Computer generated holography
Encyclopedia
Computer Generated Holography (CGH) is the method of digitally generating holographic
interference patterns. A holographic image can be generated e.g. by digitally computing a holographic interference pattern and printing it onto a mask or film for subsequent illumination by suitable coherent light source.
Alternatively, the holographic image can be brought to life by a holographic 3D display
(a display which operates on the basis of interference of coherent light), bypassing the need of having to fabricate a "hardcopy" of the holographic interference pattern each time. Consequently, in recent times the term "computer generated holography" is increasingly being used to denote the whole process chain of synthetically preparing holographic light wavefronts suitable for observation.
Computer generated holograms have the advantage that the objects which one wants to show do not have to possess any physical reality at all (completely synthetic hologram generation). On the other hand, if holographic data of existing objects is generated optically, but digitally recorded and processed, and brought to display subsequently, this is termed CGH as well. Ultimately, computer generated holography might serve all the roles of current computer generated imagery: holographic computer
displays for a wide range of applications from CAD
to gaming, holographic video and TV programs, automotive and communication applications (cell phone displays) and many more.
is a technique originally invented by Hungarian physicist Dennis Gabor
(1900-1979) to improve the resolving power on electron microscopes. An object is illuminated with a coherent (usually monochromatic) light beam; the scattered light is brought to interference with a reference beam of the same source, recording the interference pattern. CGH as defined in the introduction has broadly three tasks:
Note that it is not always justified to make a strict distinction between these steps; however it helps the discussion to structure it in this way.
.
Unfortunately, the researchers soon realized that there are noticeable lower and upper bounds in terms of computational speed and image quality and fidelity respectively. Wavefront calculations are computationally very intensive; even with modern mathematical techniques and high-end computing equipment, real-time computation is tricky. There are many different methods for calculating the interference pattern for a CGH.
In the next 25 years a lot of methods for CGHs
have been proposed in the fields of holographic information and computational reduction as well as in computational and quantization techniques. In the field of computational techniques the reported algorithms can be categorized in two main concepts.
with the detour phase method leading to cell oriented holograms. A coding technique suggested by Burch
replaced the cell oriented holograms by point holograms and made this kind of computer generated holograms more attractive.
In a Fourier Transform
hologram the reconstruction of the image occurs in the far field. This is usually achieved by using the Fourier transforming properties of a positive lens for reconstruction. So there are two steps in this process: computing the light field in the far observer plane, and then Fourier transforming this field back to the lens plane. These holograms are called Fourier Based Holograms. First CGHs based on the Fourier transform could reconstruct only 2D images. Brown and Lohmann
introduced a technique to calculate computer generated holograms of 3D objects. Calculation of the light propagation from three-dimensional objects is performed according to the usual parabolic approximation to the Fresnel-Kirchhoff diffraction integral. The wavefront to be reconstructed by the hologram is, therefore, the superposition of the Fourier transforms of each object plane in depth, modified by a quadratic phase factor.
whose major assumption originated with Rogers
who recognized that a Fresnel zone plate could be considered a special case of the hologram proposed by Gabor. But, as far as most of the object points were non-zero the computational complexity of the point-source concept was much higher than in the Fourier
transformation concept. Some researchers tried to overcome this drawback by predefining and storing all the possible elementary holograms using on top special data storage techniques
because of the huge capacity that is needed in this case, others by using special hardware
In the point-source concept the major problem that has to be circumvented is the competition among data storage capacity and computational speed. In particular, algorithms that rise the computational speed need usually very high data storage capabilities
while on the other side algorithms that lower the need of data storage capacity lead to high computational complexity
though some optimizations could be achieved
.
Another concept which leads to Point Source CGHs is the Ray tracing method. Ray tracing is perhaps the simplest method of computer generated holography to visualize. Essentially, the path length difference between the distance a virtual "reference beam" and a virtual "object beam" have to travel is calculated; this will give the relative phase of the scattered object beam.
Over the last three decades both concepts have made a remarkable progress improving computational speed and image quality. However, some technical restraints like computation and storage capacity still burden digital holography making potential real-time applications with current standard computer hardware almost impossible.
(SLM), abusing this term to include not only LCD displays or similar devices, but also films and masks. Basically, there are different types of SLMs available: Pure phase modulators (retarding the illuminating wave), pure amplitude modulators (blocking the illumination light), and SLMs which have the capability of combined phase/amplitude modulation
.
In the case of pure phase or amplitude modulation, clearly quality losses are unavoidable. Early forms of pure amplitude holograms were simply printed in black and white, meaning that the amplitude had to be encoded with one bit of depth only
.
Similarly, the kinoform is a pure-phase encoding invented at IBM
in the early days of CGH
.
Even if a fully complex phase/amplitude modulation would be ideal, a pure phase or pure amplitude solution is normally preferred because it is much easier to implement technologically.
exposure. Holographic displays are currently yet a challenge (as of 2008), although successful prototypes have been built. An ideal display for computer generated holograms would consist of pixels smaller than a wavelength of light with adjustable phase and brightness. Such displays have been called phased array optics
. Further progress in nanotechnology
is required to build them.
Holography
Holography is a technique that allows the light scattered from an object to be recorded and later reconstructed so that when an imaging system is placed in the reconstructed beam, an image of the object will be seen even when the object is no longer present...
interference patterns. A holographic image can be generated e.g. by digitally computing a holographic interference pattern and printing it onto a mask or film for subsequent illumination by suitable coherent light source.
Alternatively, the holographic image can be brought to life by a holographic 3D display
3D display
A 3D display is any display device capable of conveying a stereoscopic perception of 3-D depth to the viewer. The basic requirement is to present offset images that are displayed separately to the left and right eye. Both of these 2-D offset images are then combined in the brain to give the...
(a display which operates on the basis of interference of coherent light), bypassing the need of having to fabricate a "hardcopy" of the holographic interference pattern each time. Consequently, in recent times the term "computer generated holography" is increasingly being used to denote the whole process chain of synthetically preparing holographic light wavefronts suitable for observation.
Computer generated holograms have the advantage that the objects which one wants to show do not have to possess any physical reality at all (completely synthetic hologram generation). On the other hand, if holographic data of existing objects is generated optically, but digitally recorded and processed, and brought to display subsequently, this is termed CGH as well. Ultimately, computer generated holography might serve all the roles of current computer generated imagery: holographic computer
Computer
A computer is a programmable machine designed to sequentially and automatically carry out a sequence of arithmetic or logical operations. The particular sequence of operations can be changed readily, allowing the computer to solve more than one kind of problem...
displays for a wide range of applications from CAD
Computer-aided design
Computer-aided design , also known as computer-aided design and drafting , is the use of computer technology for the process of design and design-documentation. Computer Aided Drafting describes the process of drafting with a computer...
to gaming, holographic video and TV programs, automotive and communication applications (cell phone displays) and many more.
Overview
HolographyHolography
Holography is a technique that allows the light scattered from an object to be recorded and later reconstructed so that when an imaging system is placed in the reconstructed beam, an image of the object will be seen even when the object is no longer present...
is a technique originally invented by Hungarian physicist Dennis Gabor
Dennis Gabor
Dennis Gabor CBE, FRS was a Hungarian-British electrical engineer and inventor, most notable for inventing holography, for which he later received the 1971 Nobel Prize in Physics....
(1900-1979) to improve the resolving power on electron microscopes. An object is illuminated with a coherent (usually monochromatic) light beam; the scattered light is brought to interference with a reference beam of the same source, recording the interference pattern. CGH as defined in the introduction has broadly three tasks:
- Computation of the virtual scattered wavefront
- Encoding the wavefront data, preparing it for display
- Reconstruction: Modulating the interference pattern onto a coherent light beam by technological means, to transport it to the user observing the hologram.
Note that it is not always justified to make a strict distinction between these steps; however it helps the discussion to structure it in this way.
Wavefront computation
Computer generated holograms offer important advantages over the optical holograms since there is no need for a real object. Because of this a breakthrough in three-dimensional display was expected when the first algorithms were reported at 1966..
Unfortunately, the researchers soon realized that there are noticeable lower and upper bounds in terms of computational speed and image quality and fidelity respectively. Wavefront calculations are computationally very intensive; even with modern mathematical techniques and high-end computing equipment, real-time computation is tricky. There are many different methods for calculating the interference pattern for a CGH.
In the next 25 years a lot of methods for CGHs
have been proposed in the fields of holographic information and computational reduction as well as in computational and quantization techniques. In the field of computational techniques the reported algorithms can be categorized in two main concepts.
Fourier transform method
In the first one the Fourier transformation is used to simulate the propagation of each plane of depth of the object to the hologram plane. The Fourier transformation concept was first introduced by Brown and Lohmannwith the detour phase method leading to cell oriented holograms. A coding technique suggested by Burch
replaced the cell oriented holograms by point holograms and made this kind of computer generated holograms more attractive.
In a Fourier Transform
Fourier transform
In mathematics, Fourier analysis is a subject area which grew from the study of Fourier series. The subject began with the study of the way general functions may be represented by sums of simpler trigonometric functions...
hologram the reconstruction of the image occurs in the far field. This is usually achieved by using the Fourier transforming properties of a positive lens for reconstruction. So there are two steps in this process: computing the light field in the far observer plane, and then Fourier transforming this field back to the lens plane. These holograms are called Fourier Based Holograms. First CGHs based on the Fourier transform could reconstruct only 2D images. Brown and Lohmann
introduced a technique to calculate computer generated holograms of 3D objects. Calculation of the light propagation from three-dimensional objects is performed according to the usual parabolic approximation to the Fresnel-Kirchhoff diffraction integral. The wavefront to be reconstructed by the hologram is, therefore, the superposition of the Fourier transforms of each object plane in depth, modified by a quadratic phase factor.
Point Source Holograms
The second computational strategy is based on the point source concept, where the object is broken down in self-luminous points. An elementary hologram is calculated for every point source and the final hologram is synthesized by superimposing all the elementary holograms. This concept has been first reported by Waterswhose major assumption originated with Rogers
who recognized that a Fresnel zone plate could be considered a special case of the hologram proposed by Gabor. But, as far as most of the object points were non-zero the computational complexity of the point-source concept was much higher than in the Fourier
because of the huge capacity that is needed in this case, others by using special hardware
In the point-source concept the major problem that has to be circumvented is the competition among data storage capacity and computational speed. In particular, algorithms that rise the computational speed need usually very high data storage capabilities
while on the other side algorithms that lower the need of data storage capacity lead to high computational complexity
though some optimizations could be achieved
.
Another concept which leads to Point Source CGHs is the Ray tracing method. Ray tracing is perhaps the simplest method of computer generated holography to visualize. Essentially, the path length difference between the distance a virtual "reference beam" and a virtual "object beam" have to travel is calculated; this will give the relative phase of the scattered object beam.
Over the last three decades both concepts have made a remarkable progress improving computational speed and image quality. However, some technical restraints like computation and storage capacity still burden digital holography making potential real-time applications with current standard computer hardware almost impossible.
Interference pattern encoding
Once it is known what the scattered wavefront of the object looks like or how it may be computed, it must be fixed on a spatial light modulatorSpatial light modulator
A spatial light modulator is an object that imposes some form of spatially-varying modulation on a beam of light. A simple example is an overhead projector transparency. Usually when the phrase SLM is used, it means that the transparency can be controlled by a computer. In the 1980s, large SLMs...
(SLM), abusing this term to include not only LCD displays or similar devices, but also films and masks. Basically, there are different types of SLMs available: Pure phase modulators (retarding the illuminating wave), pure amplitude modulators (blocking the illumination light), and SLMs which have the capability of combined phase/amplitude modulation
.
In the case of pure phase or amplitude modulation, clearly quality losses are unavoidable. Early forms of pure amplitude holograms were simply printed in black and white, meaning that the amplitude had to be encoded with one bit of depth only
.
Similarly, the kinoform is a pure-phase encoding invented at IBM
IBM
International Business Machines Corporation or IBM is an American multinational technology and consulting corporation headquartered in Armonk, New York, United States. IBM manufactures and sells computer hardware and software, and it offers infrastructure, hosting and consulting services in areas...
in the early days of CGH
.
Even if a fully complex phase/amplitude modulation would be ideal, a pure phase or pure amplitude solution is normally preferred because it is much easier to implement technologically.
Reconstruction
The third (technical) issue is beam modulation and actual wavefront reconstruction. Masks may be printed, resulting often in a grained pattern structure since most printers can make only dots (although very small ones). Films may be developed by laserLaser
A laser is a device that emits light through a process of optical amplification based on the stimulated emission of photons. The term "laser" originated as an acronym for Light Amplification by Stimulated Emission of Radiation...
exposure. Holographic displays are currently yet a challenge (as of 2008), although successful prototypes have been built. An ideal display for computer generated holograms would consist of pixels smaller than a wavelength of light with adjustable phase and brightness. Such displays have been called phased array optics
Phased array optics
Phased array optics is the technology of controlling the phase of light waves transmitting or reflecting from a two-dimensional surface by means of adjustable surface elements. It is the optical analog of phased array radar...
. Further progress in nanotechnology
Nanotechnology
Nanotechnology is the study of manipulating matter on an atomic and molecular scale. Generally, nanotechnology deals with developing materials, devices, or other structures possessing at least one dimension sized from 1 to 100 nanometres...
is required to build them.
Available CGH devices
Currently, several companies and university departments are researching on the field of CGH devices:- MIT Media Lab has developed the "Holovideo" CGH display
- SeeReal TechnologiesSeeReal TechnologiesSeeReal Technologies GmbH is a Dresden-based company focusing on the development of 3D display solutions. It is owned by its Luxembourg parent company SeeReal Technologies S.A., which is responsible for marketing, partnering and IP licensing....
have prototyped a CGH display - Cortical Cafe CGH Kit is a CGH related hobbyist site with instructions, source code, and a web-application for CGH creation.