Zoom lens
A zoom lens is a mechanical assembly of lens elements for which the focal length can be varied, as opposed to a fixed focal length lens. A true zoom lens called a parfocal lens, is one that maintains focus when its focal length changes. A lens that loses focus during zooming is more properly called a varifocal lens. Despite being marketed as zoom lenses all consumer lenses with variable focal lengths use varifocal design; the convenience of variable focal length comes at the cost of complexity - and some compromises on image quality, dimensions, autofocus performance, cost. For example, all zoom lenses suffer from at least slight, if not considerable, loss of image resolution at their maximum aperture at the extremes of their focal length range; this effect is evident in the corners of the image, when displayed in a large format or high resolution. The greater the range of focal length a zoom lens offers, the more exaggerated these compromises must become. Zoom lenses are described by the ratio of their longest to shortest focal lengths.
For example, a zoom lens with focal lengths ranging from 100 mm to 400 mm may be described as a 4:1 or "4×" zoom. The term superzoom or hyperzoom is used to describe photographic zoom lenses with large focal length factors more than 5× and ranging up to 19× in SLR camera lenses and 83× in amateur digital cameras; this ratio can be as high as 300× in professional television cameras. As of 2009, photographic zoom lenses beyond about 3× cannot produce imaging quality on par with prime lenses. Constant fast aperture zooms are restricted to this zoom range. Quality degradation is less perceptible when recording moving images at low resolution, why professional video and TV lenses are able to feature high zoom ratios. Digital photography can accommodate algorithms that compensate for optical flaws, both within in-camera processors and post-production software; some photographic zoom lenses are long-focus lenses, with focal lengths longer than a normal lens, some are wide-angle lenses, others cover a range from wide-angle to long-focus.
Lenses in the latter group of zoom lenses, sometimes referred to as "normal" zooms, have displaced the fixed focal length lens as the popular one-lens selection on many contemporary cameras. The markings on these lenses say W and T for "Wide" and "Telephoto". Telephoto is designated because the longer focal length supplied by the negative diverging lens is longer than the overall lens assembly; some digital cameras allow cropping and enlarging of a captured image, in order to emulate the effect of a longer focal length zoom lens. This is known as digital zoom and produces an image of lower optical resolution than optical zoom; the same effect can be obtained by using digital image processing software on a computer to crop the digital image and enlarge the cropped area. Many digital cameras have both, combining them by first using the optical the digital zoom. Zoom and superzoom lenses are used with still, motion picture cameras, some binoculars, telescopes, telescopic sights, other optical instruments.
In addition, the afocal part of a zoom lens can be used as a telescope of variable magnification to make an adjustable beam expander. This can be used, for example, to change the size of a laser beam so that the irradiance of the beam can be varied. Early forms of zoom lenses were used in optical telescopes to provide continuous variation of the magnification of the image, this was first reported in the proceedings of the Royal Society in 1834. Early patents for telephoto lenses included movable lens elements which could be adjusted to change the overall focal length of the lens. Lenses of this kind are now called varifocal lenses, since when the focal length is changed, the position of the focal plane moves, requiring refocusing of the lens after each change; the first true zoom lens, which retained near-sharp focus while the effective focal length of the lens assembly was changed, was patented in 1902 by Clile C. Allen. An early use of the zoom lens in cinema can be seen in the opening shot of the movie "It" starring Clara Bow, from 1927.
The first industrial production was the Bell and Howell Cooke "Varo" 40–120 mm lens for 35mm movie cameras introduced in 1932. The most impressive early TV Zoom lens was the VAROTAL III, from Rank Taylor Hobson from UK built in 1953; the Kilfitt 36–82 mm/2.8 Zoomar introduced in 1959 was the first varifocal lens in regular production for still 35mm photography. The first modern film zoom lens, the Pan-Cinor, was designed around 1950 by Roger Cuvillier, a French engineer working for SOM-Berthiot, it had an optical compensation zoom system. In 1956, Pierre Angénieux introduced the mechanical compensation system, enabling precise focus while zooming, in his 17-68mm lens for 16mm released in 1958; the same year a prototype of the 35mm version of the Angénieux 4x zoom, the 35-140mm was first used by cinematographer Roger Fellous for the production of Julie La Rousse. Angénieux received a 1964 technical award from the academy of motion pictures for the design of the 10 to 1 zoom lenses, including the 12-120mm for 16mm film cameras and the 25-250mm for 35mm film cameras.
Since advances in optical design the use of computers for optical ray tracing, has made the design and construction of zoom lenses much easier, they are now used in professional and amateur photography. There are many possible designs for zoom lenses, the most complex ones having upwards of thirty individu
Curvilinear perspective
Curvilinear perspective is a graphical projection used to draw 3D objects on 2D surfaces. It was formally codified in 1968 by the artists and art historians André Barre and Albert Flocon in the book La Perspective curviligne, translated into English in 1987 as Curvilinear Perspective: From Visual Space to the Constructed Image and published by the University of California Press. Earlier, less mathematically precise versions can be seen in the work of the miniaturist Jean Fouquet. Leonardo da Vinci in a lost notebook spoke of curved perspective lines. Examples of approximated five-point perspective can be found in the self-portrait of the mannerist painter Parmigianino seen through a shaving mirror. Another example would be the curved mirror in Arnolfini's Wedding by the Flemish painter Jan van Eyck; the book Vanishing Point: Perspective for Comics from the Ground Up by Jason Cheeseman-Meyer teaches five and four point perspective. In 1959, Flocon had acquired a copy of Grafiek en tekeningen by M. C.
Escher who impressed him with his use of bent and curved perspective, which influenced the theory Flocon and Barre were developing. They started a long correspondence, in which Escher called Flocon a "kindred spirit"; the system uses curving perspective lines instead of straight converging ones to approximate the image on the retina of the eye, itself spherical, more than the traditional linear perspective, which uses straight lines and gets strangely distorted at the edges. It uses either four, five or more vanishing points: In five-point perspective: Four vanishing points are placed around in a circle, they are named N, W, S, E, plus one vanishing point in the center of the circle. Four, or infinite-point perspective is the one that most approximates the perspective of the human eye, while at the same time being effective for making impossible spaces, while five point is the curvilinear equivalent of one point perspective, so is four point the equivalent of two point perspective; this technique can, like two-point perspective, use a vertical line as a horizon line, creating both a worms and birds eye view at the same time.
It uses four or more points spaced along a horizon line, all vertical lines are made perpendicular to the horizon line, while orthogonals are created using a compass set on a line made at a 90-degree angle through each of the four vanishing points. Distances a and c between the viewer and the wall are greater than the b distance, so adopting the principle that when an object is a greater distance from the observer, it becomes smaller, the wall is reduced and thus appears distorted at the edges. If a point has the 3D Cartesian coordinates: P 3 D = Denoting distance from the point to the origin by d = √x2 + y2 + z2 the transformation of the point to a curvilinear reference system of radius R is P 2 D = This is derived by first projecting the 3D point onto a sphere with radius R that centers on the origin, so that we obtain an image of the point that has coordinates P s p h e r e = ∗ Then, we do a parallel projection, parallel with the z-axis to project the point on the sphere onto the paper at z = R, thus obtaining P i m a g e = Since we are not concerned with the fact that the paper is resting on the z = R plane, we ignore the z-coordinate of the image point, thus obtaining P 2 D = = R ∗ Since changing R only amounts to a scaling, it is defined to be unity, simplifying the formula further to: P 2 D = = ( x x 2 + y 2 +
Computer graphics
Computer graphics are pictures and films created using computers. The term refers to computer-generated image data created with the help of specialized graphical hardware and software, it is a vast and developed area of computer science. The phrase was coined in 1960, by computer graphics researchers Verne Hudson and William Fetter of Boeing, it is abbreviated as CG, though sometimes erroneously referred to as computer-generated imagery. Some topics in computer graphics include user interface design, sprite graphics, vector graphics, 3D modeling, shaders, GPU design, implicit surface visualization with ray tracing, computer vision, among others; the overall methodology depends on the underlying sciences of geometry and physics. Computer graphics is responsible for displaying art and image data and meaningfully to the consumer, it is used for processing image data received from the physical world. Computer graphics development has had a significant impact on many types of media and has revolutionized animation, advertising, video games, graphic design in general.
The term computer graphics has been used in a broad sense to describe "almost everything on computers, not text or sound". The term computer graphics refers to several different things: the representation and manipulation of image data by a computer the various technologies used to create and manipulate images the sub-field of computer science which studies methods for digitally synthesizing and manipulating visual content, see study of computer graphicsToday, computer graphics is widespread; such imagery is found in and on television, weather reports, in a variety of medical investigations and surgical procedures. A well-constructed graph can present complex statistics in a form, easier to understand and interpret. In the media "such graphs are used to illustrate papers, theses", other presentation material. Many tools have been developed to visualize data. Computer generated imagery can be categorized into several different types: two dimensional, three dimensional, animated graphics; as technology has improved, 3D computer graphics have become more common, but 2D computer graphics are still used.
Computer graphics has emerged as a sub-field of computer science which studies methods for digitally synthesizing and manipulating visual content. Over the past decade, other specialized fields have been developed like information visualization, scientific visualization more concerned with "the visualization of three dimensional phenomena, where the emphasis is on realistic renderings of volumes, illumination sources, so forth with a dynamic component"; the precursor sciences to the development of modern computer graphics were the advances in electrical engineering and television that took place during the first half of the twentieth century. Screens could display art since the Lumiere brothers' use of mattes to create special effects for the earliest films dating from 1895, but such displays were limited and not interactive; the first cathode ray tube, the Braun tube, was invented in 1897 – it in turn would permit the oscilloscope and the military control panel – the more direct precursors of the field, as they provided the first two-dimensional electronic displays that responded to programmatic or user input.
Computer graphics remained unknown as a discipline until the 1950s and the post-World War II period – during which time the discipline emerged from a combination of both pure university and laboratory academic research into more advanced computers and the United States military's further development of technologies like radar, advanced aviation, rocketry developed during the war. New kinds of displays were needed to process the wealth of information resulting from such projects, leading to the development of computer graphics as a discipline. Early projects like the Whirlwind and SAGE Projects introduced the CRT as a viable display and interaction interface and introduced the light pen as an input device. Douglas T. Ross of the Whirlwind SAGE system performed a personal experiment in which a small program he wrote captured the movement of his finger and displayed its vector on a display scope. One of the first interactive video games to feature recognizable, interactive graphics – Tennis for Two – was created for an oscilloscope by William Higinbotham to entertain visitors in 1958 at Brookhaven National Laboratory and simulated a tennis match.
In 1959, Douglas T. Ross innovated again while working at MIT on transforming mathematic statements into computer generated 3D machine tool vectors by taking the opportunity to create a display scope image of a Disney cartoon character. Electronics pioneer Hewlett-Packard went public in 1957 after incorporating the decade prior, established strong ties with Stanford University through its founders, who were alumni; this began the decades-long transformation of the southern San Francisco Bay Area into the world's leading computer technology hub - now known as Silicon Valley. The field of computer graphics developed with the emergence of computer graphics hardware. Further advances in computing led to greater advancements in interactive computer graphics. In 1959, the TX-2 computer was developed at MIT's Lincoln Laboratory; the TX-2 integrated a number of new man-machine interfaces. A light pen could be used to draw sketches on the computer using Ivan Sutherland's revolutionary Sketchpad software.
Using a light pen, Sketchpad allowed one to draw simple shapes on the computer screen, save them and recall them later. The light pen itself had a small photoelectric cell in its tip. T
Axonometric projection
Axonometric projection is a type of orthographic projection used for creating a pictorial drawing of an object, where the lines of sight are perpendicular to the plane of projection, the object is rotated around one or more of its axes to reveal multiple sides. "Axonometry" means "to measure along axes". In German literature, axonometry is based on Pohlke's theorem, so that the scope of axonometric projection encompasses every type of parallel projection, including not only oblique projection, but orthographic projection and therefore multiview projection. However, outside of German literature, the term "axonometric" is used to make an explicit distinction from multiview projection, because axonometric projection allows for the depiction of more than one "side" of an object, whereas a multiview projection allows for the depiction of only one "side" of an object: A multiview projection depicts an object from one of six primary views; because multiview projections are a fundamental facet of technical illustration, a depiction that results from another type of projection is called an "auxiliary" view.
In contrast, an axonometric projection may depict an object such that none of the principal axes of the object is perpendicular to the projection plane, thus more than one "side" of an object may be represented simultaneously. When it is possible to depict more than one side of an object, it may be said that the object is being viewed from a "skew" angle. Furthermore, in English literature, the term "axonometric projection" implies an orthographic projection, such as an isometric projection. With an axonometric projection, the scale of an object does not depend on its location along any particular axis; this distortion, the direct result of a presence or absence of foreshortening, is evident if the object is composed of rectangular features. Despite this limitation, axonometric projection can be useful for purposes of illustration because it allows for relaying precise measurements; the three types of axonometric projection are isometric projection, dimetric projection, trimetric projection, depending on the exact angle at which the view deviates from the orthogonal.
In axonometric drawing, as in other types of pictorials, one axis of space is shown as the vertical. In isometric projection, the most used form of axonometric projection in engineering drawing, the direction of viewing is such that the three axes of space appear foreshortened, there is a common angle of 120° between them; as the distortion caused by foreshortening is uniform, the proportionality between lengths is preserved, the axes share a common scale. Another advantage is that 120° angles are constructed using only a compass and straightedge. In dimetric projection, the direction of viewing is such that two of the three axes of space appear foreshortened, of which the attendant scale and angles of presentation are determined according to the angle of viewing. Dimensional approximations are common in dimetric drawings. In trimetric projection, the direction of viewing is such that all of the three axes of space appear unequally foreshortened; the scale along each of the three axes and the angles among them are determined separately as dictated by the angle of viewing.
Dimensional approximations in trimetric drawings are common, trimetric perspective is used in technical drawings. The concept of isometry had existed in a rough empirical form for centuries, well before Professor William Farish of Cambridge University was the first to provide detailed rules for isometric drawing. Farish published his ideas in the 1822 paper "On Isometrical Perspective", in which he recognized the "need for accurate technical working drawings free of optical distortion; this would lead him to formulate isometry. Isometry means "equal measures" because the same scale is used for height and depth". From the middle of the 19th century, according to Jan Krikke isometry became an "invaluable tool for engineers, soon thereafter axonometry and isometry were incorporated in the curriculum of architectural training courses in Europe and the U. S; the popular acceptance of axonometry came in the 1920s, when modernist architects from the Bauhaus and De Stijl embraced it". De Stijl architects like Theo van Doesburg used axonometry for their architectural designs, which caused a sensation when exhibited in Paris in 1923".
Since the 1920s axonometry, or parallel perspective, has provided an important graphic technique for artists and engineers. Like linear perspective, axonometry helps depict three-dimensional space on a two-dimensional picture plane, it comes as a standard feature of CAD systems and other visual computing tools. According to Jan Krikke, "axonometry originated in China, its function in Chinese art was similar to linear perspective in European art. Axonometry, the pic
Pythagorean theorem
In mathematics, the Pythagorean theorem known as Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse is equal to the sum of the squares of the other two sides; the theorem can be written as an equation relating the lengths of the sides a, b and c called the "Pythagorean equation": a 2 + b 2 = c 2, where c represents the length of the hypotenuse and a and b the lengths of the triangle's other two sides. Although it is argued that knowledge of the theorem predates him, the theorem is named after the ancient Greek mathematician Pythagoras as it is he who, by tradition, is credited with its first proof, although no evidence of it exists. There is some evidence that Babylonian mathematicians understood the formula, although little of it indicates an application within a mathematical framework. Mesopotamian and Chinese mathematicians all discovered the theorem independently and, in some cases, provided proofs for special cases.
The theorem has been given numerous proofs – the most for any mathematical theorem. They are diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years; the theorem can be generalized in various ways, including higher-dimensional spaces, to spaces that are not Euclidean, to objects that are not right triangles, indeed, to objects that are not triangles at all, but n-dimensional solids. The Pythagorean theorem has attracted interest outside mathematics as a symbol of mathematical abstruseness, mystique, or intellectual power; the Pythagorean theorem was known long before Pythagoras, but he may well have been the first to prove it. In any event, the proof attributed to him is simple, is called a proof by rearrangement; the two large squares shown in the figure each contain four identical triangles, the only difference between the two large squares is that the triangles are arranged differently. Therefore, the white space within each of the two large squares must have equal area.
Equating the area of the white space yields the Pythagorean theorem, Q. E. D; that Pythagoras originated this simple proof is sometimes inferred from the writings of the Greek philosopher and mathematician Proclus. Several other proofs of this theorem are described below. If c denotes the length of the hypotenuse and a and b denote the lengths of the other two sides, the Pythagorean theorem can be expressed as the Pythagorean equation: a 2 + b 2 = c 2. If the length of both a and b are known c can be calculated as c = a 2 + b 2. If the length of the hypotenuse c and of one side are known the length of the other side can be calculated as a = c 2 − b 2 or b = c 2 − a 2; the Pythagorean equation relates the sides of a right triangle in a simple way, so that if the lengths of any two sides are known the length of the third side can be found. Another corollary of the theorem is that in any right triangle, the hypotenuse is greater than any one of the other sides, but less than their sum. A generalization of this theorem is the law of cosines, which allows the computation of the length of any side of any triangle, given the lengths of the other two sides and the angle between them.
If the angle between the other sides is a right angle, the law of cosines reduces to the Pythagorean equation. This theorem may have more known proofs than any other; this proof is based on the proportionality of the sides of two similar triangles, that is, upon the fact that the ratio of any two corresponding sides of similar triangles is the same regardless of the size of the triangles. Let ABC represent a right triangle, with the right angle located at C. Draw the altitude from point C, call H its intersection with the side AB. Point H divides the length of the hypotenuse c into parts d and e; the new triangle ACH is similar to triangle ABC, because they both have a right angle, they share the angle at A, meaning that the third angle will be the same in both triangles as well, marked as θ in the figure. By a similar reasoning, the triangle CBH is similar to ABC; the proof of similarity of the triangles requires the triangle postulate: the sum of the angles in a triangle is two right angles, is equivalent to the parallel postulate.
Similarity of the triangles leads to the equality of ratios of corresponding sides: B C A B = B H B C and A C A B = A H A C. The first result equates
Inverse trigonometric functions
In mathematics, the inverse trigonometric functions are the inverse functions of the trigonometric functions. They are the inverses of the sine, tangent, cotangent and cosecant functions, are used to obtain an angle from any of the angle's trigonometric ratios. Inverse trigonometric functions are used in engineering, navigation and geometry. There are several notations used for the inverse trigonometric functions; the most common convention is to name inverse trigonometric functions using an arc- prefix: arcsin, arctan, etc. This notation arises from the following geometric relationships: When measuring in radians, an angle of θ radians will correspond to an arc whose length is rθ, where r is the radius of the circle. Thus, in the unit circle, "the arc whose cosine is x" is the same as "the angle whose cosine is x", because the length of the arc of the circle in radii is the same as the measurement of the angle in radians. In computer programming languages the inverse trigonometric functions are called by the abbreviated forms asin, atan.
The notations sin−1, cos−1, tan−1, etc. as introduced by John Herschel in 1813, are used as well in English-language sources, this convention complies with the notation of an inverse function. This might appear to conflict logically with the common semantics for expressions like sin2, which refer to numeric power rather than function composition, therefore may result in confusion between multiplicative inverse and compositional inverse; the confusion is somewhat ameliorated by the fact that each of the reciprocal trigonometric functions has its own name—for example, −1 = sec. Certain authors advise against using it for its ambiguity. Another convention used by a few authors is to use a majuscule first letter along with a −1 superscript: Sin−1, Cos−1, Tan−1, etc; this avoids confusion with the multiplicative inverse, which should be represented by sin−1, cos−1, etc. Since 2009, the ISO 80000-2 standard has specified the "arc" prefix for the inverse functions. Since none of the six trigonometric functions are one-to-one, they are restricted in order to have inverse functions.
Therefore the ranges of the inverse functions are proper subsets of the domains of the original functions. For example, using function in the sense of multivalued functions, just as the square root function y = √x could be defined from y2 = x, the function y = arcsin is defined so that sin = x. For a given real number x, with − 1 ≤ x ≤ 1, there are multiple numbers; when only one value is desired, the function may be restricted to its principal branch. With this restriction, for each x in the domain the expression arcsin will evaluate only to a single value, called its principal value; these properties apply to all the inverse trigonometric functions. The principal inverses are listed in the following table. If x is allowed to be a complex number the range of y applies only to its real part. Trigonometric functions of inverse trigonometric functions are tabulated below. A quick way to derive them is by considering the geometry of a right-angled triangle, with one side of length 1, another side of length x applying the Pythagorean theorem and definitions of the trigonometric ratios.
Purely algebraic derivations are longer. Complementary angles: arccos = π 2 − arcsin arccot = π 2 − arctan arccsc = π 2 − arcsec Negative arguments: arcsin = − arcsin arccos = π − arccos arct
Fisheye lens
A fisheye lens is an ultra wide-angle lens that produces strong visual distortion intended to create a wide panoramic or hemispherical image. Fisheye lenses achieve wide angles of view. Instead of producing images with straight lines of perspective, fisheye lenses use a special mapping, which gives images a characteristic convex non-rectilinear appearance; the term fisheye was coined in 1906 by American physicist and inventor Robert W. Wood based on how a fish would see an ultrawide hemispherical view from beneath the water, their first practical use was in the 1920s for use in meteorology to study cloud formation giving them the name "whole-sky lenses". The angle of view of a fisheye lens is between 100 and 180 degrees while the focal lengths depend on the film format they are designed for. Mass-produced fisheye lenses for photography first appeared in the early 1960s and are used for their unique, distorted appearance. For the popular 35 mm film format, typical focal lengths of fisheye lenses are between 8 mm and 10 mm for circular images, 15–16 mm for full-frame images.
For digital cameras using smaller electronic imagers such as 1⁄4" and 1⁄3" format CCD or CMOS sensors, the focal length of "miniature" fisheye lenses can be as short as 1 to 2 mm. These types of lenses have other applications such as re-projecting images that were filmed through a fisheye lens, or created via computer generated graphics, onto hemispherical screens. Fisheye lenses are used for scientific photography such as recording of aurora and meteors, to study plant canopy geometry and to calculate near-ground solar radiation, they are most encountered as peephole door viewers to give the user a wide field of view. In 1906, Wood published a paper detailing an experiment in which he built a camera in a water-filled pail starting with a photographic plate at the bottom, a short focus lens with a pinhole diaphragm located halfway up the pail, a sheet of glass at the rim to suppress ripples in the water; the experiment was Wood's attempt "to ascertain how the external world appears to the fish" and hence the title of the paper was "Fish-Eye Views, Vision under Water".
Wood subsequently built an improved "horizontal" version of the camera omitting the lens, instead using a pinhole pierced in the side of a tank, filled with water and a photographic plate. In the text, he described a third "Fish-Eye" camera built using sheet brass, the primary advantages being that this one was more portable than the other two cameras, was "absolutely leaktight". In his conclusion, Wood thought that "the device will photograph the entire sky a sunshine recorder could be made on this principle, which would require no adjustment for latitude or month" but wryly noted "the views used for the illustration of this paper savour somewhat of the'freak' pictures of the magazines." W. N. Bond described an improvement to Wood's apparatus in 1922 which replaced the tank of water with a simple hemispheric glass lens, making the camera more portable; the focal length depended on the refractive index and radius of the hemispherical lens, the maximum aperture was f/50. Bond noted the new lens could be used to record cloud cover or lightning strikes at a given location.
Bond's hemispheric lens reduced the need for a pinhole aperture to ensure sharp focus, so exposure times were reduced. In 1924, Robin Hill first described a lens with 180° coverage, used for a cloud survey in September 1923 The lens, designed by Hill and R. & J. Beck, Ltd. was patented in December 1923. The Hill Sky Lens is now credited as the first fisheye lens. Hill described three different mapping functions of a lens designed to capture an entire hemisphere. Distortion is unavoidable in a lens that encompasses an angle of view exceeding 125°, but Hill and Beck claimed in the patent that stereographic or equidistant projection were the preferred mapping functions; the three-element, three-group lens design uses a divergent meniscus lens as the first element to bring in light over a wide view followed by a converging lens system to project the view onto a flat photographic plate. The Hill Sky Lens was fitted to a whole sky camera used in a pair separated by 500 metres for stereo imaging, equipped with a red filter for contrast.
Conrad Beck described the camera system in an article published in 1925. At least one has been reconstructed. In 1932, the German firm Allgemeine Elektricitäts-Gesellschaft AG filed for a patent on the Weitwinkelobjektiv, a 5-element, 4-group development of the Hill Sky Lens. Compared to the 1923 Hill Sky Lens, the 1932 Weitwinkelobjektiv featured two diverging meniscus elements ahead of the stop and used a cemented achromatic group in the converging section. Miyamoto credits Dr Hans Schulz with the design of the Weitwinkelobjektiv; the basic patented design was produced for cloud recording as a 17 mm f/6.3 lens, the artist known as Umbo used the AEG lens for artistic purposes, with photographs published in a 1937 issue of Volk und Welt. The AEG Weitwinkelobjektiv formed the basis of the Fish-eye-Nikkor 16 mm f/8 lens of 1938, used for military and scientific purposes. Nikon, which had a contract to supply optics to the Imperial Japanese Navy gained access to the AEG design under the Pact of Steel.
After the war, the lens was mated to a
