Note: Descriptions are shown in the official language in which they were submitted.
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INTRAVOLLTME DIFFRACTIVE OPTICAL ELEMENTS
FIELD OF THE 1NVENTION
The present invention relates to the field of intravolume diffractive optical
elements, especially those produced in transparent materials by means of
digital
laser engraving at very high energy densities.
BACKGROUND OF THE INVENTION
Diffractive optical elements (DOE'S) are well known and fulfill important
roles in industrial and military applications, in imaging, in medicine, in the
storage, processing and transmission of information, and elsewhere. Digital
DOE's, have been described by B.R.Brown and A.W.Lohmann in the article
"Complex Spatial Filtering with Binary Masks", published in Applied Optics,
Vol. 5, p. 967ff, (1966). Such digital DOE's have generally been produced by
means of mechanical micro-engraving, electron beam, ion beam or chemical
etching, electron lithography or photolithography, or by other suitable
techniques.
The mathematical functionality of a DOE can be expressed in terms of the
field R(r) produced after imaging by the DOE of an incident light field S(n) .
This image field is given by equation 1:
R(r) = f S(u)T(n) exp(ikd (r, n)) / d (r, u)ds ( 1 )
D
where S(n) is the incident light field at the surface, s, of the DOE,
T(a) is the complex transmission coefficient of the DOE,
d(r,n) is the optical path from point r to n in the imaging space, and
f is the integral over the surface, s, of the DOE.
D
Equation (1) is the Kirchhoff approximation for the solution of the scalar
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Dirichlet problem with infinite boundary conditions, and with Sommerfeld
radiation conditions. Equation (1) can alternatively be interpreted as the
Fresnel
transformation of the field S(u)T(u) from the surface of the DOE to the point
r .
In order to construct the desired DOE, the inverse problem has to be solved,
whereby the incident field S(u) and the transmitted field R(u) are known and
the
appropriate complex transmission function of the DOE - T(n) , has to be
calculated. Such a DOE then produces the desired transformation of the
incident
field such that the correct field is formed in the image plane. The method of
representing the DOE by means of a function T(n) is performed by assigning
complex values of the transmission function to discrete pixels of the DOE. The
number of pixels chosen depends on the size of the DOE and its resolution. The
values of the transmission function for each pixel can be calculated by means
of
scalar diffraction theory, and form a Fourier transform of the model field.
Evaluation of this Fourier series requires some approximations. Several
numerical methods and procedures for the calculation of DOE's, both direct and
indirect, have been proposed in the prior art. Examples of such methods are
given, for instance by D. Brown and A. Kathman, in the article "Multi-element
diffractive optical designs using evolutionary programming" published in SPIE
Vol. 2404, p.l7ff, 1995; by J. N. Mait, in "Review of multi-phase Fourier
grating
design for array generation", published in SPIE Vol. 1211, p. 67ff, 1990; by
V.A.
Soifer, et al., in "Multifocal diffractive elements", published in Optical
Engineering, Vol. 33, p. 3610ff, Nov. 1994; and by N.L. Kazansky and V.V.
Kotlyar, in "Computer-aided design of diffractive optical elements", published
in
Optical Engineering, Vol. 33, p. 3156ff, (October 1994). These different
methods
are intended for different types of DOE and field transformations. A review of
the problems associated with these methods, and various discretization
quantization and errors are discussed in "Some effects of Fourier domain phase
quantization" by J.W.Goodman and A.M.Silvestri, published in IBM Journal of
Research and Development, Vol. 14, p. 478ff, (1970) and in "Aliasing errors in
digital holography" by J. Buklew and N.C. Galaher, published in Journal of
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Applied Optics, Vol. 15, p. 2183ff, (1976).
A major drawback of the prior art conventional methods of producing
computer-generated DOE's is that they are principally two dimensional in
nature
and are located on the surface of the DOE. Such DOE's have found limited use
because of the complexity of constructing integrated multi-element devices
from
an assembly of 2-dimensional devices. The need to maintain correct alignment
of
a number of separate elements, also reduces the reliability of such a device.
A
further serious limitation is the inability to produce a coherent arrangement
of
independent sequential devices and a 3-dimensional spatial diffractive
structure.
These problems are analogous to the differences found in the prior art between
conventional 2-D Gabor holograms and 3-D Lipman-Denisyuk holograms, as
described by Denisyuk in the article "Optical Properties of an Object as
Mirrored
in the Wave Field of its Scattered Radiation", published in Optics and
Spectroscopy, Vol. 15, pp. 522-532, (1963). This difference is analyzed by Van
Heerden in the article "Theory of optical information storage in solids",
published in Applied Optics, Vol. 2, pp.764ff, (1963).
A number of different types of DOE's, produced according to prior art
methods and apparatus, are described in the following documents: U.S. Patent
No. 5,291,317, to Newswanger et al, describes methods and apparatus for
creating a plurality of holographic diffraction grating patterns in a raster
scan
fashion; U.S. Patent No. 3,905,674, to Ruell et al, describes apparatus for
producing one-dimensional holograms; U.S. Patent No. 4,140,362, to Tien et al,
describes a method for forming focusing diffraction gratings by production of
a
predetermined interference pattern on photosensitive film; U.S. Patent No.
4,516,833, to R. L. Fusek describes the production of high performance optical
spatial filters; U.S. Patent No. 4,846,552, to W.B.Veldkamp et al, describes a
method of fabricating high efficiency binary planar optical elements based on
photolithographic techniques; U.S. Patent No. 5,428,479, to R.A. Lee describes
a
method of manufacture of a diffraction grating with assembled point gratings;
and U.S. Patent No. 5,818,988 to R.A. Modavis describes a method of forming a
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grating in an optical waveguide utilizing photosensitive materials. All of the
above-cited prior art methods have one or more of the disadvantages mentioned
in the previous paragraph.
Furthermore, in U.S. Patent No. 5,761,111 to E. N. Glezer, are described
methods of providing 2- or 3-dimensional optical information storage in
transparent materials by controllably focusing ultra-short laser pulses into a
transparent medium. Volume DOE's are mentioned therein as one of the
applications for the method. However, no details are provided, nor are any
methods suggested of how to calculate the necessary "information" for storage
in
the transparent medium to produce such a DOE.
There therefore exists a serious need for a method of constructing
intravolume mufti-element DOE's, which overcome disadvantages of prior art
DOE's.
All of the documents mentioned in this section, and in the other sections of
this specification, are hereby incorporated by reference, each in its
entirety.
SUMMARY OF THE INVENTION
The present invention seeks to provide a new method of producing
3-dimensional intravolume DOE's, including both polychromatic and achromatic
DOE's, in transparent materials, by creating inside the material a set of
scattering
centers. The position of every point of this set of scattering centers is
computed,
so that the set of secondary waves of light scattered from these points is
such as
to create the desired field by means of a suitable transformation of the
incident
electromagnetic field. Unfortunately, no accurate mathematical techniques
exist
for calculation of such an accumulated scattered secondary wave. The methods
described in the above-mentioned references can be applied only to two
dimensional structures or to an incoherent set of two-dimensional devices.
In the zero level approximation, the resulting scattered wave from such a set
of points can be written as:
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isr
R(r) _ ~', S(n; )a1 (r) exp(ikd (r, nt )) ~ d(r, nt ) (2)
i-i
where i is used to enumerate the scattering centers from 1 to I,
ui is the position of i th center, and
a; (r; ) is the complex scattering coefficient of the i th center in direction
rj .
The other variables have the same meaning as in equation (1).
Equation 2 is the analog of equation 1 for the 3-dimensional discrete case,
but it is only a zero level approximation. Equation 2 can be evaluated in an
analytical form, but an analytic solution of the inverse problem of finding a;
(r; )
when It (rj ) and s (u; ) are given, cannot be achieved. The inverse problem
can,
however, be converted to one of functional extremum searching:
.l~f i5r
I,ni,ai(rj)>_min ~ D(rj)-~S(n;)a;(rj)exp(ikd(r;,u;))~d(r;,y)
j=1 i=1
where rj, j =1...J are reference points, and D(rj) is the desired resulting
field.
A solution of equation (3) for the value of a; (r j ) can be obtained both for
fixed positions of the scattering centers and for a discrete set of real
scattering
coefficients. The solution of this problem for a fixed set of scattering
centers at
a i can be performed by means of a number of well known methods. One example
is by the use of the modified genetic algorithm, as discussed in "Multi-
element
diffractive optical designs using evolutionary programming", by D.Brown and
A.Kathman, published in SPIE, Vol. 2404, pp.l7-27,(1995), hereby incorporated
in its entirety by reference.
Simplifying assumptions can be made for specific geometrical applications.
Thus, for instance, if the DOE is to be used in an application with a
spherical
incident wavefront, then the set of scattering points may be limited to points
located on a spherical shell. In such a situation, the configuration becomes a
scalar scattering problem, since the E-field vector of the incident field is
always
perpendicular to the scattering plane. This then enables the same result to be
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achieved as that obtained using a DOE having scattering points arranged in the
entire volume of the sample, but with fewer scattering points.
A more accurate mathematical model of a three-dimensional discrete DOE
can be obtained using an analog to Faddeev's approach of T-matrix formalism
for
a multi-body system, as described in L. D. Faddeev and S. P. Merkuriev,
"Quantum Scattering Theory for Several Particle Systems", published by Kluver,
Dordrech, 1993.
The stationary wave equation in a solid medium is expressed as:
(-~x -k2)~o(X~k)=~
where
fro (X, k) is a solution of the wave equation for a specific wave vector k, k
= IkI
and ~x is the Laplace operator in x space.
For a domain SZ of scattering centers, equation (4) can be written as:
(-Ox -k2co2 /c12(ac))tV(x~~) _ ~ (4a).
where
co is the velocity of wave propagation in the given media,
c1 (x) is the velocity of wave propagation in the domain Sz of scattering
centers.
Equations (4) and (4a) can be combined into one equation:
(-Ox -k2 +~'(k2~X))~(X~k) _ ~
where the following notations have been introduced:
1V(k2,X) =k2 (1-C~Z /Clz(X)) ~ W(k2,X) _ ~,X ~
With regard to the radiation conditions for a scattering center located at the
origin, an asymptotic solution of (5) is assumed, as follows:
exp~ikx~
yr(X,k,k) ~ exp~ik(X,k)}+a(x,k,k) (6)
x
where x = ~ I x , k = k l k, and a(x, k, k) is the scattering amplitude.
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Defining a Green's function:
go (z) _ (-~x - z)-i
g(2) _ (-~x -Z + W(z,X)) 1 .
The perturbed Green's function can then be represented as:
g(Z) = go (~) - go (Z)t(Z)go (Z)
t(z) is called the T matrix and obeys the integral equation:
t(z) = w(z~.) - W(~~.)go (Z)t(Z)
This is equivalent to the equation for the kernels of the Fourier
transformation of
participating operators:
t(PaP~~z)=w(Z~P-P~)- f dP~~~'(z~P-P~~)(Pn2 -z) lt(P~~~P~~z) (8a)
General scattering theory gives the basic relation between the solution of
(5), the
scattering amplitude in (6) and the T-matrix
a(x,k,k) _-i2~tt(kx,kk,kz +i0)
lim
~(x~k) ' ~ -~ 0 iEg(k2 +is)Y~o(X~~)
The wave equation for a set of scattering centers reads:
(-0x - k2 + W (k2, X))'I'{X, k) = 0 ( 10)
The perturbation W(kZ,X) is a summation over all scattering centers of the
local
perturbations W(kz,X) _ ~Wt(k2,x) . The T matrix for (10) obeys the following
equation:
Z'(z) = W (k2 ~ z) - W (k2 > z)go (z)Z'(z) ( 11 )
Defining the components of the T matrix as:
T(z)=~'~'(z~~-y)-~'i'(z~~-u~)go(z)~'(Z)~ Z'(z)=~,T(Z) (12)
After transformation, equation (12) gives:
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g
T (z) = t; (z) - to (z)go (z)~T; (z) ( 13)
;~r
Here T matrix t; (z) for the j-th scattering center has been introduced:
A solution of (13) can be presented as a series:
T (z) = t~ (Z) - ti (Z)go (~)~ t~ (Z) +t~ (Z)go (~)~, tr (Z)go (Z)~, tx (Z) -
... ..
*a ;~r k~;
T(z) _ ~ Ol (z)t(z) , (14)
r=o
where O(z) is an operator matrix with components Oj = t; (z)go (z)(8~ -1) ,
and
T(z) and t(z) are vectors with components T,. (z) and t; (z) respectively.
In most cases, this is a convergent series and it has a clear physical meaning
of sequential one fold, twofold and . . ... scattering.
The total resulting scattering amplitude A(x, k, k) according to (9) can be
presented as:
A(x,k,k) =-i2r~l'(kx,kk,k2 +i0)
In the zero level approximation, T(z) _ ~T,. (z) _~ t; (z) , after averaging
1 !
over the wave vector of the incident field, a result similar to (2) is
obtained with
a; (r; ) = f dka; (r; l r, k, k) .
The use of series (14) allows obtaining the correct problem definition for
manifold scattering. The great advantage of equation (3) is the possibility of
sequential evaluation of the extremum according to the level of approximation,
or
in the present case, to the degree of operator O(z) . On the other hand,
equation
(9) allows another interpretation of Green's function G(k2 ) as a propagation
operator for the wave function and the solution ~(X, k) as a result of
transformation of the incident field fro (x, k) .
Denoting this transformation as G(aouo, alul, a2ua, a3u3,...aln1 ) .
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It should be emphasized that this transformation depends on scattering
properties
of i~' center a; and it's location n; . Hence the problem expressed in (3)
becomes:
'II(X, k) = G(aono , alnl, a2n2 , a3u3,..., alnl )~0 (X, k) _ G( lafui ~)~o
(X~ k)
I,ut,ai =>min ,~~D(ri)-~G(~a~ur~)S~ri)~
j=1
There is thus provided, in accordance with a preferred embodiment of the
present invention, a method of producing a 3-dimensional DOE, using the
phenomenon of intravolume optical breakdown. Intravolume optical breakdown
involves the focusing of the beam from a laser emitting ultra-short pulses, of
the
order of tens of picoseconds or less, into the volume of a transparent
material, by
means of a high quality objective lens, such that a focal spot of size close
to the
diffraction limit for the laser wavelength, is obtained within the material.
At very
high power densities, of the order of 1013 Watts/cm2, the material undergoes
optical breakdown, since the power density of the focused beam far exceeds the
threshold above which non-linear effects occur in the transmission properties
of
the otherwise transparent materials, and the material strongly absorbs the
focused
beam. Because of the intense power density, atomic and molecular bonds of the
material are broken down, and the material decomposes almost instantaneously
into its basic components, generally highly ionized component atoms, leaving
behind a tiny diffuse scattering center. The optical breakdown damage zones
constituting these scattering centers define the pixels of the DOE. The
position of
these scattering centers is calculated according to the function of the DOE
planned, using one of the methods described hereinabove, such as by the
modified genetic algorithm. The production of such optical breakdown damage
centers has been described in Russian Patent No. RU 2,008,288 to S.V.
Oshemkov, one of the current applicants, entitled "Process for Laser Forming
of
Images in Solid Media". This document is hereby incorporated by reference in
its
entirety.
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Alternatively and preferably, the DOE may be produced in a transparent
molecularly porous material, such as Corning Glass type Porous Vicor 7930, and
the voids created at the optical breakdown damage zones filled with a liquid
having a different refractive index to that of the transparent material, for
instance
by immersion in the liquid. The scattering then takes place from those points
of
different refractive index. The liquids used can preferably be organic
solvents
such as acetone, alcohol or toluene, or other suitable liquids such as oils,
having
suitably different refractive index from the host material. A sealant layer is
preferably applied to the DOE so produced in order to avoid loss of the
filling
liquid.
According to further preferred embodiments of liquid filled DOE's, the
liquid used can act as a carrier of another active material, such as a
phosphorescent or a fluorescent dye, or a simple absorbent dye, and the DOE
operative by scattering from this dye under the relevant conditions of
activation
or view. Details of the production of such fluid-filled voids are described in
the
co-pending PCT Patent Application No. PCT/RU 98/00241 entitled "Method for
Forming Images" to one of the inventors of the present application. The
published Application is herewith incorporated by reference in its entirety.
It should be noted that use of the term transparent throughout this
specification is taken to refer to the transparency of the material at the
processing
laser wavelength, and it is thus quite feasible for a DOE to be produced,
according to the present invention, in materials which are opaque at visible
wavelengths.
The above method is capable of producing pixels of size close to the
diffraction limit for the laser light used, of the order of 0.5 ~,m, and at
distances
apart of less then 1 ~.m. In order to produce a periodic diffraction grating
of
period O, the maximum diffraction angle, a, is defined by the equation
k0 sin(a) = 2~z . This means that the diffraction angle, even for a plane DOE,
may
be greater than 60 degrees.
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There is thus provided, in accordance with another preferred embodiment of
the present invention, a method for producing a computer generated,
intravolume
diffractive optical element in a transparent material by means of the
controlled
production of scattering centers by means of optical breakdown in the
material,
resulting from the focusing of high intensity laser pulses therein. Since they
are
computer generated, such DOE's are called digital DOE's. In the case where the
scattering points essentially consist of a series of digital ones or zeros, in
so far as
their scattering ability is concerned, such DOE's are also known as binary
DOE's. For binary DOE's equation (14) allows some simplifications to be made.
Every scattering center can be assumed to have the same perturbation operator
~'r(kZ~~)-n'(k2~x-ui)~
which is shifted to a location of the center n; .
Hence according to equation (6), t~ (k, k', z) = t(k, k', z) exp~i(u~ , k -k')
.
The last expression obviously gives Bragg's scattering condition for a
periodic
grid of scattering centers.
The accuracy of the arrangement of pixels inside the transparent material
depends on the quality of the optical and mechanical beam positioning system,
and on the size of the pixels produced. In practice, with good quality
focusing
optics, it is possible to create pixels of size close to ~,/2 of the engraving
light,
which is the theoretical limit for such a focusing process, and with a
location
accuracy of greater than ~, / 8 . Pixel sizes and location accuracies of this
order
should thus be sufficient for the production of intravolume DOE's for use in
the
visible range, by means of the methods of this invention.
The DOE's constructed according to the present invention can be used for a
number of purposes in the field of optics, including, but not limited to,
focusing,
beam shaping, wavefront correction, beam splitting, optical filtering,
diffracting,
partial reflecting, and others. According to a further preferred embodiment of
the
invention, if the scattering points are produced throughout the volume of the
transparent material in a random manner, an optical diffuser is obtained,
whose
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density is dependent on the density of scattering centers produced.
Most of the known prior art DOE's are monochromatic and are designed
for one specific wavelength. DOE's constructed according to preferred
embodiments of the present invention are primarily three dimensional, and this
enables the selection of a wide range of spatial wave vectors for achieving
polychromatic design. This means that it is possible to control the scattering
of a
set of electromagnetic waves with different wavelengths. This feature allows
achromatic DOE's to be achieved, when the element is designed such that all
the
waves with different wavelength are scattered in the same way.
In addition to correcting the imaging functions of light beams, DOE's
according to other embodiments of the present invention, can be utilized for
transformation of an incident electromagnetic field in a predetermined manner.
It
is thus possible to compensate a beam emitted from a light source, such as,
for
instance, a laser diode, or a LED, for undesired properties therein. In this
application, the light emitted from the source is measured, and the results
analyzed and compared with the desired output of the source. A set of data
according to the differences between the measured and desired beam
characteristics is used to produce a DOE according to preferred methods of the
present invention. When this DOE is incorporated into the front envelope of
the
source, or elsewhere in its beam path, it compensates the emitted light to
achieve
the desired beam characteristic. Depending on the type of incident wave
analysis
performed, correction can be achieved for undesired characteristics in spatial
intensity (mode form), phase or even chromatic variations of the beam. Thus,
for
spatial intensity corrections, a simple beam profile is sufficient, for phase
correction, a full phase profile of the incident beam is necessary, and for
chromatic correction, a wavelength profile is preferably used. The correcting
DOE is calculated according to the differences between the undesired beam
characteristics and the desired beam characteristics.
Since the DOE's constructed according to the present invention are
intravolume elements, using all three dimensions of the support material, they
are
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well suited for multielement designs, since all the elements can be located in
one
piece of glass, and do not need any adjustment or maintenance. Such a
multi-element device can also be constructed by locating the scattering points
in a
plurality of separate planes, thus constituting a sequential set of
diffractive
elements. Furthermore, the DOE's constructed according to the present
invention
can be used in hybrid optical assemblies by locating them inside the volume of
classic refractive elements constituting a hybrid optical device.
In accordance with yet another preferred embodiment of the present
invention, there is provided a method of producing in a solid transparent
material,
a diffractive optical element for the predefined transformation of an incident
wave, consisting of the steps of developing a mathematical model of the
diffractive optical element in terms of the transformation, using the
mathematical
model for determining a set of points which form the diffractive optical
element,
and focusing at least one pulsed laser beam onto the points, such that it
causes
optical breakdown damage at the points.
In accordance with yet another preferred embodiment of the present
invention the mathematical model may review the discrete structure of the set
of
points and take into account the amplitude and phase properties of their
scattering
diagram.
In accordance with still another preferred embodiment of the present
invention, there is provided in the method described above, the determining is
performed by finding a numerical solution to the equation
I,u;,a; =>min ~~~D~r~)yGya~u~~)S~(r;)~
where the symbols have the meaning used in the above-mentioned disclosure.
The numerical solution may be found by use of a modified genetic algorithm.
There is further provided in accordance with still another preferred
embodiment of the present invention, a method as described above, and wherein
the set of points is determined by taking into account twofold or multifold
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scattering of the scattered wave by the set of points.
In accordance with a further preferred embodiment of the present invention,
there is also provided a method as described above, wherein the solid
transparent
material is a porous material, and wherein the points of the optical breakdown
damage may be filled with a liquid having a refraction index different from
that
of the transparent material.
There is also provided in accordance with yet further preferred
embodiments of the present invention, any of the methods described above, and
wherein the set of points lies on a curved two-dimensional surface, or
consists of
a plurality of planes which form a sequential set of diffractive elements, or
are
located in substantially any location in the three dimensional volume of the
material, or form a binary diffractive optical element.
In accordance with yet another preferred embodiment of the present
invention, there is provided a method as described above, and wherein the
points
are located on a fixed grid, have sizes determined from a defnite set and form
a
digital diffractive optical element. The sizes may be variable and are
achieved by
varying the number of pulses of the pulsed laser beam used to form each point.
There is further provided in accordance with yet another preferred
embodiment of the present invention, a method as described above, and wherein
the step of developing a mathematical model is performed by analysis of the
incident wave.
In accordance with still another preferred embodiment of the present
invention, the diffractive optical element may be operative to compensate for
undesired properties of the incident wave.
There is further provided in accordance with still another preferred
embodiment of the present invention, a method as described above, and wherein
the step of developing a mathematical model is performed during production of
the diffractive optical element, by analysis of the scattered wave.
In accordance with a further preferred embodiment of the present invention,
there is also provided a method as described above, and also consisting of the
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step of impinging a monitoring incident wave onto the diffractive optical
element
during at least part of the step of focusing a pulsed laser beam onto each of
the
points sequentially, and correcting the diffractive optical element during
production in accordance with the scattered wave obtained in real time.
In accordance with yet a further preferred embodiment of the present
invention, any of the methods described above may be used to correct an
aberration in an optical element by the formation of a diffractive optical
element
within the element. In accordance with another preferred embodiment of the
present invention, a monitoring incident wave is impinged onto the optical
element during at least part of the step of focusing a pulsed laser beam onto
each
of the points sequentially, and the diffractive optical element corrected
during
production in accordance with aberrations obtained from the optical element in
real time.
In accordance with more preferred embodiments of the present invention,
the diffractive optical element may be a wave front corrector, or a lens, or a
grating, or a beam splitter or a filter, or has a predefined reflectance to
the
incident wave, or is an optical diffuser.
Furthermore, in accordance with yet another preferred embodiment of the
present invention, there is provided a method as described above, and wherein
the
laser beam is focused onto the points sequentially by mutual motion of the
laser
beam and the solid transparent material.
There is also provided in accordance with further preferred embodiments of
the present invention, a method wherein the laser beam is focused onto a
plurality
of the points simultaneously by transmitting the beam through a master
diffractive optical element operative to focus the beam onto the plurality of
points.
In accordance with yet another preferred embodiment of the present
invention, the at least one laser beam may be a plurality of laser beams,
operative
to simultaneously produce a plurality of diffractive optical elements.
There is even further provided in accordance with a preferred embodiment
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of the present invention, a laser system for simultaneous production of a
plurality
of damage points in a solid transparent material, consisting of a pulsed laser
beam
capable, when focused, of causing optical breakdown damage at the points in
the
material, and a master diffractive optical element, through which the pulsed
laser
beam is passed, the master diffractive optical element being predefined such
as to
focus the laser beam onto the locations of the plurality of damage points.
Furthermore, in accordance with yet more preferred embodiments of the present
invention, the laser system can further include a computer control system for
relative displacement of the sample and the laser beam, and can further
include a
focusing optical system.
There is also provided in accordance with a further preferred embodiment
of the present invention, a laser system for producing a diffractive optical
element
in a solid transparent material, consisting of a pulsed first laser beam
capable,
when focused, of causing optical breakdown damage at points in the material,
an
optical system for focusing the first laser beam, a computer controlled motion
system for moving the solid transparent material in the first laser beam, such
that
the optical breakdown damage is formed at the desired points, a second laser
beam, projected through the solid transparent material, operative as a probing
beam, and an imaging system consisting of a camera for monitoring the
diffraction of the second laser beam through the diffractive optical element,
the
imaging system providing data to the computer controlled motion system, such
that the diffractive optical element is correctly formed in real time
according to
the diffractive effects obtained.
BRIEF DESCRIPTION OF THE DRAWINGS
The present invention will be understood and appreciated more fully from
the following detailed description, taken in conjunction with the drawings in
which:
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Fig. 1 is a schematic illustration of a computer controlled system for the
production of computer generated intravolume 3-dimensional DOE's, constructed
and operative according to a preferred embodiment of the present invention;
Fig. 2(a) is a schematic illustration of the use of a DOE, constructed and
operative according to a preferred embodiment of the present invention, for
beam
focusing; Fig. 2(b) shows a typical DOE pixel arrangement for performing the
focusing functions shown in Fig. 2(a); and Fig. 2(c) is a view of the
logarithm of
the energy distribution of the resulting field in the focal plane;
Fig. 3(a) is a schematic illustration of the use of a DOE, constructed and
operative according to a preferred embodiment of the present invention, for
beam
shaping; Fig. 3(b) shows a typical example of a DOE pixel arrangement for
performing the shaping functions shown in Fig. 3(a); and Fig. 3(c) is a view
of
the energy distribution of the resulting field in the object plane;
Fig. 4(a) is a schematic illustration of using a DOE, constructed and
operative according to a preferred embodiment of the present invention, as a
wave front corrector, Fig. 4(b) is an illustration of the known energy
distribution
in the incident field, which may have aberrations which it is desired to
remove.
Fig. 4(c) shows the desired energy distribution, Fig. 4(d) shows a sample of a
DOE pixel arrangement; and Fig. 4(e) illustrates the energy distribution
obtained
in the refracted field;
Fig. 5 is a schematic illustration of a system, according to a further
preferred
embodiment of the present invention, whereby replication of DOE's can be
performed without the need for auxiliary focussing or scanning, by means of
passing a writing laser beam through a master DOE; and
Fig. 6 is a schematic illustration of a system, according to a further
preferred
embodiment of the present invention, in which the DOE being engraved is
dynamically inspected by means of a probe laser beam transmitted through the
DOE and imaged thereby, and the laser engraving system adjusted in real time
to
obtain the desired DOE according to the image obtained.
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DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS
Reference is now made to Fig. 1, which illustrates schematically a
computer-controlled system for the production of 3-dimensional intravolume
Diffractive Optical Elements, constructed and operative according to a
preferred
embodiment of the present invention. A femtosecond pulsed laser 10 emits a
beam 12 which is deflected by beam deflector 14 and focused by means of a high
quality optical system 16, into a transparent sample 18 in which the DOE is to
be
produced. The laser pulse peak power is sufficiently high to achieve optical
breakdown for the particular material of the sample.
The sample is disposed on a CNC-controlled three-axis precision stage 20.
The motions along the X-Y-Z axes are executed by means of motors 22, 24, 26.
Selection of the position at which the spot is to be focused is performed
either by
motion of the sample using the CNC-controlled motion stage 20, or by means of
a the fast optical beam scanner 14, which operates in the x-y plane only, or
by a
combination of both. A computer 27, supplies data to a CNC controller unit 28,
which supervises all of the functions of the system, synchronizing the firing
of
the laser pulses with the motion of the X-Y-Z stage and deflector, such that
the
required arrangement of scattering points is formed throughout the volume of
the
sample, in accordance with a predefined program. The method by which the
predefined program determines the location of each scattering center is
described
hereinabove.
Reference is now made to Figs. 2(a), which schematically illustrates the use
of a DOE 30, constructed and operative according to a preferred embodiment of
the present invention, in a beam focusing application. The beam from the laser
33
is focused at the point 31. Fig. 2(b) is a typical DOE pixel arrangement for
performing the focusing function shown in Fig. 2(a). Fig. 2(c) is a view of
the
logarithm of the energy distribution of the resulting field in the focal
plane. This
beam focusing element resembles a Fresnel Zone plate, but is constructed from
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scattering points. It differs from a Zone plate due to the phase properties of
the T-
matrix (i.e. scattering amplitude equation (9) A(x, k, k) ).
Reference is now made to Fig. 3(a), which is a schematic illustration of the
use for beam shaping of a DOE 32, constructed and operative according to
another preferred embodiment of the present invention. The laser 33 produces a
plane coherent wavefront 34, which is directed to be incident on the DOE 32.
The
arrangement of scattering centers produced by the methods of the present
invention within the volume of the DOE, are such as to cause the plane wave 34
to diverge to produce the desired high contrast image 3 5 in the image plane.
Fig.
3(b) shows a typical example of a DOE pixel arrangement for performing the
shaping functions shown in Fig. 3(a). Fig. 3(c) is a view of the energy
distribution
of the resulting field in the obj ect plane. Such a DOE can be used in
encoding,
encryption or marking applications.
Reference is now made to Fig. 4(a), which is a schematic illustration of the
use of a DOE 36, constructed and operative according to a preferred embodiment
of the present invention, as a wave front corrector. The DOE operates by
preferentially spatially diffracting the incident beam 37 in such a way that
the
incident field E(x,y) is refracted to a value U(x,y) for every point in the
transmitted beam 38.
Fig. 4(b) is an illustration of the known energy distribution in the incident
field, which may have aberrations which it is desired to remove. Fig. 4(c)
shows
the desired energy distribution. Fig. 4(d) shows a sample of a DOE pixel
arrangement. Fig. 4(e) illustrates the energy distribution obtained in the
refracted
field after passage through the field-correcting DOE. Such an aberration-
correcting DOE may also be produced inside another optical element, whether
conventional or a DOE, in order to correct aberrations present in that optical
element.
Reference is now made to Fig. 5, which is a schematic illustration of
another preferred embodiment of the present invention, wherein repeated
samples
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of a DOE 40 are produced by means of passing a writing beam 42 produced by a
laser 33, through a master DOE 43, to provide the desired image of the desired
DOE in the focal plane 44. The master DOE 43 may be calculated and produced
according to any of the previous embodiments described hereinabove, or by any
other suitable method. In the focal plane, the laser beam is focused so as to
produce an assembly of scattering points by means of optical breakdown, such
that multiply repeated samples of the desired DOE is obtained. If the laser
beam
is sufficiently energetic, it can produce several scattering points
simultaneously
for each incident laser pulse, by differently diffracted beams of the writing
laser
beam. Although in Fig. 5, only one DOE sample is shown, according to another
preferred embodiment of the present invention, it is possible for the writing
beam
to be diffracted by the master DOE such that it cari engrave several DOE
samples
simultaneously, thereby increasing productivity of the system.
Reference is now made to Fig. 6, which is a schematic illustration of yet
another preferred embodiment of the present invention, whereby active feedback
is used to control the properties of a DOE during production in a transparent
material by means of optical breakdown. The DOE is dynamically inspected by
means of a second probe laser beam transmitted through the DOE and imaged by
it, and the laser engraving system adjusted in real time to obtain the desired
DOE
characteristics according to the resulting image obtained.
The DOE production system is similar to that shown in Fig. 1, and consists
of an engraving laser S0, whose beam is focused by means of an objective lens
onto the sample 54 in which the DOE is to be engraved. The sample 54 is
mounted on a motor driven CNC-controlled motion table 56. For simplicity, no
beam scanning system is shown, though it is understood that such a system
could
also be preferably used for directing the focused laser beam. A probe laser 60
provides a collimated beam 62 which is used as the probe beam for testing the
DOE under production 54. The probe laser beam is preferably directed onto the
optical axis of the DOE by means of a dichroic beam combiner 64. After being
focused by the DOE, the image is recorded by means of a CCD camera 66
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mounted on an inspection microscope 68. This CCD camera provides data in real
time to the control system 70, about the actual focusing performance of the
DOE
being produced. The image is compared with the known image expected from the
desired DOE performance, and the control system then adjusts the engraving
laser and motion system to correct the DOE characteristics to provide the
desired
DOE performance.
According to a further embodiment of the present invention, a set of
scattering centers can be produced for the purpose of amending the optical
properties of a material in a predetermined manner. The refraction coefficient
or
transparency are examples of the properties of the material that can be thus
amended.
It will be appreciated by persons skilled in the art that the present
invention is not limited by what has been particularly shown and described
hereinabove. Rather the scope of the present invention includes both
combinations and subcombinations of various features described hereinabove as
well as variations and modifications thereto which would occur to a person of
skill in the art upon reading the above description and which are not in the
prior
art.
