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Cooke triplet

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Cooke triplet
Introduced in1893
AuthorDennis Taylor
Construction3 elements in 3 groups
Aperturef/3.5 (early)
f/2.8 (rare-earth optical glass)

The Cooke triplet is a photographic lens designed and patented in 1893 by Dennis Taylor who was employed as chief engineer by T. Cooke & Sons of York. It was the first lens system that allowed the elimination of most of the optical distortion or aberration at the outer edge of the image.[citation needed]

The Cooke triplet is noted for being able to correct the five Seidel aberrations.[1] The compound lens design consists of three air-spaced simple lens elements: two biconvex (positive) lenses surrounding a biconcave (negative) lens in the middle.[2] It is one of the most important objective designs in the history of photography.[2]

Design

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Cooke triplet

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.[a] 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;[3] although he patented versions in which either the negative or positive element was split, in his preferred embodiment, he split the positive element.[4]: 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.

Impact and production

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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.[2] 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.[4]: 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.

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)[2]

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.[4]: 105 

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

Further development

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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."[14]: 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.[4]: 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.[4]: 107–108  Anecdotal evidence indicates that a Heliar was used to take official portraits of Emperor Hirohito.[15] 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.[16]: 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.[4]: 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.[4]: 113 

Application

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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.[4]: 104 

  • Triotar-Triplet on a Rollei scale-focus camera
    Triotar-Triplet on a Rollei scale-focus camera
  • Projection objective Patrinast for a 35 mm slide projector by Ed. Liesegang; 1:2.8/85
    Projection objective Patrinast for a 35 mm slide projector by Ed. Liesegang; 1:2.8/85
  • Projection objective Maginon by Wilhelm Will, Wetzlar, 1:2.8/100
    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.[17]

See also

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Notes

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  1. ^ 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.
  2. ^ Entry-level normal lens offered for Ihagee Exakta SLR cameras.[5]
  3. ^ After c. 1932–35, a fourth element was added to Anticomar lenses, making them more similar to Tessar designs.[6][7]
  4. ^ Novar lenses were manufactured by Rodenstock or Steinheil [de] for Zeiss Ikon cameras.[8]

References

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  1. ^ Kidger, Michael J. (2002). Fundamental Optical Design. SPIE Press. ISBN 9780819439154.
  2. ^ a b c d Vasiljević, Darko (2002). "13: The Cooke triplet optimizations". Classical and Evolutionary Algorithms in the Optimization of Optical Systems. Springer US. pp. 187–211. doi:10.1007/978-1-4615-1051-2_13. ISBN 9781461510512.
  3. ^ Taylor, H. Dennis (1923). "Optical designing as an art". Transactions of the Optical Society. 24 (3): 143. doi:10.1088/1475-4878/24/3/302.
  4. ^ a b c d e f g h Kingslake, Rudolf (1989). "7. The Triplet Lens and its Modifications". A History of the Photographic Lens. San Diego: Academic Press. pp. 103–116. ISBN 0-12-408640-3. Retrieved 28 December 2024.
  5. ^ "E. Ludwig Meritar 50mm f2.9 Review". lens-legend. April 3, 2020. Retrieved 22 August 2023.
  6. ^ "Anticomar | Plaubel". only images. 14 October 2019. Retrieved 22 August 2023.
  7. ^ "Chapter: P" (PDF). lens-club.ru. Retrieved 22 August 2023.
  8. ^ Gubas, Larry (Autumn 1982). "The Super Ikontas" (PDF). Zeiss Historica. Vol. 4, no. 2. Zeiss Historica Society of America. NOVAR: These triplet lenses were made to Stuttgart's specifications by Rodenstock and possibly also by Steinheil. Both firms were located in Munich.
  9. ^ US Patent 568052A, H. D. Taylor, "Lens", issued September 22, 1896 
  10. ^ US Patent 716035A, Carl August Hans Harting, "Lens", issued December 16, 1902 
  11. ^ US Patent 765006A, Hans Harting, "Lens", issued July 12, 1904 
  12. ^ US Patent 1739512A, Horace William Lee, "Photographic Objective", issued December 17, 1929 
  13. ^ DE Patent 458499C, Ludwig Bertele, "Photographisches Objektiv", issued April 13, 1928 
  14. ^ Cox, Arthur (1966). "Basic Lens Types". Photographic optics: a modern approach to the technique of definition (Thirteenth ed.). London & New York: Focal Press. pp. 233–314. Retrieved 21 August 2023.
  15. ^ "Additional info about the APO-LANTHAR" (PDF). Cosina Voigtländer. Retrieved 21 August 2023.
  16. ^ Kingslake, Rudolf (1989). "6. The First Anastigmats". A History of the Photographic Lens. San Diego: Academic Press. pp. 81–102. ISBN 0-12-408640-3. Retrieved 28 December 2024.
  17. ^ Sharma, K. D. (1979-12-01). "Design of a new five-element Cooke triplet derivative". Applied Optics. 18 (23): 3933–3937. doi:10.1364/AO.18.003933. ISSN 1559-128X. PMID 20216728.
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