Cooke triplet

File:Cooke triplet.JPG

According to Taylor, the lens design was derived by considering a cemented achromatic doublet consisting of one thin negative element and one thin positive element, both of equal power; such a doublet would result in a compound lens with zero net power but also a flat field of focus.{{efn|The field of focus is expressed by the Petzval field curvature, also known as Petzval sum. This was defined by the mathematician Joseph Petzval as the sum of the product of the radii of curvature and refractive index for each lens element.}} However, by separating the elements, the resulting air gap would act as an additional lens element, giving the system a positive overall power while retaining the flat-field characteristic. To correct the oblique aberrations, Taylor recommended splitting one element and mounting them on either side of the remaining element;{{cite journal |doi=10.1088/1475-4878/24/3/302 |title=Optical designing as an art |author=Taylor, H. Dennis |author-link=Harold Dennis Taylor |date=1923 |journal=Transactions of the Optical Society |volume=24 |number=3 |page=143}} although he patented versions in which either the negative or positive element was split, in his preferred embodiment, he split the positive element.{{Kingslake-lens-history |chapter=7}}{{rp|103}}

A Cooke triplet comprises a negative flint glass element in the centre with a positive crown glass element on each side. In this design, the Petzval sum is zero, so the field of focus is flat. In other words, the negative lens can be as strong as the outer two combined, when one measures in dioptres, yet the lens will converge light, because the rays strike the middle element close to the optical axis. The curvature of field is determined by the sum of the dioptres, but the focal length is not.

At the time, the Cooke triplet was a major advancement in lens design. For one wavelength, the design can correct, using only three elements, spherical aberration, coma, astigmatism, field curvature, and distortion. However, Kingslake noted "there is no symmetry to help the designer, and there is no control over distortion", leading to a trial-and-error design process.{{rp|104–105}} It was surpassed by later designs in high-end cameras, including the double Gauss design, but is still widely used in inexpensive cameras, including variations using aspheric elements, particularly in cell-phone cameras.

{{quote2|The Cooke triplet consists of three separated lenses positioned at the finite distance. It is often considered that the triplet is one of the most important discoveries in the field of photographic objectives|The Cooke triplet optimizations (2002)}}

T. Cooke & Sons were reluctant to manufacture the lens, possibly because of the difficulty in grinding the strong central negative element, and the design was licensed to Taylor, Taylor and Hobson, who named the product the Cooke triplet.{{rp|105}}

Starting from the early 1900s, the Cooke triplet was adopted by other major optical lens manufacturers and were produced for many decades.

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• Agfa Agnar, Apotar
• Argus Cintar
• Corfield Lumar
• {{ill|Enna Werk|de|lt=Enna}} Ennagon
• {{ill|ISCO Göttingen|de|lt=ISCO}} Iscotar
• Kodak Anaston
• E.Ludwig Meritar,{{efn|Entry-level normal lens offered for Ihagee Exakta SLR cameras.{{cite web |url=https://lenslegend.com/e-ludwig-meritar-50mm-f2-9-review/ |title=E. Ludwig Meritar 50mm f2.9 Review |date=April 3, 2020 |website=lens-legend |access-date=22 August 2023}}}} Victar
• Meyer Optik Domiplan, Trioplan
• Piesker Piconar
• Plaubel Anticomar (early){{efn|After {{circa|1932–35}}, a fourth element was added to Anticomar lenses, making them more similar to Tessar designs.{{cite web |url=https://apenasimagens.com/en/anticomar-plaubel-2/ |title=Anticomar {{!}} Plaubel |date=14 October 2019 |website=only images |access-date=22 August 2023}}{{cite web |url=https://lens-club.ru/public/files/pdfs/0d4d0d70363bbeae3caf5bda84ecb0a6.PDF |title=Chapter: P |website=lens-club.ru |access-date=22 August 2023}}}}
• Rodenstock Eurygon, Trinar
• Schacht Travegar
• Schneider Kreuznach Radionar
• {{ill|C. A. Steinheil & Söhne|de|lt=Steinheil}} Cassar, Cassarit
• Voigtländer Vaskar, Voigtar
• Zeiss Pantar, Novar-Anastigmat,{{efn|Novar lenses were manufactured by Rodenstock or {{ill|C. A. Steinheil & Söhne|de|lt=Steinheil}} for Zeiss Ikon cameras.{{cite magazine |url=https://www.mikeeckman.com/wp-content/uploads/2019/02/ZeissAutumn1982.pdf |title=The Super Ikontas |author=Gubas, Larry |magazine=Zeiss Historica |date=Autumn 1982 |volume=4 |number=2 |publisher=Zeiss Historica Society of America |quote=NOVAR: These triplet lenses were made to Stuttgart's specifications by Rodenstock and possibly also by Steinheil. Both firms were located in Munich.}}}} Triotar

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File:Taylor US568052A (Cooke Triplet, 1893 Fig 11).svg|Cooke triplet (Taylor, 1893){{cite patent |country=US |status=Patent |number=568052A |title=Lens |inventor=H. D. Taylor |gdate=September 22, 1896}}

File:Harting US716035A (Heliar, 1901).svg|Voigtländer Heliar (Harting, 1900){{cite patent |country=US |status=Patent |number=716035A |title=Lens |inventor=Carl August Hans Harting |fdate=February 4, 1901 |gdate=December 16, 1902}}

File:Harting US765006A (Dynar, 1904).svg|Voigtländer Dynar (Harting, 1903){{cite patent |country=US |status=Patent |number=765006A |title=Lens |inventor=Hans Harting |fdate=February 17, 1904 |gdate=July 12, 1904}}

File:Lee US1739512A (Speedic, 1924).svg|Taylor Hobson Speedic (Lee, 1924){{cite patent |country=US |status=Patent |number=1739512A |title=Photographic Objective |inventor=Horace William Lee |fdate=January 29, 1925 |pridate=February 6, 1924 |gdate=December 17, 1929}}

File:Bertele DE458499C (Ernostar, 1924).svg| Ernostar f/2.0 (Bertele, 1924){{cite patent |country=DE |status=Patent |number=458499C |title=Photographisches Objektiv |inventor=Ludwig Bertele |fdate=July 22, 1924 |gdate=April 13, 1928}}

Arthur Cox noted that anastigmat lenses were "almost exclusively, the logical development of two main types, the symmetrical lens, and the Cooke triplet of H. D. Taylor."{{cite book |url=https://archive.org/details/photographicopti00coxa/ |title=Photographic optics: a modern approach to the technique of definition |author=Cox, Arthur |date=1966 |edition=Thirteenth |publisher=Focal Press |location=London & New York |access-date=21 August 2023 |chapter=Basic Lens Types |url-access=registration |pages=233–314}}{{rp|241}} One of the first derivatives was the Voigtländer Heliar, developed by Hans Harting in 1900 as a symmetrical modification of the original Cooke triplet.{{rp|106}} Harting continued to develop the lens, resulting in the Dynar (1903), whose design was later adopted as a new version of the Heliar after World War I.{{rp|107–108}} Anecdotal evidence indicates that a Heliar was used to take official portraits of Emperor Hirohito.{{cite web |url=https://allphotolenses.com/public/files/pdfs/9842628bf65e4cf32df53c0daac7a09a.pdf |title=Additional info about the APO-LANTHAR |publisher=Cosina Voigtländer |access-date=21 August 2023}} Although the contemporary Zeiss Tessar (1902) is said to be a development of the Cooke triplet, it is more accurately considered a parallel development descended from earlier, four-element designs by Paul Rudolph, including the Protar and Unar.{{Kingslake-lens-history |chapter=6}}{{rp|90}}

To increase the lens speed, either the rear element was further split into two, as patented by Edward Bausch in 1900 and H.W. Lee as the Speedic in 1924, or a positive meniscus element was inserted into the front air space, as in Ludwig Bertele's enduring Ernostar and Sonnar designs for Ernemann and Carl Zeiss AG, respectively.{{rp|108–111}}

Several of the early lenses used with the Leica camera were derived from the Cooke triplet by splitting one or more of the three elements into a cemented doublet, including the Elmar, Elmarit, Hektor, and Thambar.{{rp|113}}

Binoculars as well as refracting telescopes often use triplets. The same holds for many projection lenses, e.g., for 35 mm slide projectors.

Rudolf Kingslake notes the Hologon is a triplet in which the negative element was split to surround a positive element.{{rp|104}}

Image: Rollei B 35 black.jpg|Triotar-Triplet on a Rollei scale-focus camera

Image: Ed LiesegangPatrinast1-28 85 d37 zebra top.jpg|Projection objective Patrinast for a 35 mm slide projector by Ed. Liesegang; 1:2.8/85

Image: Will-Wetzlar-Maginon 1-2.8 100 d42Obl.jpg|Projection objective Maginon by Wilhelm Will, Wetzlar, 1:2.8/100

The Cooke triplet has provided the basis for additional designs, including a derivative with five lens elements.{{Cite journal|last=Sharma|first=K. D.|date=1979-12-01|title=Design of a new five-element Cooke triplet derivative|journal=Applied Optics|volume=18|issue=23|pages=3933–3937|doi=10.1364/AO.18.003933|issn=1559-128X|pmid=20216728}}

• Achromatic lens
• Chromatic aberration
• Triplet lens

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{{Reflist}}

• {{cite patent |country=GB |status=Patent |number=189322607A |title=A Simplified Form and Improved Type of Photographic Lens |inventor=Harold Dennis Taylor |fdate=November 25, 1893 |gdate=October 6, 1894}}
• {{cite patent |country=GB |status=Patent |number=189515107A |title=Improvements in Lenses |inventor=Harold Dennis Taylor |fdate=August 10, 1895 |gdate=July 18, 1896}}
• [https://spie.org/publications/pm92_101_triplets?SSO=1 Explanation of triplets from Fundamental Optical Design]

Category:Photographic lens designs