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Photographic Zoom Fisheye Lens Design for DSLR Cameras Photographic zoom fisheye lens design for DSLR cameras Item Type Article Authors Yan, Yufeng; Sasian, Jose Citation Photographic zoom fisheye lens design for DSLR cameras 2017, 56 (09):1 Optical Engineering DOI 10.1117/1.OE.56.9.095103 Publisher SPIE-SOC PHOTO-OPTICAL INSTRUMENTATION ENGINEERS Journal Optical Engineering Rights © 2017 SPIE. Download date 07/10/2021 10:47:58 Item License http://rightsstatements.org/vocab/InC/1.0/ Version Final published version Link to Item http://hdl.handle.net/10150/626080 Photographic zoom fisheye lens design for DSLR cameras Yufeng Yan Jose Sasian Yufeng Yan, Jose Sasian, “Photographic zoom fisheye lens design for DSLR cameras,” Opt. Eng. 56(9), 095103 (2017), doi: 10.1117/1.OE.56.9.095103. Downloaded From: https://www.spiedigitallibrary.org/journals/Optical-Engineering on 11/14/2017 Terms of Use: https://www.spiedigitallibrary.org/terms-of-use Optical Engineering 56(9), 095103 (September 2017) Photographic zoom fisheye lens design for DSLR cameras Yufeng Yan* and Jose Sasian University of Arizona, College of Optical Sciences, Tucson, Arizona, United States Abstract. Photographic fisheye lenses with fixed focal length for cameras with different sensor formats have been well developed for decades. However, photographic fisheye lenses with variable focal length are rare on the market due in part to the greater design difficulty. This paper presents a large aperture zoom fisheye lens for DSLR cameras that produces both circular and diagonal fisheye imaging for 35-mm sensors and diagonal fish- eye imaging for APS-C sensors. The history and optical characteristics of fisheye lenses are briefly reviewed. Then, a 9.2- to 16.1-mm F ∕2.8 to F ∕3.5 zoom fisheye lens design is presented, including the design approach and aberration control. Image quality and tolerance performance analysis for this lens are also presented. © 2017 Society of Photo-Optical Instrumentation Engineers (SPIE) [DOI: 10.1117/1.OE.56.9.095103] Keywords: fisheye lenses; zoom lenses; two group zooms; lens design; aberration compensation. Paper 170893 received Jun. 12, 2017; accepted for publication Sep. 6, 2017; published online Sep. 27, 2017. 1 Introduction curvature, oblique spherical aberration, and lateral color Among the various types of imaging lenses that exist, fisheye challenging. These challenges become greater when the lenses are outstanding for their ultrawide-angle field of view lens must be optimized for different focal lengths, this is and for their unusual image mapping. Fisheye lenses can for a zoom lens. Over the last decade, a few zoom fisheye lens designs have been patented. For example, the lens in cover more than a hemispherical (180 deg) field of view 2 and were initially used for meteorology purposes to record U.S. Patent #6,987,623 assigned to Nikon, the lens in U.S. Patent #7,317,5813 assigned to Pentax, and the lens in U.S. the entire visible sky. Today, fisheye lenses are utilized for 4 many applications such as creative photography, surveil- Patent #8,456,751 assigned to Canon. Among these patents, lance, photogrammetry, art, and advertising. Fisheye lenses the design by Canon has been mass-produced. Apparently, suffer from a large amount of barrel distortion, which is used this lens is the only photographic zoom fisheye lens on in creative photography. Some photographic fisheye lenses the market that maintains its field of view at all zoom posi- tions. Furthermore, this lens provides a focal length that with extreme fields of view have been commercially manu- varies in the range of 8 to 15 mm at a relative aperture of factured, such as the Nikon 6-mm fisheye lens with a hyper F∕4 across the zoom range, which is relatively slow com- 220-deg full field of view.1 However, many photographers pared to some fixed focal length fisheye lenses. have come to realize that a full field of view of 180 deg Lens design details for zoom fisheye lenses are scarce in is most desirable for photography and this field has become the literature. However, this paper presents design details of a a standard. An important specification of a photographic zoom fisheye for diagonal and circular imaging with an aper- fisheye lens is how the object hemisphere is imaged on ture of F∕2.8 at the shortest focal position of 9.2 mm and the active area of the camera sensor. There are currently F∕3.5 at the longest focal position of 16.1 mm. The high- two types of fisheye lenses on the market, these are diagonal lights of the design are its simplicity, aberration control, fisheye lenses that cover the full field of view along the and image quality. This paper begins with an overview of diagonal of the sensor so that the sensor is fully illuminated fisheye lenses, discusses relevant optical characteristics, with the image, and the circular fisheye lenses that project an presents the design philosophy, provides lens data and analy- entire circular image within the camera sensor. This imaging sis, and then concludes. is shown in Fig. 1. To provide different image sizes, these fisheye lenses 2 Fisheye Lenses require different focal lengths for a given sensor size. In addi- The concept of a fisheye lens was inspired by considering the tion, fisheye lenses for cameras having different image for- eyes of fish under water. A fisheye model was first intro- mats, such as 35-mm format and APS-C format [a smaller duced by Wood5 [Fig. 2(a)]. He placed a photographic sensor format that is used on many compact digital sin- plate in a water-tight box filled with water with a pinhole gle-lens reflex camera (DSLR) cameras], also call for a dif- on the top. Then, he added a cover glass on the top of ferent focal length. Thus, a fisheye lens with a variable focal the pinhole to seal the water box so it could be pointed hori- length would be convenient and desirable for photographers zontally. Thus, the optical system was simply a water-filled as to provide full sensor imaging or circular imaging. pinhole camera with no lens involved. Some sample photos However, the extreme field of view of a fisheye lens, its opti- taken by this camera were published in Wood’s paper. Wood cal asymmetry, and the required long back focal distance also pointed out that this kind of wide-angle camera could be (BFD) make correcting off-axis aberrations, such as field used for sky recording. *Address all correspondence to: Yufeng Yan, E-mail: [email protected] 0091-3286/2017/$25.00 © 2017 SPIE Optical Engineering 095103-1 September 2017 • Vol. 56(9) Downloaded From: https://www.spiedigitallibrary.org/journals/Optical-Engineering on 11/14/2017 Terms of Use: https://www.spiedigitallibrary.org/terms-of-use Yan and Sasian: Photographic zoom fisheye lens design for DSLR cameras Fig. 1 Images taken by (a) a diagonal fisheye lens and (b) a circular fisheye lens. Fig. 2 Early development of fisheye lenses: (a) pinhole camera with water tank by Wood, (b) pinhole camera with hemispherical lens by Bond, (c) Hill sky lens, and (d) Allgemeine Elektricitäts-Gesellschaft (AEG) fisheye lens. The fisheye pinhole camera was then improved to a more Shortly after Bond’s fisheye pinhole camera was intro- practical design by Bond6 [Fig. 2(b)]. A single hemispherical duced, Robin7 published a paper on his famous “Hill sky lens was used to replace the water in Wood’s design, so the lens” [Fig. 2(c)]. Instead of a pinhole, he used a negative new design contained no water. In this design, all light would meniscus lens in the front to guide light into the stop aper- go through the small aperture located at the center top of the ture, then he used two additional lenses behind the stop for lens and form the image onto an almost hemispherical image imaging and aberration control. This lens was later mass-pro- surface. Bond’s design should be still considered as a fisheye duced as a sky recording device by Beck of London.8 With pinhole camera, rather than as a fisheye lens. Due to the lack the control of coma, astigmatism, and field curvature, the of aberration control in this system, the aperture needed to be lens could operate at F∕22. Lack of control of spherical aber- very small, which made the entire system so slow that it ration became the limiting factor on aperture size. Color cor- could be operated only at about F∕50. Also, field curvature rection was non-existent as well, so the lens could produce of the image was so large that the entire image could never monochromatic images only with a color filter. Nevertheless, been fully focused on a single photographic plate. Hill’s fisheye lens was truly a milestone in the history of Optical Engineering 095103-2 September 2017 • Vol. 56(9) Downloaded From: https://www.spiedigitallibrary.org/journals/Optical-Engineering on 11/14/2017 Terms of Use: https://www.spiedigitallibrary.org/terms-of-use Yan and Sasian: Photographic zoom fisheye lens design for DSLR cameras fisheye lens design. It was the first actual fisheye lens in the photographic fisheye lenses, image quality usually controls world. The optical structure of his design became common to the design, and the resulting mapping can be described by later fisheye lens designs. The negative meniscus shape of the first element has become common on all modern fisheye Y ¼ a f ðθ∕bÞ; EQ-TARGET;temp:intralink-;e001;326;730 · sin (1) lenses. Another remarkable design that rarely is mentioned is the a b AEG fisheye lens9 [Fig. 2(d)]. It was patented by the AEG where and are the coefficients that define the mapping.
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