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The light field is a function that describes the amount of light faring in every direction through every point in space. Michael Faraday was the first to propose (in an 1846 lecture entitled "Thoughts on Ray Vibrations") that light should be interpreted as a field, much like the magnetic fields on which he had been working for several years. The phrase light field was coined by Alexander Gershun in a classic paper on the radiometric properties of light in three-dimensional space (1936). The phrase has been redefined by researchers in computer graphics to mean something slightly different.^{[citation needed]}

The 5D plenoptic function[link]

Radiance L along a ray can be thought of as the amount of light traveling along all possible straight lines through a tube whose size is determined by its solid angle and cross-sectional area.

If the concept is restricted to geometric optics—i.e. to incoherent light and to objects larger than the wavelength of light—then the fundamental carrier of light is a ray. The measure for the amount of light faring along a ray is radiance, denoted by L and measured in watts (W) per steradian (sr) per meter squared (m²). The steradian is a measure of solid angle, and meters squared are used here as a measure of cross-sectional area, as shown at right.

Parameterizing a ray in 3D space by position (x,y,z) and direction (Failed to parse (Missing texvc executable; please see math/README to configure.): \theta

,Failed to parse (Missing texvc executable; please see math/README to configure.): \phi

).

The radiance along all such rays in a region of three-dimensional space illuminated by an unchanging arrangement of lights is called the plenoptic function (Adelson 1991). The plenoptic illumination function is an idealized function used in computer vision and computer graphics to express the image of a scene from any possible viewing position at any viewing angle at any point in time. It is never actually used in practice computationally, but is conceptually useful in understanding other concepts in vision and graphics.^{[citation needed]} Since rays in space can be parameterized by three coordinates, x, y, and z and two angles Failed to parse (Missing texvc executable; please see math/README to configure.): \theta

and Failed to parse (Missing texvc executable; please see math/README to configure.): \phi

, as shown at left, it is a five-dimensional function.

Summing the irradiance vectors Failed to parse (Missing texvc executable; please see math/README to configure.): D_1

and Failed to parse (Missing texvc executable; please see math/README to configure.): D_2
arising from two light sources Failed to parse (Missing texvc executable; please see math/README to configure.): I_1
and Failed to parse (Missing texvc executable; please see math/README to configure.): I_2
produces a resultant vector Failed to parse (Missing texvc executable; please see math/README to configure.): D

having the magnitude and direction shown (Gershun, fig 17).

Like Adelson, Gershun defined the light field at each point in space as a 5D function. However, he treated it as an infinite collection of vectors, one per direction impinging on the point, with lengths proportional to their radiances.

Integrating these vectors over any collection of lights, or over the entire sphere of directions, produces a single scalar value—the total irradiance at that point, and a resultant direction. The figure at right, reproduced from Gershun's paper, shows this calculation for the case of two light sources. In computer graphics, this vector-valued function of 3D space is called the vector irradiance field (Arvo, 1994). The vector direction at each point in the field can be interpreted as the orientation one would face a flat surface placed at that point to most brightly illuminate it.

Higher dimensionality[link]

One can consider time, wavelength, and polarization angle as additional variables, yielding higher-dimensional functions.

The 4D light field[link]

Within a scene, light may encounter objects and is described by a 5D plenoptic function. Outside of a scene, such as outside of the sphere of a snow globe, light from the scene does not encounter objects, which drops the dimension by one and it can thus be described as a 4D light field.

Radiance along a ray remains constant if there are no blockers.

In a plenoptic function, if the region of interest contains a concave object (think of a cupped hand), then light leaving one point on the object may travel only a short distance before being blocked by another point on the object. No practical device could measure the function in such a region.

However, if we restrict ourselves to locations outside the convex hull (think shrink-wrap) of the object, then we can measure the plenoptic function easily using a digital camera. Moreover, in this case the function contains redundant information, because the radiance along a ray remains constant from point to point along its length, as shown at left. In fact, the redundant information is exactly one dimension, leaving us with a four-dimensional function. Parry Moon dubbed this function the photic field (1981), while researchers in computer graphics call it the 4D light field (Levoy 1996) or Lumigraph (Gortler 1996). Formally, the 4D light field is defined as radiance along rays in empty space.

The set of rays in a light field can be parameterized in a variety of ways, a few of which are shown below. Of these, the most common is the two-plane parameterization shown at right (below). While this parameterization cannot represent all rays, for example rays parallel to the two planes if the planes are parallel to each other, it has the advantage of relating closely to the analytic geometry of perspective imaging. Indeed, a simple way to think about a two-plane light field is as a collection of perspective images of the st plane (and any objects that may lie astride or beyond it), each taken from an observer position on the uv plane. A light field parameterized this way is sometimes called a light slab.

Note that a light slab does not mean that the 4D light field is equivalent to capturing two 2D planes of information (this latter is only two dimensional). For example, a pair of points at position (0,0) in the st plane and (1,1) in the uv plane correspond to a ray in space, but other rays may pass through (0,0) in the st plane and through (1,1) in the uv plane—this pair of points correspond only to the one ray, not all these other rays.

Some alternative parameterizations of the 4D light field, which represents the flow of light through an empty region of three-dimensional space. Left: points on a plane or curved surface and directions leaving each point. Center: pairs of points on the surface of a sphere. Right: pairs of points on two planes in general (meaning any) position.

Sound analog[link]

The analog of the 4D light field for sound is the sound field or wave field, as in wave field synthesis, and the corresponding parametrization is the Kirchhoff-Helmholtz integral, which states that, in the absence of obstacles, a sound field over time is given by the pressure on a plane. Thus this is 2D of information at any point, and over time a 3D field.

This 2D, compared with the 4D of light, is because light travels in rays (0D at a point in time, 1D over time), while by Huygens' Principle, a sound wave front can be modeled as spherical waves (2D at a point in time, 3D over time): light moves in a single direction (2D of information), while sound simply expands in every direction.

Ways to create light fields[link]

Light fields are a fundamental representation for light. As such, there are as many ways of creating light fields as there are computer programs capable of creating images or instruments capable of capturing them.

In computer graphics, light fields are typically produced either by rendering a 3D model or by photographing a real scene. In either case, to produce a light field views must be obtained for a large collection of viewpoints. Depending on the parameterization employed, this collection will typically span some portion of a line, circle, plane, sphere, or other shape, although unstructured collections of viewpoints are also possible (Buehler 2001).

Devices for capturing light fields photographically may include a moving handheld camera, a robotically controlled camera (Levoy, 2002), an arc of cameras (as in the bullet time effect used in The Matrix), a dense array of cameras (Kanade 1998; Yang 2002; Wilburn 2005), or a handheld camera (Ng 2005; Georgiev 2006), microscope (Levoy 2006), or other optical system in which an array of microlenses has been inserted in the optical path.

How many images should be in a light field? The largest known light field (of Michelangelo's statue of Night) contains 24,000 1.3-megapixel images. At a deeper level, the answer depends on the application. For light field rendering (see the Application section below), if you want to walk completely around an opaque object, then of course you need to photograph its back side. Less obviously, if you want to walk close to the object, and the object lies astride the st plane, then you need images taken at finely spaced positions on the uv plane (in the two-plane parameterization shown above), which is now behind you, and these images need to have high spatial resolution.

The number and arrangement of images in a light field, and the resolution of each image, are together called the "sampling" of the 4D light field. Analyses of light field sampling have been undertaken by many researchers; a good starting point is Chai (2000). Also of interest is Durand (2005) for the effects of occlusion, Ramamoorthi (2006) for the effects of lighting and reflection, and Ng (2005) and Zwicker (2006) for applications to plenoptic cameras and 3D displays, respectively.

Applications of light fields[link]

Computational imaging refers to any image formation method that involves a digital computer. Many of these methods operate at visible wavelengths, and many of those produce light fields. As a result, listing all applications of light fields would require surveying all uses of computational imaging in art, science, engineering, and medicine. In computer graphics, some selected applications are:

A downward-facing light source (F-F') induces a light field whose irradiance vectors curve outwards. Using calculus, Gershun could compute the irradiance falling on points (Failed to parse (Missing texvc executable; please see math/README to configure.): P_1, P_2 ) on a surface. (Gershun, fig 24)

• Illumination engineering. Gershun's reason for studying the light field was to derive (in closed form if possible) the illumination patterns that would be observed on surfaces due to light sources of various shapes positioned above these surface. An example is shown at right. A more modern study is (Ashdown 1993).
• Light field rendering. By extracting appropriate 2D slices from the 4D light field of a scene, one can produce novel views of the scene (Levoy 1996; Gortler 1996). Depending on the parameterization of the light field and slices, these views might be perspective, orthographic, crossed-slit (Zomet 2003), multi-perspective (Rademacher 1998), or another type of projection. Light field rendering is one form of image-based rendering.
• Synthetic aperture photography. By integrating an appropriate 4D subset of the samples in a light field, one can approximate the view that would be captured by a camera having a finite (i.e. non-pinhole) aperture. Such a view has a finite depth of field. By shearing or warping the light field before performing this integration, one can focus on different fronto-parallel (Isaksen 2000) or oblique (Vaish 2005) planes in the scene. If the light field is captured using a handheld camera (Ng 2005), this essentially constitutes a digital camera whose photographs can be refocused after they are taken.
  
• 3D display. By presenting a light field using technology that maps each sample to the appropriate ray in physical space, one obtains an autostereoscopic visual effect akin to viewing the original scene. Non-digital technologies for doing this include integral photography, parallax panoramagrams, and holography; digital technologies include placing an array of lenslets over a high-resolution display screen, or projecting the imagery onto an array of lenslets using an array of video projectors. If the latter is combined with an array of video cameras, one can capture and display a time-varying light field. This essentially constitutes a 3D television system (Javidi 2002; Matusik 2004). Image generation and predistortion of synthetic imagery for holographic stereograms is one of the earliest examples of computed light fields, anticipating and later motivating the geometry used in Levoy and Hanrahan's work (Halle 1991, 1994).
• Glare reduction. Glare arises due to multiple scattering of light inside the camera’s body and lens optics and reduces image contrast. While glare has been analyzed in 2D image space (Talvala 2007), it is useful to identify it as a 4D ray-space phenomenon (Raskar 2008). By statistically analyzing the ray-space inside a camera, one can classify and remove glare artifacts. In ray-space, glare behaves as high frequency noise and can be reduced by outlier rejection. Such analysis can be performed by capturing the light field inside the camera, but it results in the loss of spatial resolution. Uniform and non-uniform ray sampling could be used to reduce glare without significantly compromising image resolution (Raskar 2008).
• Biology. The compound eyes of Arthropods may be collecting and making use of the 4D light field for ranging and discriminating predators and prey.

References[link]

Theory[link]

• Adelson, E.H., Bergen, J.R. (1991). "The plenoptic function and the elements of early vision", In Computation Models of Visual Processing, M. Landy and J.A. Movshon, eds., MIT Press, Cambridge, 1991, pp. 3–20.
• Arvo, J. (1994). "The Irradiance Jacobian for Partially Occluded Polyhedral Sources", Proc. ACM SIGGRAPH, ACM Press, pp. 335–342.
• Faraday, M., "Thoughts on Ray Vibrations", Philosophical Magazine, S.3, Vol XXVIII, N188, May 1846.
• Gershun, A. (1936). "The Light Field", Moscow, 1936. Translated by P. Moon and G. Timoshenko in Journal of Mathematics and Physics, Vol. XVIII, MIT, 1939, pp. 51–151.
• Gortler, S.J., Grzeszczuk, R., Szeliski, R., Cohen, M. (1996). "The Lumigraph", Proc. ACM SIGGRAPH, ACM Press, pp. 43–54.
• Levoy, M., Hanrahan, P. (1996). "Light Field Rendering", Proc. ACM SIGGRAPH, ACM Press, pp. 31–42.
• Moon, P., Spencer, D.E. (1981). The Photic Field, MIT Press.
• Wigner Distribution Function and Light Fields

Analysis[link]

• Ramamoorthi, R., Mahajan, D., Belhumeur, P. (2006). "A First Order Analysis of Lighting, Shading, and Shadows", ACM TOG.
• Zwicker, M., Matusik, W., Durand, F., Pfister, H. (2006). "Antialiasing for Automultiscopic 3D Displays", Eurographics Symposium on Rendering, 2006.
• Ng, R. (2005). "Fourier Slice Photography", Proc. ACM SIGGRAPH, ACM Press, pp. 735–744.
• Durand, F., Holzschuch, N., Soler, C., Chan, E., Sillion, F. X. (2005). "A Frequency analysis of Light Transport", Proc. ACM SIGGRAPH, ACM Press, pp. 1115–1126.
• Chai, J.-X., Tong, X., Chan, S.-C., Shum, H. (2000). "Plenoptic Sampling", Proc. ACM SIGGRAPH, ACM Press, pp. 307–318.
• Halle, M. (1994) "Holographic stereograms as discrete imaging systems", in SPIE Proc. Vol. #2176: Practical Holography VIII, S.A. Benton, ed., pp. 73–84.

Devices[link]

• Liang, C.K., Lin, T.H., Wong, B.Y., Liu, C., Chen, H. H. (2008). "Programmable Aperture Photography:Multiplexed Light Field Acquisition", Proc. ACM SIGGRAPH.
• Veeraraghavan, A., Raskar, R., Agrawal, A., Mohan, A., Tumblin, J. (2007). "Dappled Photography: Mask Enhanced Cameras for Heterodyned Light Fields and Coded Aperture Refocusing", Proc. ACM SIGGRAPH.
• Georgiev, T., Zheng, C., Nayar, S., Curless, B., Salesin, D., Intwala, C. (2006). "Spatio-angular Resolution Trade-offs in Integral Photography", Proc. EGSR 2006.
• Kanade, T., Saito, H., Vedula, S. (1998). "The 3D Room: Digitizing Time-Varying 3D Events by Synchronized Multiple Video Streams", Tech report CMU-RI-TR-98-34, December 1998.
• Levoy, M. (2002). Stanford Spherical Gantry.
• Levoy, M., Ng, R., Adams, A., Footer, M., Horowitz, M. (2006). "Light field microscopy", ACM Transactions on Graphics (Proc. SIGGRAPH), Vol. 25, No. 3.
• Ng, R., Levoy, M., Brédif, M., Duval, G., Horowitz, M., Hanrahan, P. (2005). "Light Field Photography with a Hand-Held Plenoptic Camera", Stanford Tech Report CTSR 2005-02, April, 2005.
• Wilburn, B., Joshi, N., Vaish, V., Talvala, E., Antunez, E., Barth, A., Adams, A., Levoy, M., Horowitz, M. (2005). "High Performance Imaging Using Large Camera Arrays", ACM Transactions on Graphics (Proc. SIGGRAPH), Vol. 24, No. 3, pp. 765–776.
• Yang, J.C., Everett, M., Buehler, C., McMillan, L. (2002). "A real-time distributed light field camera", Proc. Eurographics Rendering Workshop 2002.
• "The CAFADIS camera"

Archives of light fields[link]

• "The Stanford Light Field Archive"
• "UCSD/MERL Light Field Repository"

Applications[link]

• Ashdown, I. (1993). "Near-Field Photometry: A New Approach", Journal of the Illuminating Engineering Society, Vol. 22, No. 1, Winter, 1993, pp. 163–180.
• Buehler, C., Bosse, M., McMillan, L., Gortler, S., Cohen, M. (2001). "Unstructured Lumigraph rendering", Proc. ACM SIGGRAPH, ACM Press.
• Isaksen, A., McMillan, L., Gortler, S.J. (2000). "Dynamically Reparameterized Light Fields", Proc. ACM SIGGRAPH, ACM Press, pp. 297–306.
• Javidi, B., Okano, F., eds. (2002). Three-Dimensional Television, Video and Display Technologies, Springer-Verlag.
• Matusik, W., Pfister, H. (2004). "3D TV: a scalable system for real-time acquisition, transmission, and autostereoscopic display of dynamic scenes", Proc. ACM SIGGRAPH, ACM Press.
• Rademacher, P., Bishop, G. (1998). "Multiple-Center-of-Projection Images", Proc. ACM SIGGRAPH, ACM Press.
• Vaish, V., Garg, G., Talvala, E., Antunez, E., Wilburn, B., Horowitz, M., Levoy, M. (2005). "Synthetic Aperture Focusing using a Shear-Warp Factorization of the Viewing Transform", Proc. Workshop on Advanced 3D Imaging for Safety and Security, in conjunction with CVPR 2005.
• Zomet, A., Feldman, D., Peleg, S., Weinshall, D. (2003). "Mosaicing new views: the crossed-slits projection", IEEE Transactions on Pattern Analysis and Machine Intelligence (PAMI), Vol. 25, No. 6, June 2003, pp. 741–754.
• Halle, M., Benton, S., Klug, M., Underkoffler, J. (1991). "The UltraGram: a generalized holographic stereogram", SPIE Vol. 1461, Practical Holography V, S.A. Benton, ed., pp. 142–155.
• Talvala, E-V., Adams, A., Horowitz, M., Levoy, M. (2007). "Veiling glare in high dynamic range imaging", Proc. ACM SIGGRAPH.
• Raskar, R., Agrawal, A., Wilson, C., Veeraraghavan, A. (2008). "Glare Aware Photography: 4D Ray Sampling for Reducing Glare Effects of Camera Lenses", Proc. ACM SIGGRAPH.
• Pérez, F., Marichal, J. G., Rodriguez, J.M. (2008). "The Discrete Focal Stack Transform", Proc. EUSIPCO

Ren Ng
Ren Ng with Lytro light field camera in 2012.
Born	Yi-Ren Ng (1979-09-21) September 21, 1979 (age 32) Malaysia
Occupation	CEO, Lytro

Yi-Ren Ng (born September 21, 1979) is the founder and chief executive officer of Lytro, a Mountain View, California-based startup company.^[1][2] Lytro is developing consumer light-field cameras based on Ng's graduate research at Stanford University.^[3]

Background[link]

Ng was born in Malaysia, and emigrated to Australia at the age of 9.^[4] He earned a B.S. degree in mathematical and computational science in 2001, a M.S. in computer science in 2002, and a Ph.D. in computer science in 2006, all from Stanford University^[5]. His doctoral advisor was Pat Hanrahan and Ng's dissertation, Digital Light Field Photography [1], received the 2006 ACM Doctoral Dissertation Award.^[6]

References[link]

1. ^ Manu Kumar (June 22, 2011). "The Making of Lytro". http://k9ventures.com/blog/2011/06/22/the-making-of-lytro/. Retrieved June 23, 2011. 
2. ^ Ina Fried (June 21, 2011). "Meet the Stealthy Start-Up That Aims to Sharpen Focus of Entire Camera Industry". http://allthingsd.com/20110621/meet-the-stealthy-start-up-that-aims-to-sharpen-focus-of-entire-camera-industry/. Retrieved June 23, 2011. 
3. ^ Rachel Metz (November 21, 2005). "Say Sayonara to Blurry Pics". Wired News. http://www.wired.com/science/discoveries/news/2005/11/69594. Retrieved June 23, 2011. 
4. ^ http://thephenomlist.com/lists/5/people/21
5. ^ http://www.kdkfactory.com/perspactive/conversation-dr-ren-ng-camera-inventor/
6. ^ "ACM Recognizes Contributors Who Advanced The Computing Field". March 29, 2007. http://www.acm.org/press-room/news-releases-2007/internal/. 

External links[link]

• Lytro - Company Website
• Ren Ng biography - Lytro, Inc.

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Bruce Munro is a British lighting designer and installation artist.^[1] Munro is best known for lighting installations such as Field of Light,^[2] which was first exhibited at the V&A Museum in 2004. His work was featured as an example of outstanding lighting design in the book by Design Museum titled How to Design a Light, published by Conran Octopus in October 2010.^{[citation needed]}

Bruce Munro was born in Salcombe in Devon in 1959 and studied fine art at Bristol Polytechnic. He moved to Australia in 1984, where he created a commercial design company providing illuminated signage for large corporations such as Quantas and Honda. On his return to the UK in 2002 he worked for Kevin McCloud at his eponymous light manufacturing company before settling in West Wiltshire and branching out on his own as a lighting designer.^{[citation needed]}

Since then Munro has designed contemporary chandeliers and feature lights for The Royal Society, ZSL London Zoo, Liberty & Co, and the Royal Institute of Chartered Surveyors (RICS).^{[citation needed]} He took part in a group exhibition at the Solomon R. Guggenheim Museum in New York called 'Contemplating the Void' from February–April 2010, celebrating the inspirational rotunda of the building designed by Frank Lloyd Wright.^[3]

Shortly after Field of Light was exhibited at the Brilliant! exhibition at the Victoria and Albert Museum in 2004, Munro developed a larger scale version for Long Knoll Field in Wiltshire; a field adjacent to his workshop that is bisected by a public footpath.^[4] Munro was then invited to create Field of Light at the Eden Project in Cornwall (Winter 2008/9).^[5] Installed between the Mediterranean and Rainforest 'biomes' at the Eden Project, the installation consisted of 6,000 acrylic stems toped by clear glass spheres, each laced with optic fibre and planted into the grass roof of the visitor's centre.^[6]

Munro's next art installation was CDSea, made of 6000,000 unwanted CDs donated by the general public from across the world. It was installed at Long Knoll Field in Wiltshire in June 2010 by Munro and a group of 140 friends and volunteers, including Kevin McCloud the presenter of the Grand Designs TV series on Channel 4. Conceived as a glittering inland 'sea', lit by natural sunlight, moonlight, reflecting on the CDs. Under the light of fireworks, the installation was renamed 'CDSea Regatta'.^[7] Independent Article Munro is also known for 'Light Shower', an installation made for the spire cross within Salisbury Cathedral. Light Shower was designed to be switched on for the cathedral's 'Darkness into Light' candle-lit procession to mark the start of Advent on 29 November 2010.^[8][9]
In an article in the Financial Times dated January 28th 2011 entitled New Light Through Old Windows, the curator, Turner prize judge and broadcaster Richard Cork called Bruce Munro's Light Shower 'spectacular'. 'Admirably site-specific' he wrote, 'It encourages us to respond to the gothic architecture in a fresh way." FT Visual Arts Munro's second large installation at Salisbury Cathedral called Water-Towers, was a large-scale illuminated maze that changed colours in reaction to choral music. It took Munro 10 days to build it in the Cloister of Salisbury Cathedral, and was open to the public from January 15 to February 27, 2011.^{[10][11][12][unreliable source?]}
Salisbury Cathedral News

In November 2011, a 5,200 stem Field of Light was installed in the gardens at the back of the Holburne Museum in Bath, and remained in place until 8th January 2012. On the 21st December 2011, Munro unveiled a new installation named Star-Turn, which was a one-night-only piece to raise funds for the Help for Heroes charity. Star-Turn was lit with candles turned by sponsored riders on a 'bicycle'. It was Munro's second artwork for Help for Heroes, following a 'Light Shower' which he installed in the rehabilitation centre at Tedworth House PRC at Tidworth, earlier in 2011. Crossing into the world of high fashion, Munro created a catwalk chandelier (7m long x 4m wide) for the Alexander McQueen catwalk show for Autumn/Winter 2012/2013, designed by Sarah Burton who created the wedding dress for The Duchess of Cambridge. Evening Standard Fashion Daily Telegraph Fashion

First One-Man Show[link]

Longwood Gardens, one of the great display gardens in America, originally created by Pierre S. du Pont and the Pierce family, announced that it has commissioned Bruce Munro to create his first one-man show across the gardens from June-October 2012. Longwood Gardens Exhibitions

Notes[link]