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Claims  |
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What is claimed is:
1. An optical processor apparatus comprising:
a light source for providing a coherent source beam,
a spatial light modulator for modulating the source beam with an input
information signal to produce a modulated beam, said modulated beam
diverging into spacially separated frequency components including a zero
frequency component from said source beam,
reference beam generator means for forming a reference beam from said zero
frequency component such that said reference beam appears to diverge from
a reference point,
an optical detector having an aperture positioned for receiving said
reference bean and particular ones of said spatially separated frequency
components whereby said particular ones of said spatially separated
frequency components are coherently detected to produce an output
information signal as a function of the input information signal.
2. The apparatus of claim 1 in which said reference beam generator means
includes,
a transform lens for transforming said frequency components, including said
zero frequency component, of said modulated beam, and
an optical mask positioned to diffract said zero frequency component to
form said reference beam.
3. The apparatus of claim 2 in which said optical mask is a holographic
mask.
4. The apparatus of claim 2 in which said optical mask is located between
said transform lens and said aperture at a position which optimizes the
energy in said reference beam.
5. The apparatus of claim 2 in which said source beam has a wavelength
.lambda..sub.L, in which said input information signal has a minimum
frequency f.sub.min, in which said spatial light modulator propagates
signals with a velocity v, and in which said optical mask is displaced
from said modulator a displacement distance to insure sufficient energy in
said reference beam.
6. The apparatus of claim 5 in which said displacement distance is greater
than the quantity v.sup.2 /(.lambda..sub.L f.sub.min.sup.2).
7. The apparatus of claim 2 in which said optical mask diffracts the zero
frequency component from said transform lens to form said reference beam
in a manner such that said reference beam diverges from said mask to cover
said aperture and has said reference point located at said spatial light
modulator.
8. The apparatus of claim 7 in which said spatial light modulator is
oriented to receive said source beam in a first direction through an
aperture opening between first and second aperture ends, said aperture
extending parallel to an axis of modulation substantially normal to said
first direction, said modulator functioning to spatially modulate said
source beam by propagating signals from the first end to the second end of
said aperture along the axis of modulation, and in which said reference
point is located along the axis of modulation between said first and
second ends and displaced from said first end by an offset distance
whereby the output information signal is delayed from the input
information signal an amount proportional to said offset distance.
9. The apparatus of claim 7 wherein said zero frequency component is
delimited by a converging cone of light converging at a point in a plane
extending through said aperture, wherein said reference beam is delimited
by a diverging cone originating from said reference point in said spatial
light modulator and diverging through said mask to fill said aperture, and
wherein said optical mask is located such that the ratio of the width of
said diverging cone to the width of said converging cone at said mask is
approximately a maximum.
10. The apparatus of claim 2 in which said transform lens has a focal
distance, said optical mask is located between said lens and said focal
distance and said optical detector is located approximately at said focal
distance.
11. The apparatus of claim 1 in which said input information signal has a
bandwidth defined by a minimum frequency f.sub.min and a maximum frequency
f.sub.max, in which said spatial light modulator propagates signals with a
velocity v, in which said reference beam generator means generates said
reference beam which appears to be delimited by a cone of diverging light
from said reference point such that the width of said cone at the plane of
said spatial light modulator does not exceed said velocity v divided by
said bandwidth.
12. An optical processor apparatus comprising:
a light source for providing a coherent source beam,
a spatial light modulator for modulating the source beam with an input
information signal to produce a modulated beam, said modulated beam
diverging into spacially separated frequency components including a zero
frequency component from said source beam,
a transform lens for transforming said frequency components, including said
zero frequency component, of said modulated beam, and
an optical mask positioned to diffract said zero frequency component from
said transform lens to form said reference beam,
an optical detector having an aperture positioned for receiving said
reference beam and particular ones of said spatially separated frequency
components whereby said particular ones of said spatially separated
frequency components are coherently detected to produce an output
information signal as a function of the input information signal.
13. The apparatus of claim 12 in which said optical mask is a holographic
mask.
14. The apparatus of claim 12 in which said optical mask is located between
said transform lens and said aperture at a position which optimizes the
energy in said reference beam.
15. The apparatus of claim 12 in which said source beam has a wavelength
.lambda..sub.L, in which said input information signal has a minimum
frequency f.sub.min, in which said spatial light modulator propagates
signals with a velocity v, and in which said optical mask is displaced
from said modulator a displacement distance to insure sufficient energy in
said reference beam.
16. The apparatus of claim 15 in which said displacement distance is
greater than the quantity v.sup.2 /(.lambda..sub.L f.sub.min.sup.2).
17. The apparatus of claim 12 in which said optical mask diffracts the zero
frequency component from said transform lens to form said reference beam
in a manner such that said reference beam diverges from said mask to cover
said aperture and has a reference point located at or near said spatial
light modulator.
18. The apparatus of claim 17 in which said reference point is a virtual
image point.
19. The apparatus of claim 17 in which said spatial light modulator is
oriented to receive said source beam in a first direction through an
aperture opening between first and second aperture ends, said aperture
extending parallel to an axis of modulation substantially normal to said
first direction, said modulator functioning to spatially modulate said
source beam by propagating signals from the first end to the second end of
said aperture along the axis of modulation, and in which said reference
point is located along the axis of modulation between said first and
second ends and displaced from said first end by an offset distance
whereby the output information signal is delayed from the input
information signal an amount proportional to said offset distance.
20. The apparatus of claim 17 wherein said zero frequency component is
delimited by a converging cone of light converging at a point in a plane
extending through said aperture, wherein said reference beam is delimited
by a diverging cone originating from said reference point in said spatial
light modulator and diverging through said mask to fill said aperture, and
wherein said optical mask is located such that the ratio of the width of
said diverging cone to the width of said converging cone at said mask is a
maximum.
21. The apparatus of claim 12 in which said transform lens has a focal
distance, said optical mask is located between said lens and said focal
distance and said optical detector is located approximately at said focal
distance.
22. The apparatus of claim 12 in which said input information signal has a
bandwidth defined by a minimum frequency f.sub.min and a maximum frequency
f.sub.max, in which said spatial light modulator propagates signals with a
velocity v, in which said reference beam is delimited by a cone of
diverging light from said reference point such that the width of said cone
at the plane of said spatial light modulator does not exceed said velocity
v divided by said bandwidth.
23. A method of optical processing comprising:
providing a coherent source beam,
modulating the source beam in a spatial light modulator with an input
information signal to produce a modulated beam, said modulated beam
diverging into spacially separated frequency components including a zero
frequency component from said source beam,
forming a reference beam from said zero frequency component such that said
reference beam appears to diverge from a reference point,
receiving said reference beam and particular ones of said spatially
separated frequency components in the aperture of an optical detector to
coherently detect said particular ones of said spatially separated
frequency components and produce an output information signal as a
function of the input information signal.
24. The method of claim 23 including the steps of
transforming said frequency components, including said zero frequency
component, of said modulated beam with a transform lens, and
diffracting said zero frequency component from said transform lens with an
optical mask to form said reference beam.
25. The method of claim 24 in which said diffracting step is performed in a
manner such that said reference beam diverges from said mask to cover said
aperture and has said reference point located at said spatial light
modulator.
26. The method of claim 25 in which said reference point is a virtual image
point. |
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Claims |
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Description |
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BACKGROUND OF THE INVENTION
This invention relates to the field of signal processing, and in
particular, to optical signal processing utilizing coherent detection.
Signal processing typically involves the modulation of a source signal by
an information signal to produce a modulated signal. The modulated signal,
after transmission and any appropriate processing, is demodulated to
recover the information signal, as modified by the processing.
Coherent detection, sometimes called synchronous detection, is a method of
detection in which the demodulation employs a reference signal, sometimes
called a local oscillator signal, that is in synchronisim with the source
signal.
In optical processors, the input information signals are typically
time-varying electrical signals which modulate optical source signals to
produce optical, modulated signal. The optical, modulated signals are
processed and then demodulated to produce electrical output information
signals. The modulation converts the electrical signals to optical signals
and the demodulation converts the optical signals back to electrical
signals. The conversion from electrical to optical signals is undertaken
because the desired signal processing can be performed better optically
than it can be electrically.
In laboratory environments, coherent-detection optical processors have been
known in the prior art. In such processors, coherent light from a laser
source is diverted into two paths by means of beam-splitters and mirrors.
One path passes the optical source beam through a modulator to modulate
the source beam with an appropriate input information signal. The other
path from the laser source is transmitted withot modulation to form a
coherent reference signal. The reference signal is added to the modulated
signal to enable coherent detection. Because the reference signal and the
modulated signal travel in different paths, careful alignment of the
beam-splitters, mirrors, and other optical elements is required in order
to achieve satisfactory coherent detection. Relative displacement between
the modulated signal and the reference signal by one-half of a wavelength
(for example, less than a micron) can cause complete phase reversals which
change the phase of the output information signal by 180 degrees. Because
ot the careful alignment and high stability required in prior art
coherent-detection optical processors, they have been generally regarded
as impractical except in laboratory environments.
Optical processors for real-life cross-correlation have recognized the
extreme alignment sensitivity of the modulated signal and the reference
signal beams. Vibration of the apparatus or inhomogeneities of the optical
mediums usually cause optical path differences which substantially
interfere with the desired processing. In order to overcome such problems,
collinear heterodyning has been proposed.
Collinear hetrodyning is described, for example, in the article "Collinear
Heterodyning and Optical Processors" by Herbert R. Carlton, William T.
Maloney and Gerald Meltz, Proceedings of the IEEE, Vol. 57, #5, May 1969,
pages 769-775. In that article, a real-time cross-correlator is described
in which the reference signal and the modulated signal are collinear and
hence are not subject to error-causing optical path differences and other
problems created by the use of separate optical paths.
Other optical processors have been known which employ collinear optical
processing. Such systems, however, have not provided a satisfactory method
of and apparatus for processing wide-bandwidth information signals to
provide wide-bandwidth output signals.
In light of the above background, there is a need for a wide-bandwidth,
high-resolution stable optical processor employing coherent detection.
BRIEF SUMMARY OF THE INVENTION
The present invention is a method of and an apparatus for coherently
detecting modulated optical signals employing optical mask-generated
signals.
A coherent light source generates a source beam which is incident on a
spatial light modulator. The spatial light modulator modulates the source
beam with an information signal. The information signal, typically a
wide-band radio frequency signal, is composed of one or more frequency
components within its frequency bandwidth. The modulated beam output from
the spatial light modulator includes corresponding frequency components
resulting from the modulation. The frequency components output from the
modulator diverge and become spatially separated. One of the frequency
components of the modulated beam is the zero frequency component (DC
component) which corresponds to the unmodulated source beam.
A reference beam is formed from the zero frequency component by a reference
beam generator. The reference beam is generated so as to appear to diverge
from a reference point located at or near the spatial light modulator.
An optical detector is located to receive the reference beam and particular
ones of the spatially separated frequency components corresponding to the
frequency components of the input signal.
The optical detector performs coherent detection by squaring the sum of the
frequency components and the reference beam to provide an output
information signal as a function of the input information signal.
In accordance with a preferred embodiment, the reference beam generator is
formed by a Fourier transform lens and an optical mask.
The Fourier transform lens transforms the modulated beam to spatially
separate the frequency components. At the transform lens focal plane, the
zero frequency component appears at one point and the other frequency
components appear at different points displaced from the zero frequency
point. The optical detector aperture is offset from the zero frequency
point to receive only those frequency components which correspond to the
frequency components of the input information signal. The detector is
typically located at or near the transform lens focal plane.
In order to enable coherent detection, an optical mask is provided for
diffracting the zero frequency component to provide a coherent reference
beam across the full detector aperture. The resultant signal at the
detector aperture is the sum of the coherent reference beam, produced by
the optical mask, and the spatially distributed frequency components
falling within the aperture. In general, the optical mask is located
anywhere between the light source and a position in front of the detector;
and hence, the optical mask can be placed on either side of the spatial
light modulator or on either side of the Fourier transform lens.
The optical mask utilized to produce the coherent reference signal is
produced by holographic, digital or any other suitable technique. In a
holographic method, a coherent light beam is split by a beam splitter into
two spatially separate paths. The beam in one path is analogous to the
modulated beam previously described but it is unmodulated as it passes
through the Fourier transform lens. The beam in the other path is focused
and recombined with the unmodulated beam to expose a photographic or other
plate located at the position that the optical mask is to be placed.
Exposure and development of the plate produces the desired optical mask.
In accordance with a preferred embodiment of the present invention, the
optical mask is located between a Fourier transform lens and the detector
aperture at a position which optimizes the coherent reference beam signal
strength. The location of the mask is determined by the geometrical
relationship between the zero frequency component and the optical
elements. The zero frequency component forms a cone of light from the
Fourier transform lens converging at a point at the Fourier transform
focal plane. A portion of the converging zero frequency component is
diffracted by the optical mask to form the reference beam. The reference
beam is a diverging cone which fills the detector aperture such that a
virtual image point appears to be a point located in a plane passing
through the spatial light modulator. For maximum efficiency, the optical
mask is located approximately at a point such that the ratio of the width
of the diverging reference cone as it passes through the optical mask and
the width of the converging zero frequency cone at the position of the
optical mask is a maximum.
With the coherent reference beam provided in the manner summarized above,
the objective of providing stable coherent detection for wide-bandwidth
optical processors of many types is achieved.
Additional objects and features of the present invention will appear from
the following description in which the preferred embodiments of the
invention have been set forth in detail in conjunction with the drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a block diagram depicting an optical processor, employing
coherent detection in accordance with the present invention positioned to
receive an input information signal S(t) and to produce an output
information signal I(t).
FIG. 2 is a block diagram of an optical processor in accordance with one
embodiment of the present invention.
FIG. 3 is a more detailed schematic diagram of the optical processor of
FIG. 2.
FIG. 4 is a schematic optical diagram further depicting optical ray traces
between optical elements of the FIG. 3 device.
FIG. 5 is a schematic representation of the optical configuration employed
for holographically generating an optical mask for use in the apparatus of
the present invention.
DETAILED DESCRIPTION
FIG. 1--General Environment
In FIG. 1, the signal source 10 provides an input information signal S(t)
on line 13 to the optical processor 11. The signal S(t) is typically a
radio frequency signal with wide bandwidth. A typical signal has a 200 MHz
center frequency with a 100 MHz bandwidth.
Optical processor 11 receives the S(t) signal and optically processes that
signal. The optical processing in one example delays the signal S(t).
Other types of processing include frequency filtering, excising (removing
unwanted frequency components), matched filtering, correlation, and
phaseshifting. In order to perform such other types of processing, optical
elements, in addition to those shown in FIGS. 2, 3 and 4, are generally
required. For example, a frequency plane modulator can be added when
frequency filtering or excising is desired.
After optical processing, the processor 11 forms the output information
signal I(t) on line 14 where I(t) is a function of the input information
signal S(t). The output device 12 receives the signal I(t) for further
processing and/or use.
The FIG. 1 apparatus is employed in many applications. In a typical
application, the signal S(t) is a frequency down-shifted radar signal in a
radar receiver where wide-bandwidth processing of the signal S(t) is
required. For example, unwanted frequency components can be removed from
the signal S(t) and/or the signal S(t) may be suitably delayed.
FIG. 2--Optical Processor Block Diagram
In FIG. 2, the optical processor 11 of FIG. 1 is shown in further detail.
Coherent light source (CLS) 15 is any source which produces spatially
coherent light. Typically, source 15 is a conventional gas or solid-state
laser together with appropriate lenses. A suitable gas (HeNe) laser
commercially available has a center frequency of 4.741 times 10.sup.14 Hz
and produces approximately five milliwatts of output power. Alternatively,
a conventional source directed through a pinhole filter can be employed
for source 15. While the source can have relatively high temporal
coherence (for example, a fractional bandwidth of 10.sup.-6), sources with
relatively low temporal coherence (for example, fractional bandwidths of
10.sup.-3 or greater) are acceptable.
The spatial light modulator (SLM) 16 receives the coherent source beam 22
from the coherent light source 15 and modulates the source beam with the
input information signal S(t). The spatial light modulator 16 is typically
a Bragg cell or other acousto-optical modulator. The modulated beam 23 is
received by the Fourier transform lens (FTL) 17 which functions to
transform beam 23 into beam 24 which has spatially separate frequency
components at the back focal plane 33 of lens 17. The beam 24 includes
frequency components corresponding to the frequency components in the
input information signal S(t) and also includes the zero frequency or
unmodulated frequency component derived directly from the source beam 22.
The optical mask 18 operates on the unmodulated zero frequency component
of the beam 24 to provide a coherent reference component to the beam 25.
The beam 25 is incident, through the aperture 20, on the photodetector
(PD) 19. The photodetector 19 coherently detects the modulated beam
employing the coherent reference beam added by the optical mask 18.
The photodetector (PD) 19 is a conventional detector. Vacuum tube
multipliers, avalanche photodiodes, PIN photodiodes and other conventional
wide-band photodetectors are suitable large-bandwidth devices. The
bandwidth of commercially available detectors can be as much as 2
gigahertz. Such detectors are squaring devices which respond to the
incident optical power appearing at the aperture 20. In the present
invention, the detector squares the vector sum of the incident optical
signals, specifically, the incident modulated beam and the incident
reference beam. The output signal I(t) on line 14 is a time-varying
electrical signal having a readily isolatable frequency component
proportional to the input signal S(t). Typically, the signal on line 14 is
passband or high-pass filtered to isolate the component proportional to
the signal S(t) from other unwanted components. Such filtering devices are
conventional and can form a part of output device 12 of FIG. 1.
FIG. 3--Optical Beams
In FIG. 3, further details of the optical processor in accordance with the
present invention are shown. In FIG. 3, the coherent light source (CLS) 15
includes a conventional highly coherent laser 27, a cylindrical lens 28
for diverging the light 28 to an appropriate size for the aperture of the
spatial light modulator 16. The lens 29 receives the beam from lens 28 and
forms the collimated source beam 22. Of course, other methods of
generating a collimated source beam can be employed. The source beam 22 is
incident on the spatial light modulator 16 in a direction substantially
parallel to the X axis and normal to the Y axis where the Y axis is normal
in the positive direction into the plane of the drawing.
The spatial light modulator 16 receives the input information signal S(t)
on line 13 which causes acoustical waves to be propagated through the
modulator in the direction of the negative Z axis. The acoustical waves
transmitted through the modulator 16 create, as a function of time and
position, points of varying index of refraction. The source beam 22 is
diffracted differently, therefore, as a function of time and of spatial
position along the Z axis. The acoustical wave is propagated as a function
of the frequency components in the input information signal S(t).
Therefore, the output beam 23 includes optical frequency components
directly resulting, by the modulation process, from the electrical
frequency components in the input information signal S(t). In order to
enhance the diffraction of beam 22, the spatial light modulator 16 is
normally rotated in a counter-clockwise direction by a small angle,
.phi..sub.i (not shown in FIG. 3).
The Fourier transform lens (FTL) 17 forms at the back focal plane 33 the
Fourier transformed image of the beam 23. The transformed image includes
the image from the zero frequency component cone 30 (delimited by
single-headed rays) which is incident at a central point of the back focal
plane 33. Additionally, the beam 24 includes one or more frequency
components each converging to a different point within aperture 20. The
converging cone 31 (delimited by the triple-headed rays) is shown as
typical and represents a single component frequency. The cone 31 is
representative of one frequency within the bandwidth of the signal S(t).
Each different frequency within the bandwidth of the signal S(t) will
produce a different cone, like cone 31, incident at a different position
in the direction of the Z axis and in the aperture 20 in FIG. 3.
In FIG. 3, the optical mask (OM) 18 is positioned at some displacement x
from lens 17 and some displacement g from the modulator 16 as measured
along the X axis. The mask 18 is positioned to receive at least a portion
of the zero frequency component represented by cone 30 (delimited by the
single-headed rays). Optical mask 18 diffracts the zero frequency
component to form a coherent reference beam (delimited by the
double-headed rays in FIG. 3) across the full opening of aperture 20. The
incident beam at the aperture 20 is, therefore, the sum of the coherent
reference beam from mask 18 and the modulated components (such as the cone
31 component) falling within the aperture 20.
Although the optical mask 18 is shown in FIG. 3 positioned in the positive
X axis direction relative to the spatial light modulator 16, the mask can
be located in general any place between source 15 and a position in front
of detector 19. Specifically, the mask 18 can be located before or after
modulator 16 and before or after lens 17. If mask 18 is located in a
positive X axis direction such that x is greater than some value x.sub.1
as hereinafter defined, then the reference beam will not appear over the
full detector aperture and therefore the bandwidth of the output signal on
line 14 will be restricted.
FIG. 3--Mathematical Model
In order to further explain the coherent detection operation of the present
invention, a mathematical model of FIG. 3 is described. This model assumes
a weak acousto-optic interaction for the spatial light modulator 16 so
that the diffracted light amplitude in modulated beam 23 is linearly
related to the input information signal amplitude S(t).
The acoustic wave in the modulator 16 is defined to be propagating in the
-Z axis direction and imposes a dielectric modulation .epsilon.
proportional to S(t+z/v) where t is time, z is the Z axis coordinate and v
is the velocity of the wave in the modulator 16 along the Z axis. Also,
the optical beam 22 incident on the modulator 16 is defined to propagate
in the XZ plane with a Y axis polarization, and all spatial variations in
the Y axis direction may be ignored. Finally, the incident optical beam 22
is defined to propagate through free space at an angle .phi..sub.i to an
axis normal to a plane through modulator 16 such that the diffracted
energy of the modulated optical beam is concentrated in the m=-1
diffraction order with a negative doppler shift. The desired angle,
.phi..sub.i, is obtained, for example, when modulator 16 is rotated in the
counter-clockwise direction by the angle .phi..sub.i as shown hereafter in
FIG. 4. With these defined conditions, the diffracted optical amplitude
E.sub.-1 in the m=-1 diffraction order for the beam 31 from modulator 16
has a free space representation which can be described in the X axis
plane, X=0, through the spatial light modulator 16 as follows:
E.sub.-1.sbsb.[X=0] =CW(z)S.sub.+
(t+z/v)e.sup.-j2(.pi./.lambda..sbsp.L.sup.) sin
.phi..sbsp.i.sup.z-j2.pi.f.sbsp.L.sup.t Eq.(1)
In Eq.(1), C is a complex constant, W(z) is the spatial apodization of the
window of acousto-optic modulator 16, and .lambda..sub.L is the free space
wavelength of source beam 22. The plus subscript for the signal S.sub.+
(t+z/v) is used to signify that the diffracted optical beam 23 has a
negative doppler shift. The analytic signal S.sub.+ (t+z/v) may be
expressed in terms of the Fourier transform, S(f.sub.a), of the input
signal as follows:
##EQU1##
To clearly see that Eq.(1) contains a negative doppler shift, Eq.(2) is
substituted into Eq.(1) to derive Eq.(3) as follows:
##EQU2##
The optical time frequencies in Eq.(3) are given by f.sub.L -f.sub.a where
f.sub.a >0 so that the dopper shift is negative.
The signal beam optical amplitude E.sub.-1 described by Eq.(3) is located a
distance d in front of lens 17 in FIG. 3. In the back focal plane 33
(Fourier transform plane) of the lens 17, the signal beam optical
amplitude E.sub.SF is described by the spatial Fourier transform of Eq.(3)
multiplied by a quadratic phase factor yielding:
##EQU3##
In Eq.(4), z' is the spatial Z axis coordinate in the Fourier transform
plane, .lambda. is the average optical wavelength and F is the lens 17
focal length. By inserting Eq.(1) into Eq.(4) and substituting the
following normalized and displaced Fourier transform variable:
.gamma.=z'/.lambda.F+sin .phi..sub.i /.lambda..sub.L, the signal beam
optical amplitude E.sub.SF in the Fourier transform plane is expressed as
follows,
E.sub.SF =CW(.gamma.).COPYRGT.[vS.sub.+ (.gamma.v)e.sup.j2.pi..gamma.vt
]e.sup.-j2.pi.f.sbsp.L.sup.t Eq.(5)
For Eq.(5), W(.gamma.) is the spatial Fourier transform at the window
apodization W(z) while the .COPYRGT. symbol denotes convolution over the
variable .gamma.. Since the variable .gamma. is proportional to spatial
distance in the lens focal plane, the convolution of Eq.(5) acts to spread
each doppler-shifted, spectral component vS.sub.+ (.gamma.v) exp
(j2.pi..gamma.vt) of the input signal S(t) over a spatial width in the
transform plane determined by W(.gamma.). The number of spatially
resolvable spots in the Fourier transform plane is thus limited by
W(.gamma.) and the number of spatially resolvable spots is, to a good
approximation, determined by the bandwidth product of the apodized spatial
light modulator 16.
The signal beam optical amplitude of Eq.(5) is coherently detected by
adding the optical reference beam, which is typically not doppler shifted,
produced by the mask 18 in FIG. 3. The optical reference beam amplitude
E.sub.RF in the Fourier transform plane 33 is in general a function of
spatial position and may also be expressed in terms of the normalized and
displaced Fourier transform plane variable .gamma. as follows:
E.sub.RF =e.sup.j(.pi./.lambda.F)(1-d/F)(z').spsp.2
R(.gamma.)e.sup.-j2.pi.f.sbsp.L.sup.t Eq.(6)
The optical intensity I(.gamma.,t) in the Fourier transform plane in the
proximity of the detector aperture 20 is expressed as follows:
I(.gamma.,t)=1/2.vertline.E.sub.SF +E.sub.RF .vertline..sup.2 Eq.(7)
The optical intensity distribution defined by Eq.(7) is collected by the
large-area photodetector 19 in FIG. 3. The photocurrent output information
signal I(t) from the photodetector 19 is given by:
##EQU4##
By combining Eqs. (5), (6), (7) and (8), the output information signal,
I(t), is the sum of the three terms in Eq.(9a) as follows:
I(t)=i.sub.R +i.sub.S (t)+i.sub.HET (t) Eq.(9a)
and where the terms in Eq.(9a) are as follows:
##EQU5##
The i.sub.R component of the photocurrent defined by Eq.(9b) represents the
total reference beam (delimited by double-headed rays in FIG. 3) optical
power collected by the photodetector. The reference beam power is
independent of time. The i.sub.S (t) component defined by Eq.(9c) of the
output signal I(t) represents the total diffracted signal beam optical
power collected by the photodetector. The i.sub.S (t) component of the
photocurrent is a low frequency term with the majority of its power near
DC and has an absolute maximum time frequency less than (f.sub.max
-f.sub.min) where f.sub.max and f.sub.min are the maximum and minimum
frequencies of the input information signal S(t). The i.sub.HET (t)
component defined by Eq.(9d) of the photocurrent is the desired linear
output of the detection process. From Eq.(9d) it appears that each
spectral component S.sub.+ (f) of the input signal S(t) contributes a time
frequency component exp (j2.pi.ft) to the output component signal
i.sub.HET (t) so that a linear filter operation exists. To more clearly
define the linear filter response, Eq.(9d) is rewritten as follows:
##EQU6##
where
H.sub.+ (f)=1/2C[W(-.gamma.).COPYRGT.[R*(.gamma.)]] Eq.(10b)
evaluated at .gamma.=f/v.
Eq.(10a) implies that the response for positive frequencies f>0 is defined
by H.sub.+ (f). From Eq.(10b), it appears that the response H.sub.+ (f) is
basically equal to R*(f/v) convolved with the inverted window transform
W(-f/v).
Eq.(10a) is not quite in the final form of a linear response due to the Re
operator (real part of) and the restriction to positive frequencies f>0.
To clearly express the linear response for positive and negative
frequencies, Eq.(10a) is rewritten using the fact that S(t) is real so
that S(f) is equal to S*(-f). Rewriting Eq.(10a) yields the following
Eq.(11):
##EQU7##
In Eq.(11), the linear frequency response of the optical system from the
input signal S(t) to the heterodyne component i.sub.HET (t) of the
photocurrent is defined by H(f). Furthermore, H(f) is equal to H*(-f) as
is required of real valued input and output signals.
Since the heterodyne component i.sub.HET (f) of the photocurrent is a
linear version of the input signal, the time frequencies f of i.sub.HET
(t) are bandlimited to the frequency range f.sub.min <f<f.sub.max. As
before, f.sub.max and f.sub.min are the maximum and minimum frequencies of
the input signal S(t). Thus if the input signal has less than an octave
bandwidth so that (f.sub.max -f.sub.min)<f.sub.min, then i.sub.HET (t) may
be electronically separated from i.sub.R and i.sub.S (t) by the use of a
highpass filter. Typically, a bandpass filter is used at the output
instead of a highpass filter since this minimizes the wideband shot noise
and rejects signal harmonics which can be present when multi-longitudinal
mode lasers are used as the optical source.
The linear response characteristics at the optical processor may be
understood by a close examination of H.sub.+ (f) from Eq.(10b). The
simplest situation occurs with a plane wave optical reference beam, that
is, with R(.gamma.) equal to 1. In this case, it is apparent from Eq.
(10b) that:
H.sub.+ (f)=1/2CW(0) for R(.gamma.)=1 Eq.(12)
In other words, the response H(f) is constant, independent of frequency, so
that the system acts like an electrical short circuit from the input to
output. In actual practice with R(.gamma.)=1 there is a constant time
delay from the input S(t) to the output i.sub.HET (t) caused by the
constant acoustic transit time from the acoustic transducer boundary to
the effective reference beam origin 35 shown at the X=0 plane in the
modulator 16.
For other types of processing, a mask or other optical element is typically
provided in front of the aperture 20. A blocking mask may be employed, for
example, to block one or more selected frequency components thereby
removing such components from the output signal.
Optical Mask Location--FIG. 4
In FIG. 4, an expanded view of the optical components between the spatial
light modulator 16 and the photodetector aperature 20 of the FIG. 3
apparatus is shown. In FIG. 4, the spatial light modulator (SLM) 16, the
Fourier transform lens (FTL) 17, the optical mask (OM) 18 and the detector
aperture 20 are the same as shown in FIG. 3.
The spatial light modulator 16 is rotated counter-clockwise to the position
shown by modulator 16 at an angle .phi..sub.i relative to the X and Z
axes. When thus rotated, the diffracted frequency components
(triple-headed rays) form an angle .theta. with the zero frequency
component (single-headed rays). The angle .theta. ranges between
.theta..sub.max and .theta..sub.min.
In FIG. 4, modulator 16 has a window or aperture 53 with a dimension w in
the Z axis direction extending between a first aperture end 51 and a
second aperture end 52. The axis of modulation of modulator 16 is in the
negative Z axis direction.
The mask 18 is located at some displacement x from the center of the
Fourier transform lens 17. In FIG. 4, the optical mask 18', shown in
broken line, represents the optimum location when the displacement x is
equal to x.sub.1 for the optical mask 18. In FIG. 4, the single-headed
rays for cone 30 represent the zero frequency beam. The double-headed rays
represent the the reference beam diffracted by the mask 18 and which falls
within the aperture 20. The triple-headed rays depict a typical cone 31 of
one modulated frequency component.
The following TABLE I defines various parameters in FIG. 4.
TABLE I
h(x)=the distance in the Z axis direction, at the X axis displacement x, to
the top most part of the optical mask utilized and the distance
corresponds to the lowest portion through which the zero frequency beam
must pass in order to deflect the reference beam onto the entire detector
aperture.
k(x)=the distance in the Z axis direction, at the X axis displacement x, to
the bottom most part of the optical mask utilized and the distance
corresponds to the highest portion through which the zero frequency beam
must pass in order to deflect the reference beam onto the entire detector
aperture.
m(x)=the distance in the Z axis direction, at the X axis displacement x, to
the bottom of the zero frequency beam.
j(x)=the distance in the Z axis direction, at the X axis displacement x, to
the top of the zero frequency beam.
a=the distance in the Z axis direction to the point where the lowest
frequency component signal falls within the detector aperture.
b=the distance in the Z axis direction to the point where the highest
frequency component signal falls within the detector aperture.
c=the distance in the Z axis direction to the virtual focal point 35 of the
reference beam.
d=the virtual focus distance of the reference beam.
e=the distance in the X axis direction between the optical light modulator
16 and the Fourier transform lens 17.
F=focal length of the Fourier transform lens 17.
g=the distance in the positive or negative X axis direction of optical mask
18 from the spatial light modulator 16.
u=the distance in the Z axis direction from the center point 36 of
modulator 16 to the virtual image point 35.
w=width in the Z axis direction of the aperture of the spacial light
modulator 16.
x=the distance in the X axis direction between the Fourier transform lens
17 and the optical mask 18.
In FIG. 4, the portion of the optical mask 18 which is utilized to deflect
the reference beam over the entire aperture is equal to the quantity
h(x)-k(x). Note that the extension of the double-headed rays from the
aperture 20 back to the virtual image point 35, in the X=0 plane,
determines what portion of the optical mask is utilized.
The quantity h(x)-k(x) is the "width" of the cone of the reference beam.
The width of the zero frequency cone 30, delimited by the single-headed
rays at the displacement x of the optical mask 18, is given by j(x)-m(x).
The ratio, Q, of the width of the utilized portion of the optical mask,
given by the quantity h(x)-k(x), and the width of the zero frequency cone
given by the quantity j(x)-m(x) is the controlling factor in the strength
of the reference beam as it appears in the aperture 20 at the Fourier
transform plane 33.
The ratio Q will be a maximum at a point where x is equal to x.sub.1 at
which h(x) is equal to j(x). The optical mask 18' is located at the point
where is x equal to x.sub.1 so that h(x.sub.1) is equal to j(x.sub.1).
Although the optical mask 18 can be placed at any location between the
spatial light modulator 16 and the plane at x=x.sub.1, the reference beam
will have the highest strength when x is equal to x.sub.1 if the input
source beam 22 has a uniform intensity in the Z axis direction. The
highest strength of the reference beam occurs at x equal to x.sub.1
because, at that location, the highest percentage of the zero frequency
beam passes through the utilized portion of the optical mask. The higher
the percentage of the zero frequency beam passing through the utilized
portion of the optical mask, the higher the reference beam strength at the
aperture 20. The high reference beam strength is desirable to maximize the
signal-to-noise ratio of the coherent detection process.
When the source beam 22 has a non-uniform intensity distribution in the Z
axis direction, for example a Gaussian distribution, then the maximum
intensity reference beam is obtained when the optical mask is located at a
value of x somewhat less than x.sub.1.
The following TABLE II lists typical parameters for the FIG. 4 device in
accordance with the present invention.
TABLE II
______________________________________
bandwidth = 100 M Hz
center frequency
= 200 M Hz
.phi..sub.i = 0.56 degrees
.theta..sub.max
= 1.39 degrees
.theta..sub.min
= 0.84 degrees
v = 6.5 .times. 10.sup.3 m/sec
.lambda. = 6.328 .times. 10 .sup.-7 m
a = 2.30 cm
b = 2.88 cm
c = 1.425 cm
d = 10 cm
e = 8 cm
F = 50 cm
g = 37.8 cm
u = 0.2 cm
x.sub.1 = 27.8 cm
h(x.sub.1) = 2.35 cm
j(x.sub.1) = 2.35 cm
k(x.sub.1) = 1.98 cm
m(x.sub.1) = 0.90 cm
______________________________________
The distance g in FIG. 4 can be measured along the positive or negative X
axis such that optical mask 18 is located on the right of (after) or left
of (before) spatial light modulator 16. For high frequency applications
(500 M Hz or more), mask 18 is typically placed before lens 17 or before
modulator 16. In any case, however, the absolute value of g should not be
too small since, if g is too small, the reference beam will not have
sufficient energy to permit reliable coherent detection when a point
source reference source is employed. In the limit, if g equals zero, the
reference beam will have zero energy. As a general guide, g should be
greater than the quantity given by the following expression,
g>v.sup.2 /(f.sub.min.sup.2 .lambda.)
where,
v=velocity of wave in modulator 16
f.sub.min =minimum frequency of input information signal
.lambda.=wavelength of source beam
Although the reference point 35 has been specified as a virtual image point
lying in the X=0 plane passing through the center of modulator 16,
reference point 35 can be displaced to a location 35' by a distance p
displaced in the minus X axis direction such that the virtual image cone
(delimited by double-headed broken-line rays) has some width p(z)
(measured in the Z axis direction) in the X=0 plane. In general, in order
not to introduce additional components into the output | | |
