Optical: systems and elements – Holographic system or element – For synthetically generating a hologram
Reexamination Certificate
1999-11-05
2002-07-09
Spyrou, Cassandra (Department: 2872)
Optical: systems and elements
Holographic system or element
For synthetically generating a hologram
C359S566000, C359S575000
Reexamination Certificate
active
06417940
ABSTRACT:
FIELD OF THE INVENTION AND RELATED ART
This invention relates to a phase type computer hologram and an optical instrument suitably usable in an optical system such as an optical interconnection system, a lens surface shape measuring system or an illumination optical system, for example.
A process for producing a hologram by use of a computer is called “computer hologram”. In an earlier stage, it is directed to reproduction of a virtual three-dimensional object. Currently, however, because of its ability of deforming a wavefront of light as desired, it is applied to various optical systems such as an optical interconnection system, a lens surface shape measuring system and an illumination system, for example.
In the computer hologram, amplitudes or phases of incident light rays at different positions on a hologram are changed so that a desired deformation is produced in the wavefront of the incident light, and a desired image is produced through propagation of the deformed wavefront. As an example of a method of causing wavefront deformation, there is a coding method called a “binary hologram” wherein a complex amplitude of a deformed wavefront such as described above is approximated on the basis of a transmission factor distribution of binary levels of black and white. Because a complex amplitude distribution can be reproduced and the process is relatively simple, this method is used widely at present. However, because it is an amplitude type hologram, it involves inconveniences such as a low diffraction efficiency and production of a ghost image due to higher-order diffraction light.
On the other hand, there is a kind of phase type hologram, called a “Kinoform” wherein the phase of incident light is changed. It is known that, if an idealistic Kinoform is produced, the diffraction efficiency thereof becomes equal to 100%. Such Kinoform may be used as a phase type computer hologram.
A phase type computer hologram can be produced by a method wherein an original with a pattern having a multiple-value density distribution, determined by calculation, is produced by use of an intermediate-tone plotter, and wherein the pattern of the original is transferred onto a dry plate in reduced magnification, the dray plate being thereafter bleached to produce a phase type hologram. Recently, however, a method in which a shape is directly produced upon a substrate surface by cutting, and a method in which a binary optics is produced while approximating a Kinoform-like shape with a step-like shape by use of a photolithographic process, are used widely. Particularly, because a very fine structure can be produced at a good precision, the latter method is used in many cases for production of surface relief type diffraction optical elements, in general, not only for production of hologram.
In phase type diffraction optical elements such as a Kinoform described above, the phase of light impinging on the element is changed by an amount determined by a phase function applied. While such phase function can be expressed by a function &phgr;(x, y) of the position (x, y) upon the element, since the phase term of light has a period of 2&pgr;, a change of &phgr;(x, y) (mod2&pgr;) will be sufficient in practice. Such a phase change may be applied by forming an appropriate curved surface upon a substrate to produce a suitable optical path difference. However, if &phgr;(x, y) is a continuous function, then &phgr;(x, y) (mod2&pgr;) will change continuously within a certain zone, while, at a position as folded by “mod”, it takes discontinuous points having a difference 2&pgr;.
Considering this in terms of the surface of a substrate, while the shape changes smoothly within a certain zone, there is produced, at the discontinuous points, a surface step (level difference) of optical path length &lgr; corresponding to the phase 2&pgr;. As regards the shape which is continuous only in a certain zone, it becomes very difficult to form such shape if the width of the zone is small. In consideration of it, there is a method in which the shape in that zone is approximated by a step-like shape.
The concept described above basically applies to a phase type computer hologram. However, usually, no curved surface is formed on a substrate in accordance with a phase function-applied. Rather, in many cases, from the size and resolution of an image desired, the size of cells as a whole as well as the size of each cell necessary for a phase type computer hologram are calculated and, on the basis of which, phase values for the cells are optimized. Here, “cells” refer to small areas as divided by what is called a “mesh”.
Here, the phases of the cells may be set continuously, in a range from 0-2&pgr;. In order to provide these phase values on the basis of the surface shape, the depth direction has to be controlled continuously. If this is done through an etching process, the control has to be made separately with respect to individual cells and, therefore, the process for continuous depth control is difficult to accomplish. In consideration of it, the phase values of the cells may be set to 2&pgr;j/N (where N is a natural number and 0≦j<N−1) and a solution for phase distribution may be obtained. On the basis of it, an etching process may be repeated N times, at the maximum, by which a phase type computer hologram may be produced.
However, as regards a binary optics element such as shown in
FIG. 7
, for example, having a sectional shape corresponding to a phase type computer hologram where N=4, particularly when an element equivalent to a lens is considered, although the phase function usually changes monotonously, there is no such monotonous change present in the case of a phase type computer hologram which requires complicated wavefront deformation as compared with the lens. Therefore, when considered one-dimensionally, there may be a case wherein the phase value of successive three cells once skips by more than &pgr;, at the position of a cell
3
and then turns back. In terms of surface shape, this corresponds to a protrusion or a recess having a height (depth) of &lgr;/2 or more. Particularly where the size of the cells is small, it is very difficult to produce such shape with a good precision,
SUMMARY OF THE INVENTION
It is accordingly an object of the present invention to provide a phase type computer hologram having a good shape precision.
In accordance with an aspect of the present invention, there is provided a phase type computer hologram, characterized by a plurality of cells for applying a predetermined phase to different portions of a wavefront of light, wherein no phase skip larger than it is present in the cells.
In accordance with another aspect of the present invention, there is provided a method of producing a phase type computer hologram, comprising the steps of: determining phases for a plurality of cells, respectively; smoothening a distribution of the phases of the cells, by shifting the phase of at least one of the cells by 2&pgr;; and forming, on a substrate, the cells whose phase distribution is smoothened in said smoothening step.
The smoothening step may include shifting the phase of at least one cell by 2&pgr; so that a least square error related to the cell phase is reduced.
The smoothening step may further include (i) a process for separating the cells into plural groups and detecting, with respect to each groups, a least square error related to the cell phase, and (ii) a process for shifting, by 2&pgr;, the phase of said at least one cell in a cell group or groups where the detected least square error is larger than a threshold value, to thereby reduce the least square error related to the cell phase.
The phase type computer hologram may be a hologram having a phase distribution.
The phase type computer hologram may be a hologram having a phase distribution and an amplitude distribution.
In accordance with a further aspect of the present invention, there is provided a system including a hologram produced in accordance with a method as described above.
In accordance with a yet further
Boutsikaris Leo
Fitzpatrick ,Cella, Harper & Scinto
Spyrou Cassandra
LandOfFree
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