Optical: systems and elements – Holographic system or element – Fourier transform holography
Reexamination Certificate
2000-06-22
2004-01-06
Chang, Audrey (Department: 2872)
Optical: systems and elements
Holographic system or element
Fourier transform holography
C359S030000, C359S035000, C359S022000
Reexamination Certificate
active
06674555
ABSTRACT:
FIELD OF THE INVENTION
This invention relates to the holographic storage of information. More particularly, the invention relates to methods in which information associated with a patterned object is recorded in the form of a Fourier transform hologram.
BACKGROUND OF THE INVENTION
It has long been known that the methods of holography can be used to create records of digital data. For example, data are initially provided in the form of a two-dimensional array of elements such as spots or rectangular pixels. Each of the individual data elements can assume a binary value of 1 or 0 or represent several bits by encoding the light intensity (gray scale) transmitted through the optical system. For example, a totally opaque element may represent 0, whereas a totally transparent element may represent 1. An array of this kind has been referred to as a data mask.
The technique of Fourier transform holography relies on the physical principle that when an object is placed in the front focal plane of a converging lens, the optical field at the back focal plane corresponds to the Fourier transform of that object. (More generally, shifting the object out of the front focal plane of the lens will simply add phase terms to the Fourier transform observed at or near the back focal plane.)
The Fourier transform is a representation of the spatial characteristics of the object. Like an optical image, the Fourier transform has an amplitude that varies meaningfully from place to place. However, the amplitude at a given location in the Fourier transform does not correspond directly to, e.g., the luminance of the object at a given point (as would be the case in an image). Instead, each small region of the Fourier transform receives contributions from essentially every point on the object. As a result of the manner in which these contributions are combined, the amplitude in a given small region expresses the relative contribution that a given spatial frequency makes to the overall pattern represented by the object. Each place within the Fourier transform relates to a corresponding spatial frequency. In this sense, a record of the Fourier transform provides a spatial frequency spectrum of the object.
The Fourier transform may be recorded by placing a suitable recording medium in the back focal plane of the transforming lens. The earliest such media were photographic plates. In addition to photographic media, which are still in use, currently available media include photopolymers, as well as photochromic, photorefractive, and thermoplastic media.
The recording takes place by forming an interference pattern that impinges on the recording medium. Two light beams, referred to as the object beam and the reference beam, are used to form this interference pattern. In order to interfere, these beams must be at least partially coherent, that is, they must be at least partially correlated in phase. In many cases, these beams are generated by passing a single laser beam through a beam splitter.
An illustrative recording setup using a transmissive data mask is shown in FIG.
1
. Object beam
05
is created by modulating a plane wave by data mask
10
, which is, e.g., a spatial light modulator (SLM). Modulation may be transmissive, as shown, or alternatively, it may be reflective. The object beam then passes through transforming lenses
15
,
20
, and
25
, and impinges on storage medium
30
. In a typical arrangement, the lenses are spaced in a standard
4
F configuration. (In such a configuration, the spacing between adjacent lenses is equal to the sum of their respective focal lengths. The spacing between a lens and an adjacent element such as data mask
10
is one focal length of that lens.) Reference beam
35
does not pass through the data mask or the system of transforming lenses, but instead is combined directly with object beam
05
on storage medium
30
to form the interference pattern that is recorded as a hologram. The object and reference beams overlap in region
40
of medium
30
.
An image of the original object is reconstructed by impinging on medium
30
an excitation beam having the same angle of incidence, wavelength, or wavefront (or combination of these properties) as the reference beam used to create the hologram. Diffraction of the excitation beam by the hologram gives rise to a further, reconstructed output beam
45
that is Fourier transformed by the system of lenses
50
,
55
,
60
to produce the image. For automatic reading of data, the image is usefully projected onto an array of sensors
65
. Such an array is readily provided as, for example, a CCD array or a CMOS optical sensor array.
One practical difficulty posed by photographic emulsions and other holographic media is that none of these exhibit a perfectly linear dynamic range. That is, the optical density of the exposed medium will be proportional to the exposure for only a limited range of exposures. In addition, diffraction efficiency even in a perfect material varies with a figure of merit referred to as the modulation depth. The modulation depth at a given location within the recording medium is the intensity ratio of the object beam to the reference beam at that location.
Practitioners have observed that when the Fourier transform of an object is recorded holographically, as described here, the exposure in significant parts of the hologram that are displaced from the optical axis often tends to be much weaker in intensity than parts lying at or near the optical axis.
This occurs because in the Fourier transform plane, a significant fraction of the total illumination tends to be concentrated in a relatively small spot about the optical axis. This spot corresponds to those few spatial frequencies (generally zero and low-valued frequencies) that are highly represented in any data mask, including data masks that are inherently random in amplitude. We refer to this spot as the “dc spot”, in analogy to direct electrical current (dc), which has only a zero frequency component.
If the reference beam is adjusted to match the high intensity of the dc spot, the higher frequencies will have much less diffraction efficiency relative to the low frequencies. Conversely, if the reference beam is adjusted to match the lower intensity present in the higher frequency area of the object beam, the lower frequencies will have much less diffraction efficiency relative to the high frequencies. When the diffraction efficiency is distorted in this way, the reconstructed image will be a corrupted representation of the original object, and as a result, incorrect bit values may be retrieved from the stored data. In addition, this modulation mismatch causes the resulting hologram to have a lower overall diffraction efficiency. Given a fixed amount of laser power, such a reduction in overall diffraction efficiency decreases the attainable read-out rate of the hologram, and thus it limits the rate at which data can be transferred out of a storage device incorporating the hologram.
Various attempts have been made to alleviate this problem. These attempts have been based on the principle that what defines a pattern (for purposes of visual observation or detection by photosensors) is its corresponding pattern of luminous intensity, not its complex amplitude. What distinguishes these quantities (for simplicity of presentation, polarization is here neglected) is that the field quantity described by complex amplitude has both magnitude and phase, and is thus conveniently represented as a complex number, whereas intensity is represented by the (phaseless) real number obtained by multiplying the corresponding amplitude by its complex conjugate: I=A*·A. The properties of the Fourier transform are determined, in part, by the phases of the optical wavelets arriving at the Fourier transform plane (i.e., at the back focal plane of the transforming lens or lens system). Thus, by altering the phases of these wavelets as they emanate from the data mask, it is possible to manipulate the Fourier transform without (in principle) affecting the intensity distribution in t
Curtis Kevin Richard
Mitra Partha Pratim
Tackitt Michael C.
Chang Audrey
Lucent Technologies - Inc.
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