{{Short description|Compound lens}} {{Infobox lens design | name =Double Gauss | scheme =Double gauss.png | caption =The "Opic" type double Gauss design with optical ray traces | year ={{ubl| * 1888 (Clark) * 1896 (Rudolph; ''Zeiss Planar'') * 1920 (Lee; Taylor, Taylor and Hobson ''Opic'')}} | author = Alvan Graham Clark, Paul Rudolph, and Horace William Lee | elements =4–6 | groups =4+ | aperture = }} The '''double Gauss lens''' is a compound lens used mostly in camera lenses that reduces optical aberrations over a large focal plane.

==Design== right|thumb|upright=1|Development of the Double Gauss The earliest double Gauss lens, patented by Alvan Graham Clark in 1888, consists of two symmetrically-arranged Gauss lenses. Each Gauss lens is a two-element achromatic lens with a positive meniscus lens on the object side and a negative meniscus lens on the image side. In Clark's symmetric arrangement, this makes four elements in four groups: two positive meniscus lenses on the outside with two negative meniscus lenses inside them. The symmetry of the system and the splitting of the optical power into many elements reduces the optical aberrations within the system.

There are many variations of the design. Sometimes extra lens elements are added. The basic lens type is one of the most developed and used photographic lenses. The design forms the basis for many camera lenses in use today, especially the wide-aperture standard lenses used with 35 mm and other small-format cameras. It can offer good results up to {{f/|1.4|link=yes}} with a wide field of view, usually with seven elements for extra aberration control. Modern super wide aperture models of {{f/}}1.0 can have eight or more elements, while more moderate aperture {{f/|2.8}} versions can be simplified to five elements.

The Double Gauss was likely the most intensively studied lens formula of the twentieth century,<ref name=Cox>{{cite book|last=Cox|first=Arthur|title=Photographic Optics, a Modern Approach to the Technique of Definition|year=1971|publisher=Focal Press|location=London|isbn=0817406654 |url=https://archive.org/details/photographicopti0000coxa |url-access=registration}}</ref>{{rp|245}} producing dozens of major variants, scores of minor variants, hundreds of marketed lenses and tens of millions of unit sales.<ref name=Cox/>{{rp|444–452}}<ref name=Kingslake>{{Kingslake-lens-history |chapter=8}}</ref>{{rp|123–128}} It has few flaws, most notably a small amount of oblique spherical aberration, which could lower peripheral contrast.<ref name=Cox/>{{rp|245–248}} Double Gauss/Planar tweaks formed the basis for most normal and near-normal prime lens designs with wide apertures for sixty years.

==History== ===Early development=== The original two element ''Gauss'' was a telescope objective lens consisting of closely spaced positive and negative menisci, invented in 1817 by Carl Friedrich Gauss as an improvement to the Fraunhofer Achromatic telescope objective lens by adding a meniscus lens to its single convex and concave lens design.<ref name=Kingslake/>{{rp|117–118}} Alvan Graham Clark and Bausch & Lomb further refined the design in 1888 by taking two of these lenses and placing them back to back, making a "double Gauss" design,<ref>{{US patent reference |inventor=Alvan G. Clark |title=Photographic Lens |number=399499 |d=12 |m=March |y=1889}}</ref> albeit with indifferent photographic results.<ref name=Kingslake/>{{rp|118}}

Current double Gauss lenses can be traced back to an 1895 improved design, when Paul Rudolph of Carl Zeiss Jena thickened the interior negative menisci and converted to them to cemented doublets of two elements of equal refraction but differing dispersion for the ''Zeiss Planar'' design of 1896<ref>{{US patent reference |inventor=Paul Rudolph |title=Objective Glass |number=583336 |d=25 |m=May |y=1897}}</ref> to correct for chromatic aberration. It was the original six element symmetric {{f/|4.5}} double Gauss lens.<ref name=Kingslake/>{{rp|121–122}} Horace William Lee added a slight asymmetry to the Planar in 1920, and created the ''Taylor, Taylor & Hobson Series 0'' (also called the ''Lee Opic'', UK) {{f/|2}} lens.<ref name=Kingslake/>{{rp|122}} It was commercially unsuccessful, but its asymmetry is the foundation of the modern double Gauss, including the Zeiss ''Biotar''.<ref name=Cox/>{{rp|243–245}}

===Modern designs=== thumb|right|Zeiss ''Biotar'' 58mm {{f/|2}} Later the design was developed with additional glasses to give high-performance lenses of wide aperture. The main development was due to Taylor Hobson in the 1920s, resulting in the {{f/|2.0}} ''Opic'' and later the ''Speed Panchro'' designs, which were licensed to various other manufacturers. In 1927, Lee modified the Opic design and increased the maximum aperture up to {{f/|1.4}}, which was named the ''Ultra Panchro'' lens. Further improvement was done by Lee in 1930, the ''Super Speed Panchro''.<ref>{{cite patent |country=US |number=2019985 |inventor=Horace William Lee |pridate=December 26, 1930 |pubdate=November 5, 1935 |title=Lens}}</ref> It was a {{f/|1.5}} fast design with seven elements in five groups, which influenced later fast speed lens designs, being cited by many lens manufacturers until the 1960s.

left|thumb|Zeiss ''Biotar'' diagram The ''Biotar'' is another competitor of British ''Panchro'' series. In the same year of 1927, Zeiss designed the ''Biotar'' 50mm {{f/|1.4}}<ref>{{cite patent |country=DE |number=485798 |pubdate=Sep 30, 1927}}</ref> for cinematography. Its still photography version, the Zeiss ''Biotar'' 58mm {{f/|2}} (Germany) appeared on the Ihagee Kine Exakta (1936, Germany), the first widely available 35mm single-lens reflex cameras, in 1939. It was also the standard lens on the VEB Zeiss Ikon (Dresden) Contax S (1949, East Germany), the first pentaprism eye-level viewing 35mm SLR.<ref>{{cite magazine |first=Herbert |last=Keppler |title=Inside Straight: Optical Miracle: The amazing story of the Biotar |pages=32–33 |magazine=Popular Photography & Imaging |volume=71 |number=5 |date=May 2007 |issn=1542-0337 |url=https://books.google.com/books?id=QRZmyE_0cHAC&pg=PA32}}</ref> The ''Biotar'', originally designed in 1927, had a six element asymmetric double Gauss formula. Post-World War II Zeiss (Oberkochen, West Germany) no longer uses the ''Biotar'' name; instead lumping all double Gauss variants under the ''Planar'' name. The Soviet 58mm {{f/|2}} ''Helios-44'' lens of the Zenit camera was the most common version/clone of the ''Biotar'',<ref>{{Cite web|url=http://www.photohistory.ru/1207248188431861.html|title=PHOTOHISTORY - Г.Абрамов, "Этапы развития отечественного фотоаппаратостроения"|website=www.photohistory.ru|access-date=2018-08-24}}</ref> making an excellent value-for-money accessory today for any digital camera with APS-C and Full-Frame sized sensor, though an appropriate M42 adaptor is required for this particular lens.

Several contemporaneous competing, but less famous lenses, were similar to the Biotar, such as Albrecht Tronnier's ''Xenon'' for Schneider Kreuznach (1925, Germany).<ref name=Kingslake/>{{rp|122–123}}<ref>{{cite patent |inventor=Albrecht Wilhelm Tronnier |title=Photographisches Objektiv |country=DE |number=439556 |pubdate=30 April 1925}}</ref> For example, three asymmetric Double Gauss lenses were produced in 1934 for Ihagee VP Exakta (1933, Germany) the type 127 roll film SLR camera: 8&nbsp;cm {{f/|2}} versions of both the ''Biotar'' and ''Xenon'', as well as the Dallmeyer ''Super Six'' 3&nbsp;inch {{f/|1.9}} (UK).<ref>{{cite book |first1=Clément |last1=Aguila |first2=Michel |last2=Rouah |title=Exakta Cameras, 1933–1978 |edition=2003 reprint |location=Small Dole, West Sussex, UK |publisher=Hove Collectors Books |date=1987 |isbn=0-906447-38-0 |pages=25–26}}</ref>

Other early Double Gauss variants for 35mm cameras included the Kodak ''Ektar'' 45mm {{f/|2}}<ref>{{Cite book |author=<!--Anonymous--> |title=Kodak Lenses & Shutters (Promotional book) |location=Rochester, NY |publisher=Eastman Kodak Co. |date=c. 1939 |pages=36}}</ref> on the Kodak Bantam Special (1936, USA), the Kodak ''Ektar'' 50mm {{f/|1.9}}<ref>{{Cite book |author=Anonymous |title=Kodak Ektra (Instruction manual) |location=Rochester, NY |publisher=Eastman Kodak Co. |date=c. 1941 |pages=9}}</ref> for the Kodak Ektra (1941, USA), the Voigtländer ''Ultron'' 50mm {{f/|2}}<ref>{{Cite web |author=Frank Mechelhoff |title=History of fast 35mm and small format film lenses |url=http://www.taunusreiter.de/Cameras/Biotar_en.html |accessdate=30 April 2008}}</ref> on the Voigtländer Vitessa (1951, West Germany) and the Leitz ''Summicron'' 50mm {{f/|2}}<ref name=Kingslake/>{{rp|125}} for the Leica M3 (1953, West Germany). A notable, but largely-forgotten, use of the Double-Gauss formula was in the Canon 28mm {{f/|3.5}} (1951, Japan) <ref>{{Cite web |publisher=Canon INC |title=Canon Serenar 28mm f/3.5 I |url=http://www.canon.com/camera-museum/camera/lens/s/data/19-35/s_sere_28_35.html?p=1 |accessdate=26 December 2012}}</ref> in M39 mount for Rangefinder cameras. By enlarging the rear group significantly (compared to a Double-Gauss type of more traditional focal length), the field of view was increased while keeping the aperture relatively large- making it, for a time, the fastest 28mm lens available for 35mm cameras by a large margin.<ref>{{Cite web |publisher=Canon INC |title=Canon Serenar 28mm f/3.5 I Block Diagram |url=http://www.canon.com/camera-museum/camera/lens/s/data/19-35/s_sere_28_35.html?p=2 |accessdate=26 December 2012 |archive-date=23 May 2013 |archive-url=https://web.archive.org/web/20130523232829/http://www.canon.com/camera-museum/camera/lens/s/data/19-35/s_sere_28_35.html?p=2 |url-status=dead }}</ref>

===Later development and proliferation=== In 1966, ''Asahi Pentax'' combined the ''Super Speed Panchro'' type and the ''Xenon'' type, developing the seven-element, six-group ''Super Takumar'' 50mm {{f/|1.4}} (v2).<ref>{{cite patent |country=US |number=3451745 |title=Large aperture seven-lens objective lens system |inventor=Tomokazu Kazamaki |invent2=Yasuo Takahashi |assign=Asahi Kogaku Kogyo Kabushiki Kaisha |pridate=February 28, 1966 |pubdate=June 24, 1969}}</ref> During the 1960s to early 80s every optical house had ''Super Panchro'' type or ''Super Takumar'' type double Gauss normal lenses jockeying for sales. For example, compare the Tokyo Optical ''RE Auto-Topcor'' 5.8&nbsp;cm {{f/|1.4}}<ref>{{Cite book |author=Anonymous |title=Beseler Topcon Super D: With Behind Mirror Meter System. (Instruction manual) |date=c. 1966 |pages=40 |url=https://www.pacificrimcamera.com/rl/02325/02325.pdf}}</ref> for the Topcon RE Super/Super D (1963), Olympus ''G. Zuiko'' Auto-S 40mm {{f/|1.4}}<ref>{{cite book |author=Anonymous |title=An Outline of Facts You Should Know About: Olympus FTography. (Dealer information guide) |location=Los Angeles, CA |publisher=Ponder & Best |date=c. 1966 |page=6 |url=https://www.pacificrimcamera.com/rl/01029/01029.pdf}}</ref> for the Olympus Pen F (lens 1964, camera 1963), Yashica ''Auto Yashinon'' DX 50mm {{f/|1.4}}<ref>Anonymous, ''Yashinon Lenses.'' (Brochure) no publication data, but circa 1974. p. 13.</ref> for the Yashica TL Super (1967), Canon FL 50mm {{f/|1.4}} (v2)<ref>{{Cite web |author=Anonymous |work=Canon Camera Museum: Camera Hall |title=Lenses (FL Mount): FL50mm f/1.4II: specifications |url=http://www.canon.com/camera-museum/camera/lens/fl/data/19-85/fl_50_14v2.html |accessdate=7 January 2010 |archive-date=24 February 2010 |archive-url=https://web.archive.org/web/20100224005045/http://www.canon.com/camera-museum/camera/lens/fl/data/19-85/fl_50_14v2.html |url-status=dead }}</ref><ref>{{Cite web |author=Anonymous |work=Canon Camera Museum: Camera Hall |title=Lenses (FL Mount): FL50mm f/1.4II: block diagram |url=http://www.canon.com/camera-museum/camera/lens/fl/data/19-85/fl_50_14v2.html?p=2 |accessdate=7 January 2010}}</ref> for the Canon FT (lens 1968, camera 1966), Asahi Optical ''Super Takumar'' 50mm {{f/|1.4}} (v2)<ref>Anonymous, ''Asahi Pentax Spotmatic II Operating Manual.'' Tokyo, Japan: Asahi Optical Co., Ltd., September 1972. p. 28.</ref> for the Pentax Spotmatic (lens 1968, camera 1964), Fuji ''Fujinon'' 50mm {{f/|1.4}}<ref>{{Cite web |author=Anonymous |title=EBC FUJINON 50MM F1.4 |url=http://www.pentax-manuals.com/fujica/lenses/m42_50_14.htm |accessdate=25 January 2010}}</ref> for the Fujica ST701 (1971), Minolta MC ''Rokkor-PG'' 50mm {{f/|1.4}}<ref>{{Cite web |author=Anonymous |title=ОПТИЧЕСКИЕ СХЕМЫ ОБЪЕКТИВОВ MINOLTA MC/MD ROKKOR |trans-title=The optical schemata of Minolta MC/MD Rokkor lenses |url=http://www.rokkor-x.narod.ru/user_manuals/rokkors_schems |accessdate=25 January 2010}}</ref> for the Minolta XK/XM/X-1 (1973), Zeiss ''Planar HFT'' 50mm {{f/|1.4}}<ref>{{Cite web |author=Frank Mechelhoff |title=The Last German 35mm film cameras / Rolleiflex SL350 |url=http://www.taunusreiter.de/Cameras/Rolleiflex350_en.html |accessdate=30 April 2008}}</ref> for the Rolleiflex SL350 (1974), Konica ''Hexanon AR'' 50mm {{f/|1.4}}<ref>{{Cite web |author=Andreas Buhl |title=Konica SLR lenses 1960–1987: Konica Hexanon AR 50 mm / F1.4 |url=http://www.buhla.de/Foto/Konica/Objektive/e50_14.html |accessdate=22 February 2010}}</ref> for the Konica Autoreflex T3 (lens 1974, camera 1973) and Nippon Kogaku ''Nikkor'' (K) 50mm {{f/|1.4}} (New)<ref>{{Cite book |author=Anonymous |title=Nikon: Dealer Catalogue |location=Garden City, NY |publisher=Nikon Corp. |date=c. 1987 |pages=26}}</ref> for the Nikon F2 (lens 1976, camera 1971); all from Japan except the Zeiss which was designed in West Germany.

<gallery caption="History of Double Gauss lens designs" mode=packed widths=240px heights=360px class="skin-invert-image"> Image:DoubleGauss2text.svg|1936–1964 Image:DoubleGauss3text.svg|1964–1977 Image:DoubleGauss4text.svg|1978–2010 </gallery>

===Current status=== Zoom lenses have been dominant since the 1980s and so there have been few newly designed Double Gauss normal lenses, but many new prestige low production Double Gauss lenses have been released. Compare the Canon EF 50mm {{f/|1.2}}''L'' USM (2007, Japan),<ref name=EF50-1.2L-spec>{{Cite web |author=Anonymous |work=Canon Camera Museum: Camera Hall |title=Lenses (EF Mount): EF50mm f/1.2L USM: specifications |url=http://www.canon.com/camera-museum/camera/lens/ef/data/standard/ef_50_f1.2l_usm.html |accessdate=4 January 2010 |archive-url=https://web.archive.org/web/20071022043202/http://www.canon.com/camera-museum/camera/lens/ef/data/standard/ef_50_f1.2l_usm.html |archive-date=22 October 2007 |url-status=dead }}</ref><ref name=EF50-1.2L-diagram>{{Cite web |author=Anonymous |work=Canon Camera Museum: Camera Hall |title=Lenses (EF Mount): EF50mm f/1.2L USM: block diagram |url=http://www.canon.com/camera-museum/camera/lens/ef/data/standard/ef_50_f1.2l_usm.html?p=2 |accessdate=4 January 2010}}</ref> Nikon ''AF-S Nikkor'' 50mm {{f/|1.4}}G (2008, Japan/China),<ref>{{Cite web |author=Anonymous |title=AF-S NIKKOR 50mm f/1.4G |url=http://imaging.nikon.com/products/imaging/lineup/lens/af/normal/af_50mmf_14g/index.htm |accessdate=4 January 2010 }}{{Dead link|date=November 2019 |bot=InternetArchiveBot |fix-attempted=yes }}</ref> Sigma EX DG HSM 50mm {{f/|1.4}} (2008, Japan),<ref>{{Cite book |author=Anonymous |title=SIGMA: Lens Catalogue |location=Kawasaki, Kanagawa, Japan |publisher=Sigma Corp. |date=June 2008 |pages=15}}</ref> (''Cosina'') Voigtländer ''Nokton'' 50mm {{f/|1.1}} (2009, Japan),<ref>{{Cite web |author=Anonymous |title=L&VM standard- Lens |url=http://www.cosina.co.jp/seihin/voigt/english/standard-e.html |accessdate=4 January 2010 |archive-url=https://web.archive.org/web/20091226081247/http://www.cosina.co.jp/seihin/voigt/english/standard-e.html |archive-date=26 December 2009 |url-status=dead }}</ref> ''Leica Noctilux-M 50mm f/0.95 ASPH'' (2009, Germany)<ref>{{Cite book |author=Anonymous |title=LEICA NOCTILUX-M 50 mm f/0.95 ASPH. (Brochure) |location=Solms, Germany |publisher=Leica Camera AG |year=2009 |pages=1}}</ref> with their antecedents, or SLR Magic ''HyperPrime'' 50mm CINE T0.95 (2012, Hong Kong, China).<ref>{{Cite web |work=Digital Photography Review |title=SLR Magic announces HyperPrime CINE 50mm T0.95 M-mount lens |url=http://www.dpreview.com/news/2012/01/01/SLRMagic50mm0p95 |accessdate=1 January 2012}}</ref>

The design is presently used in inexpensive-but-high-quality fast lenses such as the Sony FE 50mm {{f/}}1.8, the Canon EF 50mm {{f/}}1.8 and the Nikon 50 mm {{f/}}1.8D AF Nikkor. It is also used as the basis for faster designs, with elements added, such as a seventh element as in both Canon<ref>{{Cite web |url=https://global.canon/en/c-museum/product/ef318.html |title=EF50mm f/1.4 USM |website=Canon Camera Museum: Lens Hall}}</ref> and Nikon's 50&nbsp;mm {{f/}}1.4 offerings<ref>{{Cite web |url=http://imaging.nikon.com/products/imaging/lineup/lens/singlefocal/normal/af_50mmf_14d/index.htm |title=AF Nikkor 50mm f/1.4D |website=Nikon Imaging |access-date=2010-07-01 |archive-date=2011-02-20 |archive-url=https://web.archive.org/web/20110220144720/http://imaging.nikon.com/products/imaging/lineup/lens/singlefocal/normal/af_50mmf_14d/index.htm |url-status=dead }}</ref> or an aspherical seventh element in Canon's 50&nbsp;mm {{f/}}1.2''L''.<ref name=EF50-1.2L-diagram/> The design appears in other applications where a simple fast normal lens is required (≈53° diagonal) such as in projectors.

==References== {{reflist}}

==External links== *[http://www.cartage.org.lb/en/themes/Arts/photography/photproces/photogralens/carlzeiss/carlzeiss.htm A brief description of the double Gauss design] {{Webarchive|url=https://web.archive.org/web/20060517124505/http://www.cartage.org.lb/en/themes/Arts/photography/photproces/photogralens/carlzeiss/carlzeiss.htm |date=2006-05-17 }}

Category:Photographic lenses Category:Photographic lens designs