Abstract:
A new differential technique for forming optical images using a synthetic aperture is introduced. This differential technique utilizes a single aperture to obtain unique (N) phases that can be processed to produce a synthetic aperture image at points along a trajectory. This is accomplished by dividing the aperture into two equal “subapertures”, each having a width that is less than the actual aperture, along the direction of flight. As the platform flies along a given trajectory, a source illuminates objects and the two subapertures are configured to collect return signals. The techniques of the invention is designed to cancel common-mode errors, trajectory deviations from a straight line, and laser phase noise to provide the set of resultant (N) phases that can produce an image having a spatial resolution corresponding to a synthetic aperture.

Description:
RELATED APPLICATION 
   This application is a Continuation-In-Part of application Ser. No. 10/342,726 filed Jan. 14, 2003 now abandoned, and claims priority thereto. 

   The United States Government has rights in this invention pursuant to Contract No. W-7405-ENG-48 between the United States Department of Energy and the University of California for the operation of Lawrence Livermore National Laboratory. 

   BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to remote high-resolution imaging, and specifically to a system and method for forming high-resolution optical and RF images using a differential synthetic aperture radar technique. 
   2. State of Technology 
   Synthetic Aperture Radars (SARs) are used in military and non-military applications to provide high-resolution images using a predetermined frequency of electromagnetic radiation. Their spatial resolution is approximately given by the ratio of the wavelength and the effective antenna size. By forming a synthetic aperture, along the direction of flight, much larger than the physical size of the antenna, greatly improved resolution can be obtained along that direction. This is most commonly achieved by generating a profile of target return phase versus position along the synthetic aperture, at spacings equal to about half the physical antenna size (Nyquist rate) or less, while maintaining a linear trajectory. 
   A normal operating mode of SAR, called Stripmap mode SAR, includes imaging a strip having a length determined by the synthetic aperture as it is flown by a moving platform over a target area. The antenna pointing direction is kept fixed while image data are collected. The length of the strip is determined by a time window over which back-scattered radiation is collected using a series of pulses from an illuminated target area. The collected radiation is processed and an accumulation of data is used to construct a synthesized image of a target area. To form images, the platform is required to fly in a straight line or, if not, deviations from a straight line require corrections during processing. 
   Another mode of operation, i.e., Spotlight SAR, includes imaging a target by directing an antenna at the center of the imaging scene during the entire pass of the platform to provide a longer illumination time, (i.e., a spotlight aperture). 
   Accordingly, the present invention provides a Differential Synthetic Aperture Radar imaging technique that reduces system platform constraints to produce higher resolution images. 
   SUMMARY OF THE INVENTION 
   Accordingly, the present invention provides a differential synthetic aperture radar method to produce an image having a spatial resolution corresponding to a synthetic aperture of about Nd/4. 
   Another aspect of the present invention provides an imaging method from a moving platform that includes illuminating an object with electromagnetic radiation from an aperture of size d and collecting, from a plurality of platform positions separated by about d/4, a reflected radiation from the object by a first and a second sub-aperture, each sub-aperture having a predetermined width of about d/2. A plurality of differential phases from each of the plurality of platform positions is measured by optically splitting the collected radiation by the first sub-aperture into a first and a second optical beam that are directed to the first quadrature receiver and optically splitting the collected radiation by the second sub-aperture into a third and a fourth optical beam that are directed to the second quadrature receiver. A pair of common in-phase (I) local oscillator reference beams and a pair of common quadrature (Q) local oscillator reference beams are generated such that the (I) beams are directed to operationally heterodyne with the first and the third optical beams and the (Q) beams are directed to operationally heterodyne with the second and the fourth optical beams respectively. The heterodyne signals are processed to produce a first phase φm j  and a second phase φm j+1  with respect to the common local oscillator such that a phase differential φm j+1 −φm j  between the sub-apertures is capable of being produced. A plurality of resultant (N) phases are calculated by summing the phase differentials at each of the platform positions according to [φ j+1 =φ j +(φm j+1 −φm j )] to produce an image having a spatial resolution corresponding to a synthetic aperture of length of about Nd/4. 
   Accordingly, the present invention provides a differential synthetic radar method and apparatus that would relax stability requirements, compared to conventional SARs, such as: deviations from a straight line platform trajectory during the image formation time, both line-of-sight and out-of-plane, laser frequency stability (bandwidth), and speckle and turbulence distortion. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The accompanying drawings, which are incorporated into and form a part of the disclosure, illustrate an embodiment of the invention and, together with the description, serve to explain the principles of the invention. 
     FIG.  1 ( a ) illustrates a Differential SAR Stripmap mode geometry. 
     FIG.  1 ( b ) illustrates a simplified schematic of the two sub-apertures incorporated as part of the present invention. 
     FIG.  2 ( a ) illustrates the differential phase measurement technique disclosed in the present invention. 
     FIG.  2 ( b ) further illustrates the differential phase measurement technique. 
     FIG.  3 ( a ) shows a simplified schematic of a top down receiver. 
     FIG.  3 ( b ) shows a schematic of an exemplary DSAR optical receiver. 
     FIG.  4 ( a ) illustrates theoretical phase profiles versus target position. 
     FIG.  4 ( b ) shows a resultant theoretical plot of differential phase versus target position. 
       FIG. 5  shows a plot number of required pulses to form a synthetic image for three different wavelengths. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   Referring now to the following detailed information, and to incorporated materials; a detailed description of the invention, including specific embodiments, is presented. 
   Unless otherwise indicated, numbers expressing quantities of ingredients, constituents, reaction conditions and so forth used in the specification and claims are to be understood as being modified by the term “about.” Accordingly, unless indicated to the contrary, the numerical parameters set forth in the specification and attached claims are approximations that may vary depending upon the desired properties sought to be obtained by the subject matter presented herein. At the very least, and not as an attempt to limit the application of the doctrine of equivalents to the scope of the claims, each numerical parameter should at least be construed in light of the number of reported significant digits and by applying ordinary rounding techniques. Notwithstanding that the numerical ranges and parameters setting forth the broad scope of the subject matter presented herein are approximations, the numerical values set forth in the specific examples are reported as precisely as possible. Any numerical value, however, inherently contain certain errors necessarily resulting from the standard deviation found in their respective testing measurements. 
   General Description 
   Conventional Radio Frequency (RF) Synthetic Aperture Radars (SARs) are well understood and extensively used for imaging of remote targets, but their extension to optical wavelengths is at an early stage of development. Issues include the required frequency stability of the laser and the precision within which the position of the phase sensor must be known during the time to acquire a complete synthetic image (i.e., a synthetic aperture size divided by platform velocity). To form images, the SAR platform must fly in a straight line or, if not, deviations from a straight line must be sensed or measured so that they can be corrected during processing. The deviation from a straight line must be a fraction of a wavelength of about λ/10. As an example, for an optical wavelength of 2 μm, this corresponds to 0.2 μm. At RF wavelengths, the tolerances are correspondingly larger. Even though the tolerances are small in the optical regime, the time over which they have to be maintained, (i.e., the length of the synthetic aperture), is also proportional to the wavelength and therefore much shorter, typically less than about 0.6 to about 6 milliseconds instead of seconds for average platform velocities of about 150 m/sec. 
   The present invention, Differential Synthetic Aperture Radar (DSAR) is analogous to “Stripmap mode” SAR (discussed herein before), but incorporates a differential technique that is capable of operating in the optical regime (e.g., from about 850 nm to about 10.0 microns) and the short-wavelength RF regime. 
   Specific Description 
   DSAR Geometry 
   FIG.  1 ( a ) and FIG.  1 ( b ) illustrate the basic DSAR geometry. The real aperture (not shown) from a moving platform  2 , such as an aerial vehicle, is divided into a first sub-aperture  4 , and a second sub-aperture  6 , as shown in FIG.  1 ( b ). Each sub-aperture  4 ,  6 , having a width from about 0.1 m to about 0.5 m, measures a phase for each laser illumination pulse (illustrated as an illumination source beam  8 ). A beam footprint  10  approximately equal to λR/d, (with λ as the illumination wavelength, R is the range to target, and d the combined physical size of the two sub-apertures) is created by beam  8  and carried along a strip  12  having a length  14 . A phase profile along the synthetic aperture is then obtained by summing a predetermined number of phase differentials, and an image is subsequently extracted. The pointing direction of the illumination beam can be kept fixed, to a fraction of the diffraction-limit corresponding to the sub-aperture size, during an image formation time. Instruments such as gyroscopes can be used to keep the pointing of the illumination beam stable. 
   DSAR Concept 
   FIG.  2 ( a ) illustrates the DSAR concept. Phase measurements of an incident reflected field  11  are made, for a first sub-aperture  14 , and a second sub-aperture  16 , at a number of platform positions  18 ,  20 ,  22  along a trajectory  23 . The upper part of FIG.  2 ( a ) shows “effective” platform translations, such as between platform positions  18  and  20 , of d/2. The corresponding “physical” platform translations are d/4 because the path length from the transmitter to the target and the path length from the target to the receiver aperture both change. Since the collected reflected fields at the two sub-apertures  14 ,  16  result from the same transmitted pulse, and because a local oscillator (LO) (not shown), having a phase β, is common to both quadrature receivers (not shown), phase errors resulting from (small) deviations from a linear trajectory and from illumination and LO noise, cancel out when phases are calculated from a plurality of differential phases  30 ,  32 , and  34 , which are measured at each of platform positions  18 ,  20 , and  22 . Such differential phases  30 ,  32 , and  34 , are obtained by measuring the phases of the two sub-aperture fields and subtracting them, or from a correlation of the heterodyne output signals. 
   FIG.  2 ( b ) further illustrates the DSAR concept. Thus, with sub-apertures  14  and  16 , separated by d/2 as denoted, at positions (x−d/2) and (x) respectively, and a target point reflector  35  at position y, the differential phase can be computed from the following equation: 
         Δ   ⁢           ⁢     φ   ⁡     (     x   ,   y   ,   z     )         ≈       π     λ   ⁢           ⁢   z       ⁡     [         (     y   -   x     )     ⁢   d     +       (     d   2     )     2       ]           
 
where λ=wavelength, d=aperture size, x=platform position, y=target position, and z=target range. For a translation of both sub-apertures by δz, 
         δ   ⁡     (     Δ   ⁢           ⁢   φ     )       ≈     Δ   ⁢           ⁢   φ   ⁢           ⁢       δ   ⁢           ⁢   z     z           
 
which is negligible for realistic platform motions since the maximum value of Δφ is about a radian and δz/z&lt;&lt;1. Similarly, out-of-plane translation produces a negligible change in differential phase. In addition, unlike conventional SAR, temporal coherence of the laser transmitter is required over only a single roundtrip time to the target area, not the transit time of the synthetic aperture time because of the differential method of the present invention, thereby relaxing laser frequency stability requirements.
 
   The differential phases do not depend on target axial motion/Doppler. However, target motion can still be obtained from the Doppler shift measured using either of the sub-aperture receivers. 
   Source Bandwidth 
   A source of electromagnetic radiation for illuminating a target is typically a frequency-chirped laser or a short pulse laser. As an example, for a range resolution of 10 cm, a frequency chirp of about 4 GHz is required. Equivalently, a short pulse laser having a pulse-width less than about 250 picoseconds can be used. As stated herein before, if the source transmitter (i.e., a laser source) has phase-distortions/noise, they will appear in the return at both sub-apertures, and therefore cancel out when calculating the phase differentials. This cancellation relaxes the requirement on maximum phase noise, and therefore the laser source transmitter requirements. With atmospheric transmission properties and eye-safety concerns as design considerations, a source of electromagnetic radiation, such as one or more laser systems, provides illumination wavelengths, having a range between about 850 nm and about 10.0 μm, and more particularly at 2 μm, and 4 μm, and even more particularly at 1.5 μm. Exemplary laser source materials include carbon-diode gas, Yb or Er in the proper host material, and optical parametric oscillators. However, any type of amplifier means capable of operating within the parameters set forth herein can be employed in practice of the invention. Moreover, the application of using the differential technique of the present invention is additionally capable of operating at conventional SAR frequencies (i.e., RF frequencies) that are compatible with platform constraints, in particular, antenna size limitations. 
   Receiver 
   FIG.  3 ( a ) shows a basic schematic of a receiver system of the present invention, generally designated by the reference numeral  300 , including a pair of sub-apertures  38 ,  40 , capable of receiving return signals that vary with time (i.e., s 1 (t) and s 2 (t)), a pair of high bandwidth heterodyne detectors  42 ,  44 , a common local oscillator source  46  having a phase denoted as β, commercially available electronic amplifiers  48 ,  50  and commercially available A/D converters (not shown) as well as other conventional operationally connected processing electronics (not shown). Such architecture is similar to conventional SAR detection arrangements as described in a textbook by Fitch, J. P.,  Synthetic Aperture Radar , Springer-Verlag New York Inc., 1988. p. 11-18. TK 6592.S95F58. 
   FIG.  3 ( b ) shows an example of a DSAR optical receiver apparatus and is generally designated by reference numeral  400 . In an exemplary method of the present invention, a linearly polarized illumination beam A from an electromagnetic source  52 , is reflected by a polarizing beam-splitter  53  (shown as two polarizing beam splitters to illustrate the principles of the embodiment) and output through an aperture (not shown) that has a width of d. Sub-aperture receivers  38  and  40 , as shown in FIG.  3 ( a ), each having a width of d/2, collect a reflected radiation from a target (not shown) as shown as denoted return signals s 1 (t) and s 2 (t) respectively. A Faraday rotator  51 , (i.e., a transparent material that rotates a plane of polarization of a polarized beam, with a direction of rotation dependent upon an applied dc magnetic field), causes a rotation of the plane of polarization of beam A from source  52 , such as for example by 45 degrees, upon output of apparatus  400 . Return signal s 1 (t) and s 2 (t) have their plane of polarization rotated an additional 45 degrees with respect to beam A upon transmission back though rotator  51 . Such a technique enables a total of 90 degrees of rotation of the initial polarization state (i.e., of source  52 ) that enables return signals s 1 (t) and s 2 (t) to pass through beam-splitter  53  for detection and which also optically isolates s 1 (t) and s 2 (t) from source  52 . 
   Local oscillator (LO)  46 , having a linear output polarization, is transmitted through a quarter-wave plate  56 , (i.e., an optical component that enables two polarization components of a polarized beam to be 90 degrees out-of-phase with respect to one another and thus be circularly polarized), and directed to a first beam-splitter  55  capable of transmitting between about 80 and about 90% of return signal s 2 (t) and capable of reflecting between about 10 and about 20% of an output of LO  46 . A second beam-splitter  54 , additionally capable of transmitting between about 80 and about 90% of return signal s 1 (t) and capable of reflecting between about 10 and about 20% of LO  46  that is transmitted through beam-splitter  55 , reflects LO  46  and transmits s 1 (t). Both, s 1 (t) and LO  46  are substantially co-linear at the denoted point B after transmission through a first half-wave plate  57  designed for an operating wavelength of source  52 . Half-wave plate  57  rotates incident linearly polarized return beam s 1 (t) by 45 degrees of rotation, while the beam of LO  46  remains circularly polarized. Both s 1 (t) and LO  46  are further directed to a first Wollaston prism  59  to produce orthogonally polarized and separated beams denoted as C and D. Beam C includes, for example, a vector component of s 1 (t) and an in-phase component of LO  46  while Beam D includes, for example, a vector component of s 1 (t) and a quadrature (i.e. a 90 degree out-of-phase component) component of LO  46 . An optical component, such as lens  61 , having a predetermined focal length then is arranged to direct beams C and D to a first in-phase  63  and a first quadrature  64  high-speed heterodyne detectors. Received beams C and D are then processed using conventional operationally connected electronics and heterodyne methods, to produce a phase (φm j ) of return signal s 1 (t) with respect to common LO  46 . 
   Similarly, operationally coupled electronics and optical components are capable of receiving and processing return signal s 2 (t) such that a phase information (φm j+1 ) may be extracted. Therefore, similar to the description for the optical path of return signal s 1 (t), between about 80 and about 90% of return signal s 2 (t) is transmitted through beam-splitter  55 . Beam-splitter  55  also reflects and directs the output of LO  46  after passing through quarter-wave plate  56 . LO  46  and s 2 (t) are substantially collinear at denoted point E after transmission through a second half-wave wave plate  58  also designed for an operating wavelength of source  52 . Half-wave plate  58  rotates incident linearly-polarized return beam s 2 (t) by 45 degrees of rotation, while the beam of LO  46  remains circular. Both s 2 (t) and LO  46  are further directed to a second Wollaston prism  60  to produce orthogonally polarized and separated beams denoted as F and G. Beam F includes a vector component of s 2 (t) and an in-phase component of LO  46  while Beam G includes a vector component of s 2 (t) and a quadrature (i.e. a 90 degree out-of-phase component) component of LO  46 . A second optical component, such as lens  62 , having a predetermined focal length then is arranged to direct beams F and G to a second in-phase  65  and a second quadrature  66  high-speed heterodyne detectors. Similar to processed beams C and D, beams F and G are processed using conventional operationally connected electronics and methods, to produce phase (φm j+1 ), of return signal s 2 (t,) with respect to common LO  46 . 
   Phases φm j  and φm j+1  that are measured through the two sub-apertures for a given illumination pulse, can be written as the sum of the actual (correct) phase values and errors. The phase errors can further be divided into a common mode error ε cm  and non-common-mode errors, if any. Non-common-mode errors, if any, are not considered in the present invention and, therefore, φm j =φ j +ε cm  and φm j+1 =φ j+1 +ε cm , where φ j  and φ j+1  are the actual (correct) phase values. The common mode phase error, ε cm , cancels out when computing the actual phase values, and may be different for different illumination pulses. Accordingly, a measured phase differential φm j+1 −φm j  between the sub-apertures is capable of being produced and a plurality of resultant (N) phases are calculated by summing the phase differentials at each of the platform positions according to [φ j+1 =φ j +(φm j+1 −φm j )] to produce a image having a spatial resolution corresponding to a synthetic aperture of length of about Nd/4. 
   Phase Profiles and Phase Differentials 
   FIG.  4 ( a ) shows exemplary theoretical sub-aperture phase profiles,  68  and  69 , versus platform position from a DSAR apparatus, for a point-reflector target returning a phase front to a varying platform position, and with the following example input parameters: a wavelength λ=4 μm, an aperture d=0.25 m, denoted as numeral  13  as shown in  FIG. 2 , and a length L=100 km, denoted as numeral  14  as shown in FIG.  1 ( a ). FIG.  4 ( b ) illustrates a theoretical plot of differential phases  70  versus platform position after applying the method of the present invention to the theoretical (error-free) received phase profiles  68  and  69 , as shown in FIG.  4 ( a ). 
   Phase Error Buildup 
     FIG. 5  shows a plot of the number of pulses needed to form a synthetic image versus range in kilometers for three wavelengths, 10 μm  72 , 4 μm  74 , and 2 μm  76 , that are capable of being used as an illumination source for the present invention. As examples, from the given plot, for λ=10 μm, R=100 km, and d=0.25 m, N p =64 pulses, while for λ=4 μm, R=50 km, and d=0.25 m, N p =13 pulses. 
   As discussed herein before, a phase profile by the method of the present invention is obtained by summing phase differentials along the synthetic aperture. Since the phase profile is acquired by adding phase differentials, errors in the measured phases, in particular those resulting from intrinsic heterodyne detection shot noise, add in a random manner as a function of the number of pulses needed to form an image. This number (N p ) as shown in  FIG. 5  on the vertical axis, is approximately 4λR/d 2 , and is derived as follows: an effective length of the synthetic aperture is about λR/d, which is the size, at range R (i.e., antenna distance to the target), of a coherent beam having an illumination wavelength λ, transmitted from an aperture of size d, with a corresponding beam divergence of λ/d. Accordingly, if pulses are transmitted at positions separated by d/4, then the total number of pulses fired along the synthetic aperture is N p =(λR/d)/(d/4)=4λR/d 2 , with d/2 being the physical size of each sub-aperture. 
   However, the linear (tilt) and quadratic (focus) optical aberration components of the random phase error do not significantly impact image quality, and, when they are removed or minimized, for example, by hardware or software techniques, the error buildup is small for typical numbers of pulses required. In addition, the precision of the individual phase measurements can be improved by increasing the illumination laser power and, thereby, the detection Signal to Noise Ratio (SNR). 
   While the invention may be susceptible to various modifications and alternative forms, specific embodiments have been shown by way of example in the drawings and have been described in detail herein. However, it should be understood that the invention is not intended to be limited to the particular forms disclosed. Rather, the invention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the invention as defined by the following appended claims.