### Warped Perspective:

#### a Mathematical and Aesthetic Journey with the Fisheye Lens

In 1906, optical physicist Robert W. Wood wanted to invent a lens that would show the world from the perspective of a fish, “whose view from underwater compresses the entire horizon” (Vox). His paper discussed an experiment involving “a camera in a water-filled pail starting with a photographic plate at the bottom, a short focus lens with a pinhole diaphragm located approximately halfway up the pail, and a sheet of glass at the rim to suppress ripples in the water” (Vox). The resulting fisheye lens might have remained a novel item of early photography consigned to oblivion, but instead it took on a life of its own as fisheye lenses became commercially available in the 1960s. The fisheye’s multipurpose style has proven successful and popular from the lens’s first prototypes to modern smartphone apps.

While viewing the world from the eyes of a fish may seem a peculiar goal for a physicist, Wood’s work was both a natural outgrowth of early experimentation with a relatively recent invention and highly important in furthering our understanding of light. His other inventions, from a “disk whose microscopic experiments helped determine the age of stars” to infrared photography often used in nature documentation and thermodynamics, have occupied realms of physics without influencing the art world as strongly (Vox). The fisheye lens, then, is that unique instance of math meeting pop culture. I attempted to showcase this phenomenon in my project by explaining how each image represents a unique ability of the fisheye lens to interpret the world around us, interspersed with math, physics, and scientific history lessons on how and why the fisheye lens works.

The mathematical qualities that create the fisheye mainly involve manipulation of angles, distortion, and perspective. Rectilineal lenses represent straight features as straight lines. Distortions, therefore are deviations from rectilineal projection (Wikipedia). Fisheye lenses are extremely wide, massively distorting their subject matter and creating an illusion of convexity or concavity. The result is either hemispherical, meaning all the points in the image appear to be of

equal distance from the center; or panoramic, conveying a massive scale using wide angles (Wikipedia). In other words, widest highest quality fisheye lenses will capture absolutely everything from objects directly to their left to directly to the right of the lens; some are so wide one can take a photograph of a ceiling and capture the floor (Brownlee). “While wide-angle rectilinear lenses can capture angles of view approaching 100 degrees, fisheye lenses can stretch that to 180 degrees — impossible to do without the light bending science they employ” (Cunningham). In principle, this occurrence is simple refraction, the bending of light as it changes medium, just as one sees upon placing a pencil in a glass of water, hence the connection to a fish’s worldview and the usage of water in Wood’s experiment (Hashem). “The tradeoff is distinct: Straight lines anywhere but dead center in the fisheye image appear to curve. The farther they are from center, the greater the curved distortion” (Cunningham). So, whether one reenacts Wood’s experiment with light and water; utilizes an actual fisheye lens, which functions because of its physical shape; or, like me, takes photos using an app created by computer code; the origins of the fisheye’s instantly recognizable aesthetic is deeply rooted in mathematics.

Many of its applications are scientific. In nature, landscape, astronomical, and meteorological photography, the fisheye lens is uniquely qualified to capture both tiny spaces and huge spaces. Astronomers have therefore used it to photograph both the surface of mars and the movement of stars, as well as the confined quarters of a space vessel (Vox). I unfortunately did not have access to this subject matter, so instead I juxtaposed my use of the fisheye to capture me in my bathtub to my feet dangling over a cliff at a lookout point. My photographs of trees are meant to mimic the fisheye’s portrayal of the sky as a dome rather than a vast expanse.

Of course, many common usages of the fisheye are probably completely unaware of the lens’s mathematical origins, but they nonetheless make unique use of mathematical phenomena. Countless album covers from jazz to hip hop have utilized the lens to make artists appear larger-than-life. It helped that the release of the first consumer-grade fisheye lens in 1962 roughly coincided with the advent of rock ‘n’ roll and wider youth culture (Vox). The fisheye’s ability to distort made it instantly popular among the psychedelic rock stars of the 1960s including the Birds and Jimi Hendrix, who worshipped everything surrealistic and trippy. 1990s skaters filmed countless videos with the lens to properly capture the curves and swerves of a skatepark, one invention of optical physics capturing another invention of motion physics. I attempted to pay tribute to both art movements with my fake album cover photographs. And, of course, harkening back to Wood’s original intent, fisheye lens photos of my dog’s face represent the last thing a fish sees before being eaten.

### Sources

Brownlee, Marques. “What is a Fisheye Lens?” YouTube. November 30, 2011.

Cunningham, Matt. “What is fisheye lens photography?” HowStuffWorks.

https://electronics.howstuffworks.com/cameras-photography/tips/fisheye-lens-photography.htm

“Fisheye lens.” Wikipedia, the Free Encyclopedia. https://en.wikipedia.org/wiki/Fisheye_lens

Hashem, Amin. “What Is Fisheye Lens – The Full Guide.” Ehab Photography. May 11, 2018.

“How the fisheye lens took over music.” Vox. YouTube. Film. December 17, 2019.

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