Note: Descriptions are shown in the official language in which they were submitted.
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PHASE ERROR CORRECTION IN SYNTHETIC APERTURE IMAGING
TECHNICAL FIELD
The general technical field relates to synthetic aperture imaging and, in
particular, to a
method for correcting phase errors in a synthetic aperture imaging system.
BACKGROUND
Synthetic aperture (SA) imaging is a well-known imaging technology that can be
used
to increase resolution beyond the diffraction limit of a physical aperture of
an imaging
system. In SA imaging systems, a large "virtual" aperture is synthesized along
a path
by coherently summing the amplitude and phase information of return echoes
from a
plurality of electromagnetic signals sequentially transmitted by a relatively
small
physical aperture provided on a platform moving along the path. Typical
implementations of SA imaging systems include a transmitter-receiver unit
mounted
on an airborne, spaceborne, or terrestrial platform (e.g., an aircraft, a
satellite, a
ground vehicle, a watercraft, and the like) traveling along a path over a
target region
to be imaged. The transmitter-receiver unit directs a plurality of
electromagnetic
signals onto the target region and collects a series of phase-coherent return
echoes
corresponding to the electromagnetic signals reflected by the target region.
The
return echoes can be recorded, and then coherently combined using signal
processing techniques to reconstruct a high-resolution image of the target
region.
Typical implementations of SA imaging systems achieve two-dimensional imaging
by
using phase history reconstruction along the path (also referred to as the
"azimuth" or
"along-track" direction) and ranging with chirped signals at an angle (e.g.,
perpendicularly in zero-squint mode) to the path (also referred to as the
"range" or
"beam" direction).
SA imaging technology was initially developed and has been successfully
employed
at radio frequencies, where it is referred to as "synthetic aperture radar"
(SAR)
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imaging. Conventional SAR systems typically operate in the centimeter (cm)
wavelength range and produce images with azimuth resolutions of the order of a
meter for spaceborne applications and of the order of a decimeter for airborne
applications. As resolution is generally inversely proportional to the
wavelength used
for imaging, there has been a growing interest to extend SAR technology to
shorter
wavelengths. In particular, an emerging technology referred to as "synthetic
aperture
lidar" (SAL) imaging is currently being developed in order to apply SAR
technology to
the visible and near-infrared portions of the electromagnetic spectrum, with
most
reported experimental studies of SAL dating from the last decade. It is
envisioned that
SAL could produce images with azimuth resolutions of centimeters or less, and
also
provide information complementary to that provided by SAR systems.
In addition to its promising potential in terms of resolution, the development
of SAL
imaging also poses a number of challenges, among which is the measurement and
correction of phase errors. As SA imaging relies on maintaining phase
coherence
between the return echoes collected over the length of the virtual aperture,
any
uncompensated fluctuations in the length of the optical path between the SA
imaging
system and the target region to be imaged can affect the phase of the return
echoes
and, in turn, lead to phase errors that can degrade the image reconstruction
process.
In particular, phase errors can result in images that are not uniformly
focused across
the target region. Typical sources of uncompensated optical-path-length
fluctuations
include, for example, unintended deviations in the plafform motion and
refractive-
index inhomogeneities in the atmosphere. As obtaining high-quality SA images
generally involves keeping phase errors to within a fraction of the imaging
wavelength, which becomes increasingly difficult as the imaging wavelength
decreases, phase errors are expected to be more important in SAL than in SAR.
One phase error correction method used in SAR systems employs global
positioning
system (GPS) data with an inertial navigation system (INS) to provide real-
time
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compensation of undesired platform motions, in combination with autofocus
techniques such as the phase gradient autofocus (PGA) algorithm. The PGA
algorithm is a state-of-the-art technique for phase error correction that
exploits the
redundancy of phase error information among range bins by selecting and
synthesizing the strongest scatterers (which may be in situ corner-cube
retroreflectors) for each range bin. However, implementing an integrated
INS/GPS
system is generally complex and may not be sufficiently accurate for SAL
requirements. Also, the PGA algorithm tends to be less efficient for large
phase
errors, and may therefore not be suitable for being used alone in SAL, due to
the high
level of blurring generally observed in uncorrected SAL images.
Accordingly, various challenges still exist in the field of phase error
correction in SA
imaging applications, particularly in SAL applications.
SUMMARY
According to an aspect of the invention, there is provided a method for phase
error
correction in a synthetic aperture (SA) imaging system configured for imaging
a target
region of a scene from a platform in relative movement with respect to the
scene. The
method includes the steps of:
a) acquiring target SA data from the target region and reference SA data from
a
reference region of the scene, using a SA acquisition unit provided on the
platform;
b) determining one or more phase correction factors from the reference SA data
based on an assumption that the reference region has a known topography,
the one or more phase correction factors being representative of
uncompensated optical-path-length fluctuations along a round-trip optical path
between the reference region and the SA acquisition unit; and
c) applying a phase correction to the target SA data based on the one or more
phase correction factors so as to obtain phase-corrected target SA data.
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According to another aspect of the invention, there is provided a synthetic
aperture
(SA) imaging system for obtaining a phase error-corrected image of a target
region of
a scene from a platform in relative movement with respect to the scene. The SA
imaging system includes:
- a SA acquisition unit provided on the platform and configured to acquire
target
SA data from the target region and reference SA data from a reference region
of the scene; and
- a SA processing unit including:
o a determination module configured to determine one or more phase
correction factors from the reference SA data based on an assumption
that the reference region has a known topography, the one or more
phase correction factors being representative of uncompensated optical-
path-length fluctuations along a round-trip optical path between the
reference region and the SA acquisition unit; and
o a correction module configured to apply a phase correction to the target
SA data based on the one or more phase correction factors so as to
obtain phase-corrected target SA data.
Other features and advantages of the embodiments of the present invention will
be
better understood upon reading of preferred embodiments thereof with reference
to
the appended drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
Fig 1 is a flow chart of a method for phase error correction in a SA imaging
system, in
accordance with an embodiment.
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Fig 2 is a schematic perspective view of a SA imaging system mounted on a
platform
moving relative to a scene along a flight trajectory, in accordance with an
embodiment.
5 Fig 3 is a schematic front elevation view of the SA imaging system of Fig
2, illustrating
the spatial arrangement of the components of the SA acquisition unit on the
platform.
Fig 4 is a simplified block diagram of the SA imaging system of Fig 2.
Figs 5A to 5C are schematic front elevation views of three embodiments of a SA
imaging system, illustrating different implementations of the SA acquisition
unit.
Fig 6 is a plot of simulated SA raw data obtained after demodulation of the
reflected
signal collected by the second receiver in the simplified block diagram of Fig
4.
Fig 7 is a plot of the simulated SA raw data of Fig 6, after range
compression. Fig 7A
is an enlargement of a portion of Fig 7, delineated by dashed lines in Fig 7,
to better
illustrate the reference SA signal received from the reference region.
Fig 8A is a photograph of a target used in a laboratory-scaled experiment
conducted
to illustrate the capabilities of the phase error correction method described
herein.
Fig 8B is a SAL image of the target reconstructed without applying phase error
correction. Fig 8C is a SAL image of the target which was corrected for phase
errors
using an implementation of the method described herein.
DETAILED DESCRIPTION
In the following description, similar features in the drawings have been given
similar
reference numerals, and, in order to not unduly encumber the figures, some
elements
may not be indicated on some figures if they were already identified in
preceding
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figures. It should also be understood herein that the elements of the drawings
are not
necessarily depicted to scale, since emphasis is placed upon clearly
illustrating the
elements and structures of the present embodiments.
General overview of phase errors in synthetic aperture imaging
The present description generally relates to a method for phase error
correction in a
synthetic aperture (SA) imaging system configured to image a target region of
a
scene from a platform in relative movement with respect to the scene. The
present
description also generally relates to a SA imaging system capable of
implementing
the method.
A conventional SA imaging system typically includes a transmitter that
produces an
electromagnetic signal which is directed toward a target region to be imaged,
for
example a ground surface of the Earth, while the SA imaging system is moving
with
respect to the target region. The electromagnetic signal is reflected by the
target
region, producing a return signal that is subsequently collected by a receiver
of the
SA imaging system. The range to the target region can be deduced from the
amplitude of the return signal and the round-trip delay from transmission to
reception.
A processing unit can analyze data indicative of the return signal in order to
reconstruct an image representative of the target region.
Basic SA processing generally assumes that the platform on which is mounted
the SA
imaging system follows a straight trajectory during the image formation time.
In
practice, however, wind, atmospheric turbulence and other environmental
factors
cause the platform to deviate from the assumed ideal trajectory, resulting in
undesired
range fluctuations during data acquisition. As the formation of a SA image is
based on
the coherent combination of the amplitude and phase information of a plurality
of
return signals received at different platform positions throughout the SA
formation
time, a range shift of AR between the platform and the target region leads to
a
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corresponding round-trip phase shift of 0 = 2 x (2-rrAR/A) in the SA data.
This phase
shift, in turn, introduces errors in the phase history of the return signals.
These phase
errors can manifest themselves as image artifacts, a loss of resolution, and a
reduction in the signal-to-noise ratio (SNR) that combine to blur or otherwise
degrade
the quality of the reconstructed images.
Thus, in order to form SA images of sufficiently high quality, it is desirable
that
deviations of the platform from the ideal trajectory (e.g., deviations in
altitude, pitch,
roll, yaw, and the like) be measured or calculated so that they can be
corrected during
the image reconstruction process. As SA images can be quite sensitive to
platform
deviations, it also desirable that phase errors be kept to within a fraction
of the
wavelength (e.g., about a tenth of a wavelength or less) for the duration of
the SA
formation time, which becomes increasingly stringent as the wavelength
decreases.
Accordingly, phase errors are expected to be more important in SAL than in
SAR, as
in SAL any instability in the platform motion of the order of a micrometer
(pm) could
lead to 2-rr phase errors.
It is also to be noted that phase errors in SA data can arise not only from
deviations of
the platform from its ideal trajectory, but also from any other sources of
uncompensated fluctuations in the optical length of the round-trip optical
path
between the SA imaging system and the target region to be imaged. Other
sources of
phase errors can include, for example, atmospheric refractive-index
inhomogeneities
along the optical path between the SA imaging system and the target region.
Embodiments of the present invention may be particularly suitable for use in
SAL
applications employing wavelengths in the visible or near-infrared portions of
the
electromagnetic spectrum, where phase errors are expected to have a greater
impact
than in longer-wavelength SA imaging applications. Those skilled in the art
will
recognize, however, that the methods and systems described herein also apply
to
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other types of SA imaging modalities, including, but not limited to, SAR
imaging, SA
terahertz imaging, SA infrared imaging, SA sonar (SAS) imaging, and SA
ultrasound
(SAU) imaging. It will also be understood that in the context of the present
description, the terms "light" and "optical" are understood to refer to
electromagnetic
radiation in any appropriate portion of the electromagnetic spectrum. In
particular, the
terms "light" and "optical" are not limited to visible light, but can include,
for example,
the radio, microwave, terahertz, infrared, and visible wavelength ranges.
In this context, embodiments of the present invention provide a method for
correcting
phase errors in a SA imaging system configured to image a target region of a
scene from a platform in relative movement with respect to the scene. Fig 1
shows a
flow chart of an embodiment of the method 100, which can, by way of example,
be
implemented in a SA imaging system 10 mounted on a moving platform 12 flying
over
a scene 14 along a flight trajectory 16, such as that illustrated in Figs 2
and 3. In
particular, in Figs 2 and 3, the SA imaging system 10 is implemented in a
typical side-
looking stripmap operation mode, with the platform moving along the azimuth or
along-track direction 18 and the SA imaging system 10 pointing perpendicular
to the
flight trajectory 16 (zero-squint mode) in the range or beam direction 20.
Of course, the phase error correction method 100 of Fig 1 is also applicable
to any
other suitable SA imaging systems or operation modes (e.g., scanning or
spotlight
modes) capable of performing the appropriate method steps. Also, while the
platform
provided with the SA imaging system is an airplane in Figs 2 and 3, various
other
types of manned or unmanned airborne, spaceborne and terrestrial vehicles
could be
used in other embodiments. Furthermore, in Figs 2 and 3, the platform travels
over a
stationary scene, while in other embodiments it is the scene that moves past a
stationary platform. In some embodiments both the platform and the scene may
move. Those skilled in the art will appreciate that each of these scenarios is
meant to
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be encompassed by the expression "platform in relative movement with respect
to the
scene".
Acquisition of synthetic aperture imaging data
Referring to Fig 1, the method first includes a step 102 of acquiring SA data
from two
regions of the scene, namely a target region and a reference region. The SA
data
associated with the target and reference regions are respectively referred to
as target
and reference SA data, and are acquired using a SA acquisition unit. More
regarding
the operational and structural features of the SA acquisition unit will be
described in
greater detail below, with reference to Fig 4.
Turning to Fig 2, first, the target region 22 corresponds to an area, object
or feature of
interest of the scene 14, whose image is to be obtained through appropriate
processing of the target SA data, as in conventional SA imaging applications.
Second, the reference region 24 corresponds to a region of the scene 14 having
a
topography which is assumed to be known, and preferably substantially uniform,
over
the extent of the reference region 24.
In the present specification, the term "topography" generally refers to the
overall relief
and surface elevation of the reference region. It will be understood that the
term
"known" when referring to the topography of the reference region is to be used
as a
practical term depending on the specific implementation of the phase error
correction
method. In particular, the term "known topography" generally refers to the
fact that the
topography of the reference region is known, or uniform, to a degree
sufficient to
justifiably assume that its effect on unexpected phase shifts in the reference
SA data
is known, or negligible, as will described in greater detail below. In some
embodiments, it may also be advantageous that the reflectance characteristics
(e.g.,
reflection coefficient and reflection type) of the reference region be known.
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Depending on the implementation of the method, the reference region 24 may or
may
not overlap the target region 22. The reference region 24 is also generally
smaller
than the target region 22, as there is typically a practical size limit above
which a
reference region 24 of the scene 14 having a uniform, or at least known,
topography
5 can no longer be defined. As described below, the reference SA data from the
reference region 24 can be processed to determine phase correction factors,
which
can then be applied to the target SA data to reduce phase errors and improve
the
quality of the reconstructed image of the target region. More regarding the
reasons for
and advantages of acquiring SA data from such a reference region 24 in view of
10 correcting phase errors in the SA data from the target region 22
will become apparent
from the description provided below.
Referring still to Fig 2, the acquisition of the SA data from the target
region 22 can
involve illuminating the target region 22 with a target optical signal 26, and
collecting
return echoes produced by reflection of the target optical signal 26 from the
target
region 22. The area of the scene 14 which is illuminated by the target optical
signal 26 at a given time, corresponding to a given position of the platform
12 along
the flight trajectory 16, is referred to as the footprint 80 of the target
optical signal 26.
As the platform 12 travels along the flight trajectory 16, the footprint 80 of
the target
optical signal 26 is also moving, thereby defining the target region 22 of the
scene 14.
Similarly, the acquisition of the SA data from the reference region 24 can
involve
illuminating the reference region 24 with a reference optical signal 28, and
collecting
return echoes produced by reflection of the reference optical signal 28 from
the
reference region 24. The area of the scene 14 which is illuminated by the
reference
optical signal 28 at a given time is referred to as the footprint 82 of the
reference
optical signal 28. As the platform 12 travels along the flight trajectory 16,
the
footprint 82 of the reference optical signal 28 is also moving, thereby
defining the
reference region 24 of the scene 14. It will be understood that while the
footprints 80,
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82 of the target and reference optical signals 26, 28 are ellipses in Fig 2,
they may
assume other shapes in other embodiments.
As the general principles underlying the acquisition of SA data of a target
region of a
scene from a platform traveling over the scene along a flight trajectory are
well-known
to those skilled in the art, they need not be covered in detail herein.
Turning now to Fig 4, there is provided a simplified block diagram of an
embodiment
of a SA acquisition unit 30 configured to acquire the target and reference SA
data
from the target and reference regions, respectively. In the illustrated
embodiment, the
SA acquisition unit 30 is configured for SAL applications in the near-
infrared, but
could be readily adapted for SA imaging in other wavelength ranges without
departing
from the scope of the present invention. For example, in other embodiments,
the
target and reference signals each has a wavelength from a few hundreds of
nanometers to a few decimeters. For example, wavelengths ranging from a few
centimeters to a few decimeters may be employed for SAR applications, while
wavelengths ranging from a few hundreds of nanometers to a few micrometers may
be employed for SAL applications. In yet other embodiments, acoustic waves may
be
employed to form the synthetic aperture, such as in SAS imaging applications.
In Fig 4, the SA acquisition unit 30 includes an optical source 32 for
generating a
source optical signal 34, and an optical splitter 36 for splitting the source
optical
signal 34 into the target optical signal 26 and the reference optical signal
28. The
optical source 32 can be embodied by any appropriate device or combination of
devices apt to generate a source optical signal 34 suitable for SA imaging.
For SAL
applications, the optical source 32 is generally a laser source, which may be
operated
in continuous wave or pulsed regime, and which may or may not be modulated.
For
example, in the illustrated embodiment, the optical source 32 is a pulsed
fiber laser
emitting at a wavelength of 1.55 pm and provided with an optical modulator 38
that
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performs a linear frequency modulation on the source optical signal 34, of
increasing
or decreasing frequency (up-chirp or down-chirp, respectively). Those skilled
in the
art will understand that various other types of optical sources can be used in
other
embodiments including, but not limited to, a gas laser, a solid-state laser, a
diode
laser, a dye laser, a fiber laser, and the like. The choice of the optical
source can be
dictated by several factors, notably the desired wavelength, peak power,
coherence,
pulse duration and repetition rate of the optical source signal.
The time-dependent electric field of each linear frequency-modulated (LFM)
pulse of
the source optical signal 34 may be written as:
E (t) = Eorect () cos(2n-fot + n-Kt2),
(1)
where r is the pulse duration, fo is the center frequency of the pulse (which
is equal to
193 THz at a wavelength of 1.55 pi,m), and K is the chirp rate. It will be
understood
that Equation (1) describes pulses with a rectangular temporal profile. For
example, in
SAL applications, the pulses each may have a pulse duration ranging from a few
nanoseconds to a few microseconds.
The optical splitter 36, for example a fiber splitter, splits the source
optical signal 34
into the target and reference optical signals 26, 28, each of which therefore
also has
an LFM phase-encoded waveform. As known in the art of SA imaging, the
inclusion of
an up-chirp (K> 0) or a down chirp (K> 0) can improve the detection accuracy
since
it allows achieving both the average transmitted power of a relatively long
pulse and
the range resolution of a relatively short pulse. In the illustrated
embodiment, the
optical splitter 36 is a 90/10 fiber splitter, whereby 90% and 10% of the
power of the
source optical signal 34 are used to form the target and reference optical
signals 26,
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28, respectively. Of course, it is envisioned that optical splitters with
various power-
dividing ratios may be used without departing from scope of the present
invention.
It is to be noted that depending on the intended application, the target and
reference
optical signals 26, 28 may or may not be phase-coherently synchronized with
each
other. It will also be appreciated that while the target and reference optical
signals 26,
28 are generated using the same optical source 32 in the embodiment of Fig 4,
other
embodiments of the SA acquisition unit 30 can generate the target and
reference
optical signals 26, 28 using different optical sources, which may operate in
the same
or in different portions of the electromagnetic spectrum. Furthermore, while
the SA
acquisition unit 30 in Fig 4 is fiber-based, its fiber components could be
replaced by
bulk components in other embodiments.
Referring still to Fig 4, the SA acquisition unit 30 can include a target
transmitter 40
for illuminating the target region 22 with the target optical signal 26, and a
reference
transmitter 42 for illuminating the reference region 24 with the reference
optical
signal 28. Each of the target and reference transmitters 40, 42 can include
appropriate transmitting optics (e.g., lens, mirrors, optical fibers)
configured to direct,
focus and/or condition the target and reference optical signals 26, 28 in
order to
efficiently illuminate the target and reference regions 22, 24, as illustrated
in Figs 2
and 3.
It is to be noted that, while in Figs 2 and 3 the target and reference
transmitters 40, 42
are incident from the same side of the platform 12, due to the target and
reference
regions 22, 24 being located on the same side of the flight trajectory 16, the
target
and reference transmitters 40, 42 can be incident from opposite sides of the
platform 12 in scenarios where the target and reference regions 22, 24 are
located on
corresponding opposite sides of the flight trajectory 16. Also, more than one
reference
optical signal may be used in some embodiments. More regarding possible
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alternative arrangements of the SA acquisition unit 30 on the platform 12 will
be
discussed further below, with reference to Figs 5A to 5C.
In the embodiment of Fig 4, the reference transmitter 42 includes collimating
optics 44
for collimating the reference optical signal 28 prior to directing the
reference optical
signal 28 onto the reference region 24. Then, as a result of collimation, the
reference
optical signal 28 can achieve low divergence and be focused at higher power
density
to have a relatively small footprint on the scene.
Those skilled in the art will understand that by converting the reference
optical
signal 28 into a collimated beam having a relatively small footprint on the
ground, the
condition of having a known, and preferably substantially uniform, topography
over
the extent of the reference region 24 can more easily be fulfilled, thereby
facilitating
the implementation of the phase error correction method described herein. It
will also
be understood that when the collimated reference optical signal 28 is incident
onto
the reference region 24 with a high power density, the reference SA data can
exhibit
a better SNR, which can make the determination of phase correction factors
from the
reference SA data easier. For example, in some embodiments, the power density
of
the reference optical signal 28 can be as much as ten times higher than the
power
density of the target optical signal 26. Additionally, when the reference
optical
signal 28 is collimated, only a modest portion of the source optical signal 34
may
need to be extracted from the source optical signal 34. In this way, in some
implementations, the generation of the reference optical signal 28 to acquire
the
reference SA data does not or only slightly impact the optical power budget
compared
to conventional SA imaging systems, while providing additional phase error
correction
capabilities, as described below.
Referring still to Fig 4, the SA acquisition unit 30 can also include a first
receiver 46
associated with the target transmitter 40, and a second receiver 48 associated
with
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the reference transmitter 42. Each of the first and second receivers 46, 48
can include
appropriate receiving optics (e.g., lens, mirrors, optical fibers) for
collecting radiation
from the scene 14.
5 Referring to Fig 3, the first and second receivers 46, 48 are spaced from
each other
on the platform 12 by a distance D, which is along the range direction 20 in
Fig 3.
Also, the target transmitter 40 and the first receiver 46 are two physically
distinct
components on the platform 12, separated by a distance d along the range
direction,
while the reference transmitter 42 and the second receiver 48 together form a
10 collimated transceiver 50. Referring to Fig 4, in such a configuration,
an optical
circulator 52 can be provided to separate signals coming in and out of the
collimated
transceiver 50. Of course, depending on the intended application, each
transmitter-
receiver pair of the SA acquisition unit 30 may be physically distinct
components or
be combined as a transceiver. In particular, the distance d would become zero
if the
15 target transmitter 40 and the first receiver 46 were to be combined into
a single
transceiver.
Referring to Figs 3 and 4, the first receiver 46 is configured to collect a
first reflected
signal 54 produced by reflection of the target and reference optical signals
26, 28
respectively from the target and reference regions 22, 24. Meanwhile, the
second
receiver 48 is configured to collect a second reflected signal 56 also
produced by
reflection of the target and reference optical signals 26, 28 respectively
from the
target and reference regions 22, 24. More specifically, the target optical
signal 26
emitted by the target transmitter 40 is reflected by the target region 22,
such that a
portion of the reflected optical power is collected by the first receiver 46
and another
portion is collected by the second receiver 48. Likewise, the reference
optical
signal 28 emitted by the reference transmitter 42 is reflected by the
reference
region 24, such that a portion of the reflected optical power is collected by
the first
receiver 46 and another portion is collected by the second receiver 48.
Therefore, in
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the illustrated embodiment, each of the first and second reflected signals 54,
56 is a
superposition of phase-coherent return echoes reflected by the target region
22 and
phase-coherent return echoes reflected by the reference region 24.
It is to be noted that, in other embodiments, the number of receivers in the
SA
acquisition unit and the nature of the reflected signals collected by the
receivers may
be varied to suit a particular application, as will now be discussed with
reference to
Figs 5A to 5C, which illustrate alternative embodiments for the SA acquisition
unit 30
of the SA imaging system 10.
Referring to Fig 5A, a first alternative configuration for the SA acquisition
unit 30 is
provided. In this configuration, the target and reference transmitters 40, 42
illuminate
the scene 14 respectively with the target and reference optical signals 26, 28
from
opposite sides of the platform 12, due to the target and reference regions 22,
24
being located on opposite sides of the flight trajectory 16. The SA
acquisition unit 30
also includes a target receiver 46' configured to collect a target reflected
signal 54'
produced by reflection of the target optical signal 26 from the target region
22, and a
reference receiver 48' configured to collect a reference reflected signal 56'
produced
by reflection of the reference optical signal 28 (which may or may not be
collimated)
from the reference region 24. It is to be noted that, in this configuration,
each
receiver 46', 48' collects a signal 54', 56' reflected from either the target
region 22 or
the reference region 24, but not from both. This can be achieved, for example,
by
proper orientation of the receivers 46', 48' and/or using an appropriate set
of mirrors.
It will also be recognized that, in this configuration, the target and
reference SA data
acquired by the SA acquisition unit 30 are not mixed with each other, thus
avoiding
the need to separate them in a subsequent processing step.
Turning now to Fig 5B, a second alternative configuration for the SA
acquisition
unit 30 is illustrated. As in Fig 5A, the target and reference transmitters
40, 42 also
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illuminate the scene 14 from opposite sides of the platform 12. The SA
acquisition unit 30 includes a target receiver 46' configured to collect a
target
reflected signal 54' produced by reflection of the target optical signal 26
from the
target region 22, and first and second reference receivers 48a, 48b configured
to
collect first and second reference reflected signals 56a, 56b produced by
reflection of
the reference optical signal 28 (which may or may not be collimated) from the
reference region 24. Again, in this configuration, each receiver collects a
signal
reflected from either the target or the reference region, but not from both.
Finally, referring to Fig 5C, a third alternative configuration for the SA
acquisition
unit 30 is illustrated. The SA acquisition unit 30 includes a target
transmitter 40
illuminating the target region 22 from one side of the platform 12, and first
and second
spaced-apart reference transceivers 50a, 50b illuminating the reference region
24
from the other side of the platform 12 with respective first and second
reference
optical signals 28a, 28b, each of which may or may not be collimated. The
first and
second reference transceivers 50a, 50b are also configured to respectively
collect a
first and a second reference reflected signal 56a, 56b, each produced by
reflection of
the first and second reference optical signals 28a, 28b from the reference
region 24.
In other words, the first reference optical signal 28a emitted by the first
reference
transceiver 50a is reflected by the reference region 24, such that a portion
of the
reflected optical power is collected by the first reference transceiver 50a
and another
portion is collected by the second transceiver 50b. Likewise, the second
reference
optical signal 28b emitted by the second reference transceiver 50b is
reflected by the
reference region 24, such that a portion of the reflected optical power is
collected by
the first reference transceiver 50a and another portion is collected by the
second
transceiver 50b.
Referring back to Fig 4, the SA acquisition unit 30 can further include an
optical
demodulator 58 configured to demodulate the first and second reflected
CA 02864501 2014-09-19
18
signals 54, 56 and provide therefrom a first SA data set Si and a second SA
data
set S2, respectively. As an example, the optical demodulator 58 can be an in-
phase/quadrature (IQ) demodulator configured to perform a quadrature
demodulation
process on each of the first and second reflected signals 54, 56. In the
illustrated
embodiment, the optical demodulator 58 includes two demodulation sub-
units 58a, 58b, each of which for demodulating one of the first and second
reflected
signals 54, 56. The quadrature demodulation process can be accomplished by
mixing
each of the first and second reflected signals 54, 56 with a local oscillator
signal 60, 62 coherent with the source optical signal 34 or with a delayed
version of
the source optical signal 34. In Fig 4, a local oscillator 64 (e.g., a fiber
laser emitting
at a wavelength of 1.55 pm) and an optical splitter 66 are used to generate
the local
oscillator signals 60, 62, but other configurations can be used in other
embodiments.
IQ demodulation processes are known to those skilled in the art and need not
be
further described. After demodulation, the first and second SA data sets Si
and S2
can be directed onto and detected by a light detector (not shown), which can
convert
the first and second SA data sets Si and S2 into electrical signals. In some
embodiments, the light detector is a PIN photodiode or an avalanche
photodiode, but
other types of light detector could be used in other embodiments. The
electrical
signals may then be digitally sampled at a frequency satisfying the Nyquist
criterion,
and digitally stored for later processing.
The first SA data set Si and the second SA data set S2 respectively obtained
from the
first and second reflected signals 54, 56 can be referred to as "SA raw data".
Each of
Si and S2 can be represented as a two-dimensional complex-valued array of data
points organized in rows along the azimuth direction and in columns along the
range
direction, where each data point of the array is associated with an amplitude
value
and a phase value. Fig 6 is a gray-scale-coded plot of simulated SA raw data
corresponding to the absolute value of the second SA data set S2 after
demodulation.
The first SA data set Si would lead to a similar plot. As can be seen from Fig
6, at this
CA 02864501 2014-09-19
19
stage, the SA raw data generally does not form an interpretable image, but
rather has
a noise-like appearance, due to the fact that the data points are spread out
in azimuth
and ground range and include information from both the target and reference
regions
of the scene.
Referring back to Fig 4, the first SA data set Si is composed of two signals:
a first
target SA signal Sir, which corresponds to the signal emitted by the target
transmitter 40 and collected by the first receiver 46, and a first reference
SA signal
Sir, which corresponds to the signal emitted by the reference transmitter 42
and
collected by the first receiver 46. The second SA data set S2 is also composed
of two
signals: a second target SA signal S2t, which corresponds to the signal
emitted by the
target transmitter 40 and collected by the second receiver 48, and a second
reference
SA signal S2r, which corresponds to the signal emitted by the reference
transmitter 42
and collected by the second receiver 48. It is to be noted that the first and
second
target SA signals Sit and S2t together form the target SA data, while the
first and
second reference SA signals Sir and S2, together form the reference SA data.
The extraction of the first target and reference SA signals Sit and Sir from
the stored
first SA data set Si and of the second target and reference SA signals S2t and
S2r
from the stored second SA data set S2 can be performed using various
techniques
and algorithms based on numerical processing, optronic processing, or a
combination
of numerical and optronic processing. For example, in some embodiments, a
numerical extraction of Sit and Sir can involve performing a range compression
on Si,
while a numerical extraction of S2t and S2r can involve performing a range
compression on 52. Range compression techniques to improve ground range
resolution and SNR are well-known in the art, and can be done efficiently in
the
frequency domain by using fast Fourier transform (FFT) techniques. For
example, in
SAL applications, range compression can involve performing a FFT on each
column
of Si and 52, while in SAR applications, range compression can involve
successively
CA 02864501 2014-09-19
performing a FFT, applying a matched filter, and performing an inverse FFT on
each
column of Si and S2.
After range compression, the data points in the two-dimensional arrays Si and
52 can
5 be associated with a position in ground range. Accordingly, the signals
Sit and Sir
can become easier to identify in the range-compressed data set Si, and the
signals
S2t and S2r can become more easily recognizable in the range-compressed data
set
S2. To better illustrate this effect, reference is made to Fig 7, which is a
plot of the
second SA data set S2 of Fig 6 after range compression, as well as to Fig 7A,
which is
10 an enlargement of the portion of Fig 7 that better illustrates the
signal S2r received
from the reference region. Looking at Fig 7, it is seen that the range signals
S2t and
S2r can now be distinguished, in particular S2r which, as seen in Fig 7A, is
characterized by a high amplitude response resulting from the collimation and
associated high power density of the reference optical signal. In some
embodiments,
15 an optical delay may be introduced between the target and reference optical
signals
to further facilitate the identification of Sit and Sir from Si and the
identification of S2t
and S2r from S2.
Those skilled in the art will recognize that in conventional SA imaging
systems, only
20 the complex demodulated signal Sit is obtained from the series of phase-
coherent
return echoes produced by reflection of the target optical signal from the
target
region. As will be now be described, in some embodiments of the method
described
herein, once the first and second reference SA signals Sir and S2r have been
extracted, calculated or otherwise obtained, they can be used in the method
described herein to correct phase errors in the first target SA signal Sit.
Determination of phase correction factors
Referring back to Fig 1, the phase error correction method 100 also includes a
step 104 of determining one or more phase correction factors from the
reference SA
CA 02864501 2014-09-19
,
21
data based on the assumption, introduced above, that the reference region has
known, and preferably substantially uniform, topographic characteristics over
its
extent.
Referring to Fig 2, it will be recognized that when the topography of the
reference
region 24 is assumed to be known, the phase of each of the return echoes
reflected
by the reference region also has a known expected value when no phase error is
present. Accordingly, any unexpected phase shift observed in the reference SA
data
can be interpreted as phase errors arising from uncompensated optical-path-
length
fluctuations along a round-trip optical path 68 between the reference region
24 and
the SA acquisition unit 30 as the platform 12 travels along the flight
trajectory 16. The
uncompensated optical-path-length fluctuations can be indicative of at least
one of
unintended platform motions and refractive-index inhomogeneities along the
round-
trip optical path 68 between the reference region 24 and the SA acquisition
unit 30.
Therefore, by acquiring SA data from such a reference region 24, the method
100 can
allow for the determination of one or more phase correction factors which are
representative of these uncompensated optical-path-length fluctuations such
as, for
example, undesired platform motions and atmospheric refractive-index
inhomogeneities.
It is to be noted that once the reference region is assumed to have known
topographic characteristics, various analysis, computational and processing
techniques may be employed to derive phase correction factors to apply a phase
correction to the target SA data. In the following, an exemplary, non-limiting
approach
for obtaining phase correction factors from the reference SA data will be
described.
The approach is based on the SA acquisition unit 30 described above with
reference
to Figs 3 and 4 and including a target transmitter 40, a first receiver
associated with
and separated by a distance d from the target transmitter 40, and a collimated
CA 02864501 2014-09-19
22
transceiver 50 separated by a distance D from the first receiver 46 and
including a
reference transmitter 42 and a second receiver 48. The approach described
below
also assumes that the reference region 24 has a uniform topography. Of course,
in
other embodiments, phase correction factors could be determined from the
reference
SA data using a different approach without departing from the scope of the
present
invention.
First, when the source optical signal is given by Equation (1), and after
range
compression, the first target and reference SA signals Su and Sir and the
second
target and reference SA signal S2t and S2r introduced above may be
approximated as
follows:
i27rfo[111(x)+G t(x)]Hi(x) + G1(x)1)
Sit(t,x) ,-4.-: ZAie c W (xi, yi, x)sinc (KT Ft ,
(2a)
c
I
1271 fo[R 1(4+ H i(x)]R 1(4 + H 1(41)
S ir(t , X) r-t,' X Ale c w(xi,yi,x)sinc (KT {t
(2b)
,
c
1
i2n fo[R i(x)+G i(x)]Ri(x) + Gi(x)1)
,
S2t(t,x) =-=.:: ZBie c W (xi, yi, x)sinc (KT [t
(2c)
c
I
i4ir foRt(x)
5.2r (t , X) 1-'-' X Bie c w(xi,yi, x)sinc (Kr t-2R1(x) .
(2d)
c
t
In Equations (2a) to (2d), t is the range time, x is the azimuth position of
the
platform 12, (xi, yi) is the ground coordinates of a scatterer /within the
scene 14, W is
the irradiance of the target optical signal 26 on the ground, w is the
irradiance of the
collimated reference optical signal 28 on the ground, K is the chirp rate, r
is the pulse
duration, fo is the center frequency, and c is the speed of light in vacuum.
Also, the
coefficients A/ and a represent the amplitude of the return signals collected
by the
first receiver 46 and the collimated transceiver 50, respectively, taking into
account
CA 02864501 2014-09-19
23
the collection efficiency, while the functions HI, G, and RI correspond to the
slant
ranges from the scatterer / to the first receiver 46, the target transmitter
40 and the
collimated transceiver 50, respectively.
The slant range functions HI, GI and RI generally depend on the azimuth
position x of
the platform 12 along the flight trajectory 16. In the presence of phase
errors caused
by uncompensated optical-path-length fluctuations from transmission to
reception, the
slant range functions HI, G1and RI may be approximated as follows:
R 1 (x) -,.: RI + a(x) ¨ D 13 (x),
(3a)
2
(x ¨ .x1)
_________________________________________ + a(x) + dfl(x),
(3b)
2 GI
(x ¨ x 1)2
H1(x)=-=,' Hi + ______________________________ + a(x),
21/1
(3c)
where a is a first phase correction factor and fl is a second phase correction
factor.
As will be described below, each of the first and second correction factors a
and 16 will
be determined as a function of the first and second reference SA signals
Sir(t, x) and
S2r(t, x) given by Equations (2b) and (2d). The first phase correction factor
a is
associated with "common phase errors" arising from one or more sources of
uncompensated optical-path-length fluctuations that are independent of the
spatial
arrangement of the reference transmitter 42, the first receiver 46 and the
second
receiver 48 on the platform 12, which is accounted for by the distances D and
din the
present example. Meanwhile, the second phase correction factor # is associated
with
"non-common phase errors" arising from one or more sources of uncompensated
optical-path-length fluctuations that depend on the spatial arrangement the
reference
transmitter 42, the first receiver 46 and the second receiver 48 on the
platform 12. In
CA 02864501 2014-09-19
24
other words, the first phase correction factor a is meant to account for phase
errors
induced by uncompensated optical-path-length fluctuations that affect the SA
signals
identically, irrespective of their transmission and reception locations on the
platform 12, while the second phase correction factor p is meant to account
for phase
errors induced by uncompensated optical-path-length fluctuations that affect
the SA
signals differently based on their transmission and reception locations on the
platform 12.
Common phase errors can include, for example, altitude fluctuations and
lateral-
position fluctuations, as well as local inhomogeneities in the refractive
index of the
atmosphere that are the same for all the signals transmitted and received by
the SA
imaging system. Meanwhile, non-common phase errors can arise as a result of
uncompensated rotational motions of the platform such as, for example, roll
fluctuations.
It is to be noted that because the reference optical signal 28 is collimated,
the
expression for the slant range function R,(x) in Equation (3a) does not
possess the
typical quadratic dependence as a function of azimuth position x exhibited by
the
slant range functions Gi(x) and El,(x), which can simplify the calculation of
the first and
second correction factors a and p. However, the principles of the method
described
herein could also be applied to SA imaging system implementations where the
reference optical signal 28 is not collimated.
Assuming that the uncompensated optical-path-length fluctuations remain
relatively
small compared to the ground range cell resolution, the range compressed first
and
second reference SA signals Si,(t, x) and S21-(t, x) may be written as:
CA 02864501 2014-09-19
121rf0[2a(x)¨D J3(x)1 fo(Ri+Ht) _in
fo(x¨x1)2 (-1¨)
Sir(t ,X) c ilie c e c kH11
1
(4a)
(Hi + Ri)l)
x w(xbyt,x)sinc (KT {t
i2n10[2a(x)-2D13(41 i4irf0R1 2R1
52,(t, x) e Bie c w(xbyi, x)sinc (KT [t ¨
where it can be seen that the first and second phase correction factors a and
16 in the
exponential function have been taken outside the summation.
5 It is to be noted that a range migration correction has been applied to
Equations (4a)
and (4b) to correct the effect of range migration, which, as known in the art,
results
from the variation of the slant range between the platform and the reference
region
during the SA formation time. Range migration correction allows correcting the
ground range variation of the return echoes corresponding to each data point
in the
10 two-dimensional arrays Sir(t, x) and S2,-(t, x). It is also to be noted
that in a scenario
where the uncompensated optical-path-length fluctuations would be larger than
the
ground range cell resolution, the first and second phase correction factors a
and 16
would initially remain in the sinc function, but would be taken out by
applying a range
migration correction under the assumption of a uniform reference region 24,
thus
15 recovering the expressions of Equations (4a) and (4b).
Under the assumption of a narrow collimated beam fulfilling the condition
cH 2
2ir for the reference optical signal 28, the quadratic phase term can be
ignored in Sir
and S2r so that a particular range bin ti in Equations (4a) and (4b) may be
written as:
CA 02864501 2014-09-19
26
f0[2a(x)-Dgx)]
SD(t X)==-1 e [6' (x,ti)lec'(''ti),
(5a)
i2nf0[2a(x)-2DP(x)]
S2r(ti) X) e c IC(x,ti)lei0c(x,ti).
(5b)
It is to be noted that Equations (5a) and (5b) generally are valid over a
limited interval
of range bin values ti, where the complex amplitude of S11-(t1, x) and S2,-
(t1, x) is
sufficiently large. For example, in the range-compressed SA raw data of Fig 7
the
interval of range bin values ti over which Equation (5b) for S21.(ti, x) is
valid would be
expected to approximately coincide with the interval of range bin values
ranging from
about 175 to 200 and illustrated in Fig 7A.
The x dependence of the complex functions C and C' is due to speckle,
providing that
the reference region has a relatively homogeneous topography at the operating
wavelength. In this embodiment, the use of a collimated reference optical
signal
allows the quadratic phase term to be neglected in Equation (3a). This, in
turn, leads
to a smoother speckle pattern that can be markedly reduced after averaging
over
multiple range bins. As known in the art, speckle is a SA imaging specific
noise effect
resulting from constructive and destructive interference from multiple
scatterers within
a resolution cell of the SA imaging system that gives the SA images a grainy
or
textured appearance.
The method can then involve using a phase gradient method which, as known in
the
art, is a linear minimum-variance estimator for phase error that can
efficiently
combine measurements from a plurality of range bins. The method may first
include
taking the derivative of Sir(ti, x) and S21.(t1, x) with respect to the
azimuth position x, as
follows:
CA 02864501 2014-09-19
27
aSir(ti,x) i2n-
ax __ = ¨1V AxIFFik = FFT(Sir(ti, x))), (6a)
aS2r(ti,x)
ax __ = ¨NAxIFFTtic = FFTf,S2r (ti, x)}}, (6b)
where IFFT denotes the inverse fast Fourier transform, Ax is the displacement
of the
platform between the emission of two consecutive pulses by the reference
transmitter 42, N is the number of pulses emitted and k = [0 1 ... N-1] is the
spectral
index vector. Using Equations (6a) and (6b), the derivative of the phase
signal of
x) and S21(t1, x) with respect to the azimuth position x may then be written
as:
asir(ti,x)
aCr(ti,x) Lai{ ax slr(ti,x)1
(7a)
ax x)12
1052r (ti, x)
acp2r (ti, x) ax .5;7. (ti, x)1 (7b)
Ox IS2r (ti, x)12
where Im and * respectively denote the imaginary part and the complex
conjugate of
a complex number.
Next, the method may involve averaging over multiple range bins, to reduce the
speckle, and integrating the result over x, which yield:
asrPi (t. X) 2Thfo[2a(x) ¨ Dig(x)]
1r =j dx ( r ) (8a)
Ox
ao2r(t1 X) 2Thfo[2a(X) 2Di3(X)]
1:132r = f dx ( ) x c (8b)
a
CA 02864501 2014-09-19
28
Equations (8a) and (8b) provide a link between the phase of the first and
second
reference SA signals Sir and S2r and the uncompensated optical-path-length
fluctuations along the round-trip optical paths (i.e., R/(x) + H/(x) for Sir
and 2R1(x) for
S2,-) between transmission and reception. The first and second phase
correction
factors a and 16 can finally be extracted from Equations (8a) and (8b) and be
written
as:
a(x) = 4n-f0 (20
- lr CD2r), (9a)
C
11(x) = 27r f oD lC1:11r (1)2r)= (9b)
As mentioned above, the phase correction factors a and fi represent phase
errors
resulting from common and non-common uncompensated optical-path-length
fluctuations, respectively. It will be understood that the determination of
two phase
correction factors a and 16 is made possible by the fact that two reflected
signals from
the reflection regions are measured at two different locations on the
platform. This is
the case for the SA acquisition unit 30 illustrated in Fig 4, but also for the
alternative
configurations of Figs 5B and 5C. However, for the SA acquisition unit 30
illustrated in
Fig 5A, only one reflected signal is measured from the reference region so
that only
one phase correction factor would generally be obtained using the exemplary
approach described above with reference to Equations (2a) to (9b). This single
phase
correction factor would account for both common and non-common phase errors at
the same time, but would not be able to directly isolate their individual
contributions.
Correction of phase errors
Referring back to Fig 1, the method 100 further includes a step 106 of
applying a
phase correction to the target SA data based on the one or more phase
correction
CA 02864501 2014-09-19
29
factors so as to obtain phase-corrected target SA data. In the exemplary
approach
described above with reference to Equations (2a) to (9b), the correction step
106 can
include applying a phase correction to the first target SA signal Sit(t, x)
based on the
first and second phase correction factors a and
Indeed, the first target SA signal
Sit(t, X) corresponds to the signal emitted by the target transmitter and
collected by
the first receiver after reflection by the target region, which is the region
of interest of
the scene whose SA image is desired to be reconstructed, and thus corrected
for
phase errors.
Referring to Fig 2 as well as to Equation (2a), a round-trip optical path 78
associated
with the first target SA signal S1 1(t, x) may be written as the sum of the
slant ranges
G/(x) and Hi(x). Furthermore, in view of Equations (3a) and (3b), the
uncompensated
optical-path-length fluctuations in the round-trip optical path 78 result in a
round-trip
range shift of ARit= 2a(x) d/3(x) during data acquisition and, in turn, to a
corresponding round-trip phase shift Oit in the first target SA signal Sit(t,
x), which
may be written as:
[2a(x) + dgx)]
(10)
The phase shift Olt can introduce errors in the phase history of the first
target SA
signal Sit(t, x). In some embodiments of the method described herein,
correcting
phase errors in the first target SA signal Sit (t, x) can involve subjecting
Sit (t, x) to an
equal but opposite phase shift -Olt as follows:
git(t, x) [Sit(t, x)] x e41t,
(11)
where Slit(t,x) is the phase-corrected first target SA signal. It is seen
that, in this
implementation of the method, the phase correction of the first target SA
signal
CA 02864501 2014-09-19
Sit(t, x) is applied based on the first and second phase correction factors a
and II and
in view of the relative spatial arrangement of the target transmitter and the
first
receiver on the platform, which is accounted for by their spacing d.
5 Referring now to Figs 8A to 8C, a laboratory-scaled experimental
demonstration was
conducted to illustrate the capabilities of the phase error correction method
described
herein. The experimental demonstration was performed with a home-built system
configured for SAL imaging. The target consisted of a retroreflective tape
with the
number "4" painted thereon. A photograph of the actual target is shown in Fig
8A. The
10 reference region consisted of a white sheet of paper. Optical fibers for
transmitting
and receiving optical signals and a collimator for collimating the reference
optical
signal were mounted on a translation stage disposed 25 centimeters away from
the
target. The laser output power was 15 milliwatts and the wavelength was
continuously
linearly swept from 1535 to 1565 nanometers. Fig 8B is a SAL image of the
target
15 reconstructed without phase error correction, while Fig 8C is a
reconstructed SAL
image of the target which was corrected for phase errors using the various
techniques
described herein. It is seen that the phase-corrected image in Fig 8C is more
properly
focused and enables distinguishing individual retroreflecting elements of the
tape,
which is not possible for the image shown in Fig 8B.
The phase-corrected target SA data thus obtained may then be processed using
known SA processing techniques involving, for example, FFT and matched
filtering
algorithms, or optronic processing to reconstruct an image of the target
region in
which the impact of phase errors is mitigated. In some embodiments, the phase
error
correction method described herein allows for the estimation and compensation
of the
bulk of the phase errors affecting the SA data. If desired or required, in
such
embodiments, a subsequent correction of residual phase errors could be
performed
CA 02864501 2014-09-19
31
based, for example, on the PGA algorithm, which generally tends to be more
efficient
when the magnitude of the phase errors is relatively small.
Synthetic aperture processing unit
Referring back to Fig 4, the SA imaging system 10 includes a SA processing
unit 70,
which may be embodied by any type of appropriate processing unit capable of
processing the SA data collected and stored by the SA acquisition unit 30. In
the
context of the present specification, the term "processing unit" denotes an
entity of the
SA imaging system 10 that controls and executes the operations required for
correcting phase errors in SA data. For this purpose, the SA processing unit
can
include a determination module 72 configured to determine the one or more
phase
correction factors from the reference SA data based on an assumption that the
reference region has a known topography, as well as a correction module 74
configured to apply a phase correction to the target SA data based on the one
or
more phase correction factors so as to obtain phase-corrected target SA data.
In
some embodiments, the determination module 72 of the SA processing unit 70 may
also include a range compression sub-module 76 to perform a range compression
on
each of the first and second SA data sets S1 and S2 obtained from the SA
acquisition
unit 30, as described above.
Those skilled in the art will recognize that the SA processing unit 70 may be
implemented as a single unit or as a plurality of interconnected processing
sub-units,
and may be embodied by a microprocessor, a central processing unit (CPU), a
microcontroller, or by any other processing resource or any combination of
such
processing resources configured to operate collectively as a processing unit.
Alternatively, the SA processing unit 70 can be implemented as an optronic
processor. The SA processing unit 70 can be described as a series of modules,
each
of which performing one or more different functions, such as the determination
module 72, the correction module 74 and the range compression sub-module 76
CA 02864501 2014-09-19
32
introduced in the previous paragraph. However, it will be understood that the
subdivision into such modules is made from a conceptual standpoint only and
that, in
practice, a given hardware or software component may be shared by different
modules, and that components of different modules may be combined together
physically and logically without departing from the scope of the present
invention.
Referring still to Fig 4, in some embodiments, the SA processing unit 70 may
be
physically located on the same platform 12 as the SA acquisition unit 30.
However, it
may be envisioned that certain aspects of the determination of the phase
correction
factors from the SA reference data and certain aspects of the phase correction
of the
SA target data may be performed remotely, for example from a remote ground-
based
processing station. In such scenarios, the target and reference SA data
acquired and
stored by the SA acquisition unit 30 could be transmitted wirelessly to the
remote
processing station while the platform is moving relative to the scene.
Alternatively, the
SA data acquired and stored by the SA acquisition unit 30 could be transferred
to the
SA processing unit 70 via wired or wireless transmission after the SA target
and
reference data have been acquired and the SA acquisition unit 30 has returned
to the
ground.
As mentioned above, the phase error correction method may be carried out
numerically and/or optronically, and may include processing the target and
reference
SA data using conventional techniques based on the theory of SA imaging. In
this
regard, it will be understood by those skilled in the art that various such
techniques
could be employed, given the many approaches and algorithms available for
numerically and/or optronically processing SA data.
Of course, numerous modifications could be made to the embodiments described
above without departing from the scope of the present invention.
