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Description  |
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BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a method and apparatus for locating moving
or stationary objects and, more specifically, to a method and apparatus
for locating the distance of an object to a reference point and/or the
angle of an object to a reference point for objects within a large range
and with high accuracy through the use of reflected optical radiation
comprising a plurality of different wavelengths.
2. Description of the Related Art
Various laser interferometric techniques have been utilized to measure the
distance to an object. One of these techniques involves analyzing the
fringes of an interference pattern created by the intersection of light
waves transmitted to and reflected off an object. Although these fringe
analyzing techniques can be highly accurate, their absolute range is
limited to the ambiguity length of the system, i.e., the wavelength of
light. Therefore, the distance to an object cannot be determined beyond
the ambiguity length.
Fringe analysis, however, can be used to measure the distance to an object
beyond the ambiguity wavelength by continuously directing light waves onto
an object and counting the number of interference fringes produced by the
intersecting transmitted and reflected waves as the object moves. However,
only relative and not absolute distances can be measured with this
technique. In addition, if the light waves incident on the object are
interrupted, even the relative distance information is lost.
In lieu of these fringe counting techniques, multiwave techniques, wherein
the phase differences are measured between a plurality of transmitted and
respective reflected light waves of a different optical wavelength have
been utilized to calculate absolute distances within a large range and
with high accuracy. In one such method, a plurality of optical waves each
having a different wavelength are sequentially reflected off an object.
The phase differences between the transmitted waves and respective
reflected waves are then sequentially detected and analyzed. If the object
moves, however, even by an amount equal to a portion of an optical
wavelength, the method of sequential phase measurements will be invalid
and the measured distance will be in error. Therefore, only the distance
to an object which is stationary can be determined by this sequential
multiwave technique (see, Williams, C.C. and Wickramasinghe, H.K.,
"Optical Ranging by Wavelength Multiplexed Interferometry", Journal of
Applied Physics, Vol. 60, No. 6, pp. 1900-1903, Sept. 5, 1986; Beheim, G.,
"Fiber-optic Interferometry Using Frequency Modulated Laser Diodes",
Applied Optics, Vol. 25, No. 19, pp. 3469-3472, Oct. 1, 1986; and Kikuta,
H., Iwata, K., and Nagata, R., "Distance Measurement by the Wavelength
Shift of Laser Diode Light", Applied Optics, Vol. 25, No. 17, pp.
2976-2980, Sept. 1, 1986).
In another multiwave technique, two optical waves of distinct wavelengths
and polarized at 90.degree. to each other are directed onto an object. The
phase differences between the transmitted waves and the respective
reflected waves are then simultaneously detected. Before the phases can be
analyzed, however, two signals created by the intersecting waves must be
separated. Because, at most, only two polarizations can be separated at
any one time, this method is limited to the simultaneous measurement of
only two phases, i.e., the phase difference between the first transmitted
optical wave and the respective reflected wave, and the phase difference
between the second transmitted optical wave and the respective reflected
wave. In addition, this method is limited to locating objects which are
very smooth because when a light beam is reflected off a rough surface its
polarization changes. This unwanted change in polarization produces
crosstalk between signals thereby reducing the accuracy of the system.
Thus, the polarization technique is limited to slowly moving and very
smooth objects (see, den Boef, A.J., "Two-Wavelength Scanning Spot
Interferometry Using Single Frequency Diode Lasers", Applied Optics, Vol.
27, No. 2, pp. 306-311, Jan. 15, 1988).
In another multiwave technique, two optical waves of different wavelengths
are directed onto an object and their reflection is detected. The two
wavelengths are mechanically separated by a dispersion prism and their
phases are measured. In practice this method is limited to the
simultaneous detection of just a few wavelengths since only a few
wavelengths can be mechanically separated at any one time. Also, the
wavelengths of the optical waves cannot be changed or tuned without
modifying the optical hardware (see, A.F. Fercher, H.Z. Hu, and U. Vry
"Rough Surface Interferometry with a Two-Wavelength Heterodyne Speckle
Interferometer", Applied Optics, Vol. 24, No. 14).
SUMMARY OF THE INVENTION
Accordingly, it is an object of the present invention to provide a method
and apparatus for determining the location of a moving or stationary
object within a large range and with high accuracy.
Additional objects and advantages of the invention will be set fourth in
the description which follows, and in part will be obvious from the
description, or may be learned by practice of the invention. The objects
and advantages of the invention may be realized and obtained by means of
the instrumentalities and combinations particularly pointed out in the
appended claims.
To achieve the foregoing objectives, and remove the limitations of the
techniques in the prior art, a method is provided wherein any number of
distinct optical wavelength measurement beams and corresponding same
optical wavelength reference beams are used in an interferometric
configuration to measure an unknown distance absolutely. The limitations
of the prior art are removed by emitting, combining and measuring the
phases of multiple wavelengths simultaneously. Simultaneous measurements
of phase are provided by inducing a distinct frequency shift between each
reference beam and corresponding measurement beam, separating the signals
created by the combined reference and measurement beams corresponding to
each wavelength and measuring the relative phases of the separated
signals. Simultaneous, multiple phase measurements allow determination of
absolute location even while the object is moving due to the fact that a
long equivalent wavelength can be achieved by combining two distinct
wavelengths.
Any number of wavelengths may be simultaneously combined in the present
invention by techniques wherein the reference and corresponding
measurement beams of each wavelength are assigned a different frequency.
Various methods exist to create the distinct frequency shifts including
but not limited to, acoustooptic modulators, magnetic field splitting of
the emission lines of a gas laser, optical parametric amplifiers in
addition to mechanical means whereby small mirrors are piezoelectrically
vibrated to modify the path difference for each distinct wavelength at a
distinct frequency. Different wavelengths may be created by use of
separate laser sources and/or injection current tuning of such sources.
In a preferred embodiment, a method of measuring the distance between an
object and a reference point using first and third optical beams which
have the same first wavelength and are coherent with each other, and
second and fourth optical beams which have the same second wavelength and
are coherent with each other, the second wavelength being different from
the first wavelength, is provided comprising the steps of frequency
shifting one of the first and third beams using a first reference signal
having a first reference frequency, frequency shifting one of the second
and fourth beams using a second reference signal having a second reference
frequency different from the first reference frequency, directing the
first and second beams from the reference point onto a surface of the
object so that portions of the first and second beams are reflected from
the object, simultaneously combining the reflected first and second beams
with the third and fourth beams at a reference location a fixed optical
distance from the reference point to produce a combined optical signal,
simultaneously detecting from the combined optical signal a first
heterodyne signal having a first beat frequency equal to the first
reference frequency, and a second heterodyne signal having a second beat
frequency equal to the second reference frequency, measuring the phase
difference between the first heterodyne signal and the first reference
signal, and the phase difference between the second heterodyne signal and
the second reference signal, and employing the phase differences to
determine the distance between the object and the reference point.
Preferably, the method comprises the preliminary steps of splitting the
output of a first laser diode into the first and third optical beams and
splitting the output of a second laser diode into the second and fourth
optical beams.
Still further, the measurement method of the present invention is repeated
in three nonplanar axes to determine the position and orientation of the
object with respect to the reference point.
The measurement method of the present invention may also be used to measure
the angular bearing of the object with respect to a reference line.
BRIEF DESCRIPTION OF THE DRAWINGS
The accompanying drawings, which are incorporated in and constitute a part
of the specification, illustrate the presently preferred apparatus and
method of the invention and, together with the general description given
above and the detailed description of the preferred embodiment given
below, serve to explain the principles of the invention. Of the drawings:
FIG. 1 is a block diagram of a multiwave interferometer which incorporates
the teachings of the present invention;
FIG. 2 is an illustration of a position and orientation sensor which is
used according to the teachings of the present invention;
FIG. 3 illustrates the position and orientation sensor of FIG. 2 attached
to a robot arm;
FIG. 4 is a block diagram of a multiwave optical phased array target
tracking system incorporating the teachings of the present invention;
FIG. 5 is a block diagram of the transmitter electronics and optics of the
system of FIG. 4;
FIG. 6 is a block diagram of the electronics of a single receiving element
of the system of FIG. 4; and
FIG. 7 illustrates various reception patterns created by the system of FIG.
4.
DESCRIPTION OF THE PREFERRED EMBODIMENTS AND METHOD
Reference will now be made in detail to the presently preferred apparatus
and method incorporating the invention as illustrated in the accompanying
drawings, in which like reference characters designate like or
corresponding parts throughout the several drawings.
Embodiment 1
As shown in FIG. 1, there is provided a multiwave interferometer which
comprises laser sources 20 and 22, beam splitters 28 and 30, acoustooptic
modulators 32 and 36, reference oscillators 34 and 38, optical combiners
40 and 42, beam splitter 53, optical fibers 44 and 45, measurement head
48, measurement head lens 46, PIN diode 54, transimpedence amplifier 56,
power splitter 58, filter bank 60, analog electronics 62, and computer 64.
Laser sources 20 and 22 operate at different electronically variable
wavelengths each determined by computer 64 and comprise, for example,
laser diodes. The outputs of laser sources 20 and 22 are, thus, distinct
wavelength beams. The output of laser source 20 is directed to beam
splitter 28 where it is split into coherent measurement beam 1 and
reference beam 3. The output of laser source 22 is directed to beam
splitter 30 and split into coherent measurement beam 2 and reference beam
4.
Reference beam 3 is directed to acoustooptic modulator 32 driven by a first
reference signal generated by RF reference oscillator 34. Acoustooptic
modulator 32 shifts the frequency of reference beam 3 by an amount equal
to the frequency of the first reference signal generated by RF reference
oscillator 34. Because RF reference oscillator 34 operates in the RF band,
the amount by which the wavelength of reference beam 3 is shifted is
relatively small as compared to the wavelength of measurement beam 1.
Thus, reference beam 3 may be said to maintain the same wavelength as
measurement beam 1. Reference beam 3 is maintained coherent to measurement
beam 1. It should be noted that, in the alternative, measurement beam 1
instead of reference beam 3 can be directed to acoustooptic modulator 32
and frequency shifted.
Similarly, reference beam 4 is directed to acoustooptic modulator 36 driven
by a second reference signal generated by RF reference oscillator 38. The
frequency of RF reference oscillator 38 is different than (i.e., distinct
from) the frequency of RF reference oscillator 34. Acoustooptic modulator
36 shifts the frequency of reference beam 4 by an amount equal to the
second reference signal generated by RF reference oscillator 38. Because
RF reference oscillator 38, like RF reference oscillator 34, operates in
the RF band, the amount by which the wavelength of reference beam 4 is
shifted is relatively small as compared to the wavelength of measurement
beam 2. Thus, reference beam 4 may be said to maintain the same wavelength
as measurement beam 2. Reference beam 4 is maintained coherent to
measurement beam 2. It should also be noted that, in the alternative,
measurement beam 2 instead of reference beam 4 can be directed to
acoustooptic modulator 36 and frequency shifted.
As should be apparent to those skilled in the art, it is also possible to
induce the distinct frequency shifts between measurement beam 1 and
reference beam 3 and between measurement beam 2 and reference beam 4, for
example, by splitting the magnetic field of the emission lines of a gas
laser, or by using optical parametric amplifiers, optical rotators, or
piezoelectrically vibrated mirrors in place of acoustooptic modulators 28
and 30.
In addition, the wavelength of laser source 22 can be made variable by
tuning the injection current of the laser diode of source 22. This allows
the relationship between the wavelength or beams 1 and 3 and the
wavelength of beams 2 and 4 to be adjusted to accommodate the need for
balance between resolution and range.
Frequency-shifted reference beams 3 and 4 are directed to optical combiner
40 where they are coaxially combined, and then directed, via optical fiber
45, to beam splitter 53 located a fixed optical distance from measurement
head lens 46. Measurement beams 1 and 2 are directed to optical combiner
42 where they are coaxially combined and then directed, to beam splitter
53, through optical fiber 44 and out of measurement head lens 46 of
measurement head 48. Optical fiber 44 and measurement head lens 46 thus
direct coaxially-combined measurement beams 1 and 2 to a surface of object
50. Object 50 is at an unknown distance d from measurement head lens 46.
Optical combiners 40 and 42 comprise, for example, common glass beam
splitters or fiber optical beam splitters.
As thus described, laser sources 20 and 22, beam splitters 28 and 30,
acoustooptic modulators 32 and 36, optical combiners 40 and 42, and beam
splitter 53 are connected in one example of an interferometric
configuration.
The portions of coaxially-combined measurement beams 1 and 2 reflected from
object 50 are received by measurement head lens 46 redirected back through
optical fiber 44, and directed to beam splitter 53. Beam splitter 53
simultaneously combines the portions of coaxially-combined measurement
beams 1 and 2 reflected from object 50 with frequency-shifted reference
beams 3 and 4 to produce a combined optical signal. It should be noted
that the combined optical signal comprises the portions of measurement
beams 1 and 2 reflected from object 50 as well as frequency-shifted
reference beams 3 and 4 and, therefore, includes the frequency components
associated with each of them. The lengths of optical fibers 44 and 45 are
preferably selected such that measurement beams 1 and 2, and reference
beams 3 and 4 travel approximately the same total optical distance.
The combined optical signal is directed to photodetector 54 which
comprises, for example, a PIN diode. Photodetector 54 simultaneously
detects from the combined optical signal a plurality of heterodyne signals
having various beat frequencies created by the interference of the
portions of measurement beams 1 and 2 reflected from object 50 and
frequency-shifted reference beams 3 and 4. The frequency response of
photodetector 54, however, is such that only a first heterodyne signal
having a beat frequency equal to the difference between the frequencies of
the portion of measurement beam 1 reflected from object 50 and
frequency-shifted reference beam 3, and a second heterodyne signal having
a beat frequency equal to the difference between the frequencies of the
portion of measurement beam 2 reflected from object 50 and
frequency-shifted reference beam 4 are detected. All other heterodyne
signals produced by the interfering beams are outside the frequency range
of photodetector 54 and are therefore eliminated. It should be noted that
the frequency of the first heterodyne signal is equal to the frequency of
the first reference signal generated by RF reference oscillator 34 and
contains phase information corresponding to distance d. Similarly, the
frequency of the second heterodyne signal is equal to the frequency of the
second reference signal generated by RF oscillator 38 and also contains
phase information corresponding to distance d.
The first and second heterodyne signals simultaneously detected by
photodetector 54 are directed to transimpedence amplifier 56, power
splitter 58, filter bank 60, and analog electronics 62, in that order.
Transimpedence amplifier 56 amplifies both the first and second heterodyne
signals, and power splitter 58 and filter bank 60 electronically separate
the first and second heterodyne signals from each other. It should be
noted that a bank of mixers, each followed by a low pass filter, can also
be used to separate the first and second heterodyne signals.
Analog electronics 62 operates to measure the phase difference,
.PHI..sub.1, between the first heterodyne signal and the first reference
signal generated by RF reference oscillator 34, and the phase difference,
.PHI..sub.2, between the second heterodyne signal and the second reference
signal generated by RF reference oscillator 38, wherein:
##EQU1##
.lambda..sub.1 and .lambda..sub.2 being the wavelengths at which laser
sources 20 and 22 operate, respectively.
Phase differences .PHI..sub.1 and .PHI..sub.2 are between 0 and 2.sub..pi.
radians and repeat themselves whenever d changes by an amount equal to one
wavelength. In conventional interferometers, only one of .PHI..sub.1 or
.PHI..sub.2 is used to compute d which results in a nonambiguous range of
only one wavelength.
The two phase differences .PHI..sub.1 and .PHI..sub.2 measured by analog
electronics 62 are directed to computer 64. Computer 64 computes distance
d from the phase difference .DELTA..PHI. between the two phase differences
.PHI..sub.1 and .PHI..sub.2. Special analog electronics can also be
constructed to calculate the phase difference .DELTA..PHI. and thus
distance d as follows:
##EQU2##
Because .DELTA..PHI. repeats whenever d changes by .lambda..sub.eq (which
is long) rather than whenever d changes by .lambda. (which is short) as in
conventional interferometry, by using the multiwave technique of the
present invention, the nonambiguous range is extended to .lambda..sub.eq
which is long if .lambda..sub.1 and .lambda..sub.2 are close together,
allowing absolute distance measurements within the range of
.lambda..sub.eq.
In general, the multiwave technique of the present invention can be used
whether the two phase differences .PHI..sub.1 and .PHI..sub.2 in Eq. (1.0)
are measured sequentially or simultaneously. However, if the two phase
differences are measured sequentially, the object must remain stationary.
Otherwise, if the location of the object changes slightly between phase
measurements, even one half of a micron, the multiwave technique will be
invalid. To measure the location of a moving object, the two phase
differences .PHI..sub.1 and .PHI..sub.2 must be measured simultaneously.
The present invention allows simultaneous phase measurement by separating
the heterodyne signals before the phase differences are measured. Since
the wavelengths of the reference and measurement beams are assigned
different frequencies, any number of phase differences can be calculated
simultaneously.
The above method can be repeated a plurality of times, each time shifting
the wavelength of at least one of laser source 20 or 22 to sequentially
measure a plurality of phase measurement pairs. The plurality of phase
measurement pairs can then be processed by computer 64 to determine
distance d with even higher accuracy and greater range. Similarly, if
object 50 is moving at a high velocity, it may be necessary to measure a
plurality of phase measurement pairs simultaneously, in which case, as
shown in FIG. 1, an N number of laser sources 22N, beam splitters 30N,
acoustooptic modulators 36N, reference oscillators 38N, and filters 60N
may be provided, thereby increasing the number of measurement beams
reflected onto object 50 in order to accurately determine distance d.
In an example of the first embodiment, the phase difference between two
heterodyne signals and respective reference signals were calculated by
analog electronics 62 at a rate of 500 KHz which allowed distance d to be
accurately measured while object 50 was moving at a speed of 0.5
meters/second.
Embodiment 2
As shown in FIG. 2, there is provided a position and orientation sensor
which comprises object fixture 100, measurement heads 101a-f, optical
beams 102a-f, retroreflectors 104a-f, and base fixture 106.
As shown in FIG. 2, optical measurement heads 101a-f are grouped into three
pairs 101a-b, 101c-d, and 101e-f, each pair being located on one of three
distinct nonplanar surfaces of object fixture 100. Object fixture 100 can
comprise any of a number of materials such as plastic, metal, wood, etc.
Each of optical measurement heads 101a-f is substantially identical to
measurement head 48 of FIG. 1 except that it emits a parallel beam. Each
of optical measurement heads 101a-f emits a respective one of optical
beams 102a-f. Each of optical beams 102a-f is directed towards a
respective one of retroreflectors 104a-f. Retroreflectors 104a-f are
grouped into three pairs 104a-b, 104c-d, and 104e-f, each pair being
located on one of three distinct nonplanar surfaces of base fixture 106,
and comprise, for example, mirrors or other optically reflective
materials. Base fixture 106 can comprise any number of materials suitable
for holding retroreflectors 104a-f such as plastic, metal, wood, etc.
The distance from each of optical measurement heads 101a-f to the
respective one of retroreflectors 104a-f is measured using the multiwave
measurement technique of the first embodiment. The six distance
measurements are then used in any known geometric algorithm to determine
the position and orientation of object fixture 100 with respect to base
fixture 106.
As shown in FIG. 3, the position and orientation sensor of FIG. 2 can be
easily be adapted for use with robot arm 108 to accurately determine the
position of robot arm 108 with respect to surrounding retroreflector
arrays 110a-c even in the presence of high frequency vibrations caused by
nearby machinery.
Because base fixture 106 is a passive device, the position and orientation
sensor of FIG. 2 has a number of unique features. First, base fixture 106
can be placed in harsh environments without the need for special
electrical shielding. Second, base fixture 106 is relatively inexpensive
so that a number of base fixtures can be position around an object whose
position and orientation are to be measure without significantly
increasing the cost of the system. Third, base fixture 106 can be placed
throughout a factory environment without requiring electrical cabling. In
addition, because the position and orientation sensor of FIG. 2 utilizes a
noncontact measurement method, the chances of damaging the object to be
measured are reduced. Finally, the measurement range of the position and
orientation sensor of FIG. 2 can be easily expanded by increasing the size
of base fixture 106. This can easily be done by forming base fixture 106
from large retroflective arrays as shown in FIG. 3.
Embodiment 3
As shown in FIG. 4, there is provided a multiwave optical phased array
target tracking system comprising laser sources 200 and 202, transmitter
204, transmitting lens 224, receiving lens array 230, processing element
array 232, phase shifter arrays 246A and 248A, power combiner 262, squarer
circuitry 264, phase shift control unit 266 and computer 270.
Laser sources 200 and 202 operate at variable wavelengths .lambda..sub.1
and .lambda..sub.2, respectively, and comprise, for example, tunable
lasers. The output beams from laser sources 200 and 202 are directed to
transmitter 204. As shown in FIG. 5, transmitter 204 includes beam
splitters 206 and 208, acoustooptic modulators 210 and 214, RF reference
oscillators 212 and 216, RF power splitters 211 and 213, and optical
combiners 218 and 220. The output of laser source 200 is directed to beam
splitter 206 where it is split into coherent beams 1 and 3 and the output
of laser source 202 is directed to beam splitter 208 where it is split
into coherent beams 2 and 4.
Beam 3 is directed to acoustooptic modulator 210 driven by a first
reference signal generated by RF reference oscillator 212. The first
reference signal is directed to acoustooptic modulator 210 via power
splitter 211. Acoustooptic modulator 210 shifts the frequency of beam 3 by
an amount equal to the frequency of the first reference signal generated
by RF reference oscillator 212. Because RF reference oscillator 212
operates in the RF band, the amount by which the frequency of beam 3 is
shifted is relatively small as compared to the frequency of beam 3. It
should be noted that, in the alternative, beam 1 instead of beam 3 can be
directed to acoustooptic modulator 210 and frequency shifted.
Similarly, beam 4 is directed to acoustooptic modulator 214 driven by a
second reference signal generated by RF reference oscillator 216. The
second reference signal is directed to acoustooptic modulator 214 via
power splitter 213. Acoustooptic modulator 214 shifts the frequency of
beam 4 by an amount equal to the frequency of the second reference signal
generated by RF reference oscillator 216. Because RF reference oscillator
216, like RF reference oscillator 212, operates in the RF band, the amount
by which the frequency of beam 4 is shifted is relatively small as
compared to the frequency of beam 4. It should also be noted that, in the
alternative, beam 2 instead of beam 4 can be directed to acoustooptic
modulator 214 and frequency shifted.
Frequency-shifted beams 3 and 4 are directed to optical combiner 218 where
they are coaxially combined, and then directed, along with the first and
second reference signals generated by RF reference oscillators 212 and
216, respectively, to receiving element array 232 shown in FIG. 4. Beams 1
and 2 are directed to optical combiner 220 where they are coaxially
combined, and then directed to transmitting lens 224 also shown in FIG. 4.
Optical combiners 218 and 220 comprise, for example, common glass beam
splitters. Transmitting lens 224 transforms coaxially-combined beams 1 and
2 into expanding optical wave 222 and operates to direct
coaxially-combined beams 1 and 2 onto a surface of object 226. Object 226
comprises, for example, a spacecraft approaching a space station, or a
robot in a workcell. Transmitting lens 224 comprises, for example, a
concave lens.
A portion of expanding optical wave 222 is reflected from object 226 as
reflected optical wave 228 and is detected by receiving lens array 230.
Receiving lens array 230 detects reflected optical wave 228 and comprises
N receiving lenses each separated by distance a. It should be noted that
the receiving array could consist of an array of photodetractors.
Reflected optical wave 228 is incident to the line defined by receiving
lens array 230 at an unknown angle .theta. whereby the nth receiving lens
of receiving lens array 230 detects signals s.sub.1 and s.sub.2 due to
.lambda..sub.1 and .lambda..sub.2 given by:
s.sub.1 =S.sub.1 sin((.omega..sub.1 t+2.pi.na/.lambda..sub.1)sin.theta.)
(3.0a)
S.sub.2 =S.sub.2 sin((.omega..sub.2 t+2.pi.na/.lambda..sub.2)sin.theta.)
(3.0b)
where S.sub.1 and S.sub.2 are the amplitudes of s.sub.1 and s.sub.2 and
s.sub.1 and s.sub.2 are the signals comprising the portion of expanding
optical wave 222 reflected from object 226 as reflected optical wave 228
that are detected by each receiving lens of receiving lens array 230,
.omega..sub.1 and .omega..sub. 2 are the angular frequencies of the output
beams generated by laser sources 200 and 202, respectively, .lambda..sub.1
and .lambda..sub.2 are the wavelengths at which laser sources 200 and 202
operate, respectively, and n designates the nth receiving lens of
receiving lens array 230. The phases of signals s.sub.1 and s.sub.2
generated by the nth receiving lens of receiving lens array 230 are
measured with respect to the phases of signals s.sub.1 and s.sub.2
detected by the first receiving lens of receiving lens array 230. There is
also a phase shift corresponding to the distance from receiving lens array
230 to object 266 in the arguments of Eqs. (3.0a) and (3.0b). However,
this phase shift for the processed signal at the output of analog squarer
and divider circuit 258 is substantially constant for each of the
receiving lenses because the distance from receiving lens array 230 to
object 226 is very long with respect to distance a and, therefore, can be
eliminated by signal processing. It should be noted that reflected optical
wave 228 comprises beams 1 and 2 outputted from transmitter 204 and
converted to expanding optical wave 222 by transmitting lens 224, and,
therefore, includes the frequency components associated with each of them.
The output of each receiving lens of receiving lens array 230 is directed
to a corresponding processing element of processing element array 232. As
shown in FIG. 6, each processing element of processing element array 232
comprises beam splitter 234, photodetector 236, amplifier 238, power
splitter 240, filter bank 242, quadrature power splitter circuits 244,
power splitters 246 and 248, phase detection circuits 250, analog phase
shifters 246A and 248A multiplier circuits 252, summer circuit 254,
difference circuit 256, and analog squarer and divider circuit 258.
Operation of a single processing element of processing element array 232
will now be described. As shown in FIG. 6, the output of a receiving lens
of receiving lens array 230 is directed to beam splitter 234. Beam
splitter 234 combines the portion of reflected optical wave 228 detected
by the receiving lens with frequency-shifted beams 3 and 4 to produce a
combined optical signal. It should be noted that the combined optical
signal comprises the portions of beams 1 and 2 reflected from object 226
and detected by the receiving lens as well as frequency-shifted beams 3
and 4 and, therefore, includes the frequency components associated with
each of them.
The combined optical signal is directed to photodetector 236 which
comprises, for example, a photodiode. Photodetector 236 simultaneously
detects from the combined optical signal a plurality of heterodyne signals
having various beat frequencies created by the interference of the
portions of beams 1 and 2 reflected from object 226 and frequency-shifted
beams 3 and 4. The frequency response of photodetector 236, however, is
such that only a first heterodyne signal having a first beat frequency
equal to the difference between the frequencies of reflected beam 1 and
frequency-shifted beam 3, and a second heterodyne signal having a beat
frequency equal to the difference between the frequencies of reflected
beam 2 and frequency-shifted beam 4 are detected. All other heterodyne
signals produced by the interfering beams are outside the frequency range
of photodetector 236 and are therefore eliminated. It should be noted that
the frequency of the first heterodyne signal is equal to the frequency of
the first reference signal generated by RF reference oscillator 212, and
that the frequency of the second heterodyne signal is equal to the
frequency of the second reference signal generated by RF reference
oscillator 216.
The first and second heterodyne signals simultaneously detected by
photodetector 236 are directed to transimpedence amplifier 238, power
splitter 240, and filter bank 242 in that order. Transimpedence amplifier
238 amplifies both the first and second heterodyne signals, and power
splitter 240 and filter bank 242 electronically separate the first
heterodyne signal from the second heterodyne signal. Each of the first and
second heterodyne signals is directed to quadrature power splitter circuit
244 where it is separated into 0.degree. and 90.degree. quadrature
components.
Each quadrature component of the first and second heterodyne signals, in
addition to the first and second reference signals generated by RF
reference oscillators 212 and 216, respectively, are directed to phase
detection circuits 250. As shown in FIG. 6, the first and second reference
signals generated by RF reference oscillators 212 and 216 are directed to
phase detection circuits 250 via phase shifters 246A and 248A and power
splitter 246 and 248, respectively. Phase detection circuits 250 detect
the phase differences between each of the quadrature components of the
first heterodyne signal and the first reference signal generated by RF
reference oscillator 212, and the phase differences between each of the
quadrature components of the second heterodyne signal and the second
reference signal generated by RF reference oscillator 216. The signals
detected by phase detection circuits 250 are in-phase signals g.sub.1 and
g.sub.2 and quadrature signals f.sub.1 and f.sub.2 given by:
f.sub.1 =Asin((2.pi.an/.lambda..sub.1)sin.theta.) (3.1a)
f.sub.2 =Asin((2.pi.an/.lambda..sub.2)sin.theta.) (3.1b)
g.sub.1 =Acos((2.pi.an/.lambda..sub.1)sin.theta.) (3.2a)
g.sub.2 =Acos((2.pi.an/.lambda..sub.2)sin.theta.) (3.2b)
wherein A is the amplitude of signals f.sub.1, f.sub.2, g.sub.1 and
g.sub.2, and depends on the amplitude of the first and second heterodyne
signals.
In-phase signals g.sub.1 and g.sub.2 and quadrature signals f.sub.1 and
f.sub.2 are directed to analog multiplier circuits 252, summer and
difference circuits 254 and 256, and analog squarer and divider circuit
258 in that order. Analog multiplier circuit 252, summer and difference
circuits 254 and 256, and analog squarer and divider circuit 258 combine
the phase differences detected by phase detection circuit 250 in an
ordered way to produce a receiving element output.
Analog multiplier circuit 252 comprises four analog multipliers while
summer and difference circuits 254 and 256 comprise, for example,
operational amplifiers and appropriate input resistors. The signals
x.sub.1 and x.sub.2 generated by analog multiplier circuit 252 and summer
and difference circuits 254 and 256, and corresponding to equivalent
wavelength .lambda..sub.eq are given by:
x.sub.1 =f.sub.1 g.sub.2 -f.sub.2 g.sub.1 =A.sup.2
sin((2.pi.an/.lambda..sub.eq)sin.theta.) | | |
