Hospitality chain is The Key Club.


title: Kikoriki

text: Kikoriki, known in the United States as GoGoRiki or BalloonToons and in Russia as Smeshariki (), is a Russian animated television series consisting of 209 episodes of 6 minutes and 30 seconds each, aimed at children of 3 to 8 years. This series uses both flash animation and computer animation (mostly).


title: Kikoriki

text: The first episode premiered in Russia on May 17, 2004. The Kikoriki are stylized rounded animals. Its Russian name, Smeshariki, is based on the words "funny" and "little balls". The series includes complex themes and specific cultural references. The series is aired in 60 countries, is translated to 15 languages and has an everyday audience of 50 million people. The audience in China surpasses the audience in Russia. As of 2020, episodes are currently available on KinoPoisk in Russia.


title: Kikoriki

text: English-language distribution rights to the series were acquired by 4Kids Entertainment from worldwide distributor Fun Game Media, Munich and began airing as part of The CW4Kids block on The CW on September 13, 2008, under the name GoGoRiki. "GoGoRiki" began its second season in the United States on August 22, 2009. Fun Game Media was also producing a European version, which began airing on KI.KA on December 8, 2008. Since February 2017, all rights to Kikoriki and PinCode outside of the CIS territories, including Kikoriki episodes in all languages other than Russian, are owned by FUN Union.


title: Kikoriki

text: The series of Kikoriki was created as part of the cultural-educational project "World Without Violence" within the Russian federal program "Forming bulwarks of tolerance and preventing extremism in Russian society". It is made with the help of the Ministry of Culture of the Russian Federation and with the participation of the company "Master-Film" at the computer animation studio "Peterburg", which was created in March 2000 specifically for "Smeshariki".


title: Kikoriki

text: On January 24, 2007, it was announced that a "Smeshariki"/"Kikoriki" feature film was to be made by the St. Petersburg company "Marmelad-media" (which owns the brand) to be released in December 2011. This film was shot in 3D CGI, unlike the 2D Flash-animated series. An initial budget of $1 million was given to produce a "test film" to show to international partners. According to Marmelad-media's general director Ilya Popov, the final budget would depend on a number of factors, such as whether it will be sold internationally (in which case the budget would be up to $15 million) or limited to Russia (in which case it will cost around $3–4 million). Popov considered spending anything over $5 million to be unprofitable (the highest-grossing Russian animated film to date, "Ilya Muromets and Nightingale the Robber", cost $2.5 million and made just under $10 million; since around half of the profits usually go to the distributors, if it had cost over $5 million it would not have been profitable). The film was released domestically in December 2011, but received a limited release in the UK in early 2012. The film was considered a well-thought-through prequel, its plot explaining events that brought the nine animal characters together in the first place.


title: Kikoriki

text: Two other films entitled "Kikoriki: Legend of the Golden Dragon" and "Kikoriki: Deja Vu" were released on March 17, 2016 and April 26, 2018.


title: Kikoriki

text: "The ABCs of Safety of the Kikoriki" () is a series of instructional and educational short cartoons. A total of 73 episodes were issued, lasting either one minute and thirty seconds, or the conventional six minutes and thirty seconds. Each episode was part of several categories: traffic safety, , health, morals, reading skills, children's rights, etc.


title: Kikoriki

text: After a long hiatus, in August 2017, a new category of episodes, titled "ABCs of the Internet" debuted, where the characters are taught to work on the Internet.


title: Kikoriki

text: "Kikoriki. New Adventures" () is a series of 3D CGI shorts starring the original characters, designed as a continuation of the original 2D shorts. It was broadcast from October 27, 2012 to December 28, 2013, consisting of 57 episodes. This series was scheduled for November 11, 2011, but the actual premiere on the "Channel One" was held on October 27, 2012.


title: Kikoriki

text: This is a continuation of "Kikoriki. New Adventures" which also uses 3D CG graphics. The premiere is dated September 1, 2017, and took place on the official YouTube channel of this animated series.


title: Kikoriki

text: "Pin-Code" () is an educational spinoff designed to develop interest in inventing, programming and science in children from 4 to 14 years old. Initially, it was supposed to be done in flash-animation (such as the pilot episode "Runaway Rocket"), but later this idea was abandoned and production began in 3D computer animation instead. The show airs on Channel One on Sundays at 8:45 at Moscow time. From January 18, 2015 to February 7, 2016, the new season of the series aired under the title "Leap to the Future".


title: Kikoriki

text: In the first season, the characters travel on the Umflier (later renamed to Sphere-Jet), a ship invented by Pin, which can travel through the air, under the water, underground, and even in space. The adventures of the heroes are accompanied by stories of Dokko and Pin about the world around them. Each episode of the season, having the subtitle "Nobel Season", ends with information about Nobel Prize winners (narrated by Andrei Levin).


title: Kikoriki

text: The plot of the second season "Jump to the Future" is built around time travel, in which the characters are sent using the unique invention, the "Spheroscope-3000" (), capable of answering any scientific questions. Pin thinks that it is impossible to interfere with the opening of the future, and Dokko, on the contrary, is obsessed with the idea of knowing everything. Now all the Kikoriki are used to the Spheroscope and they learn about the inventions of the future.


title: Kikoriki

text: This is a preschool version of this series and was created with the same company, being named BabyRiki.


title: Kikoriki

text: In May 2019, in Beijing as part of the talks between Asian civilizations, Russian and Chinese animators have made two agreements regarding cooperation, one of which involves the joint creation of the cartoon entitled Panda and Krash (). The Chinese side of this project will be represented by the animation division of the Central Television Agency of China.


title: Kikoriki

text: After 8 years of break, the show has been renewed for official 3rd season, which serves as a continuation for the original 2D animated series; it has been sponsored by Yandex and the new 52 episodes will be available exclusively on a streaming service Kinopoisk HD.


title: Kikoriki

text: In the United States of America, the 4Kids dub aired as part of The CW4Kids block on The CW from September 13, 2008 to November 14, 2009. The FUN Union dub became available on YouTube since May 14, 2018.


title: Kikoriki

text: Character stickers on bananas depicting a Kikoriki character holding a peeled banana have been used by Russian company Navkus (Навкус) and a banana sticker promoting the show has the line "Poprobuy Mul'tik Na Vkus" ("Taste the Cartoon").


title: Kikoriki

text: A Club Penguin-like video game based on the series was released and titled in Russian "Шарарам". An English version of the game was released under the title of "RolyPolyLand", that didn't last as long.


title: Jessica Lundy

text: Jessica R. Lundy (born March 20, 1966) is an American actress best known for her television roles, especially as Joel Fleishman's fiancée/ex-fiancée Elaine Shulman on the series "Northern Exposure".


title: Jessica Lundy

text: Lundy was born in San Diego, California, the daughter of Jean (née McDonald) and Joel Lundy, a surgical oncologist. She grew up in Avon, Connecticut. Lundy has a younger sister, Judy.


title: Jessica Lundy

text: Lundy attended the Circle in the Square Theatre School. She graduated with a Bachelor of Arts in 1987 at the Tisch School of the Arts of New York University, where she majored in drama and performing arts. Lundy moved to Los Angeles in 1990.


title: Jessica Lundy

text: Lundy made her film debut with "Bright Lights, Big City" (1988). That same year, she appeared in "Caddyshack II" (1988). Lundy also appeared opposite John Larroquette in the 1990 film "Madhouse".


title: Jessica Lundy

text: From 1990 to 1991, Lundy appeared opposite Edward Woodward in the short-lived series "Over My Dead Body".


title: Jessica Lundy

text: Lundy has also performed in theater. In 1994, Lundy portrayed Rita Altabel in an Off-Broadway production of "Uncommon Women and Others".


title: Jessica Lundy

text: From 1995 to 1996, Lundy played the titular role of Gloria in the short-lived sitcom "Hope and Gloria".


title: Jessica Lundy

text: From 2015 to 2019 Lundy portrayed Inspector Amanda Wainwright in the CBS educational series "The Inspectors".


title: Jessica Lundy

text: In 2016, she won a Daytime Emmy Award for Outstanding Performer in Children's Programming for her performance on "The Inspectors".


title: Richard McGonagle

text: Richard Francis McGonagle (born October 22, 1946) is an American actor. He is perhaps best known for his voice work in various video games, movies and television shows. He is also known for his work by voicing Colonel Taggart in "Prototype", Orlovsky in "", Mr. Incredible through various "The Incredibles" projects (in lieu of Craig T. Nelson), Victor Sullivan in the "Uncharted" franchise, Four Arms and Exo-Skull in the "Ben 10" franchise, Bato in "", Dr. Peace in "No More Heroes", Eight-Armed Willy in "The Marvelous Misadventures of Flapjack", Dr. I.Q. Hi in "Duck Dodgers", Apocalypse in "", Ed Machine in "Scooby-Doo! Mystery Incorporated", Tom Sheldon in "Just Cause", Abin Sur in "", and Bill the Wrangler in "", and provided additional voices for "", "", "World in Conflict", "The Rise of the Argonauts", "", "Regular Show", "OK K.O.! Let's Be Heroes" and "Samurai Jack".


title: Richard McGonagle

text: McGonagle was born in Boston, Massachusetts on October 22, 1946, the son of Hildagard Virginia (née Hiller) and William Francis McGonagle.


title: Richard McGonagle

text: As a voice actor he has done many roles such as Four Arms and Exo-Skull on "Ben 10", several voices on the show "Samurai Jack", as , a secondary character from "", various people in "Zatch Bell", Bill the Wrangler in "", Dr. I.Q. Hi in "Duck Dodgers", Apocalypse in "", the second voice of General Grievous in "", Ed Machine in "Scooby-Doo! Mystery Incorporated", Abin Sur in "", and various teachers in "Recess". He was one of the voice directors on "Beyblade", and did various voices on "Rugrats" and "All Grown Up!" and adult voices on "The Buzz on Maggie". He also provided the voice of the Oracle in "Jak 3" and voiced Dr. Peace in "No More Heroes", and Eight-Armed Willy in "The Marvelous Misadventures of Flapjack", also voiced Herb (Starla's Father) in "Regular Show".


title: Richard McGonagle

text: He also voiced in video games such as "Baten Kaitos Origins", "", the "Uncharted" series (also motion capture), "Just Cause", "", "" and "Castle of Illusion Starring Mickey Mouse". In film, he appeared in "The Bucket List" for Warner Bros. Pictures. He narrated the acclaimed indie film "(500) Days of Summer", starring Joseph Gordon-Levitt and Zooey Deschanel. He has also narrated a number of audiobooks, including the "New York Times" bestseller "The Dark Side", by "New Yorker" journalist Jane Mayer.


title: Richard McGonagle

text: In television, he has appeared in an episode of "" and two episodes of "". He played the recurring character Judge Lathrop in the crime drama "Close to Home" and provided the voice of Sanders on the sitcom "Community" in the second-season episode "Basic Rocket Science". He appeared in the TV series "Rules of Engagement" as a doctor.


title: Diocese of Rome

text: The Diocese of Rome (; ) is the ecclesiastical district under the direct jurisdiction of the Pope, who is Bishop of Rome and hence the supreme pontiff and head of the worldwide Catholic Church. As the Holy See, the papacy is a sovereign entity with diplomatic relations, and civil jurisdiction over the Vatican City State located geographically within Rome. The Diocese of Rome is the metropolitan diocese of the Province of Rome, an ecclesiastical province in Italy. The first bishop of Rome was Saint Peter in the first century. The incumbent since 13 March 2013 is Pope Francis.


title: Diocese of Rome

text: Historically, many Rome-born men, as well as others born elsewhere on the Italian Peninsula have served as bishops of Rome. Since 1900, however, there has been only one Rome-born bishop of Rome, Pius XII (1939–1958). In addition, throughout history non-Italians have served as bishops of Rome, beginning with the first of them according to Catholic tradition, Saint Peter.


title: Diocese of Rome

text: It is the metropolitan archdiocese of the Roman ecclesiastical province and primatial see of Italy. The cathedral is the Archbasilica of Saint John Lateran. The primate of Italy is the pope, holding primacy of honor over the Italian sees and also primacy of jurisdiction over all other episcopal sees by Catholic tradition.


title: Diocese of Rome

text: The pope is the bishop of Rome. Some of his titles derive from his role as head of the diocese of Rome. Those officially listed for him in the "Annuario Pontificio" are:


title: Diocese of Rome

text: The title "pope" does not appear in the official list, but is commonly used in the titles of documents, and appears, in abbreviated form, in the signatures of the popes.


title: Diocese of Rome

text: The best evidence available for the origins of the Church in Rome is Saint Paul's Epistle to the Romans. This indicates that the church was established probably by the early 40s AD. Saint Peter became associated with this church sometime between the year 58 and the early 60s.


title: Diocese of Rome

text: The final years of the first century and the early years of the second constitute the "postapostolic" period, as reflected in the extrabiblical writings of Clement of Rome and Ignatius of Antioch. By now the church at Rome was exercising a pastoral care that extended beyond its own community, having replaced Jerusalem as the practical center of the growing universal Church. Appeals were made to Peter and Paul, with whom the Roman church was most closely identified.


title: Diocese of Rome

text: The diocese covers a territory of of which is in the Vatican City State. The diocese has 1,219 diocesan priests of its own, while 2,331 priests of other dioceses, 5,072 religious priests and 140 Opus Dei priests reside in its territory, as do 2,266 women religious. In 2004, they ministered to an estimated 2,454,000 faithful, who made up 88% of the population of the territory.


title: Diocese of Rome

text: The city of Rome has grown beyond the boundaries of the diocese. Notable parts of the city belong to the dioceses of Ostia and Porto-Santa Rufina. Ostia is administered together with the Vicariate of the city and thus included in the statistics given below, while Porto is instead administered by its own diocesan bishop. The diocese covers an area of 849 km and includes most of the city and the municipality of Rome in Italy, and the entire territory of Vatican City. The diocese is divided into two vicariates, each with its respective vicar general.


title: Diocese of Rome

text: Two vicars general exercise the episcopal ministry and pastoral government for their respective territories within the diocese of Rome. Unless the bishop of a diocese reserves some acts to himself, vicars general have by law within a diocese the power to undertake all administrative acts that pertain to the bishop except those that in law require a special mandate of the bishop.


title: Diocese of Rome

text: This vicariate has responsibility for the territory of Vatican City. It consists of two parishes: Saint Peter's Basilica and Saint Anne in Vatican. Its pastoral mission with respect to residents of its territory is minimal. It is primarily concerned with providing appropriate services to tourists, pilgrims, and others in Rome who avail themselves of services provided in Vatican City. Since 1991, the vicar general for Vatican City has been the cardinal who is the archpriest of St. Peter's Basilica, currently Cardinal Mauro Gambetti.


title: Diocese of Rome

text: The vicariate general ("Vicariatus urbis") for the diocesan territory outside of Vatican City, territory that is under Italian sovereignty, is based at the Archbasilica of Saint John Lateran, which is the cathedral of the diocese. The vicar general for the Vicariate of Rome has for centuries been called the cardinal vicar (). The vicariate has 336 active and 5 suppressed parishes in its territory. Since 1970 the vicar of the city of Rome has also been assigned the office of archpriest of the Lateran Archbasilica, where the diocesan curia has its headquarters. From a strictly pastoral point of view, the diocese is divided into five sectors: north, south, east, west, and center. Each sector is assigned an auxiliary bishop who collaborates with the vicar general and the vicegerent in the pastoral administration of the diocese. The five bishops of the sectors can be joined by other auxiliary bishops for specific pastoral areas such as health care ministry.


title: Diocese of Rome

text: Six of the dioceses of the Roman Province are described as suburbicarian. Each suburbicarian diocese has a cardinal bishop at its titular head.


title: Diocese of Rome

text: There remains the titular Suburbicarian See of Ostia, held, in addition to his previous suburbicarian see, by the cardinal bishop elected to be the dean of the College of Cardinals. The Diocese of Ostia was merged with the Diocese of Rome in 1962, and is now administered by a vicar general, in tight cooperation with the vicar general for Rome. It was also diminished to contain only the cathedral parish of Ostia (Sant'Aurea in Ostia Antica), which, however, in 2012 was divided into two parishes, who together form the present diocese of Ostia.


title: Diocese of Rome

text: Numerous ordinaries and personal prelatures outside the Province of Rome, worldwide, are "Exempt", i.e. "directly subject to the Holy See", not part of any ecclesiastical province, including:


title: Greatest hits album

text: A greatest hits album or best-of album is a type of compilation album that collects popular and commercially successful songs by a particular artist or band. While greatest hits albums are typically supported by the artist, they can also be created by record companies without express approval from the original artist as a means to generate sales. They are typically regarded as a good starting point for new fans of an artist, but are sometimes criticized by longtime fans as not inclusive enough or necessary at all.


title: Greatest hits album

text: It is also common for greatest hits albums to include new recordings, remixes or unreleased alternate takes of the hit songs, plus other new material as bonus tracks to increase appeal for longtime fans (who might otherwise already own the recordings included). At times, a greatest hits compilation marks the first album appearance of a successful single that was never attached to a previous studio album.


title: Greatest hits album

text: The first greatest hits album was Johnny Mathis's "Johnny's Greatest Hits", released in 1958. The album collected eight of Mathis's charting singles, as well as three non-charting B-sides and an altogether new track. The album spent three weeks at the number one spot on "Billboard"'s Best Selling Pop LP's chart. The greatest hits album format then gained popularity in the 1960s and 1970s among American and British rock and pop artists. One notable example was The Beach Boys 1974 album Endless Summer, which upon release was certified 3× platinum by the RIAA. It propelled them from an opening act for Crosby, Stills, Nash & Young to headlining their own tour in just a matter of weeks. Some artists were even popular enough to release multiple greatest hits albums during and after their career.


title: Greatest hits album

text: By the 1990s, greatest hits albums were common for popular artists, with some artists even releasing the greatest hits album as a music video collection concurrently with the album. It also became a commercially viable option to boost popularity for artists with dwindling careers. Some bands refuse to release a greatest hits album, such as rock groups AC/DC, Tool, and Metallica. Garth Brooks had initially refused releasing one, but he eventually agreed to it in 1994 for a limited release (the resulting record, "The Hits", sold over ten million copies).


title: Greatest hits album

text: In 2000, Sony Music Entertainment launched their "The Essential" series, which collects singles and other career-defining tracks of artists licensed to Sony. "The Essential Bob Dylan" was the first in the series, and the company has since released dozens of albums in the series with other artists under their label. In addition to artist-specific collections, the series has also released genre-specific and themed albums, such as "The Essential Christmas" (collecting pop and rock covers of Christmas songs) or "The Essential Australian Rock" (collecting a specific regional output). In 2005, Universal Music Group launched a similar line, "Gold", which collects artists' greatest hits onto two discs.


title: Greatest hits album

text: In the late 2000s and 2010s, digital downloads and music streaming services increased in popularity, which allow users to listen to their favorite tracks without the need of a greatest hits package. In 2016, "Pitchfork" noted that "in the digital era, once a catalog enters a streaming service or an MP3 store, there's no need for a reissue and, therefore, there's no reason for a label to mine the vaults, searching for old music to make new again. Users can assemble their own personalized greatest hits playlists or just scan through an act's most accessed songs", which has led to greatest hits collections becoming redundant.


title: Greatest hits album

text: Despite the popularity of streaming in 2010s and early 2020s, some artists continued to issue physical greatest hits albums, including the White Stripes, Spoon, and the Weeknd. Spoon lead singer Britt Daniel said he chose to compile 2019's "" out of an affinity for compilations such as "Standing on a Beach" by the Cure and "Substance 1987" by New Order, which had introduced him to those artists in his youth, and to provide an official introduction to Spoon's catalog for new listeners. Alex Kapranos of Franz Ferdinand echoed those sentiments when describing the decision to release the band's 2022 "Hits to the Head" compilation, stating that "I have friends who believe you’re somehow not a 'real' fan if you own a best of rather than a discography. I disagree. I think of my parents' record collection as a kid. I loved their compilation LPs. I am so grateful that they had "Changes" or "". Those LPs were my entrance point. My introduction."


title: Greatest hits album

text: Various compilation albums became in one of the best-selling albums worldwide with sales of over 20 million copies. For example, Eagles' "Their Greatest Hits (1971–1975)" is the best selling album ever in the United States, according to "Billboard," which has sold over 38 million copies. Worldwide, "The Immaculate Collection" by Madonna is the best-selling compilation by a solo artist with 30 million copies, and is the best-selling compilation ever by a female artist in major music markets such as Australia, United Kingdom and United States. In the UK, Queen's "Greatest Hits" is the biggest selling album of all time. In second place is "ABBA Gold", another greatest hits compilation which has gone on to become the longest-charting album in the UK. Queen's "Greatest Hits II" is also one of the UK's Top Ten biggest sellers.


title: Greatest hits album

text: One example of a greatest hits compilation released against the artists' intentions is British rock group the Rolling Stones' compilation "Hot Rocks 1964–1971" (1971). The music magazine "Rolling Stone" remarked that the album served as a "beautifully packaged... purely mercenary item put together by the Stones' former record company to cash in on the Christmas season and wring some more bucks out in the name of the Mod Princes they once owned." After their manager tricked the band into signing over the copyrights to their 1963–1970 song catalog, the band did succeed in changing management and record labels. However, they could neither prevent the release of "Hot Rocks" nor its successor, which was titled "More Hot Rocks (Big Hits & Fazed Cookies)". A testament to the selling power of greatest hits albums, "Hot Rocks" remains the best selling album of the Rolling Stones' career. Mick Jagger and Keith Richards continue to collect significant songwriting royalties from the "Hot Rocks" sales, but not the ownership royalties.


title: Greatest hits album

text: The concept of greatest hits compilations has been adapted to other media as well. In television, some shows have released compilations of their critically successful and highest-rated episodes to drive new viewers to watch a program, such as "Family Guy"s "Freakin' Sweet Collection" and "South Park: The Hits". Several video game companies have re-released popular games for continued sales, sometimes with discounted prices: Sony's PlayStation has released games under their Greatest Hits series; Nintendo has re-released games under the Nintendo Selects label (formerly called "Player's Choice"); Microsoft has re-released games under the Platinum Hits label. Some video game franchises have released greatest hits collections of their own content, such as "Super Mario All-Stars", "Sonic Mega Collection", and "Guitar Hero Smash Hits."


title: Colonial mentality

text: A colonial mentality is the internalized attitude of ethnic or cultural inferiority felt by people as a result of colonization, i.e. them being colonized by another group. It corresponds with the belief that the cultural values of the colonizer are inherently superior to one's own. The term has been used by postcolonial scholars to discuss the transgenerational effects of colonialism present in former colonies following decolonization. It is commonly used as an operational concept for framing ideological domination in historical colonial experiences. In psychology colonial mentality has been used to explain instances of collective depression, anxiety, and other widespread mental health issues in populations that have experienced colonization.


title: Colonial mentality

text: Notable Marxist influences on the postcolonial concept of colonial mentality include Frantz Fanon's works on the fracturing of the colonial psyche through Western cultural domination, as well as the concept of cultural hegemony developed by Italian Communist Party Founder Antonio Gramsci.


title: Colonial mentality

text: Frantz Fanon's Marxist writings on imperialism, racism, and decolonizing struggles have influenced post-colonial discussions about the internalization of colonial prejudice. Fanon first tackled the problem of, what he called, the "colonial alienation of the person" as a mental health issue through psychiatric analysis.


title: Colonial mentality

text: In "The Wretched of the Earth" (French: "Les Damnés de la Terre)," published in 1961, Fanon used psychiatry to analyze how French colonization and the carnage of the Algerian War had mentally affected Algerians' self-identity and mental health. The book argues that during the period of colonization there was a subtle and constant mental pathology that developed within the colonial psyche. Fanon argued that the colonial psyche is fractured by the lack of mental and material homogeneity as a result of the colonial power's Western culture being pressured onto the colonized population despite the existing material differences between them.


title: Colonial mentality

text: Here Fanon expands traditional Marxist understandings of historical materialism to explore how the dissonance between material existence and culture functions to transform the colonized people through the mold of the Western bourgeoisie. This meant that the native Algerian came to view their own traditional culture and identity through the lens of colonial prejudice. Fanon observed that average Algerians internalized and then openly repeated remarks that were in line with the institutionalized racist culture of the French colonizers; dismissing their own culture as backward due to the internalization of Western colonial ideologies.


title: Colonial mentality

text: According to Fanon this results in a destabilizing existential conflict within the colonized culture:"In the West, the family circle, the effects of education, and the relatively high standard of living of the working class provide a more or less efficient protection against the harmful action of these pastimes. But in an African country, where mental development is uneven, where the violent collision of two worlds has considerably shaken old traditions and thrown the universe of the perceptions out of focus, the impressionability and sensibility of the Young African are at the mercy of the various assaults made upon them by the very Nature of Western Culture."


title: Colonial mentality

text: During the period of European colonial rule in India, Europeans in India typically regarded many aspects Indian culture with disdain and supported colonial rule as a beneficial "civilizing mission". Colonial rule in India was framed as an act which was beneficial to the people of India, rather than a process of political and economic dominance by a small minority of foreigners.


title: Colonial mentality

text: Under colonial rule, many practices were outlawed, such as the practice of forcing widows to immolate themselves (known as sati) with acts being deemed idolatrous being discouraged by Evangelical missionaries, the latter of which has been claimed by some scholars to have played a large role in the developments of the modern definition of Hinduism. These claims base their assumptions on the lack of a unified Hindu identity prior to the period of colonial rule, and modern Hinduism's unprecedented outward focus on a monotheistic Vedanta worldview. These developments have been read as the result of colonial views which discouraged aspects of Indian religions which differed significantly from Christianity. It has been noted that the prominence of the Bhagavad Gita as a primary religious text in Hindu discourse was a historical response to European criticisms of Indian culture. Europeans found that the Gita had more in common with their own Christian Bible, leading to the denouncement of Hindu practices more distantly related to monotheistic world views; with some historians claiming that Indians began to characterize their faith as the equivalent of Christianity in belief (especially in terms of monotheism) and structure (in terms of providing an equivalent primary sacred text).


title: Colonial mentality

text: Hindu nationalism developed in the 19th century as an opposition to European ideological prominence; however, local Indian elites often aimed to make themselves and Indian society modern by "emulating the West". This led to the emergence of what some have termed 'neo-Hinduism': consisting of reformist rhetoric transforming Hindu tradition from above, disguised as a revivalist call to return to the traditional practises of the faith. Reflecting the same arguments made by Christian missionaries, who argued that the more superstitious elements of Hindu practice were responsible for corrupting the potential rational philosophy of the faith (i.e. the more Christian-like sentiments). Moving the definitions of Hindu practice away from more overt idol worshiping, reemphasizing the concept of Brahman as a monotheistic divinity, and focusing more on the figure of Krishna in Vaishnavism due to his role as a messianic type figure (more inline with European beliefs) which makes him a suitable alternative to the Christian figure of Jesus Christ.


title: Colonial mentality

text: The Bharatiya Janata Party (BJP), India's current ruling party, follows this tradition of nationalistic Hinduism (Hindutva), and promotes an Indian national identity infused with neo-Vedantic which has been claimed by some to have been influenced by a "colonial mentality".


title: Colonial mentality

text: Some critics have claimed that writer Rudyard Kipling's portrayals of Indian characters in his works supported the view that colonized people were incapable of living without the help of Europeans, describing these portrayals as racist. In his famous poem "The White Man's Burden", Kipling directly argues for this point by romanticizing the "civilising mission" in non-Western countries. Jaway Syed has claimed that Kipling's poems idolizes Western culture as entirely rational and civilized, while treating non-white cultures as 'childlike' and 'demonic'. Similar sentiments have been interpreted in Kipling's other works, such as his characterization of the Second Boer War as a "white man's war"; along with his presentation of 'whiteness' as a morally and culturally superior trait of the West. His portrayal of Indians in his "Jungle Book" stories have also been criticized by Jane Hotchkiss as examples of the chauvinistic infantilization of colonized peoples in popular culture. Some historians claim that Kipling's works have contributed towards the development of a colonial mentality in the ways that the colonized people in these fictional narratives are made submissive to and dependent on their white rulers.


title: Colonial mentality

text: In the overseas territories administered by the Spanish Empire, racial mixing between Spanish settlers and the indigenous peoples resulted in a prosperous union later called Mestizo. There were limitations in the racial classes only to people from African descent, this mainly for being descendants of slaves under a current state of slavery. Unlike Mestizos, castizos or indigenous people who were protected by the Leyes de las Indias "to be treated like equals, as citizens of the Spanish Empire". It was completely forbidden to enslave the "indígenas" under the death penalty charge.


title: Colonial mentality

text: Mestizos and other mixed raced combinations were categorized into different castas by viceroyalty administrators. This system was applied to Spanish territories in the Americas and the Philippines, where large populations of mixed raced individuals made up the increasing majority of the viceroyalty population (until the present day).


title: Colonial mentality

text: These racial categories punished those with Black African or Afro-Latin heritage; those of European descent were given privilege over these other mixtures. As a result of this system, people of African descent struggled to downplay their indigenous heritage and cultural trappings, in order to appear superficially more Spanish or natives. With these internalized prejudices individuals' choices of clothes, occupations, and forms of religious expression. Those of mixed racial identities who wanted to receive the institutional benefits of being Spanish (such as higher educational institutions and career opportunities), could do so by suppressing their own cultures and acting with "Spanishness". This mentality lead to commonplace racial forgery in Latin America, often accompanied by legitimizing oral accounts of a Spanish ancestor and a Spanish surname. Most mixed-white and white people in Latin America have Spanish surnames inherited from Spanish ancestors, while most other Latin Americans who have Spanish names and surnames acquired them through the Christianization and Hispanicization of the indigenous and African slave populations by Spanish friars.


title: Colonial mentality

text: However, most initial attempts at this were only partially successful, as Amerindian groups simply blended Catholicism with their traditional beliefs. Syncretism between native beliefs and Christianity is still largely prevalent in Indian and Mestizo communities in Latin America.


title: Colonial mentality

text: Prior to the arrival by the Spaniards (1565–1898), the Sulu Archipelago (located in southern Philippines) was a colony of the Majapahit Empire (1293–1527) based in Indonesia. The Americans were the last country to colonize the Philippines (1898–1946) and nationalists claim that it continues to act as a neo-colony of the US despite its formal independence in 1946. In the Philippines colonial mentality is most evident in the preference for Filipino mestizos (primarily those of mixed native Filipino and white ancestry, but also mixed indigenous Filipinos and Chinese, and other ethnic groups) in the entertainment industry and mass media, in which they have received extensive exposure despite constituting a small fraction of the population.


title: Colonial mentality

text: The Cádiz Constitution of 1812 automatically gave Spanish citizenship to all Filipinos regardless of race. The census of 1870 stated that at least one-third of the population of Luzon had partial Hispanic ancestry (from varying points of origin and ranging from Latin America to Spain).


title: Colonial mentality

text: The combined number of all types of white mestizos or Eurasians is 3.6%, according to a genetic study by Stanford University. This is contradicted by another genetic study done by California University which stated that Filipinos possess moderate amounts of European admixture.


title: Colonial mentality

text: A cultural preference for relatively light skinned people exists within the Philippines. According to Kevin Nadal and David Okazaki, light skin preference may have pre-colonial origins. However, they also suggest that this preference was strengthened by colonialism. In an undated Philippine epic, the hero covers his face with a shield so that the sun would not "lessen his handsome looks". Some regard this as proof that desire for light-colored skin predates overseas influences. Regardless of the origin of the preference, the use of skin bleaching remains prevalent among Filipino men and women, however there is also a growing embrace of darker skinned female aesthetic within the Philippines.


title: 2020 Tuscan Grand Prix

text: The 2020 Tuscan Grand Prix (officially known as the Formula 1 Pirelli Gran Premio della Toscana Ferrari 1000 2020) was a Formula One motor race held on 13 September 2020 at the Autodromo Internazionale del Mugello in Scarperia e San Piero, Tuscany, Italy. The race was the ninth round of the 2020 Formula One World Championship and the first race of the season with spectators.


title: 2020 Tuscan Grand Prix

text: The race was won by Lewis Hamilton of the Mercedes team, with teammate Valtteri Bottas in second; Mercedes scored their third 1–2 finish of the season. Alexander Albon of Red Bull Racing-Honda scored his first podium in Formula One with a third-place finish, becoming the first Thai driver to do so.


title: 2020 Tuscan Grand Prix

text: The race was the first since the 2016 Brazilian Grand Prix to have two red flags. Due to the two stoppages, the race had three standing starts.


title: 2020 Tuscan Grand Prix

text: The race was held as an event celebrating Ferrari's 1000th race in the Formula One World Championship and the safety car used a red livery, instead of its usual silver colour, to mark the occasion. The Mugello Circuit hosted a World Championship Formula One race for the first time. The Ferrari SF1000 sported a special livery: instead of the traditional rosso corsa, the car was painted dark burgundy. Both Sebastian Vettel and Charles Leclerc wore special racing overalls, and both had special helmet designs.


title: 2020 Tuscan Grand Prix

text: The championship was heavily affected by the COVID-19 pandemic. Most of the originally scheduled Grands Prix were cancelled or postponed, prompting the Fédération Internationale de l'Automobile to draft a new calendar. While the previous eight events were held behind closed doors, organizers announced that up to 2,880 spectators would be allowed for the Tuscan Grand Prix.


title: 2020 Tuscan Grand Prix

text: Ten teams (each representing a different constructor) each entered two drivers. The drivers and teams were the same as those on the season entry list with no additional stand-in drivers for either the race or practice.


title: 2020 Tuscan Grand Prix

text: Sole Formula One tyre manufacturer Pirelli brought the C1, C2, and C3 compound tyres for teams to use in the race, the three hardest compounds available.


title: 2020 Tuscan Grand Prix

text: The race was marked by several incidents. On the first lap at turn 2, Max Verstappen, Pierre Gasly, Kimi Räikkönen, and Romain Grosjean collided, resulting in Gasly and Verstappen retiring from the race and Räikkönen having to change his front wing. Verstappen's car was beached in the gravel trap. A separate incident at the same corner involved Carlos Sainz Jr. and Lance Stroll, as Sainz spun round and damaged Sebastian Vettel's front wing. These incidents together brought out the safety car. On lap 6 the safety car pulled in, but an accordion effect led the midfield drivers to accelerate up to racing speed before the leaders did and were forced to brake, triggering a collision involving Sainz, Kevin Magnussen, Antonio Giovinazzi, and Nicholas Latifi. Grosjean blamed the leader, Valtteri Bottas, for causing the accordion effect, and stated "this is the worst thing I've seen ever." All four drivers retired from the race and the red flag was brought out. During the red flag period, Esteban Ocon retired due to a brake failure; George Russell had earlier reported Ocon's brakes being on fire. The second red flag came on lap 45, after Stroll suffered a tyre failure at lap 43 turn 9, and went into the barrier. His Racing Point RP20 caught on fire, making it harder for the marshalls to clear the track.


title: 2020 Tuscan Grand Prix

text: Lewis Hamilton won the race, his 90th career win. Valtteri Bottas came in second and Alex Albon finished third; his first career podium. By finishing in ninth place, Kimi Räikkönen scored his first points of the season. A poor restart after the second red flag meant George Russell slipped from ninth to 12th and last. He eventually finished 11th leaving him out of the points. Twelve drivers were warned by the FIA for their part in the accident at the restart on lap 6. Writing for the BBC, former GP2 Series champion Jolyon Palmer praised the circuit, saying that it "defied all the [Hermann] Tilke design theories and yet provided a great spectacle in the traditional sense."


title: Respiratory tract infection

text: Respiratory tract infections (RTIs) are infectious diseases involving the respiratory tract. An infection of this type usually is further classified as an upper respiratory tract infection (URI or URTI) or a lower respiratory tract infection (LRI or LRTI). Lower respiratory infections, such as pneumonia, tend to be far more severe than upper respiratory infections, such as the common cold.


title: Respiratory tract infection

text: The upper respiratory tract is considered the airway above the glottis or vocal cords; sometimes, it is taken as the tract above the cricoid cartilage. This part of the tract includes the nose, sinuses, pharynx, and larynx.


title: Respiratory tract infection

text: Typical infections of the upper respiratory tract include tonsillitis, pharyngitis, laryngitis, sinusitis, otitis media, certain influenza types, and the common cold. Symptoms of URIs can include cough, sore throat, runny nose, nasal congestion, headache, low-grade fever, facial pressure, and sneezing.


title: Respiratory tract infection

text: The lower respiratory tract consists of the trachea (windpipe), bronchial tubes, bronchioles, and the lungs.


title: Respiratory tract infection

text: Lower respiratory tract infections are generally more severe than upper respiratory infections. LRIs are the leading cause of death among all infectious diseases. The two most common LRIs are bronchitis and pneumonia. Influenza affects both the upper and lower respiratory tracts, but more dangerous strains such as the highly pernicious H5N1 tend to bind to receptors deep in the lungs.


title: Respiratory tract infection

text: Pulmonary Function Testing (PFT) allows for the evaluation and assessment of airways, lung function, as well as specific benchmarks to diagnose an array of respiratory tract infections. Methods such as gas dilution techniques and plethysmography help determine the functional residual capacity and total lung capacity. To discover whether or not to perform a set of advanced Pulmonary Function Testing will be based on abnormally high values in previous test results. A 2014 systematic review of clinical trials does not support routine rapid viral testing to decrease antibiotic use for children in emergency departments. It is unclear if rapid viral testing in the emergency department for children with acute febrile respiratory infections reduces the rates of antibiotic use, blood testing, or urine testing. The relative risk reduction of chest x-ray utilization in children screened with rapid viral testing is 77% compared with controls. In 2013 researchers developed a breath tester that can promptly diagnose lung infections.


title: Respiratory tract infection

text: Bacteria are unicellular organisms present on Earth can thrive in various environments, including the human body. Antibiotics are a medicine designed to treat bacterial infections that need a more severe treatment course; antibiotic use is not recommended for common bacterial infections because the body is likely to treat them. This medicine does not effectively treat a viral infection like sore throats, influenza, bronchitis, sinusitis and common respiratory tract infections. This is due to antibiotic properties that only allow bacteria's termination; antibiotics were not created to treat viruses.


title: Respiratory tract infection

text: The CDC has reported that antibiotic prescription is high; 47 million prescriptions in the United States in 2018 were made for infections that do not need antibiotics to be treated with. It is recommended to avoid antibiotic use unless bacterial infections are severe, transmissible, or have a high risk of further complications if left untreated. Unnecessary use of antibiotics could increase antibiotic-resistant infections, affect the digestive system, create allergic reactions, and other intense side effects. A study published in JAMA found that narrow-spectrum antibiotics, such as amoxicillin, are just as effective as broad-spectrum alternatives for treating acute respiratory tract infections in children, but have a lower risk of side effects.


title: Respiratory tract infection

text: Despite the superior filtration capability of N95 filtering facepiece respirators measured in vitro, insufficient clinical evidence has been published to determine whether standard surgical masks and N95 filtering facepiece respirators are equivalent to preventing respiratory infections in healthcare workers.


title: Respiratory tract infection

text: Adults in intensive care units (ICU) have a higher risk of acquiring an RTI. A combination of topical and systematic antibiotics taken prophylactically can prevent infection and improve adults' overall mortality in the ICU for adult patients receiving mechanical ventilation for at least 48 hours, and topical antibiotic prophylaxis probably reduces respiratory infections but not mortality. However, the combination of treatments cannot rule out the relevant contribution in the systemic component of the observed reduction of mortality. There is no sufficient evidence to recommend that antibiotics be used to prevent complications from an RTI of unknown cause in children under the age of 5 years old. High-quality clinical research in the form of randomized controlled trials assessed the effectiveness of Vitamin D, another review of poorer quality RCTs addressed the effectiveness of immunostimulants for preventing respiratory tract infections. Despite some uncertainty due to small study sizes, there is some evidence that exercise may reduce severity of symptoms but had no impact on number of episodes or number of symptom days per episode.


title: Respiratory tract infection

text: Viruses that cause RTI are more transmissible at very high or low relative humidity; ideal humidity for indoor spaces is between 40 and 60%. Therefore, relative humidity in this range can help lessen the risk of aerosol transmission.


title: Respiratory tract infection

text: Respiratory infections often have strong seasonal patterns, with temperate climates more affected during the winter. Several factors explain winter peaks in respiratory infections, including environmental conditions and changes in human behaviors. Viruses that cause respiratory infections are affected by environmental conditions like relative humidity and temperature. Temperate climate winters have lower relative humidity, which is known to increase the transmission of influenza.


title: Respiratory tract infection

text: Of the viruses that cause respiratory infections in humans, most have seasonal variation in prevalence. Influenza, "Human orthopneumovirus" (RSV), and human coronaviruses are more prevalent in the winter. Human bocavirus and "Human metapneumovirus" occur year-round, rhinoviruses (which cause the common cold) occur mostly in the spring and fall, and human parainfluenza viruses have variable peaks depending on the specific strain. Enteroviruses, with the exception of rhinoviruses, tend to peak in the summer.


title: Optical aberration

text: In optics, aberration is a property of optical systems, such as lenses, that causes light to be spread out over some region of space rather than focused to a point. Aberrations cause the image formed by a lens to be blurred or distorted, with the nature of the distortion depending on the type of aberration. Aberration can be defined as a departure of the performance of an optical system from the predictions of paraxial optics. In an imaging system, it occurs when light from one point of an object does not converge into (or does not diverge from) a single point after transmission through the system. Aberrations occur because the simple paraxial theory is not a completely accurate model of the effect of an optical system on light, rather than due to flaws in the optical elements.


title: Optical aberration

text: An image-forming optical system with aberration will produce an image which is not sharp. Makers of optical instruments need to correct optical systems to compensate for aberration.


title: Optical aberration

text: Aberration can be analyzed with the techniques of geometrical optics. The articles on reflection, refraction and caustics discuss the general features of reflected and refracted rays.


title: Optical aberration

text: With an ideal lens, light from any given point on an object would pass through the lens and come together at a single point in the "image plane" (or, more generally, the "image surface"). Real lenses do not focus light exactly to a single point, however, even when they are perfectly made. These deviations from the idealized lens performance are called "aberrations" of the lens.


title: Optical aberration

text: Aberrations fall into two classes: "monochromatic" and "chromatic". Monochromatic aberrations are caused by the geometry of the lens or mirror and occur both when light is reflected and when it is refracted. They appear even when using monochromatic light, hence the name.


title: Optical aberration

text: Chromatic aberrations are caused by dispersion, the variation of a lens's refractive index with wavelength. Because of dispersion, different wavelengths of light come to focus at different points. Chromatic aberration does not appear when monochromatic light is used.


title: Optical aberration

text: Although defocus is technically the lowest-order of the optical aberrations, it is usually not considered as a lens aberration, since it can be corrected by moving the lens (or the image plane) to bring the image plane to the optical focus of the lens.


title: Optical aberration

text: In addition to these aberrations, piston and tilt are effects which shift the position of the focal point. Piston and tilt are not true optical aberrations, since when an otherwise perfect wavefront is altered by piston and tilt, it will still form a perfect, aberration-free image, only shifted to a different position.


title: Optical aberration

text: Chromatic aberration occurs when different wavelengths are not focussed to the same point. Types of chromatic aberration are:


title: Optical aberration

text: In a perfect optical system in the classical theory of optics, rays of light proceeding from any "object point" unite in an "image point"; and therefore the "object space" is reproduced in an "image space." The introduction of simple auxiliary terms, due to Gauss, named the focal lengths and focal planes, permits the determination of the image of any object for any system. The Gaussian theory, however, is only true so long as the angles made by all rays with the optical axis (the symmetrical axis of the system) are infinitely small, i.e., with infinitesimal objects, images and lenses; in practice these conditions may not be realized, and the images projected by uncorrected systems are, in general, ill-defined and often blurred if the aperture or field of view exceeds certain limits.


title: Optical aberration

text: The investigations of James Clerk Maxwell and Ernst Abbe showed that the properties of these reproductions, i.e., the relative position and magnitude of the images, are not special properties of optical systems, but necessary consequences of the supposition (per Abbe) of the reproduction of all points of a space in image points, and are independent of the manner in which the reproduction is effected. These authors showed, however, that no optical system can justify these suppositions, since they are contradictory to the fundamental laws of reflection and refraction. Consequently, the Gaussian theory only supplies a convenient method of approximating reality; realistic optical systems fall short of this unattainable ideal. Currently, all that can be accomplished is the projection of a single plane onto another plane; but even in this, aberrations always occurs and it may be unlikely that these will ever be entirely corrected.


title: Optical aberration

text: Let S (fig. 1) be any optical system, rays proceeding from an axis point O under an angle u1 will unite in the axis point O'1; and those under an angle u2 in the axis point O'2. If there is refraction at a collective spherical surface, or through a thin positive lens, O'2 will lie in front of O'1 so long as the angle u2 is greater than u1 ("under correction"); and conversely with a dispersive surface or lenses ("over correction"). The caustic, in the first case, resembles the sign > (greater than); in the second < (less than). If the angle u1 is very small, O'1 is the Gaussian image; and O'1 O'2 is termed the "longitudinal aberration," and O'1R the "lateral aberration" of the pencils with aperture u2. If the pencil with the angle u2 is that of the maximum aberration of all the pencils transmitted, then in a plane perpendicular to the axis at O'1 there is a circular "disk of confusion" of radius O'1R, and in a parallel plane at O'2 another one of radius O'2R2; between these two is situated the "disk of least confusion."


title: Optical aberration

text: The largest opening of the pencils, which take part in the reproduction of O, i.e., the angle u, is generally determined by the margin of one of the lenses or by a hole in a thin plate placed between, before, or behind the lenses of the system. This hole is termed the "stop" or "diaphragm"; Abbe used the term "aperture stop" for both the hole and the limiting margin of the lens. The component S1 of the system, situated between the aperture stop and the object O, projects an image of the diaphragm, termed by Abbe the "entrance pupil"; the "exit pupil" is the image formed by the component S2, which is placed behind the aperture stop. All rays which issue from O and pass through the aperture stop also pass through the entrance and exit pupils, since these are images of the aperture stop. Since the maximum aperture of the pencils issuing from O is the angle u subtended by the entrance pupil at this point, the magnitude of the aberration will be determined by the position and diameter of the entrance pupil. If the system be entirely behind the aperture stop, then this is itself the entrance pupil ("front stop"); if entirely in front, it is the exit pupil ("back stop").


title: Optical aberration

text: If the object point be infinitely distant, all rays received by the first member of the system are parallel, and their intersections, after traversing the system, vary according to their "perpendicular height of incidence," i.e. their distance from the axis. This distance replaces the angle u in the preceding considerations; and the aperture, i.e., the radius of the entrance pupil, is its maximum value.


title: Optical aberration

text: If rays issuing from O (fig. 1) are concurrent, it does not follow that points in a portion of a plane perpendicular at O to the axis will be also concurrent, even if the part of the plane be very small. As the diameter of the lens increases (i.e., with increasing aperture), the neighboring point N will be reproduced, but attended by aberrations comparable in magnitude to ON. These aberrations are avoided if, according to Abbe, the "sine condition," sin u'1/sin u1=sin u'2/sin u2, holds for all rays reproducing the point O. If the object point O is infinitely distant, u1 and u2 are to be replaced by h1 and h2, the perpendicular heights of incidence; the "sine condition" then becomes sin u'1/h1=sin u'2/h2. A system fulfilling this condition and free from spherical aberration is called "aplanatic" (Greek a-, privative, plann, a wandering). This word was first used by Robert Blair to characterize a superior achromatism, and, subsequently, by many writers to denote freedom from spherical aberration as well.


title: Optical aberration

text: Since the aberration increases with the distance of the ray from the center of the lens, the aberration increases as the lens diameter increases (or, correspondingly, with the diameter of the aperture), and hence can be minimized by reducing the aperture, at the cost of also reducing the amount of light reaching the image plane.


title: Optical aberration

text: A point O (fig. 2) at a finite distance from the axis (or with an infinitely distant object, a point which subtends a finite angle at the system) is, in general, even then not sharply reproduced if the pencil of rays issuing from it and traversing the system is made infinitely narrow by reducing the aperture stop; such a pencil consists of the rays which can pass from the object point through the now infinitely small entrance pupil. It is seen (ignoring exceptional cases) that the pencil does not meet the refracting or reflecting surface at right angles; therefore it is astigmatic (Gr. a-, privative, stigmia, a point). Naming the central ray passing through the entrance pupil the "axis of the pencil" or "principal ray," it can be said: the rays of the pencil intersect, not in one point, but in two focal lines, which can be assumed to be at right angles to the principal ray; of these, one lies in the plane containing the principal ray and the axis of the system, i.e. in the "first principal section" or "meridional section", and the other at right angles to it, i.e. in the second principal section or sagittal section. We receive, therefore, in no single intercepting plane behind the system, as, for example, a focusing screen, an image of the object point; on the other hand, in each of two planes lines O' and O" are separately formed (in neighboring planes ellipses are formed), and in a plane between O' and O" a circle of least confusion. The interval O'O", termed the astigmatic difference, increases, in general, with the angle W made by the principal ray OP with the axis of the system, i.e. with the field of view. Two "astigmatic image surfaces" correspond to one object plane; and these are in contact at the axis point; on the one lie the focal lines of the first kind, on the other those of the second. Systems in which the two astigmatic surfaces coincide are termed anastigmatic or stigmatic.


title: Optical aberration

text: Sir Isaac Newton was probably the discoverer of astigmation; the position of the astigmatic image lines was determined by Thomas Young; and the theory was developed by Allvar Gullstrand. A bibliography by P. Culmann is given in Moritz von Rohr's "Die Bilderzeugung in optischen Instrumenten".


title: Optical aberration

text: By opening the stop wider, similar deviations arise for lateral points as have been already discussed for axial points; but in this case they are much more complicated. The course of the rays in the meridional section is no longer symmetrical to the principal ray of the pencil; and on an intercepting plane there appears, instead of a luminous point, a patch of light, not symmetrical about a point, and often exhibiting a resemblance to a comet having its tail directed towards or away from the axis. From this appearance it takes its name. The unsymmetrical form of the meridional pencil—formerly the only one considered—is coma in the narrower sense only; other errors of coma have been treated by Arthur König and Moritz von Rohr, and later by Allvar Gullstrand.


title: Optical aberration

text: If the above errors be eliminated, the two astigmatic surfaces united, and a sharp image obtained with a wide aperture—there remains the necessity to correct the curvature of the image surface, especially when the image is to be received upon a plane surface, e.g. in photography. In most cases the surface is concave towards the system.


title: Optical aberration

text: Even if the image is sharp, it may be distorted compared to ideal pinhole projection. In pinhole projection, the magnification of an object is inversely proportional to its distance to the camera along the optical axis so that a camera pointing directly at a flat surface reproduces that flat surface. Distortion can be thought of as stretching the image non-uniformly, or, equivalently, as a variation in magnification across the field. While "distortion" can include arbitrary deformation of an image, the most pronounced modes of distortion produced by conventional imaging optics is "barrel distortion", in which the center of the image is magnified more than the perimeter (figure 3a). The reverse, in which the perimeter is magnified more than the center, is known as "pincushion distortion" (figure 3b). This effect is called lens distortion or image distortion, and there are algorithms to correct it.


title: Optical aberration

text: Systems free of distortion are called "orthoscopic" (orthos, right, skopein to look) or "rectilinear" (straight lines).


title: Optical aberration

text: This aberration is quite distinct from that of the sharpness of reproduction; in unsharp, reproduction, the question of distortion arises if only parts of the object can be recognized in the figure. If, in an unsharp image, a patch of light corresponds to an object point, the "center of gravity" of the patch may be regarded as the image point, this being the point where the plane receiving the image, e.g., a focusing screen, intersects the ray passing through the middle of the stop. This assumption is justified if a poor image on the focusing screen remains stationary when the aperture is diminished; in practice, this generally occurs. This ray, named by Abbe a "principal ray" (not to be confused with the "principal rays" of the Gaussian theory), passes through the center of the entrance pupil before the first refraction, and the center of the exit pupil after the last refraction. From this it follows that correctness of drawing depends solely upon the principal rays; and is independent of the sharpness or curvature of the image field. Referring to fig. 4, we have O'Q'/OQ = a' tan w'/a tan w = 1/N, where N is the "scale" or magnification of the image. For N to be constant for all values of w, a' tan w'/a tan w must also be constant. If the ratio a'/a be sufficiently constant, as is often the case, the above relation reduces to the "condition of Airy," i.e. tan w'/ tan w= a constant. This simple relation (see Camb. Phil. Trans., 1830, 3, p. 1) is fulfilled in all systems which are symmetrical with respect to their diaphragm (briefly named "symmetrical or holosymmetrical objectives"), or which consist of two like, but different-sized, components, placed from the diaphragm in the ratio of their size, and presenting the same curvature to it (hemisymmetrical objectives); in these systems tan w' / tan w = 1.


title: Optical aberration

text: The constancy of a'/a necessary for this relation to hold was pointed out by R. H. Bow (Brit. Journ. Photog., 1861), and Thomas Sutton (Photographic Notes, 1862); it has been treated by O. Lummer and by M. von Rohr (Zeit. f. Instrumentenk., 1897, 17, and 1898, 18, p. 4). It requires the middle of the aperture stop to be reproduced in the centers of the entrance and exit pupils without spherical aberration. M. von Rohr showed that for systems fulfilling neither the Airy nor the Bow-Sutton condition, the ratio a' cos w'/a tan w will be constant for one distance of the object. This combined condition is exactly fulfilled by holosymmetrical objectives reproducing with the scale 1, and by hemisymmetrical, if the scale of reproduction be equal to the ratio of the sizes of the two components.


title: Optical aberration

text: Circular wavefront profiles associated with aberrations may be mathematically modeled using Zernike polynomials. Developed by Frits Zernike in the 1930s, Zernike's polynomials are orthogonal over a circle of unit radius. A complex, aberrated wavefront profile may be curve-fitted with Zernike polynomials to yield a set of fitting coefficients that individually represent different types of aberrations. These Zernike coefficients are linearly independent, thus individual aberration contributions to an overall wavefront may be isolated and quantified separately.


title: Optical aberration

text: where "m" and "n" are nonnegative integers with formula_3, Φ is the azimuthal angle in radians, and ρ is the normalized radial distance. The radial polynomials formula_4 have no azimuthal dependence, and are defined as


title: Optical aberration

text: where formula_8 is the normalized pupil radius with formula_9, formula_10 is the azimuthal angle around the pupil with formula_11, and the fitting coefficients formula_12 are the wavefront errors in wavelengths.


title: Optical aberration

text: As in Fourier synthesis using sines and cosines, a wavefront may be perfectly represented by a sufficiently large number of higher-order Zernike polynomials. However, wavefronts with very steep gradients or very high spatial frequency structure, such as produced by propagation through atmospheric turbulence or aerodynamic flowfields, are not well modeled by Zernike polynomials, which tend to low-pass filter fine spatial definition in the wavefront. In this case, other fitting methods such as fractals or singular value decomposition may yield improved fitting results.


title: Optical aberration

text: The circle polynomials were introduced by Frits Zernike to evaluate the point image of an aberrated optical system taking into account the effects of diffraction. The perfect point image in the presence of diffraction had already been described by Airy, as early as 1835. It took almost hundred years to arrive at a comprehensive theory and modeling of the point image of aberrated systems (Zernike and Nijboer). The analysis by Nijboer and Zernike describes the intensity distribution close to the optimum focal plane. An extended theory that allows the calculation of the point image amplitude and intensity over a much larger volume in the focal region was recently developed (Extended Nijboer-Zernike theory). This Extended Nijboer-Zernike theory of point image or ‘point-spread function’ formation has found applications in general research on image formation, especially for systems with a high numerical aperture, and in characterizing optical systems with respect to their aberrations.


title: Optical aberration

text: The preceding review of the several errors of reproduction belongs to the "Abbe theory of aberrations," in which definite aberrations are discussed separately; it is well suited to practical needs, for in the construction of an optical instrument certain errors are sought to be eliminated, the selection of which is justified by experience. In the mathematical sense, however, this selection is arbitrary; the reproduction of a finite object with a finite aperture entails, in all probability, an infinite number of aberrations. This number is only finite if the object and aperture are assumed to be "infinitely small of a certain order"; and with each order of infinite smallness, i.e. with each degree of approximation to reality (to finite objects and apertures), a certain number of aberrations is associated. This connection is only supplied by theories which treat aberrations generally and analytically by means of indefinite series.


title: Optical aberration

text: A ray proceeding from an object point O (fig. 5) can be defined by the coordinates (ξ, η). Of this point O in an object plane I, at right angles to the axis, and two other coordinates (x, y), the point in which the ray intersects the entrance pupil, i.e. the plane II. Similarly the corresponding image ray may be defined by the points (ξ', η'), and (x', y'), in the planes I' and II'. The origins of these four plane coordinate systems may be collinear with the axis of the optical system; and the corresponding axes may be parallel. Each of the four coordinates ξ', η', x', y' are functions of ξ, η, x, y; and if it be assumed that the field of view and the aperture be infinitely small, then ξ, η, x, y are of the same order of infinitesimals; consequently by expanding ξ', η', x', y' in ascending powers of ξ, η, x, y, series are obtained in which it is only necessary to consider the lowest powers. It is readily seen that if the optical system be symmetrical, the origins of the coordinate systems collinear with the optical axis and the corresponding axes parallel, then by changing the signs of ξ, η, x, y, the values ξ', η', x', y' must likewise change their sign, but retain their arithmetical values; this means that the series are restricted to odd powers of the unmarked variables.


title: Optical aberration

text: The nature of the reproduction consists in the rays proceeding from a point O being united in another point O'; in general, this will not be the case, for ξ', η' vary if ξ, η be constant, but x, y variable. It may be assumed that the planes I' and II' are drawn where the images of the planes I and II are formed by rays near the axis by the ordinary Gaussian rules; and by an extension of these rules, not, however, corresponding to reality, the Gauss image point O', with coordinates ξ', η', of the point O at some distance from the axis could be constructed. Writing Dξ'=ξ'-ξ' and Dη'=η'-η', then Dξ' and Dη' are the aberrations belonging to ξ, η and x, y, and are functions of these magnitudes which, when expanded in series, contain only odd powers, for the same reasons as given above. On account of the aberrations of all rays which pass through O, a patch of light, depending in size on the lowest powers of ξ, η, x, y which the aberrations contain, will be formed in the plane I'. These degrees, named by J. Petzval "the numerical orders of the image," are consequently only odd powers; the condition for the formation of an image of the mth order is that in the series for Dξ' and Dη' the coefficients of the powers of the 3rd, 5th...(m-2)th degrees must vanish. The images of the Gauss theory being of the third order, the next problem is to obtain an image of 5th order, or to make the coefficients of the powers of 3rd degree zero. This necessitates the satisfying of five equations; in other words, there are five alterations of the 3rd order, the vanishing of which produces an image of the 5th order.


title: Optical aberration

text: The expression for these coefficients in terms of the constants of the optical system, i.e. the radii, thicknesses, refractive indices and distances between the lenses, was solved by L. Seidel; in 1840, J. Petzval constructed his portrait objective, from similar calculations which have never been published. The theory was elaborated by S. Finterswalder, who also published a posthumous paper of Seidel containing a short view of his work; a simpler form was given by A. Kerber. A. Konig and M. von Rohr have represented Kerber's method, and have deduced the Seidel formulae from geometrical considerations based on the Abbe method, and have interpreted the analytical results geometrically.


title: Optical aberration

text: The aberrations can also be expressed by means of the "characteristic function" of the system and its differential coefficients, instead of by the radii, &c., of the lenses; these formulae are not immediately applicable, but give, however, the relation between the number of aberrations and the order. Sir William Rowan Hamilton (British Assoc. Report, 1833, p. 360) thus derived the aberrations of the third order; and in later times the method was pursued by Clerk Maxwell ("Proc. London Math. Soc.," 1874–1875; (see also the treatises of R. S. Heath and L. A. Herman), M. Thiesen ("Berlin. Akad. Sitzber.," 1890, 35, p. 804), H. Bruns ("Leipzig. Math. Phys. Ber.," 1895, 21, p. 410), and particularly successfully by K. Schwarzschild ("Göttingen. Akad. Abhandl.," 1905, 4, No. 1), who thus discovered the aberrations of the 5th order (of which there are nine), and possibly the shortest proof of the practical (Seidel) formulae. A. Gullstrand (vide supra, and "Ann. d. Phys.," 1905, 18, p. 941) founded his theory of aberrations on the differential geometry of surfaces.


title: Optical aberration

text: The aberrations of the third order are: (1) aberration of the axis point; (2) aberration of points whose distance from the axis is very small, less than of the third order — the deviation from the sine condition and coma here fall together in one class; (3) astigmatism; (4) curvature of the field; (5) distortion.


title: Optical aberration

text: The classical imaging problem is to reproduce perfectly a finite plane (the object) onto another plane (the image) through a finite aperture. It is impossible to do so perfectly for "more than one" such pair of planes (this was proven with increasing generality by Maxwell in 1858, by Bruns in 1895, and by Carathéodory in 1926, see summary in Walther, A., J. Opt. Soc. Am. A 6, 415–422 (1989)). For a single pair of planes (e.g. for a single focus setting of an objective), however, the problem can in principle be solved perfectly. Examples of such a theoretically perfect system include the Luneburg lens and the Maxwell fish-eye.


title: Optical aberration

text: Practical methods solve this problem with an accuracy which mostly suffices for the special purpose of each species of instrument. The problem of finding a system which reproduces a given object upon a given plane with given magnification (insofar as aberrations must be taken into account) could be dealt with by means of the approximation theory; in most cases, however, the analytical difficulties were too great for older calculation methods but may be ameliorated by application of modern computer systems. Solutions, however, have been obtained in special cases. At the present time constructors almost always employ the inverse method: they compose a system from certain, often quite personal experiences, and test, by the trigonometrical calculation of the paths of several rays, whether the system gives the desired reproduction (examples are given in A. Gleichen, "Lehrbuch der geometrischen Optik", Leipzig and Berlin, 1902). The radii, thicknesses and distances are continually altered until the errors of the image become sufficiently small. By this method only certain errors of reproduction are investigated, especially individual members, or all, of those named above. The analytical approximation theory is often employed provisionally, since its accuracy does not generally suffice.


title: Optical aberration

text: In order to render spherical aberration and the deviation from the sine condition small throughout the whole aperture, there is given to a ray with a finite angle of aperture u* (width infinitely distant objects: with a finite height of incidence h*) the same distance of intersection, and the same sine ratio as to one neighboring the axis (u* or h* may not be much smaller than the largest aperture U or H to be used in the system). The rays with an angle of aperture smaller than u* would not have the same distance of intersection and the same sine ratio; these deviations are called "zones," and the constructor endeavors to reduce these to a minimum. The same holds for the errors depending upon the angle of the field of view, w: astigmatism, curvature of field and distortion are eliminated for a definite value, w*, "zones of astigmatism, curvature of field and distortion," attend smaller values of w. The practical optician names such systems: "corrected for the angle of aperture u* (the height of incidence h*) or the angle of field of view w*." Spherical aberration and changes of the sine ratios are often represented graphically as functions of the aperture, in the same way as the deviations of two astigmatic image surfaces of the image plane of the axis point are represented as functions of the angles of the field of view.


title: Optical aberration

text: The final form of a practical system consequently rests on compromise; enlargement of the aperture results in a diminution of the available field of view, and vice versa. But the larger aperture will give the larger resolution. The following may be regarded as typical:


title: Optical aberration

text: In optical systems composed of lenses, the position, magnitude and errors of the image depend upon the refractive indices of the glass employed (see Lens (optics) and Monochromatic aberration, above). Since the index of refraction varies with the color or wavelength of the light (see dispersion), it follows that a system of lenses (uncorrected) projects images of different colors in somewhat different places and sizes and with different aberrations; i.e. there are "chromatic differences" of the distances of intersection, of magnifications, and of monochromatic aberrations. If mixed light be employed (e.g. white light) all these images are formed and they cause a confusion, named chromatic aberration; for instance, instead of a white margin on a dark background, there is perceived a colored margin, or narrow spectrum. The absence of this error is termed achromatism, and an optical system so corrected is termed achromatic. A system is said to be "chromatically under-corrected" when it shows the same kind of chromatic error as a thin positive lens, otherwise it is said to be "overcorrected."


title: Optical aberration

text: If, in the first place, monochromatic aberrations be neglected — in other words, the Gaussian theory be accepted — then every reproduction is determined by the positions of the focal planes, and the magnitude of the focal lengths, or if the focal lengths, as ordinarily happens, be equal, by three constants of reproduction. These constants are determined by the data of the system (radii, thicknesses, distances, indices, etc., of the lenses); therefore their dependence on the refractive index, and consequently on the color, are calculable. The refractive indices for different wavelengths must be known for each kind of glass made use of. In this manner the conditions are maintained that any one constant of reproduction is equal for two different colors, i.e. this constant is achromatized. For example, it is possible, with one thick lens in air, to achromatize the position of a focal plane of the magnitude of the focal length. If all three constants of reproduction be achromatized, then the Gaussian image for all distances of objects is the same for the two colors, and the system is said to be in "stable achromatism."


title: Optical aberration

text: In practice it is more advantageous (after Abbe) to determine the chromatic aberration (for instance, that of the distance of intersection) for a fixed position of the object, and express it by a sum in which each component conlins the amount due to each refracting surface. In a plane containing the image point of one color, another colour produces a disk of confusion; this is similar to the confusion caused by two "zones" in spherical aberration. For infinitely distant objects the radius Of the chromatic disk of confusion is proportional to the linear aperture, and independent of the focal length ("vide supra", "Monochromatic Aberration of the Axis Point"); and since this disk becomes the less harmful with an increasing image of a given object, or with increasing focal length, it follows that the deterioration of the image is proportional to the ratio of the aperture to the focal length, i.e. the "relative aperture." (This explains the gigantic focal lengths in vogue before the discovery of achromatism.)


title: Optical aberration

text: Newton failed to perceive the existence of media of different dispersive powers required by achromatism; consequently he constructed large reflectors instead of refractors. James Gregory and Leonhard Euler arrived at the correct view from a false conception of the achromatism of the eye; this was determined by Chester More Hall in 1728, Klingenstierna in 1754 and by Dollond in 1757, who constructed the celebrated achromatic telescopes. (See telescope.)


title: Optical aberration

text: Glass with weaker dispersive power (greater formula_13) is named "crown glass"; that with greater dispersive power, "flint glass". For the construction of an achromatic collective lens (formula_14 positive) it follows, by means of equation (4), that a collective lens I. of crown glass and a dispersive lens II. of flint glass must be chosen; the latter, although the weaker, corrects the other chromatically by its greater dispersive power. For an achromatic dispersive lens the converse must be adopted. This is, at the present day, the ordinary type, e.g., of telescope objective; the values of the four radii must satisfy the equations (2) and (4). Two other conditions may also be postulated: one is always the elimination of the aberration on the axis; the second either the "Herschel" or "Fraunhofer Condition," the latter being the best vide supra, "Monochromatic Aberration"). In practice, however, it is often more useful to avoid the second condition by making the lenses have contact, i.e. equal radii. According to P. Rudolph (Eder's Jahrb. f. Photog., 1891, 5, p. 225; 1893, 7, p. 221), cemented objectives of thin lenses permit the elimination of spherical aberration on the axis, if, as above, the collective lens has a smaller refractive index; on the other hand, they permit the elimination of astigmatism and curvature of the field, if the collective lens has a greater refractive index (this follows from the Petzval equation; see L. Seidel, Astr. Nachr., 1856, p. 289). Should the cemented system be positive, then the more powerful lens must be positive; and, according to (4), to the greater power belongs the weaker dispersive power (greater formula_13), that is to say, crown glass; consequently the crown glass must have the greater refractive index for astigmatic and plane images. In all earlier kinds of glass, however, the dispersive power increased with the refractive index; that is, formula_13 decreased as formula_17 increased; but some of the Jena glasses by E. Abbe and O. Schott were crown glasses of high refractive index, and achromatic systems from such crown glasses, with flint glasses of lower refractive index, are called the "new achromats," and were employed by P. Rudolph in the first "anastigmats" (photographic objectives).


title: Optical aberration

text: Instead of making formula_18 vanish, a certain value can be assigned to it which will produce, by the addition of the two lenses, any desired chromatic deviation, e.g. sufficient to eliminate one present in other parts of the system. If the lenses I. and II. be cemented and have the same refractive index for one color, then its effect for that one color is that of a lens of one piece; by such decomposition of a lens it can be made chromatic or achromatic at will, without altering its spherical effect. If its chromatic effect (formula_19) be greater than that of the same lens, this being made of the more dispersive of the two glasses employed, it is termed "hyper-chromatic."


title: Optical aberration

text: For two thin lenses separated by a distance formula_20 the condition for achromatism is formula_21; if formula_22 (e.g. if the lenses be made of the same glass), this reduces to formula_23, known as the "condition for oculars."


title: Optical aberration

text: If a constant of reproduction, for instance the focal length, be made equal for two colors, then it is not the same for other colors, if two different glasses are employed. For example, the condition for achromatism (4) for two thin lenses in contact is fulfilled in only one part of the spectrum, since formula_24 varies within the spectrum. This fact was first ascertained by J. Fraunhofer, who defined the colors by means of the dark lines in the solar spectrum; and showed that the ratio of the dispersion of two glasses varied about 20% from the red to the violet (the variation for glass and water is about 50%). If, therefore, for two colors, a and b, formula_25, then for a third color, c, the focal length is different; that is, if c lies between a and b, then formula_26, and vice versa; these algebraic results follow from the fact that towards the red the dispersion of the positive crown glass preponderates, towards the violet that of the negative flint. These chromatic errors of systems, which are achromatic for two colors, are called the "secondary spectrum," and depend upon the aperture and focal length in the same manner as the primary chromatic errors do.


title: Optical aberration

text: In fig. 6, taken from M. von Rohr's "Theorie und Geschichte des photographischen Objectivs", the abscissae are focal lengths, and the ordinates wavelengths. The Fraunhofer lines used are shown in adjacent table.


title: Optical aberration

text: The focal lengths are made equal for the lines C and F. In the neighborhood of 550 nm the tangent to the curve is parallel to the axis of wavelengths; and the focal length varies least over a fairly large range of color, therefore in this neighborhood the color union is at its best. Moreover, this region of the spectrum is that which appears brightest to the human eye, and consequently this curve of the secondary on spectrum, obtained by making formula_27, is, according to the experiments of Sir G. G. Stokes (Proc. Roy. Soc., 1878), the most suitable for visual instruments ("optical achromatism,"). In a similar manner, for systems used in photography, the vertex of the color curve must be placed in the position of the maximum sensibility of the plates; this is generally supposed to be at G'; and to accomplish this the F and violet mercury lines are united. This artifice is specially adopted in objectives for astronomical photography ("pure actinic achromatism"). For ordinary photography, however, there is this disadvantage: the image on the focusing-screen and the correct adjustment of the photographic sensitive plate are not in register; in astronomical photography this difference is constant, but in other kinds it depends on the distance of the objects. On this account the lines D and G' are united for ordinary photographic objectives; the optical as well as the actinic image is chromatically inferior, but both lie in the same place; and consequently the best correction lies in F (this is known as the "actinic correction" or "freedom from chemical focus").


title: Optical aberration

text: Should there be in two lenses in contact the same focal lengths for three colours a, b, and c, i.e. formula_28, then the relative partial dispersion formula_29 must be equal for the two kinds of glass employed. This follows by considering equation (4) for the two pairs of colors ac and bc. Until recently no glasses were known with a proportional degree of absorption; but R. Blair (Trans. Edin. Soc., 1791, 3, p. 3), P. Barlow, and F. S. Archer overcame the difficulty by constructing fluid lenses between glass walls. Fraunhofer prepared glasses which reduced the secondary spectrum; but permanent success was only assured on the introduction of the Jena glasses by E. Abbe and O. Schott. In using glasses not having proportional dispersion, the deviation of a third colour can be eliminated by two lenses, if an interval be allowed between them; or by three lenses in contact, which may not all consist of the old glasses. In uniting three colors an "achromatism of a higher order" is derived; there is yet a residual "tertiary spectrum," but it can always be neglected.


title: Optical aberration

text: The Gaussian theory is only an approximation; monochromatic or spherical aberrations still occur, which will be different for different colors; and should they be compensated for one color, the image of another color would prove disturbing. The most important is the chromatic difference of aberration of the axis point, which is still present to disturb the image, after par-axial rays of different colors are united by an appropriate combination of glasses. If a collective system be corrected for the axis point for a definite wavelength, then, on account of the greater dispersion in the negative components — the flint glasses, — overcorrection will arise for the shorter wavelengths (this being the error of the negative components), and under-correction for the longer wavelengths (the error of crown glass lenses preponderating in the red). This error was treated by Jean le Rond d'Alembert, and, in special detail, by C. F. Gauss. It increases rapidly with the aperture, and is more important with medium apertures than the secondary spectrum of par-axial rays; consequently, spherical aberration must be eliminated for two colors, and if this be impossible, then it must be eliminated for those particular wavelengths which are most effectual for the instrument in question (a graphical representation of this error is given in M. von Rohr, "Theorie und Geschichte des photographischen Objectivs").


title: Optical aberration

text: The condition for the reproduction of a surface element in the place of a sharply reproduced point — the constant of the sine relationship must also be fulfilled with large apertures for several colors. E. Abbe succeeded in computing microscope objectives free from error of the axis point and satisfying the sine condition for several colors, which therefore, according to his definition, were "aplanatic for several colors"; such systems he termed "apochromatic". While, however, the magnification of the individual zones is the same, it is not the same for red as for blue; and there is a chromatic difference of magnification. This is produced in the same amount, but in the opposite sense, by the oculars, which Abbe used with these objectives ("compensating oculars"), so that it is eliminated in the image of the whole microscope. The best telescope objectives, and photographic objectives intended for three-color work, are also apochromatic, even if they do not possess quite the same quality of correction as microscope objectives do. The chromatic differences of other errors of reproduction seldom have practical importance.


title: Brooks Brothers riot

text: The Brooks Brothers riot was a demonstration at a meeting of election canvassers in Miami-Dade County, Florida, on November 22, 2000, during a recount of votes made during the 2000 United States presidential election, with the goal of shutting down the recount. After demonstrations and acts of violence, local officials shut down the recount early.


title: Brooks Brothers riot

text: The name referenced the protesters' corporate attire; described by Paul Gigot in an editorial for "The Wall Street Journal" as "50-year-old white lawyers with cell phones and Hermès ties", differentiating them from local citizens concerned about vote counting. Many of the demonstrators were Republican staffers. Both Roger Stone and Brad Blakeman take credit for managing the riot from a command post, although their accounts contradict each other. Republican New York Representative John E. Sweeney gave the signal that started the riot, telling an aide to "shut it down".


title: Brooks Brothers riot

text: In the 2000 United States presidential election between candidates George W. Bush and Al Gore, in the state of Florida, George W. Bush achieved an election night majority by 1,784 votes, a very close margin. Due to the closeness of the race, and irregularities such as hanging chads, the Gore campaign successfully advocated for a re-count of certain ballots. Miami-Dade County was one of the counties where ballots were re-counted.


title: Brooks Brothers riot

text: The Miami-Dade County Democratic Party chairman suspected that thousands of ballots in this county might have been affected by a voting machine glitch. He suspected that these ballots, after re-tallying, would help candidate Al Gore. Miami-Dade County official canvassers, in order to meet a court-ordered deadline, decided to limit the county's recount to the 10,750 ballots that their tabulation machines had been unable to tally. They moved the counting process to a smaller room, closer to the ballot-scanning equipment, to speed up the process, at a distance from the media. Republican officials objected to this change.