Catoptric cistula

Last updated March 18, 2019

A catoptric cistula, also called a catoptric theatre or chest, is a box with several sides lined with mirrors, so as to magnify or multiply images of any object placed inside the box. Of these, there are various kinds for various purposes, such as magnification, deformation, or multiplication of images.

Mirror object that reflects light or sound

A mirror is an object that reflects light in such a way that, for incident light in some range of wavelengths, the reflected light preserves many or most of the detailed physical characteristics of the original light, called specular reflection. This is different from other light-reflecting objects that do not preserve much of the original wave signal other than color and diffuse reflected light, such as flat-white paint.

The most elaborate catoptric chests known from Ancient Rome exhibited detailed scenes, including expansive libraries, forests, cities, or even vast treasures. Another form of entertainment involved placing an animal, such as a cat, inside a chest, and watching it interact with numerous other cats that appeared to surround it.^[1]

In historiography, ancient Rome is Roman civilization from the founding of the Italian city of Rome in the 8th century BC to the collapse of the Western Roman Empire in the 5th century AD, encompassing the Roman Kingdom, Roman Republic and Roman Empire until the fall of the western empire. The civilization began as an Italic settlement in the Italian Peninsula, conventionally founded in 753 BC, that grew into the city of Rome and which subsequently gave its name to the empire over which it ruled and to the widespread civilisation the empire developed. The Roman empire expanded to become one of the largest empires in the ancient world, though still ruled from the city, with an estimated 50 to 90 million inhabitants and covering 5.0 million square kilometres at its height in AD 117.

Construction

Multiple scenes in one chest

Following is an explanation of the construction of a catoptric cistula to represent several distinct scenes of objects, when looked in through several holes. Provide a polygonous cistula, or chest, in the shape of a multilateral prism ABCDEF, as shown in the figure, and divide its cavity by diagonal planes EB, FC, DA, intersecting each other in the center G, into as many triangular cells as the chest has sides; for example, a hexagonal chest will have six cells. Line the diagonal planes with plane mirrors. In the lateral planes, make round holes, through which the eye may observe cells of the chest. The holes are to be covered with plain glass, ground on the inner side, but not polished, to prevent the objects in the cells from appearing too distinctly. In each cell are placed the different objects, whose images are to be exhibited; then covering up the top of the chest with a thin transparent membrane, to permit light, the apparatus is complete.^[2]

Catoptrics deals with the phenomena of reflected light and image-forming optical systems using mirrors. A catoptric system is also called a catopter (catoptre).

By the laws of reflection, the images of the objects, placed within the angles of the mirrors, are multiplied, and some appear more distant than others, so that the objects of one cell will appear to take up more space than is contained in the entire chest. Looking through each hole will produce a new scene, each seemingly too large to be contained in the chest. According to the different angles the mirrors make with each other, the representations will be different; if the mirrors are at an angle greater than a right one, the images will be immense. (see anamorphosis)^[2]

Reflection is the change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves. The law of reflection says that for specular reflection the angle at which the wave is incident on the surface equals the angle at which it is reflected. Mirrors exhibit specular reflection.

Anamorphosis is a distorted projection or perspective requiring the viewer to occupy a specific vantage point, use special devices or both to view a recognizable image. Some of the media it is used in are painting, photography, sculpture and installation, toys, and film special effects. The word "anamorphosis" is derived from the Greek prefix ana‑, meaning "back" or "again", and the word morphe, meaning "shape" or "form". An optical anamorphism is the visualization of a mathematical operation called an affine transformation. The process of extreme anamorphosis has been used by artists to disguise caricatures, erotic and scatological scenes, and other furtive images from a casual viewer, while revealing an undistorted image to the knowledgeable spectator.

One large scene

Catoptric cistula, single scene, from 1728 Cyclopaedia, Vol 2.jpg

Following is an explanation of the construction of a catoptric cistula to represent the objects within it prodigiously multiplied, and diffused through a vast space. Make a polygonous chest, as before, but without dividing the inner cavity into any apartments or cells; see the second figure for an example. Line the lateral planes CBHI, BHLA, ALMF, etc., with plane mirrors, and at the apertures, scrape off the tin and quicksilver of the mirrors, so that the eye can see through. Place any objects in the bottom MI, e.g. a bird in a cage, etc.^[2]

Here, the eye looking through the aperture h i, will see each object placed at the bottom, vastly multiplied, and the images separated by equal distances from one another.^[2]

In culture

The torture chamber in the Phantom of the Opera is a six-sided catoptric chamber:

We were in the middle of a little six-cornered room, the sides of which were covered with mirrors from top to bottom. In the corners, we could clearly see the "joins" in the glasses, the segments intended to turn on their gear; yes, I recognized them and I recognized the iron tree in the corner, at the bottom of one of those segments...the iron tree, with its iron branch, for the hanged men.

The TARDIS of the television series Doctor Who is perhaps a modern expression, though fictional, of the effect sought to be created in the mind of the viewer of a catoptric chamber.

Jorge Luis Borges's Library of Babel is a universe which really is organized as an infinite matrix of repeating units, as it appears to be from the inside of a catoptric chamber.

Related Research Articles

A kaleidoscope is an optical instrument with two or more reflecting surfaces tilted to each other in an angle, so that one or more objects on one end of the mirrors are seen as a regular symmetrical pattern when viewed from the other end, due to repeated reflection. The reflectors are usually enclosed in a tube, often containing on one end a cell with loose, colored pieces of glass or other transparent materials to be reflected into the viewed pattern. Rotation of the cell causes motion of the materials, resulting in an ever-changing view being presented.

Camera obscura, also referred to as pinhole image, is the natural optical phenomenon that occurs when an image of a scene at the other side of a screen is projected through a small hole in that screen as a reversed and inverted image on a surface opposite to the opening. The surroundings of the projected image have to be relatively dark for the image to be clear, so many historical camera obscura experiments were performed in dark rooms.

A pinhole camera is a simple camera without a lens but with a tiny aperture, a pinhole – effectively a light-proof box with a small hole in one side. Light from a scene passes through the aperture and projects an inverted image on the opposite side of the box, which is known as the camera obscura effect.

The focal length of an optical system is a measure of how strongly the system converges or diverges light. For an optical system in air, it is the distance over which initially collimated (parallel) rays are brought to a focus. A system with a shorter focal length has greater optical power than one with a long focal length; that is, it bends the rays more sharply, bringing them to a focus in a shorter distance.

A mirror image is a reflected duplication of an object that appears almost identical, but is reversed in the direction perpendicular to the mirror surface. As an optical effect it results from reflection off of substances such as a mirror or water. It is also a concept in geometry and can be used as a conceptualization process for 3-D structures.

A camera lens is an optical lens or assembly of lenses used in conjunction with a camera body and mechanism to make images of objects either on photographic film or on other media capable of storing an image chemically or electronically.

Optical telescope telescope which is used to focus light from the visible part of the electromagnetic spectrum

An optical telescope is a telescope that gathers and focuses light, mainly from the visible part of the electromagnetic spectrum, to create a magnified image for direct view, or to make a photograph, or to collect data through electronic image sensors.

A reflecting telescope is a telescope that uses a single or a combination of curved mirrors that reflect light and form an image. The reflecting telescope was invented in the 17th century, by Isaac Newton, as an alternative to the refracting telescope which, at that time, was a design that suffered from severe chromatic aberration. Although reflecting telescopes produce other types of optical aberrations, it is a design that allows for very large diameter objectives. Almost all of the major telescopes used in astronomy research are reflectors. Reflecting telescopes come in many design variations and may employ extra optical elements to improve image quality or place the image in a mechanically advantageous position. Since reflecting telescopes use mirrors, the design is sometimes referred to as a "catoptric" telescope.

Perspective in the graphic arts is an approximate representation, generally on a flat surface, of an image as it is seen by the eye. The two most characteristic features of perspective are that objects appear smaller as their distance from the observer increases; and that they are subject to foreshortening, meaning that an object's dimensions along the line of sight appear shorter than its dimensions across the line of sight.

In geometrical optics, a focus, also called an image point, is the point where light rays originating from a point on the object converge. Although the focus is conceptually a point, physically the focus has a spatial extent, called the blur circle. This non-ideal focusing may be caused by aberrations of the imaging optics. In the absence of significant aberrations, the smallest possible blur circle is the Airy disc, which is caused by diffraction from the optical system's aperture. Aberrations tend to get worse as the aperture diameter increases, while the Airy circle is smallest for large apertures.

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$Catadioptric system optical system where refraction and reflection are combined$

A catadioptric optical system is one where refraction and reflection are combined in an optical system, usually via lenses (dioptrics) and curved mirrors (catoptrics). Catadioptric combinations are used in focusing systems such as searchlights, headlamps, early lighthouse focusing systems, optical telescopes, microscopes, and telephoto lenses. Other optical systems that use lenses and mirrors are also referred to as "catadioptric" such as surveillance catadioptric sensors.

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The Octacube is a large, steel sculpture of a mathematical object: the 24-cell or "octacube". Because a real 24-cell is four-dimensional, the artwork is actually a projection into the three-dimensional world. Octacube has very high intrinsic symmetry, which matches features in chemistry and physics.

In technical drawing and computer graphics, a multiview projection is a technique of illustration by which a standardized series of orthographic two-dimensional pictures is constructed to represent the form of a three-dimensional object. Up to six pictures of an object are produced, with each projection plane parallel to one of the coordinate axes of the object. The views are positioned relative to each other according to either of two schemes: first-angle or third-angle projection. In each, the appearances of views may be thought of as being projected onto planes that form a six-sided box around the object. Although six different sides can be drawn, usually three views of a drawing give enough information to make a three-dimensional object. These views are known as front view, top view and end view. Other names for these views include plan, elevation and section.

The sine quadrant was a type of quadrant used by medieval Arabic astronomers. It is also known as a "sinecal quadrant" in the English-speaking world. The instrument could be used to measure celestial angles, to tell time, to find directions, or to determine the apparent positions of any celestial object for any time. The name is derived from the Arabic "rub‘‘‘" meaning a quarter and "mujayyab" meaning marked with sine. It was described, according to King, by Muhammad ibn Mūsā al-Khwārizmī in 9th century Baghdad.

The first reflecting telescope built by Sir Isaac Newton in 1668 is a landmark in the history of telescopes, being the first known successful reflecting telescope. It was the prototype for a design that later came to be called a newtonian telescope.

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References

↑ Gorman, Michael John. "Between the Demonic and the Miraculous: Athanasius Kircher and the Baroque Culture of Machines Archived 2008-07-25 at the Wayback Machine .." The Great Art of Knowing: The Baroque Encyclopedia of Athanasius Kircher. Ed. Daniel Stolzenberg. Stanford: Stanford University Libraries. 2001. pp. 59-70.
1 2 3 4 This article incorporates text from a publication now in the public domain : Chambers, Ephraim, ed. (1728). "^{article name needed}". Cyclopædia, or an Universal Dictionary of Arts and Sciences (first ed.). James and John Knapton, et al.

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[Gorman-1] Gorman, Michael John. "Between the Demonic and the Miraculous: Athanasius Kircher and the Baroque Culture of Machines Archived 2008-07-25 at the Wayback Machine .." The Great Art of Knowing: The Baroque Encyclopedia of Athanasius Kircher. Ed. Daniel Stolzenberg. Stanford: Stanford University Libraries. 2001. pp. 59-70.

[cyclo-2] 1 2 3 4 This article incorporates text from a publication now in the public domain : Chambers, Ephraim, ed. (1728). "^{article name needed}". Cyclopædia, or an Universal Dictionary of Arts and Sciences (first ed.). James and John Knapton, et al.