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Claims  |
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What is claimed is:
1. A laser transmitter which produces an output by phase matching all
outputs of an array of independent laser telescopes including a first
primary telescope which has a first singular laser source which emits a
first laser beam, and a plurality of second primary telescopes each placed
in a position adjacent to said first primary telescope, each of said
second primary telescopes having their own independent and singular laser
source emitting their own independent second laser beams thereby creating
a plurality of second laser beams, said laser transmitter comprising:
a plurality of collecting telescopes facing and bridging said first and
second primary telescopes, each of said plurality of collecting telescopes
intercepting and diverting a sample of said first laser beam from said
first primary telescope and a sample of said second laser beams from one
of said plurality of second primary telescopes by partially blocking the
first and second laser beams, said plurality of collecting telescopes
reflecting all intercepted beams back in sets of focus points, each of
said focus points being a focused pair of said sample from said first
primary telescope and a sample of said second laser beam which is obtained
from the first and second primary telescopes which are bridged by that
particular collecting telescope;
a detector array means receiving said sets of focus points from said
plurality of said collecting telescopes and generating therefrom a set of
interference patterns between each second laser beam from said plurality
of second primary telescopes and the first laser beam from said first
primary telescope;
an analog-to-digital converter receiving and converting into a set of
digital signals said set of interference patterns from said detector array
means;
a data processor means receiving said set of digital signals from said
analog-to-digital converter and estimating an optical path length
adjustment amount between each of said second laser beams and said first
laser beam, said optical path adjustment amount being a measure of
distance between the optical path lengths of said first laser beam and an
associated second laser beam such that the application of said optical
path length adjustment amount to the optical path of the second laser beam
results in a matching of the phase of said second laser beam to said first
laser beam; and
a correcting means receiving said optical path length adjustment amount
from said data processor and receiving said first and second laser beams
from said first and second primary telescopes, said correcting means
performing an adjustment of the optical path length of each of said second
laser beams to match their phases with said first laser beam.
2. A laser transmitter as defined in claim 1, including:
a conducting means receiving and conducting said sets of focus points from
said plurality of collecting telescopes; and
a focusing means receiving and focusing said sets of focus points from said
conducting means onto said detector array means.
3. A laser transmitter as defined in claim 2 wherein said detector array
means comprises a charge coupled device camera which outputs an
interference pattern for each pair of focused beams input into it, said
charge coupled device camera receiving said sets of focus points from said
focusing means and generating therefrom said set of interference patterns
between each said second laser beam and said first laser beam.
4. A laser transmitter as defined in claim 3, wherein said correcting means
comprises:
a plurality of first and second correcting mirrors having an adjustable
optical path length between them, each of said first correcting mirrors
receiving and relaying to one of said second correcting mirrors one of
said second laser beams from said plurality of second primary telescopes,
each of said second correcting mirrors receiving and reflecting out of
said laser transmitter one of said second laser beams; and
an adjustment servomechanism receiving said optical path length adjustment
amount from said data processor means and adjusting the optical path
lengths between each of said first and second correcting mirrors so that
the phase of each of said second laser beams is matched to the phase of
said first laser beam from said first primary telescope.
5. A laser transmitter as defined in claim 4, wherein said conducting means
comprises:
a plurality of first and second fold mirrors with each first fold mirror
receiving and relaying one of the laser beams from said first and second
primary telescopes;
said second fold mirror receiving and relaying the laser beams from said
first fold mirror to said focusing means.
6. A laser transmitter as defined in claim 5, wherein said focusing means
comprises a plurality of lenses, with each lens receiving and focusing
said samples of said first and second laser beams on the surface of said
charge coupled device camera in a form of containing a left sample beam
having a radius of value b, and a right sample beam having a radius of
value b, and being separated from said left sample beam by a distance of 2
a, said left and right sample beams being placed in a plane having x and y
coordinates, said left sample beam having its center placed on an x axis
at a point where the value of x equals -a and the value of y equals zero,
said right sample beam having its center placed on said x axis at a point
where the value of x equals a, and the value of y equals zero.
7. A laser transmitter as defined in claim 6, wherein each of said sets of
interference patterns produced by said charged coupled device comprises:
a irradiance pattern given by the formula:
I.sub.n (r)=(2A.sub.n b/r).sup.2 J.sup.2.sub.1 (K.sub.n
rb/F).multidot.[1+cos(K.sub.n (d+2ax/F))];
where:
I.sub.n (r) is the measure of irradiance;
A.sub.n is the amplitude of incident light at wavelength .lambda.n;
b is the value for the radius of the left and right samples;
r is a measure of position on said x and y plane at position (x,y) as a
value of radial coordinate;
.lambda. is the wavelength of incident light;
K.sub.n equals 2.pi./.lambda..sub.n ;
F is the focal length of the collecting optics of said collecting
telescopes;
d is the difference in optical path length of two beams being compared;
n.sub.p is an integer which represents a detector number within said
detector array, which contains n detectors;
n.sub.F is an integer which represents a number of detectors per fringe,
between consecutive nulls in said interference pattern; and
a is one half of the value of distance of separation between the two beams
being compared.
8. A laser transmitter as defined in claim 7, wherein said data processor
means includes:
a computer which receives each of said sets of said interference patterns
in the form of a measurement of said irradiance pattern which has been
converted into a digital form by said analog to digital converter, said
computer producing each of said optical path length adjustment amounts
using the formula:
##EQU9##
where: OPD equals the optical path length adjustment amount between two
beams which are being compared, and OPD equals an amount of .lambda.,
where .lambda. equals a power weighted average of the wavelengths of said
two beams which are being compared;
wherein said computer determined said R and L values using an algorithm,
said algorithm comprising:
R=I(n.sub.p +n.sub.F);
and
L=I(n.sub.p -n.sub.F)
where: I(.sub.n) denotes an output of an n.sup.th detector in said
detector array means.
9. A laser transmitter as defined in claim 7, wherein said data processor
means includes:
a computer which receives each of said sets of said interference patterns
in the form of a measurement of said irradiance pattern which has been
converted into a digital form by said analog to digital converter, said
computer producing each of said optical path length adjustment amounts
using the formula:
##EQU10##
where OPD equals the optical path length adjustment amount between two
beams which are being compared, and OPD is defined in terms of an amount
of .lambda., where .lambda. equals a power weighted average of the
wavelengths of said two beams which are being compared; and
wherein said computer is capable of determing said R and L values using an
algorithm, said algorithm comprising:
##EQU11##
where I(.sub.n) denotes an output of an nth detector in said detector
array means, said algorithm using all the energy in subsidiary peaks of
said interference pattern which are to the left and right of a main peak.
10. A laser transmitter as defined in claim 7, wherein said data processor
means includes:
a computer which receives each of said sets of said interference patterns
in the form of a measurement of said irradiance pattern which has been
converted into a digital form by said analog to digital converter, said
computer producing each of said optical path length adjustment amounts
using the formula:
##EQU12##
where OPD equals the optical path length adjustment amount between two
beams which are being compared, and OPD is defined in terms of an amount
of .lambda., where .lambda. equals a power weighted average of the
wavelengths of said two beams which are being compared; and
wherein said computer is capable of determining said R and L values using
an algorithm, said algorithm comprising:
R=I(n.sub.p +n.sub.F)+I(n.sub.p +2n.sub.F)
L=I(n.sub.p +n.sub.F)+I(n.sub.p +2n.sub.F);
where I(.sub.n) denotes an output of an n.sup.th detector in said detector
array means, said algorithm using all peak values of irradiance in the
first two subsidiary sidelobes on either side of a central peak.
11. A laser transmitter as defined in claim 7, wherein said data processor
means includes:
a computer which receives each of said sets of said interference patterns
in the form of a measurement of said irradiance pattern which has been
converted into a digital form by said analog to digital converter, said
computer producing each of said optical path length adjustment amounts
using the formula:
##EQU13##
where OPD equals the optical path length adjustment amount between two
beams which are being compared, and OPD is defined in terms of an amount
of .lambda., where .lambda. equals a power weighted average of the
wavelengths of said two beams which are being compared; and
wherein said computer is capable of determing said R and L values using an
algorithm, said algorithm comprising:
##EQU14##
where I(.sub.n) denotes an output of an n.sup.th detector in said
detector array means, and said algorithm uses all the energy in subsidiary
peaks on either side of a main peak in said interference pattern.
12. A laser transmitter as defined in claim 7, wherein said data processor
means includes:
a computer which receives each of said sets of said interference patterns
in the form of a measurement of said irradiance pattern which has been
converted into a digital form by said analog to digital converter, said
computer producing each of said optical path length adjustment amounts
using the formula:
##EQU15##
where OPD equals the optical path length adjustment amount between two
beams which are being compared, and OPD is defined in terms of an amount
of .lambda., where .lambda. equals a power weighted average of the
wavelengths of said two beams which are being compared; and
wherein said computer is capable of determining said R and L values using
an algorithm, said algorithm comprising:
##EQU16##
where I(.sub.n) denotes an output of an nth detector in said detector
array means, said algorithm using all variations in said interference
pattern on either side of a main peak.
13. A laser transmitter as defined in claim 7, wherein said data processor
means includes:
a computer which receives each of said sets of said interference patterns
in the form of a measurement of said irradiance pattern which has been
converted into a digital form by said analog to digital converter, said
computer producing each of said optical path length adjustment amounts
using the formula:
##EQU17##
where OPD equals the optical path length adjustment amount between two
beams which are being compared, and OPD is defined in terms of an amount
of .lambda., where .lambda. equals a power weighted average of the
wavelengths of said two beams which are being compared; and
wherein said computer is capable of determining said R and L values using
an algorithm, said algorithm comprising:
##EQU18##
where I(.sub.n) denotes an output of an n.sup.th detector in said
detector array means.
14. A laser transmitter as defined in claim 13, wherein said first and
second laser beams comprises monochromatic light.
15. A laser transmitter as defined in claim 14, wherein said adjustment of
the optical path lengths of said second laser beams to match its phase
with said first laser beams comprises:
a correction of said optical path lengths of said second laser beam to
approximately equal said optical path length of said first laser beam to
within a range of one wavelength of said monochromatic light, plus
integral multiples of 2.pi. of said wavelength of monochromatic light.
16. A laser transmitter as defined in claim 13, wherein said first and
second laser beams comprise polychromatic light.
17. A laser transmitter as defined in claim 16, wherein said adjustment of
the optical path lengths of said second laser beam to match its phase with
said first laser beam comprises an adjustment of the optical path lengths
of said second laser beams within less than one wavelength of said
polychromatic light. |
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Claims |
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Description |
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BACKGROUND OF THE INVENTION
The present invention relates generally to optical laser telescopes, and
more specifically to a technique and apparatus for optically phasing an
array of multiple telescopes for use as a laser transmitter.
A synthetic aperture is formed when separate optical systems are combined
to function as a single larger aperture. When an aperture is synthesized,
independent optical systems are phased to form a common image field with
resolution determined by the maximum dimension of the array and therefore
exceeding that produced by any single element. By optically phasing an
array of multiple telescopes, a synthetic aperture is formed which can
achieve the performance of an equivalent sized, single laser transmitter.
Phased arrays are currently in use in radar systems. The successful
application of phasing an array of multiple telescopes into a synthetic
aperture extends the numerous benefits of using arrays, as experienced by
radar systems, to optical laser telescopes.
Phased arrays are modular. They can be built in stages and to some extent
be operational as soon as the first telescope is operational. An array of
independent telescopes has functional flexibility. Several simultaneous
operations can be carried out by individual telescopes within a synthetic
aperture. For example, images can be directed to different cameras or
spectrographic devices for simultaneous observations in separate imaging
modes. When operated as a transmitter, a synthetic aperture has the option
of sending beams in different directions.
Phased array apertures have virtually no size limitations. By modularly
combining telescopes in a phased configuration, laser transmitters of
previously unimaginable sizes can be constructed. Large optics fabrication
has historically posed an impermeable barrier to building large aperture
telescope systems. By phasing a number of reasonably-sized telescopes,
extremely large transmitting apertures ca be achieved with present
fabrication technology.
The optical phasing of separate transmitted beams, can be achieved by
maintaining matched optical paths, when the laser transmitter is a system
which provides inputs into multiple telescopes by dividing a single beam.
Techniques for achieving and maintaining matched optical paths fall into
four general categories:
(1) Structural or optical metering trusses;
(2) local loop phasing;
(3) target loop phasing; and
(4) hybrids or combinations of the above techniques.
The structural metering truss requires thermal control to maintain its
integrity. For large systems operating at infrared or optical wavelengths,
position monitoring of the structure is also required. An optical metering
truss can be formed by a device such as a fan beam. Tolerances associated
with the elements that produce an optical truss are a major disadvantage
to the approach.
Target loops insure that an array is phased in the far field. The target
may very well be a star in which case white light interferometry can be
employed. Difficulties include possible low signal to noise ratios and a
requirement for aperture sharing elements. Because focal arrays have an
inherently limited phased field of view, phasing on targets introduces the
prospect of an out-of-phase observation plane. Also, when phasing on
nearby fast-moving targets, Doppler effects must be taken into account.
The present invention uses local loop phasing to control the phase of
separately transmitted beams by adjusting the optical path lengths of the
beam. Local loop phasing is an indirect measurement of the quantity of
interest. Typically, a single source is injected into the system and
divided to traverse the separate paths of all telescopes to be phased.
Beams are recombined at a common plane for phase monitoring and control.
White light interferometry with a Koester prism is a good example of local
loop phasing. This technique is quite suitable for an imaging synthetic
aperture. A transmitter, however, in this configuration is limited to a
single source or a combination of local loop phasing and a separate
operation for phasing multiple sources. Furthermore, beam injection
requires an aperture sharing element which has fabrication drawbacks.
The optical phasing of separate transmitted beams of laser transmitters
with monochromatic light sources is achieved by matching the optical
paths. In systems which have polychromatic sources, the optical path
lengths are adjusted.
Monochromatic light requires phasing only within a range of one wavelength.
Polychromatic sources cannot tolerate 2.pi. ambiguities and therefore
require both coarse and fine phase adjustments for multi-wavelength
interference.
The present invention uses samples of the transmitted beams to control
optical path lengths through the separate telescopes so that the beams add
coherently at the receiver. The phasing concept is applicable both to
systems which provide inputs to the multiple telescopes by dividing a
single laser beam and to systems in which the inputs to the telescopes are
multiple, phase-locked laser beams. The approach is also compatible with
single line and multi-line lasers since all wavelengths are unambiguously
phased. The application of the technique of the present invention extends
the many benefits, described above, of using phased arrays, to optical
laser telescopes. An excellent example of the current application of laser
telescopes is contained in U.S. Pat. No. 4,295,741 issued to Gary E. Palma
et al on Oct. 20, 1981, the disclosure of which is incorporated by
reference. Palma et al disclose a laser transmitter system which achieves
phase matching between a first and second laser beam emitted through first
and second laser telescopes. While the disclosure of Palma et al is
exemplary in the art, the laser source used therein is a single multi-line
laser. The phasing of an array of separate and independent sources of
multiple laser telescopes would result in the equivalent of a single laser
transmitter, with all the advantages of phased arrays, as discussed above
and as currently incorporated in radar technology.
In view of the foregoing discussion, it is apparent that there currently
exists the need for an optical phase sensing and control system, which
allows multiple independent optical telescopes to be used as a phased
array in a laser transmitter. The present invention is directed towards
satisfying that need.
SUMMARY OF THE INVENTION
The present invention provides a means of optically phasing an array of
multiple telescopes, each of which has their own independent single laser
source, into a synthetic aperture, which potentially achieves the
performance of a single laser transmitter of an equivalent size. The
apparatus and technique of the present invention uses samples of the
transmitted beams to control optical path lengths through the separate
telescopes so that the beams add coherently at the receiver. The phasing
concept is applicable both to systems which provide inputs to the multiple
telescopes by dividing a single laser beam and to systems in which the
inputs to the telescopes are multiple, phased-locked laser beams. The
approach is also compatible with single line and multi-line lasers since
all wavelengths are unambiguously phased.
An example of the present invention consists of two optical telescopes
which become useable as a laser transmitter when combined with an optical
phase matching system consisting of: a collecting telescope, a detector
array, two fold mirrors, analog-to-digital converter, microprocessor, and
two sets of correcting mirrors.
The two optical telescopes are adjacent to each other and transmit two
separate outgoing laser beams which require phase matching. The original
source of the two outgoing beams may be either: a single laser beam, which
has been divided (monochromatic); or two separately transmitted
polychromatic laser beams.
The collecting telescope sits in front of the two optic telescopes and
bridges the gap between them. In this way, the collecting telescope is
able to intercept samples of outgoing laser beams from the edges of both
telescopes and focus them, through the two fold mirrors to the detector
array.
The detector array may be either a line scan or an area charge coupled
device (CCD), which reads out the fringe pattern by generating an
interference pattern.
The analog-to-digital converter converts the analog output of the CCD to
digital and sends it to the microprocessor which uses the interference
pattern to determine the relative phase difference between the two beams
using one of a number of phase estimating algorithms (which are part of
the invention).
Once an accurate estimate of the phase difference is determined, the
estimated error is used to adjust the phase by the correcting mirrors
which adjust the optical path lengths of the two outgoing beams.
Monochromatic light requires phasing only within a range of one wavelength.
Polychromatic sources cannot tolerate 2.pi. ambiguities and therefore
require both coarse and fine phase adjustments for multi-wavelength
interference. Both the coarse and fine tuning refer to the phase
estimating algorithms which provide adjustments to the optical path
lengths of the two beams.
By constructing a synthetic aperture and using the principles of the
example, described above, multiple independent optical telescopes can be
used as a phase array in a laser transmitter.
Note that this application incorporates by reference a patent application
filed by Richard A. Carreras entitled "Microcomputer Controlled Image
Processor" and described in U.S. patent application Ser. No. 689,700,
filed Jan. 8, 1985. Mr. Carreras, provides a detailed apparatus and
technique to calculate the optical phase difference for two signals from
an interference pattern provided by the CCD camera.
It is an object of the present invention to provide a means of optically
phasing an array of telescopes into a laser transmitter.
It is another object of the present invention to provide a laser
transmitter with virtually no size limitation.
It is another object of the present invention to provide a method of
optical phase sensing capable of detecting the difference in phase between
the transmitted beams of two adjacent telescopes.
It is another object of the present invention to provide a method of
optical phase control capable of adjusting the phase of the transmitted
beams of two adjacent telescopes by controlling the optical path length.
It is another object of the present invention to obtain matched optical
path lengths between two adjacent telescopes which emit monochromatic
beams.
It is another object of the present invention to adjust the optical path
lengths between the two adjacent telescopes which emit polychromatic
sources using both coarse and fine phase adjustments.
These together with other objects, features and advantages of the invention
will become more readily apparent from the following detailed description
when take in conjunction with the accompanying drawings wherein like
elements are given like reference numerals throughout.
DESCRIPTION OF THE DRAWINGS
FIG. 1 is a sketch of the technique of the present invention as it applies
to an array containing two primary telescopes;
FIG. 2 is a block diagram of the present invention using two primary
telescopes in an array;
FIG. 3 is an illustration of the beam geometry of two samples focused on
the detector array;
FIGS. 4, 5 and 6 are charts of interferograms imaged on the CCD camera of
FIG. 2;
FIGS. 7, 8 and 9 are charts of the far-field patterns of the interferograms
of FIGS. 4, 5 and 6 respectively;
FIG. 10 is a sketch of an interferogram output;
FIG. 11 is a focused fringe pattern;
FIG. 12 is a chart of the computer generated visibility of the fringe
patttern of FIG. 11;
FIG. 13 is a chart of estimated OPD produced by algorithm 7 versus actual
OPD;
FIG. 14 is a chart of estimated OPD produced by algorithm 1 versus actual
OPD;
FIG. 15 is the microcomputer controlled image processor of the Carreras
invention; and
FIG. 16 is an illustration of the phasing technique of the present
invention as it applies to an array of multiple telescopes.
DESCRIPTION OF THE PREFERRED EMBODIMENT
The present invention provides a technique and apparatus for optically
phasing an array of multiple telescopes for use as a laser transmitter.
The technique uses samples of the transmitted beams to control optical
path lengths through the separate telescopes so that the beams add
coherently at the receiver. The phasing concept is applicable both to
systems which provide inputs to the multiple telescopes by dividing a
single laser beam and to systems in which the inputs to the telescopes are
multiple, phase-locked laser beams. The approach is also compatible with
single line and multi-line lasers since all wavelengths are unambiguously
phased.
Optically phasing separate transmitted beams is accomplished by sampling
adjacent outgoing wavefronts. A network of auxilliary collecting optics
intercepts pairs of beams and combines them on a focal plane detector. The
relative phase of sampled beams is measured by the interference pattern
produced when the beams are combined. A symmetrical interference pattern
indicates phased beams. Small mirrors in the beam train operate as an
optical trombone to increase or decrease optical path lengths and thereby
phase match the telescopes.
This configuration does not rely on the integrity of telescope supporting
structures nor does it entail stringent alignment requirements. The key
feature of this invention is the concept of sampling outgoing wavefronts
from separate telescopes and combining them interferometrically to measure
relative phases. Telescopes are phased pair-wise which means that a huge
number of telescopes can be combined to form transmitting apertures of
sizes previously unachievable.
The technique of the present invention, as it applies to an array
consisting of only two primary telescopes, is illustrated in FIG. 1. The
two primary telescopes 101 and 102 are transmitting telescopes, which are
positioned very close to each other. Laser telescopes are known in the
art, as exemplified by the Palma et al reference, and need not be
described further other than to make clear that the two primary telescopes
101 and 102, of FIGS. 1 and 2, each possess an independent single laser
source so that each transmits a separate and independent laser beam. The
collecting telescope 103 (not drawn to scale) sits in front of the two
transmitting telescopes 101 and 102 and bridges the gap between them. In
this way, the collecting telescope 103 is able to intercept samples of
outgoing laser beams from the edges of both primary telescopes and focus
them of the detector array 104 where an interference pattern is created.
The measurement of the interference pattern will be converted to digital
and used to determine the phase difference between the two beams from the
primary telescopes.
FIG. 2 is a functional block diagram of an optically phased laser
transmitter which uses two primary telescopes in an array. As shown in
FIG. 1, the primary telescopes 101 and 102 emit two independent laser
beams A and B, which may be either monochromatic or polychromatic beams.
The collecting telescope 103 collects samples of the outgoing laser beams
from the edges of both telescopes 101 and 102. This sampling is
accomplished by the collecting telescope by partially blocking the path of
the outgoing laser beams with a mirror, and reflecting the blocked portion
of the beams back towards the fold mirrors 204 and 205. Note that FIG. 2
is intended to schematically illustrate the function of the collecting
telescope by depicting two sampled beams S.sub.1 and S.sub.2 from the
primary telescopes 101 and 102, but one skilled in the art will recognize
that the actual reflecting phenomenon of the collecting telescope is
actually accomplished as depicted in FIG. 1. The collected samples are
then conducted by fold mirrors 204 and 205 to the focusing optics 107,
which serves to focus the samples to a common point on the array of
detectors 104 where an interference pattern is created. In the embodiment
of the invention of FIG. 2, the detector array is a CCD camera, which
generates the interference pattern by reading ot the fringe pattern.
However, a line scan or other elements known in the art are also suitable
as a means of detecting the interference pattern.
From the CCD camera 104, the measurement of the interference pattern is
used by a signal processing means to determine the relative phase
difference between the two beams. This signal processing means consists of
the analog-to-digital converter 110 which digitizes the output of the CCD
camera 104, and a microprocessor 111 which uses the unique phase
generating algorithms, described below, on the interference pattern
between the two sampled beams, to estimate the difference in phase between
the two beams. Once the phase difference is known, the optical path length
of the two beams A and B from the primary telescopes 101 and 102 can be
adjusted by the set of correcting mirrors 120, as controlled by the
control mechanism 112.
Monochromatic light requires phasing only within a range of one wavelength.
Polychromatic sources cannot tolerate 2.pi. ambiguities and therefore
require both coarse and fine phase adjustments for multi-wavelength
interference. Both the coarse and fine tuning refer to the phase
estimating algorithms which provide adjustments to the optical path
lengths of the two beams.
FIG. 3 is an illustration of the beam geometry of the two samples of laser
beams, which are brought to a common focus on the detector array 104 of
FIG. 2. The two samples are separated by a distance of 2a at their
centers, and each circular sample has a radius b. If the laser beams
exiting the telescopes are pointed in the same direction and focused to
the same range, then the beam samples will focus to the same point
creating an interference pattern which will be measured by the detector
array. If the laser radiation consists of N different wavelengths
.lambda..sub.n ; (n=1,2, . . . N), then the measured irradiance pattern
will be the sum of the irradiances of the individual frequencies.
Let I.sub.n (r) denote the irradiance in the focal plane at the position
r=(x,y) and at the wavelength .lambda..sub.n. Then:
I.sub.n (r)=(2A.sub.n b/r).sup.2 J.sub.1.sup.2 (K.sub.n
rb/F).multidot.[1+cos(K.sub.n (d+2ax/F))] (1)
where
A.sub.n is the amplitude at wavelength .lambda..sub.n of the beam samples;
K.sub.n =2.pi./.lambda..sub.n ;
F is the focal length of the collecting optics; and
d is the difference in the optical path lengths of the two transmitted
beams.
As indicated in FIG. 3, the sample beams are circular with a radius b, and
are separated by a distance 2a along the x axis. The irradiance pattern,
I.sub.n (r) of Equation 1 consists of two parts: an envelope function
which is just the familiar Airy pattern which would be created by a single
sample beam and a modulation or interference term, the term in brackets.
Note that only the interference term depends on the OPD. As the OPD
varies, the interference pattern translates under a stationary envelope.
FIGS. 4, 5 and 6 are charts of interferograms which are imaged on the CCD
camera 104 of FIG. 2. FIG. 4 is a slice along the x axis in the the focal
plane, which is created by interfering the sampled beams. In FIG. 4, the
beam samples are perfectly in phase and OPD is zero waves. The vertical
axis of the chart indicates the irradiance and the horizontal axis
indicates position locations along the x axis of FIG. 3 where:
F=the focal length of the sampling optics,
.lambda.=the mean wavelength; and
b=the radius of the samples.
FIGS. 5 and 6 are also slices along the x axis, but in FIG. 5 there exists
an optical path difference of .lambda./5 between the two beam samples, and
in FIG. 4 there is an optical path difference of .lambda./2 between the
two beam samples.
FIGS. 4, 5 and 6 show the interference pattern across a central Airy disc
created by focusing two beam samples with separation and diameter in a
ratio of 10:1 and optical path length differences (the quantity d in
equation 10) of 0, 0.2, and 0.5 waves respectively. The computation
assumed that the laser output was at eight discrete frequencies. The
"waves" of optical path difference refer to the power weighted average
wavelength. If the full telescopes from which the samples originate are
contiguous, then the contribution to the far-field pattern of the two
telescopes will be as illustrated in FIGS. 7, 8 and 9.
FIG. 10 is a simplified sketch of an interferogram output of the CCD camera
104 of FIG. 2. This interferogram has a main peak and subsidiary peaks to
the right and left of the main peak. The microprocessor obtains the
digitized interference measurement from the analog-to-digital converter
110 and using one of the approaches, defined below, estimates the optical
path difference between the two beams which are being compared.
The first approach of the microprocessor to estimate the optical path
difference (OPD) is from the invention, referenced above, of Richard
Carreras, and is entitled "the linear algorithm" and is given by:
##EQU1##
where R and L are measures of the subsidiary peaks to the left and right of
the main peak. The present invention presents a variety of algorithms,
discussed below, which are used to calculate the R and L values, which are
then used by the "linear algorithm" to yield the OPD. The formula of the
"linear algorithm" compares the integrated intensity of the two adjacent
sidelobes and normalizes the quantity by their sum. The above algorithm
works well for single or multiple wavelength sources and, when solved,
yields the optical path difference in waves. The "waves" of optical path
difference refer to the power average wavelength of the two sampled laser
beams.
Because of the 2.pi. ambiguity of the linear OPD algorithm, a global
algorithm was developed by Richard A. Carreras in his invention,
referenced above, to find the zero fringe. This algorithm would be
required when phasing a multiline system since maximum interference occurs
only with zero OPD. The global algorithm used is a variation of the
classical definition of visibility, and is:
##EQU2##
where I.sub.max and I.sub.min are single values of maximum and minimum
intensities.
FIG. 11 is a focused fringe pattern which is offered to illustrate the use
of the global algorithm. In FIG. 11, points A through E are values of
intensity measured by a single pixel. The formula is easily implemented,
since A, D, E and C are always referenced to B. That is, finding B,
determines A, D, E and C to the nearest pixel. Thus, there is no
requirement to perform multiple peak and valley searches. A single search
for the peak, B, suffices.
The global algorithm of Equation 3 when applied to the interference pattern
of FIG. | | |
