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Description  |
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TECHNICAL FIELD
The present invention relates generally to optical filters and is
specifically directed to an optical filter capable of differentiating
between coherent (e.g., laser) radiation and incoherent (e.g., ambient)
radiation.
BACKGROUND ART
The optical filtering effect achieved in the present invention is based on
the well known fact that light intensity spatial distribution in the
interference region between two optical waves can change significantly
depending upon the degree of mutual coherence of the interfering waves.
This spatial distribution appears in the case of either wavefront division
(related, for example, to Young's two-beam interference) or amplitude
division (related to parallel plate interference, Fabry-Perot filter
interference, dielectric multilayer interference and, finally, to Bragg
hologram interference).
Simply speaking, the goal is to obtain an interference pattern for coherent
illumination, e.g., laser light, and no interference for incoherent
illumination, e.g., ambient light. The degree of coherence can then be
used as the key parameter for determining the interference pattern in
general and the division of reflected and transmitted beams in particular.
The net result is a spectral response (i.e., reflectivity and
transmitivity) from a plane parallel plate, Fabry-Perot filter, dielectric
multilayer, or Bragg holographic structure which differs for coherent
(laser) light relative to poorly-coherent (ambient) incident light. This
phenomenon can be significantly amplified, assuming certain
coherence/geometrical conditions are satisfied, leading to the optical
coherence dependent filtering effect of the present invention.
SUMMARY OF THE INVENTION
It is therefore an object of the present invention to construct a filter
which distinguishes between coherent and incoherent radiation.
It is another object of the present invention to construct a filter
containing a diffraction structure which constructively interferes with
incident illumination in the diffraction mode and destructively interferes
with incident illumination in the transmission mode as a function of both
temporal and spatial coherence of the incident illumination
It is yet another object of the present invention to provide a method for
making a filter capable of discriminating between coherent and incoherent
radiation.
These and other objects of the present invention are realized by arranging
a plurality of lower-hierarchy optical elements to form a higher-hierarchy
compound optical structure in a manner such that mutual constructive
interference of light occurs as a function of incident light wavelength.
Each of the lower-hierarchy optical elements contains a series of
interference structures, e.g., holographically recorded interference
patterns. The interference structures are arranged within the optical
elements, and the optical elements are spaced from one another, to take
advantage of the difference in the optical paths of rays successively
diffracted from corresponding interference structures in adjacent
lower-hierarchy elements. The spatial distribution of the various
interference structures and lower-hierarchy elements is governed according
to a set of mathematical relationships which depend upon the spatial
coherence radius and temporal coherence length of incoming radiation and
the distances between rays successively diffracted from the corresponding
interference structures. When the filter is constructed in accordance with
the set of mathematical relationships, all of the lower-hierarchy elements
in the filter can be coherently coupled for incident coherent light but
will remain randomly coupled for incident incoherent light. That is, the
interference structures within the lower-hierarchy elements will, when
subjected to incident illumination, create constructive stationary
interference in the diffraction mode and destructive interference in the
transmission mode as a function of both the temporal and spatial coherence
of the incident light. Thus, coherent light waves reflected from
lower-hierarchy elements in the filter constructively interfere with
coherent light waves diffracted by other elements, while destructive
interference occurs between any coherent light waves transmitted through
the elements. Conversely, when incoherent light strikes the filter, the
lower-hierarchy elements will remain randomly coupled and little or no
constructive interference will occur between light diffracted by or
transmitted through the filter elements.
BRIEF DESCRIPTION OF THE DRAWINGS
The foregoing objects, features and advantages of the present invention
will become more apparent upon consideration of the description provided
in the Best Mode of Carrying Out Invention, taken in conjunction with
study of the appended drawings, wherein:
FIG. 1 is a schematic representation generally depicting the operation of a
filter constructed in accordance with the present invention;
FIG. 2 depicts the reflection coefficient of a filter constructed in
accordance with the present invention, charted as a function of spatial
coherence radius of incident radiation;
FIG. 3 illustrates the general relationship between the number of
lower-hierarchy elements employed in the filter of the present invention
and the intensity reflection coefficient obtained for both coherent and
incoherent cases in the temporal domain;
FIG. 4 (A)-(I) depict a number of different Holographic Optical Elements
suitable for use in constructing the filter of the present invention;
FIG. 5A schematically illustrates a filter constructed with fully-uniform
non-Snellian Holographic Optical Elements in accordance with the teachings
of the present invention;
FIG. 5B shows a generalized version of a diffraction coherence filter;
FIG. 6A illustrates a single lower-hierarchy optical element of the type
employed in a preferred embodiment of the present invention, wherein the
optical element comprises a fully-uniform reflection subhologram in
Lippmann geometry;
FIG. 6B depicts the vector relationships (e.g., the so-called Bragg
condition) between the grating vector and the incident and diffracted
wavevectors associated with a wavefront of light incident on the
subhologram of FIG. 6A;
FIG. 7 provides a graphic representation of the interference which occurs
in the reflection and transmissions modes for radiation in the temporal
domain, using a preferred embodiment of the filter constructed with two
subholograms;
FIG. 8A depicts a filter comprised of two subholograms which receives
incoming wavefronts at slanted angles of incidence in order to demonstrate
the effect of spatial coherence on coherence filtering;
FIG. 8B charts reflectance of the filter as a function of incidence angle
for both coherent and incoherent light;
FIGS. 9A-9C illustrate a method for constructing a Lippmann subhologram for
use in the filter of the present invention;
FIGS. 10A-10C illustrate a method for constructing multiple Lippmann
subholograms of the type depicted in FIGS. 9A-9C to create a composite
filter structure;
FIG. 11A is a drawing of a filter comprised of 15 coherently coupled
subholograms in Lippmann geometry;
FIG. 11B is a filter with 8 coherently coupled subholograms in non-Snellian
geometry;
FIG. 12 is a perspective view of a diffraction coherence filter employing
subholograms in Lippmann geometry;
FIG. 13 depicts an alternative method for constructing the filter of FIG.
11A;
FIGS. 14A, 14B and 15 illustrate another modified method for constructing a
diffraction coherence filter in accordance with the teachings of the
present invention.
BEST MODE FOR CARRYING OUT INVENTION
An exemplary embodiment of the diffraction coherence filter of the present
invention is illustrated in FIG. 1. Filter 2 is a higher-hierarchy
compound optical structure comprised of some number N of lower-hierarchy
optical elements 4. Lower hierarchy elements 4 are separated from one
another by distance plates 6 fabricated from a transparent optical
material such as glass, adhesive, plastic or air to form a total filter
thickness T. If desired, filter 2 can be protected from the outside
environment by an external protective covering of optical material (not
shown in FIG. 1).
Generally speaking, a variety of different types of optical elements can be
used as the lower-hierarchy elements 4 of filter 2. Each element 4 will
characteristically contain a series of interference structures 8 which,
when subjected to incident illumination, create constructive interference
in the diffraction mode and destructive interference in the transmission
mode as a function of both the temporal and spatial coherence of the
incident illumination. Thus, as will be described more fully hereinbelow,
elements 4 may comprise any type of Bragg structure, including uniform or
non-uniform reflection or transmission Holographic Optical Elements (HOEs)
in Lippmann or non-Lippmann geometry. Alternatively, each element 4 may be
formed from non-holographic optical layers such as dielectric multilayers
with rectangular refractive profiles, blazed gratings or some form of
surface gratings.
When each lower-hierarchy element 4 of FIG. 1 is spatially distributed
according to the teachings of the present invention, a higher-hierarchy
compound optical structure is established in which mutual constructive
interference of light occurs as a function of incident light wavelength.
That is, with proper spatial distribution of elements 4, coherent (i.e.,
laser) light waves diffracted by one element 4 constructively interfere
with coherent light waves diffracted by other elements 4. This is referred
to as coherent coupling. For diffuse or incoherent (i.e., ambient) light,
on the other hand, elements 4 are randomly coupled and there is little or
no constructive interference between light waves diffracted by or
transmitted through the various elements.
In order to achieve the critical spatial distribution of lower-hierarchy
elements 4 within filter 2 necessary for coherent filtering, the distance
L between elements 4 (L=L.sub.1, L.sub.2, L.sub.3 . . . L.sub.n) must be
carefully chosen relative to the degree of spatial and temporal coherence
of the incident light radiation after taking spectral filtering into
account. Generally speaking, L need not be identical for each separation
between elements, although in the preferred embodiment equi-distant
separations are employed (L=L.sub.1 =L.sub.2 =L.sub.3 =L.sub.n).
For the first case in FIG. 1, the incident light 10 reaching filter 2 at
angle of incidence .theta..sub.i is a highly-coherent light, e.g., laser
illumination, characterized by spectrally filtered spatial coherence
radius r.sub.c and temporal coherence length l.sub.c. The radius of the
area of spatial coherence for any type of illumination can be determined
empirically as explained in Born and Wolf, Principles of Optics (Sixth Ed.
Pergammon Press), pp. 491-554. Temporal coherence length l.sub.c for
highly coherent light is calculated according to the equation:
l.sub.c =.lambda..sub.c.sup.2 /.DELTA..lambda..sub.c (1)
where .lambda..sub.c is the peak wavelength (maximum intensity of the
filter spectral characteristic) and .DELTA..lambda..sub.c is the spectral
bandwidth of the filter with respect to highly coherent light.
In the second case, incident light Il reaching filter 2 at angle
.theta..sub.i is nearly incoherent in the fashion typical of ambient
illumination, with spectrally filtered spatial coherence radius r.sub.i
and coherence length l.sub.i. Temporal coherence length l.sub.i for
incoherent light is determined according to the equation:
l.sub.i =.lambda..sub.i.sup.2 /.DELTA..lambda..sub.i (2)
where .lambda..sub.i is the peak wavelength of the filter spectral
characteristics and .DELTA..lambda..sub.i is the spectral bandwidth of the
filter with respect to incoherent light.
Coherence filtering is established by observing an exploiting the
difference in the optical paths of rays successively diffracted from
corresponding interference structures in adjacent lower-hierarchy elements
4 for each wavefront of incident light. Examining FIG. 1, d is the
distance along the normal between rays 12, 13 diffracted at an angle .psi.
from corresponding interference structures 14, 15. D is the total distance
across all rays diffracted from corresponding interference structures in
all of the elements 4 for each wavefront of incident light reaching filter
2. If the following relationships are fulfilled:
2 r.sub.i <d<2 r.sub.c (3)
##EQU1##
each pair of elements 4 may be coherently coupled for highly-coherent
light 10, but will be uncoupled for low-coherence light 11.
The coherent coupling effect can be amplified by optimizing the geometry of
filter 2 relative to the total thickness T of the filter in a manner such
that temporal coherence length l.sub.c of the highly-coherent light bears
the following relation to T:
##EQU2##
and spatial coherence radius r.sub.c is larger than D/2 (as well as d/2):
r.sub.c >D/2 (6)
Concomitantly, the temporal coherence length l.sub.i of incoherent light
maintains the following relation to L:
##EQU3##
while the radius of spatial coherence r.sub.i remains smaller than d/2:
r.sub.i <d/2 (8)
When Equations (3)-(8) are satisfied, all N lower-hierarchy elements in
filter 2 may be coherently coupled for incident coherent light 10 and will
remain uncoupled for incident incoherent light 11. The incident coherent
light will therefore be highly reflected, as indicated at 16, but the
incident incoherent light will exhibit low reflection, as indicated at 17.
This phenomenon is illustrated in FIG. 2, which charts the reflection
coefficient R of filter 2 as a function of spatial coherence radius of
incident radiation. As can be seen in FIG. 2, the smaller the coherence
radius, the lower the reflection coefficient. For values of r less than
D/2, the reflection coefficient indicated as R.sub.i is at a minimum,
i.e., an incoherent coupling situation exists and incident light,
typically ambient in nature, will be largely transmitted through the
filter. Conversely, where r is greater than D/2, conditions of
fully-coherent coupling are met and the reflection coefficient, indicated
as R.sub.c for incident coherent radiation, is high.
In a preferred embodiment of Figure lower-hierarchy elements 4 are fully
uniform reflection subholograms in Lippmann geometry. Each of the
subholograms can be thought of as a series of interference structures 8 in
the form of Bragg planes containing holographically recorded interference
patterns. Hereinafter, the Bragg planes, which are parallel to the
subhologram surface, will also be referred to as Bragg-Lippmann
holographic mirrors or holographic mirrors. The theory of each separate
subhologram is described more fully in an article entitled "Coupled Wave
Theory for Thick Hologram Gradings", by H. Kogelnik, published in the Bell
System Technical Journal (Vol. 48, P.2902; 1969).
The difference between the intensity of coherent light reflected at 16 in
FIG. 1 and incoherent light reflected at 17 in FIG. 1 can be roughly
predicted. For the so-called "on-Bragg case", where the Bragg condition is
satisfied for each separate reflection of coherent or incoherent light,
the total intensity of the reflection for coherent light is approximated
by:
R.sub.c =N.sup.2 R.sub.o (9)
with R.sub.c representing the intensity reflection coefficient of the total
filter in the case of coherent light, R.sub.o representing the intensity
reflection coefficient for each separate subhologram and N representing
the number of subholograms in the total filter. In the case of incoherent
light, the intensity reflection coefficient R.sub.i for the total filter
will be approximately:
R.sub.i =NR.sub.o (10)
The ratio of the total intensity of coherent light reflected to the total
intensity of incoherent light reflected is proportional to the ratio of
Equations (9) and (10), i.e.:
R.sub.c /R.sub.i =N (11)
In order to maximize the coherent discrimination effect of filter 2, the
number N of subholograms should be high, whereas the intensity reflection
coefficient R.sub.o for each subhologram should be kept relatively low to
permit passage of a maximum amount of incoherent light through each
subhologram. The general relationship between N and R.sub.o for both
coherent and incoherent cases in the temporal domain is illustrated in
FIG. 3.
As noted above, lower-hierarchy optical elements other than fully-uniform
reflection subholograms 4 may be employed to construct the
higher-hierarchy compound filter structure of the present invention.
Various kinds of Holographic Optical Elements, or HOEs having either fully
uniform or non-uniform configuration and either Lippmann or non-Snellian
geometries may serve as elements 4 in the filter Alternately, as also
noted above, elements 4 may be fabricated from dielectric multilayers. A
number of different HOEs suitable for use in constructing the filter of
the present invention are illustrated in FIGS. 4A-4I.
FIG. 5A depicts a diffraction coherence filter 18 made up of several
fully-uniform non-Snellian reflection HOEs 19 of the type shown in FIG.
4B, whereby reflection of coherent and incoherent light occurs in slanted
fashion As long as the critical spatial distribution requirements of
Equations (3)-(8) are met, however, a compound filter fabricated from
lower-hierarchy elements such as dielectric multilayers or the HOEs of
FIGS. 4A-4I may function as a diffraction coherence filter, differentially
transmitting coherent light relative to incoherent light.
A generalized version of a diffraction coherence filter embodying the
principles of the present invention appears in FIG. 5B. Filter 20 is
comprised of lower-hierarchy elements 21. Each element 21 contains a
series of non-uniform curved holographic reflecting surfaces B, e.g.,
non-planar Bragg surfaces which locally satisfy the Bragg condition,
arranged to provide coherent coupling for highly coherent light.
The principle of coherent coupling is best understood by reference to FIGS.
6A-6B and 7. FIG. 6A illustrates a single subhologram 22. For purposes of
the present discussion subhologram 22 is assumed to be fully uniform
structure in Lippmann geometry (such as illustrated in FIG. 4A). Hence,
subhologram 22 is comprised of a series of Bragg planes of holographically
recorded interference patterns 23. Brag planes 23 are separated from one
another by the spatial period .LAMBDA., also called the grating constant.
The value of the grating constant, which is a factor to be taken into
account in explaining coherent coupling, can be determined by reference to
physics principles governing the relationship between subhologram 22 and
radiation incident thereon.
In the exemplary case of FIG. 6A, an incident wavefront 24 of light reaches
subhologram 22 at slanted incidence characterized by angle .theta..sub.i.
Viewed locally, a portion of incident wavefront 24 passes into subhologram
22 at an angle .theta..sub.t relative to normal, indicated at 25 in FIG.
6A, and reaches a representative Bragg plane 26. .theta..sub.t is
expressed as a function of .theta..sub.i according to the well-known Snell
law:
##EQU4##
(12) where n is
the average refractive index of subhologram 22. The remaining portion of
incident wavefront 24 is reflected in Fresnel fashion from the surface of
subhologram 22 Simultaneously, reflection of wavefront 25 reaching Bragg
plane 26 occurs internal to subhologram 22, as indicated at 27 in FIG. 6A,
and a second wavefront 28 emerges from the subhologram in Bragg-reflected
fashion, as indicated at 28.
The Bragg reflection phenomenon internal to subhologram 22 can be expressed
in vector form as the algebraic relationship between the grating vector K,
the incident wavevector K, and the diffracted wavevector K.sub.o :
K=K(x,y,z) (13)
where (x,y,z) are Cartesian coordinates.
K=K-K.sub.o (14)
##EQU5##
(15)
The vector relationship of the grating vector to the incident and
diffracted wavevectors is illustrated in FIG. 6B. The length of K and
K.sub.o are determined as a function of the wavelength .lambda. of
wavefront 24.
##EQU6##
(16)
where n is again the average refractive index of the subhologram. Inasmuch
as the grating constant A is related to the grating vector:
K=2.pi./.LAMBDA. (17)
the value of the grating constant is also determined as a three-dimensional
function of (x,y,z) and incident radiation wavelength:
.LAMBDA.=f'(x,y,z) (18)
##EQU7##
(19) (20)
Equation (20) thus provides the generalized expression of the grating
constant for light reaching a subhologram at a slanted angle of incidence.
Viewing the situation locally, the phase relationship between the
wavefronts incident and reflected from any given Bragg plane, e.g., Bragg
plane 26 in FIG. 6A, depends upon the value of the grating constant. This
latter principle is explained in conjunction with FIG. 7, which depicts
the localized conditions of reflection within a subhologram structure for
the special case of radiation reaching the subhologram surface at an angle
normal to the plane of the surface, i.e., at angle of incidence
.theta..sub.i =0.degree.. FIG. 7 specifically reveals a diffraction
coherence filter 30 having two subholograms 31, 32. Each subhologram again
comprises a series of Bragg planes of holographically recorded
interference patterns separated by the grating constant or spatial period
.LAMBDA.. A fully-uniform case is assumed for subholograms 31, 32, and
hence .LAMBDA. does not change over the hologram volume. For simplicity,
the same average refractive index n for each subhologram is likewise
assumed.
Considering first a light ray or wavefront 34 reflected from the Bragg
plane in subhologram 31 containing point A and comparing it with the
wavefront 35 reflected from an adjacent Bragg plane containing point B,
the phase relationship between the two reflected wavefronts can be
expressed as:
##EQU8##
(21) where
.theta..sub.i is the angle of incidence in the holographic medium and AB
represents the distance between points A and B. Inasmuch as the distance
between point A and point B is also equal to the Bragg constant, i.e.:
AB=.LAMBDA. (22)
and further in view of the fact that:
##EQU9##
(23) Equation
(22) can be reformulated as follows:
##EQU10##
(24) (25)
Equation (21) can now be rearranged using Equation (25) above:
.DELTA..phi.=(2.pi./.lambda.) .lambda. (26)
.DELTA..phi.=2.pi. (27)
Thus, the wavefronts reflected from Bragg planes containing points A and B
are in phase with one another. This situation creates constructive
interference for reflected light, i.e., the wavefronts will be reflected
coherently in spite of the fact that they are reflected from different
Bragg planes. Conversely, the diffracted wavefronts will create
destructive interference for transmitted light.
If the thickness L of the distance plate 36 separating subholograms 31 and
32 is set at some multiple w of .LAMBDA., where w is some integer (w=1,2,3
. . . ), L can be expressed as:
##EQU11##
(28)
Now comparing the wavefront 37 reflected from the Bragg plane in
subhologram 32 containing point C with the wavefront 38 reflected from the
Bragg plane containing point A in subhologram 31, the phase relationship
between the two reflected wavefronts is:
##EQU12##
(29) where AC
represents the distance between points A and C. Because AC is the sum of
the thickness of the distance plate, L, and some integer multiple m of
.LAMBDA. represents the number of Bragg planes in subholograms 31 and 32
crossed by the wavefront between points A and C,
AC=L+m.LAMBDA. (30)
##EQU13##
(31) (32)
where w' is also an integer. Substituting Equation (32) in Equation (29)
yields:
##EQU14##
(33)
.DELTA..phi.=(2.pi./.lambda.) w'.lambda. (34)
.DELTA..phi.=w'(2.pi.) (35)
Thus, provided Equation (28) is satisfied, two wavefronts reflected from
Bragg planes respectively located in different subholograms 31 and 32 also
reflect coherently, creating constructive interference between themselves
in the reflection mode and destructive interference between themselves in
the transmission mode.
The ability of a filter constructed from multiple subholograms to
distinguish between coherent and incoherent light can be seen by examining
Equation (35) and underlying Equation (28) in relation to Equations
(1)-(8). In particular, equations (28) and (35) respectively are
wavelength-dependent functions, permitting the interference relationship
between subholograms in a diffraction filter constructed according to the
present invention to be controlled as a function of incident wavefront
coherence. In the case where the filter is constructed such that Equations
(3), (4) and (5) are satisfied, that is, in the case where the total
thickness T of the filter is adjusted such that coherence length l.sub.c
is larger than twice the thickness T, the assumption can be made that:
l.sub.c >>2L (36)
Under these conditions, coherence filtering based on temporal coherence
will occur. At the same time, when the thickness of the distance plates
separating various subholograms in the filter is chosen according to
Equation (4) for light wavelengths and associated coherence lengths in the
visible spectrum, the selection of a distance plate thickness L which
specifically does not satisfy Equation (28) will serve to prevent
interference from occurring between adjacent subholograms in the filter in
the case of incoherent light incident to the filter.
In the case where the filter is constructed such that Equations (3), (4)
and (6) are satisfied, the spatial coherence area radius r.sub.c is larger
than D/2. The assumption can then be made that
r.sub.c >>2d (37)
Hence, coherence filtering based on spatial coherence can be achieved, and
a coherence filter capable of creating differential internal reflection
characteristics as a function of the coherence of incident light can be
obtained.
FIG. 8A, like FIG. 6A, depicts the case of slanted incidence angles to
better demonstrate the effect of spatial coherence on coherence filtering.
In particular, two subholograms 39, 40 separated by a distance plate 41
receive first and second wavefronts of light 42, 43 at angle of incidence
.theta..sub.i. Regardless of the temporal coherence of wavefronts 42 and
43, the amount of interference between the two wavefronts will lessen as
.theta..sub.i increases. Consequently, the angular characteristic for
coherent radiation is narrower than for incoherent radiation. The latter
phenomenon is illustrated in FIG. 8B, which empirically charts reflectance
as a function of incidence angle for both coherent and incoherent light
(if .theta..sub.i =0 of course, the pure case of the filter functioning in
the temporal coherence domain occurs).
Fabrication of lower-hierarchy holographic elements for use in a preferred
embodiment of the present invention, employing prior art standing wave
holographic recording techniques, is illustrated in FIGS. 9A-9C. A photo
sensitive holographic medium 44 is positioned in a predetermined distance
from a mirror 45. Holographic medium 44 may comprise any suitable
holographic material, i.e., a polymer such as PVA-based or dichromated
gelatin (DCG) or a photo refractive crystal such as LiNbO.sub.3, BSO or
PLZT. Electromagnetic energy in the form of laser light (wavelength
.lambda..sub.c), indicated by arrows 46, is transmitted from a source 47
through holographic medium 44 to mirror 45 and is reflected back into the
holographic medium from the surface of mirror 45, as indicated by arrows
48. The interaction of the incident wave energy and the reflected wave
energy forms a standing wave pattern in the holographic medium, leading to
a sinusoidal distribution of electromagnetic energy throughout the
holographic medium as ill | | |
