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BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention relates to the field of optical devices, and more
specifically to the electrical detection and processing of coherent light.
2. Description of the Prior Art
The past decade and a half have seen the proposal of many approaches to the
detection of coherent light in the presence of incoherent light. Some of
these approaches have also rendered additional information about the
detected source. To perform detection and other analysis in the presence
of high levels of incoherent radiation, the detector must reject constant
and fluctuating contributions due to incoherent light. Detection based
upon both spatial and temporal coherence has been advocated.
Spatial coherence approaches have been suggested by J. Jannson, T. Jannson,
and E. Wolf: "Spatial Coherence Discrimination In Scattering," Optics
Letters, Vol. 13, No. 12, December 1988, pp. 1060-1062 and by U.S. Pat.
No. 4,874,223 to O'Meara. The effectiveness of such approaches in
detecting minute levels of coherent light obscured in incoherent light has
not been demonstrated and does not exploit the large processing gain
available to apparatus using time-integrating methods.
Many approaches have applied temporal modulation to the optical disturbance
which preferentially operates on the coherent contribution. The signature
of this modulation is then sought in detected optical intensity. Of these
approaches, several produce modulation signatures which vary substantially
with the incoming wavelength, so that searching of the signatures is
required, making detection of strongly obscured coherent light
impractical. Apparatus of this type is described by C. J. Duffy and D.
Hickman: "A Temporal Coherence-Based Optical Sensor," Sensors and
Actuators, Vol. 18, 1989, pp 17-31 and disclosed in U.S. Pat. Nos.
3,824,018 and 4,743,114 to Crane and U.S. Pat. No. 4,309,108 to Siebert.
The most promising methods for obtaining sensitivity while rejecting
incoherent light are those which apply a periodic modulation. These
produce intensity fluctuation components whose period is known precisely,
allowing nearly arbitrary gain against the random fluctuations due to
noise. Crane, in U.S. Pat. No. 4,735,507, discloses several such
arrangements which effect the modulation by undesirable mechanical means.
Crane's apparatus also permits determination of wavelength but in a manner
which does not offer gain against noise and will not function when the
coherent light is obscured by incoherent light.
Amodeo et al. in U.S. Pat. No. 4,595,292 and Krohn et al. in U.S. Pat. No.
4,600,307 have advocated the use of modulated Fabry-Perot etalons for
modulation. Thick etalons--the form required here--are difficult to
maintain in alignment. Amodeo et al. specifies the use of a liquid crystal
in the etalon, severely limiting the modulation speed and thereby
permitting only the monitoring of slow phenomena. Krohn et al. specifies
that the etalon be modulated by the presence of an ultrasonic sound wave.
Such a modulation restricts the optical aperture to less than the
wavelength of the ultrasonic wave--a very small and undesirable value for
practical systems. Neither Amodeo et al. nor Krohn et al. provides
wavelength information.
U.S. Pat. No. 4,217,036 to Chang discloses apparatus which achieves
modulation by periodic scanning of the pass band of an acoustooptic
filter. Chang's apparatus provides a detected signal whose coherent
component is impulsive, so that only a small fraction of the desired
signal component is in the low harmonics of the periodicity. This results
in great inefficiency and an attendant loss in processing gain. Moreover,
spurious harmonics of the drive frequency may be produced by variations in
the incoherent-light spectrum, even in the absence of coherent light.
Chang does not offer a wavelength measurement.
SUMMARY OF THE INVENTION
It is an object of my invention to provide a time-integrating, periodically
modulated apparatus to detect the presence of coherent light which
overcomes the limitations of the prior art.
It is a further object of my invention to provide a detector which rejects
incoherent light.
It is a still further object of my invention to provide a detector which is
simple, stable, and easily constructed.
It is another object of my invention to provide an apparatus which is
suitable for monitoring swiftly changing phenomena.
It is still another object of my invention to provide a detector which
estimates coherent light wavelength in the possible presence of incoherent
light.
An apparatus having these and other desirable features would include input
light to be studied, said light emanating from a light source; a
modulation signal source which produces a periodic electrical modulation
signal; a polarization interferometer, said interferometer comprising an
optical polarizer, an optical analyzer, and birefringent modulation means
positioned between said polarizer and said analyzer, said birefringent
modulation means possessing an optical propagation axis x and two mutually
orthogonal axes y and z orthogonal to x, said birefringent modulation
means having a first optical path length along axis x for light
propagating in the x direction with polarization parallel to the y axis
and a second optical path length along axis x for light propagating in the
x direction with polarization parallel to the z axis, said first path
length differing from said second path length by more than the coherence
length of incoherent light, said first path length differing from said
second path length by an amount which varies in accordance with said
modulation signal; collecting means positioned to receive said input light
and direct it through said interferometer; optical detection means which
produces an electrical detection signal; focusing means positioned to
receive light from said interferometer and direct it to said detection
means; and processing means which receives said detection signal, said
processing means detecting components of said detection signal which are
synchronous with said modulation signal.
BRIEF DESCRIPTION OF THE DRAWINGS
My invention may best be understood when reading the following
specification with reference to the drawings, in which:
FIG. 1 is a generalized block diagram of my invention;
FIG. 2 is a exploded view of the general polarization interferometer of
FIG. 1;
FIG. 3 illustrates an embodiment of the processor of FIG. 1;
FIG. 4 illustrates an embodiment of the birefringent modulator of FIG. 2
using a nonbirefringent electro-optic modulator;
FIG. 5 illustrates an embodiment of the birefringent modulator of FIG. 2
using two birefringent electro-optic modulators;
FIG. 6 illustrates an embodiment of the birefringent modulator of FIG. 2
using one birefringent electro-optic modulator;
FIG. 7 is an illustration of an electro-optic plate modulator found in the
prior art; and
FIG. 8 illustrates an embodiment of the birefringent modulator of FIG. 2
using the electro-optic plate modulator of FIG. 7.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
FIG. 1 illustrates my invention in its most general form. It consists of
collecting optics 10, a polarization interferometer 11, focusing optics
12, detector 13, processor 14, and modulation signal source 15. Together,
the collecting optics 10 and focusing optics 12 serve to image the field
of observation onto the detector 13 in such a way that the light of
interest 16 passes through the polarization interferometer 11 and onto
detector 13. Division of collecting and focusing optics into assemblies
before and after the interferometer is done to best accomplish this goal
for the specific application. It should be understood that for some
applications, the entire operation of collecting the light, directing it
through the interferometer, and imaging the light onto the detector may be
accomplished by either the collection optics or the focusing optics.
Hence, each of the collecting optics and the focusing optics may consist
of any combination of mirrors, lenses, and optical fibers or either may be
omitted.
The polarization interferometer 11 is driven by a modulation signal s(t),
supplied by modulation signal source 15 via a line 19. The signal s(t)
causes modulation of the interferometer's optical properties, as described
hereinbelow. The electrical output signal generated by the detector 13 is
provided via line 17 to processor 14, which recognizes the presence or
absence of the desired optical input.
The general polarization interferometer is illustrated in FIG. 2. The
purpose of the interferometer is to apply amplitude modulation to
temporally coherent light, while effecting no amplitude modulation on
incoherent light. It consists of polarizer 20, birefringent modulator 21,
and analyzer 22. The orientation and purpose of these devices is described
in detail below. Like much of the apparatus in the prior art, the
interferometer imposes a path length difference which exceeds the
coherence length of the incoherent light but not that of the coherent
light. Unlike most prior art approaches, however, my invention applies
modulation whose form is precisely known.
The interferometer 11 will be described as it operates on a single light
ray 24 passing through it, though in a practical application it will
operate on more complex and realistic optical disturbances in a similar
manner. It should also be understood that while my invention is described
herein in terms of light, it is capable of operating on radiation
throughout the electromagnetic spectrum and this disclosure should be
viewed in this more general context.
A light ray 24 entering the interferometer is incident on polarizer 20
which passes only the component having linear polarization in the
direction 45 degrees to both the y and z axes. See FIG. 2 for the
definition of these components. Let the incident light have temporal
stationary coherence function .GAMMA.(.tau.), where .tau. is time
difference. In this description, the spatial variation is suppressed, as
this analysis is carried out on a ray of light.
Light 25 leaving polarizer 20 may be resolved into its two components
having time-varying complex magnitudes A.sub.y (t) and A.sub.z (t), the
linear polarizations parallel to the y and z axes, respectively. These two
magnitudes are equal and their mutual coherence function is
A.sub.y (t)A.sub.z *(t+.tau.) =1/2.GAMMA.(.tau.),
where the asterisk indicates complex conjugation.
The two polarizations then pass through birefringent modulator 21.
Birefringent modulator 21 is aligned with its principal axes parallel with
the y and z axes so that each polarization passes through the modulator
unrotated and emerges in the same polarization. Light 26 leaving the
modulator has polarization components B.sub.y (t) and B.sub.z (t),
respectively. A modulation signal s(t) is presented to the modulator by
way of line 19. The modulator imposes a different effective path length
for each polarization. In particular,
##EQU1##
where s(t) is the modulation signal described above, c is the speed of
light, and the constants a.sub.y, a.sub.z, b.sub.y, and b.sub.z depend
upon the size and optical properties of the modulator. (Practical examples
of these constants are given below.) Thus, the mutual coherence function
of the two polarizations is
##EQU2##
Light leaving the birefringent modulator encounters analyzer 22 oriented 45
degrees to both the y and z axes. This analyzer produces linearly
polarized light whose amplitude is the sum of equal contributions from the
two impinging polarizations, reduced by a factor of .sqroot.2. Thus, the
light 27 leaving the analyzer has intensity
##EQU3##
Now let the modulator be described by the more convenient parameters
##EQU4##
The detector 13 responds in proportion to this intensity.
From the above discussion, one may see that an interferometer is formed by
polararizer 20 acting as a beam splitter, analyzer 22 acting as a beam
combiner, and birefringent modulator 21 providing two optical paths, one
for each polarization.
Let V denote the maximum absolute value of signal s(t). In order to reject
incoherent light of coherence length l, the values of a and b are chosen
so that
.vertline.a.vertline.-.vertline.b.vertline.V>l.
With this choice, the intensity for incoherent light is
I(t)=1/2.GAMMA.(0). (incoherent light)
Conversely, when light of much longer coherence length L is present, say of
wavelength .lambda., then
##EQU5##
provided that
.vertline.a.vertline.+.vertline.b.vertline.V<L.
In practice,
.vertline.a.vertline.>.vertline.b.vertline.V
so that the condition for obtaining the stated responses to incoherent and
coherent light is
L>.vertline.a.vertline.>l.
With this condition satisfied, coherent light may be recognized by the time
varying behavior of the intensity. Accordingly, processor 14 operating on
the detected signal received over line 17 is designed to look for the
time-varying behavior described above. Incoherent light, which does not
produce such time variation, is largely ignored.
Consider the case of coherent illumination with wavelength .lambda. and
sinusoidal modulation signal
s(t)=V cos (2.pi.ft).
Although it is understood that other forms of s(t) may be used in my
invention, a sinusoid is the prefered choice. In this case, the intensity
consists of terms oscillating at frequencies which are multiples of the
excitation frequency f. These terms are weighted by Bessel functions whose
arguments depend upon b and .lambda.:
##EQU6##
where the functions {J.sub.k } are the Bessel functions of the first kind.
In particular, the first four harmonics of the drive frequency have
magnitudes
##EQU7##
respectively.
The processor 14 is designed to measure h.sub.1 and h.sub.2 to detect the
presence of coherent radiation. In addition, h.sub.3 and h.sub.4 may be
measured to obtain an approximation of the wavelength of radiation.
A block diagram of one embodiment of processor 14 to be used with
sinusoidal modulation is illustrated in FIG. 3. The modulation signal
s(t), provided to polarization interferometer 11 over line 19, is also
provided to processor 14 via line 18. Processor 14 uses this signal as a
reference for detecting the modulation in the detected signal 17.
Harmonics of the reference s(t) are generated by a harmonic generator 31
for each term to be measured and these are used to downconvert the
detected signal to baseband. The nth harmonic of s(t) is a tone at
frequency nf. The detected signal arriving via line 17 is routed through a
plurality of bandpass filters 35-35 to provide a group of signals filtered
about the desired harmonics of s(t): the signal to be downconverted by the
nth harmonic of s(t) is a bandpass filtered about the frequency nf. This
rejects much of the noise which would otherwise overload the mixers 34-34.
Each harmonic of s(t) is routed over one of the lines 30-30 to one of the
mixers 34-34, where it is mixed with its corresponding filtered detected
signal on one of the lines 33-33. The phases of the tones on lines 30-30
are adjusted by generator 31 to insure they are appropriate to compensate
for phase changes throughout the rest of the electrical and optical
system.
The downconverted signals on lines 36-36 are filtered through low pass
filters 37-37 of cutoff frequency B. This cutoff frequency is small to
obtain good rejection of noise. The signal power exiting each low pass
filter, produced by squarers 38-38, is measured, producing on lines 39-39
an estimate, (H.sub.i).sup.2 of (h.sub.i) .sup.2, where i is 1, 2, 3, or
4, depending upon whether the first, second, third, or fourth harmonic of
the reference was used for downconversion, respectively.
The estimates (H.sub.1).sup.2 and (H.sub.2).sup.2 are weighted by
multipliers 40-40 and summed by summer 41 to produce on line 42 a
statistic,
##EQU8##
and where (.lambda.) is the detector responsivity, R is the detector load
resistance, and w.sub.1 and w.sub.2 are constants set to make F(.lambda.)
be as near to unity as possible over the wavelengths of interest. The
statistic S has a mean which increases with the coherent light power and
may be used to determine whether or not coherent light is present and to
provide a crude estimate of the light's power.
Denote the set of wavelengths of interest by .LAMBDA.. To overcome noise,
the product Vb is chosen so that J.sub.1 (Vb/.lambda.)and J.sub.2
(vb/.lambda.) have apreciable values for all .lambda..epsilon..LAMBDA.. In
practice, a is large number compared with the optical wavelengths, and the
sine and cosine in the function F cause the major contribution to
oscillate between h.sub.1 and h.sub.2 as the wavelength is varied. To see
how to pick w.sub.1 and w.sub.2, define the extrema
##EQU9##
for i=1, 2. To minimize the maximum possible multiplicative error, one
chooses
##EQU10##
Then the maximum possible multiplicative error (neglecting noise) is a
factor of
##EQU11##
As an example, let .LAMBDA. be the interval of 0.55 to 0.82 micron. Then a
choice of vb=2 microns results in Vb/.LAMBDA..epsilon.[2,3], with 0.33
<J.sub.1 (Vb/.lambda.) <0.58 and 0.35 <J.sub.2 (Vb/.lambda.)<0.49. With a
flat responsivity, the maximum error of measuring the light power is about
.+-.2.4 dB.
The values of (H.sub.3).sup.2 and (H.sub.4).sup.2 may be used to determine
the wavelength by comparing them to (H.sub.1).sup.2 and (H.sub.2).sup.2,
for in the absence of noise,
##EQU12##
Either of these ratios may be used to determine .lambda., provided that Vb
and .LAMBDA. are such that unique values are obtained. To avoid numerical
instability, one chooses the first or second ratio, depending upon whether
(H.sub.1).sup.2 or (H.sub.2).sup.2 is larger, respectively. The operation
of computing R.sub.1 and R.sub.2 and using these values to determine an
estimate 43 of .lambda. is carried out by wavelength estimator 44.
For the numerical example above, both R.sub.1 and R.sub.2 are monotonic in
.lambda., ensuring unique determination of .lambda. in .LAMBDA.. In fact,
over this range, R.sub.1 and R.sub.2 are nearly exponential in
Vb/.lambda., covering a range of about 12 dB for R.sub.1 and 9 dB for
R.sub.2.
Note that the value of b may vary somewhat with wavelength, causing small
modifications to the described behavior, and perhaps requiring some
modification to the interpretation of results.
The processing apparatus pictured in FIG. 3 need not be implemented in
analog hardware. Indeed, the squaring operation, performed on very low
bandwidth signals, would be realized in digital hardware much more easily.
Moreover, a system which attempts to obtain extreme sensitivity would
require large dynamic range in the mixers--a requirement met more
practically in the digital domain. In general, the preferred approach is
to implement at least a portion of the processing in digital hardware,
perhaps using software, and perhaps to the point of digitizing immediately
and implementing the entire processing operation digitally.
Now consider the details of the birefringent modulator 21. Several
embodiments of this portion of the apparatus shall be discussed here,
illustrated in FIGS. 4, 5, 6 and 8, in which the entire birefringent
modulator is shown.
According to the embodiment illustrated in FIG. 4, birefringent modulator
21 includes a fixed retarder 50 and an electro-optic modulator 51 arranged
along an axis such that a ray of light 25 will pass through them serially.
Electro-optic modulator 51 possesses no birefringence in the absence of an
applied voltage. Electro-optic modulator 51 and retarder 50 both have
their optic (z) axes perpendicular to the direction of optical
propagation.
Retarder 50 serves to introduce the constant path delay identified as
.alpha.in the above analysis. This delay arises from the difference
between the ordinary index n.sub.o experienced by light of the y
polarization and the extraordinary index n.sub.e experienced by light of z
polarization. After passing through the retarder of length s, the
difference in path lengths between the two polarizations is
a=s(n.sub.o -n.sub.e)
Electro-optic modulator 51 consists of a block of electro-optic material 53
fitted with parallel plates 54-54 perpendicular to the z axis. Wires 55-55
attached to the plates allow the modulation voltage to be applied. The
material 53 possess no quiescent birefringence, but when an electric field
is applied via the plates, a birefringence is induced which is
proportional to the field strength E. In particular, if the material is
cubic having symmetry 43 m, then the change in index in the z polarization
is
##EQU13##
where n is the quiescent index and r.sub.41 is the electro-optic
coefficient. Similarly, the change in the y-polarization index is
##EQU14##
Now, let H be the height (z extent) of the electro-optic material block and
L be the length (x extent). With the voltage s(t) applied to the
modulator, the path length difference imposed by the modulator is
##EQU15##
so that the quantity b used in the analysis above is given by the product
of a material constant and a geometric factor:
##EQU16##
As an example of this type of birefringent modulator, consider the use of
GaP as an electro-optic material 53 and quartz as the retarder 50. At
visible red wavelengths, GaP has the figure of merit r.sub.41 n.sup.3 =35
pm/V. Thus, to achieve the Vb of 2 microns suggested earlier, one would
require
##EQU17##
In quartz, n.sub.o =1.54 and n.sub.e =1.55 in the red. Thus, a=-0.01s, and
a 100 micron decorrelating distance could be achieved with a retarder of 1
cm thickness. (The indices do change with wavelength, an effect which
would not be significant here.)
The polarization interferometer described here is similar to some standard
electro-optic modulators, with the exception that a small path delay (but
much longer than optical wavelengths) has been deliberately introduced by
inclusion of retarder 50.
According to the embodiment illustrated in FIG. 5, birefringent modulator
21 includes a first electro-optic modulator 60 and a second electro-optic
modulator 61, arranged along an axis such that a ray of light 25 will pass
through them serially. Modulator 60 is constructed of a block of
electro-optic material 65 fitted with parallel plates 62-62 perpendicular
to the crystalline z axis of material 65. Modulator 61 is constructed of a
block of electro-optic material 66 fitted with parallel plates 64- 64
perpendicular to the crystalline z axis of material 66. The electro-optic
material in block 65 of this embodiment is the same as the material in
block 66. This material differs, however, from the material in block 53 of
modulator 51 of the previous embodiment. The difference is that block 65
and 66 of this embodiment each exhibit birefringence even in the absence
of applied field resulting from a voltage on lines 63-63.
Light passes serially through the two blocks perpendicular to their z axes.
The blocks 65 and 66 are oriented such that the two crystalline z axes are
perpendicular, so that the portion of light 25 polarized parallel to the
optic axis in the first block is polarized perpendicular to the optic axis
in the second block. The first block 65 is of length L.sub.1, while the
second block 66 is L.sub.2 long. In the absence of applied voltage, then,
the path difference experienced by light of the two polarizations passing
through the combination is
##EQU18##
The difference in length is chosen to effect the desired decorrelation
length.
The plates 62-62 of modulator 60 and plates 64-64 of modulator 61 are
connected in parallel by wires 63-63, but with opposing polarity. Wires
63-63 are used to apply the modulation signal. Combined with the
orthogonal orientation, this connection causes the induced index changes
to reinforce.
The structure illustrated in FIG. 5 is similar to electro-optic modulators
which have been constructed for temperature compensated modulation. The
difference here is that L.sub.1 is deliberately made different from
L.sub.2.
Consider the use of a material with 3m symmetry with field E applied along
the optic (z) axis as described. Then the y and z polarizations experience
the induced index changes
.DELTA.n.sub.y =-1/2r.sub.13 n.sub.0.sup.3 E
and
.DELTA.n.sub.z =-1/2r.sub.33 n.sub.e.sup.3 E,
where r.sub.33 and r.sub.13 are electro-optic coefficients. With a crystal
height of H, the difference in path length induced by the applied voltage
s(t) is
##EQU19##
As an example, consider LiNbO.sub.3 as the electro-optic material for
modulators 60 and 61. In the red, r.sub.33 n.sub.e.sup.2 -r.sub.13
n.sub.o.sup.2 =215 pm/V and n.sub.o -n.sub.e =0.086. Thus, to achieve Vb=2
microns, one must have
##EQU20##
In addition, to achieve a decorrelating distance of a=100 microns, one
would want
L.sub.1 -L.sub.2 =1.1 millimeters.
This value, of course, is not critical. It is only necessary that the
incoherent light be decorrelated, the coherent light of interest remain
correlated, and the imaging system be able to tolerate the differences in
path length.
It should be understood that while the use of two modulators 60 and 61 is
preferred, my invention will function with only one such modulator.
Indeed, though using one birefringent electro-optic modulator will result
in inferior performance, such an embodiment may be used to reduce
complexity and cost. The modified embodiment of the birefringent modulator
21 is pictured in FIG. 6, comprising only birefringent electro-optic
modulator 66. Modulator 66, like modulators 60 and 61, is comprised of a
block 67 of electro-optic material which is birefringent in the absence of
an electric field. Block 67 is fitted with plates 68-68 to apply a field
in the direction of the optic axis, via lines 69-69. The birefringent
modulator 21 so constructed behaves like the apparatus of FIG. 4, with the
quiescent birefringence equivalent to that introduced by retarder 50, and
the field-induced birefringence being equivalent to that introduced by
electro-optic modulator 51.
As a alternative to constructing my invention with electro-optic modulators
which use rectangular prisms with electrodes on the sides, my invention
may be constructed using electro-optic plate modulators, wherein the
optical path through the electro-optic material is small compared to the
lateral extent of the modulator. Such a device is pictured in FIG. 7. The
electro-optic plate modulator 70 is comprised of a thin plate 71 of
electro-optic material whose faces are fitted with electrodes 72-72. (In
the illustration, only one face is fitted with electrodes, through both
sides may, in general, have electrodes.) Wires 73-73 are provided to apply
a voltage to the electrodes. The electrodes are interdigitated so that an
electric field which is substantially parallel to the optic axis of the
material may be introduced by applying a voltage to wires 73-73.
Modulators similar to 70 of FIG. 7 may be used in place of modulator 51 of
FIG. 4, modulators 60 and 61 of FIG. 5, or modulator 66 of FIG. 6. In
particular, FIG. 8 illustrates an embodiment of the birefringent modulator
using electro-optic plate modulator 70 in place of electro-optic modulator
51 of FIG. 4. The plate modulator more easily accommodates a large angular
aperture.
It should also be understood that my invention may exploit the quadratic
electro-optic effect, rather than the above-described linear electro-optic
effect, in the electro-optic modulators. The quadratic electro-optic
effect produces optical pathlength variations which are proportional to
the square of the applied field. If quadratic electro-optic materials are
used in place of the linear electro-optic materials, then my invention
will behave in a similar fashion, but with the desired optical intensity
components being produced on higher harmonics. Thus, when using quadratic
electro-optic materials, detection of a coherent light source is
accomplished by examining the second and fourth harmonic of the modulation
signal. In particular, PLZT may be used as a quadratic electro-optic
material to achieve high efficiency with a small pathlength. PLZT is thus
well suited for use in a plate modulator, and the preferred embodiment of
my invention using PLZT as an electro-optic material uses the birefringent
modulator illustrated in FIG. 8.
As one of the primary objects of my invention is to detect coherent light
while ignoring the perturbations due to incoherent light, it is necessary
to consider the effects of noise arising from detector dark current,
Johnson noise, and shot noise.
The following model will be chosen for analysis: The detector is
characterized by a sensitive area A, a responsivity (. | | |
