WO2016203245A1

WO2016203245A1 - High resolution remote imaging system

Info

Publication number: WO2016203245A1
Application number: PCT/GB2016/051801
Authority: WO
Inventors: John Anthony Rogers; Christopher Pannell
Original assignee: Spectra Medical Limited
Priority date: 2015-06-16
Filing date: 2016-06-16
Publication date: 2016-12-22

Abstract

A high resolution remote imaging system one or more collectors p for receiving light returned from an image spot on a remote object illuminated by the image beam at different angles. Optical combiners at the respective collectors combine the returned reference beam with light returned from the remote object. A processor processes the OCT signals received at the respective detectors to create a 2- or 3- D image of the remote object with enhanced resolution.

Description

High Resolution Remote Imaging System

Field of the Invention

This invention relates to the field of remote imaging, and more particularly to a method and system for obtaining high-resolution images, especially, but not exclusively, to three- dimensional images, from a remote location, such as a satellite. The invention also relates to high resolution two-dimensional imaging. The invention is also applicable to terrestrial-based systems, or for example, systems installed on aircraft.

Background of the Invention

There is an ongoing need to obtain high-resolution images of ground-based objects from space for many purposes, such as land surveying, ocean monitoring, and surveillance. One such technique is described in the paper "Earth Observation from High Orbit: Pushing the limits with Synthetic Aperture Optics", L.M Mugnier, F. Cassaing, G. Rousset, B. Sorrente, Office national D'Etudes et de Recherches Aerospatiales, BP 72, 92322 Chatillon , cedex, France. This paper discusses the use of synthetic aperture optics wherein multiple collector telescopes are arranged within a single instrument. This configuration has limited resolution because of the inherent restriction on the size of the synthetic aperture, which depends on the separation of the collector telescopes. Moreover, this instrument is limited to obtaining 2D images as it does not directly collect depth information.

Other techniques for remote imaging are available including LIDAR or FMCW (Frequency Modulated Continuous Wave) radar, but these do not provide precise depth information to enable true topographic images to be created. Additionally, the horizontal resolution is generally limited by the width of the illuminating beam or spot.

Summary of the invention

Embodiments of the invention are based on a combination of three technologies. The first two are closely related: Optical Coherence Tomography (OCT) and Angle Resolved Low Coherence Interferometry (a/LCI). Both are based on the use of either low coherence or coherent tunable sources to provide high-resolution images. They respectively provide reflectivity information with depth or angular scattering information with depth, usually on the order of microns of resolution. OCT has become standard of care for imaging of the human retina since first demonstrated in 1991 . a/LCI has attracted interest for its potential to distinguish cancerous from healthy tissue in vivo. Both techniques operate at resolutions of microns and are designed for imaging highly scattering tissue samples with micron scale depth resolution. Because of the high levels of scattering in these applications, the imaging ranges are usually millimeters.

In accordance with embodiments of the invention, it is proposed that the techniques evolved for OCT are applied to imaging over hundreds of kilometers with depth resolutions of centimeters. This allows the use of synthetic aperture techniques to give resolutions of ten centimeters at remote distances of hundreds of kilometers. As will be explained the depth information provided by the OCT system also allows the lateral resolution to be improved beyond the resolution of the spot size. This is important when imaging the ground from a satellite, where the spot size can be in the order of meters. The system permits a better resolution than this making use of the amplitude and phase information provided by the OCT system. The spot is the target area on the ground illuminated by the incident beam.

Generally the invention combines the results of two or more OCT A-scans of the same illuminated spot taken at different off-axis angles on a target to compute the depth and reflectivity of sub-spots within the illuminated spot at a resolution greater than can be achieved with a single A-scan. The invention also permits a lateral resolution to be achieved that is much greater than would be determined by the spot size alone because the depth information obtained at different angles enables the reflectivity to be determined within an illuminated spot to a resolution better than the size of the spot. A feature of the invention is that it makes use of both phase and amplitude information provided by the OCT signal. While in radar applications phase information can be obtained directly, this is not true of light or infrared applications where the frequency is far too high to permit direct measurement of phase information.

The off-axis signals can be obtained either by using two or more collectors, or moving the source and changing the angle of the beam so that it tracks the target as the source moves. For example, in this case of a satellite, the source can be mounted on a single satellite and tilted as the satellite moves over the earth so as to illuminate the same point on the ground.

In a broad aspect the invention provides a high resolution remote imaging apparatus comprising an OCT source for illuminating a remote object with an imaging beam ; a reflector for generating a reference beam; one or more collectors for receiving light returned from the remote object and comparing the returned light with the reference beam at different angles to obtain a plurality of OCT signals; and a processor for extracting image data from the OCT signals.

In another aspect the invention provides a high resolution remote imaging system, comprising an OCT unit for generating an image beam and a reference beam; at least two off-axis collectors for receiving light returned from an image spot on a remote object illuminated by the image beam, said collectors being for placement in a spaced relationship; a reference path for returning the reference beam to said respective collectors; optical combiners at said respective collectors for combining the returned reference beam with light returned from the remote object; and detectors at said respective collectors for producing OCT image signals.

In yet another aspect the invention provides a method of obtaining a topographical image of a remote target, comprising: obtaining two or more OCT A-scans of an illuminated spot on the target taken at different oblique angles; and computing the topography of the target within the illuminated spot by combining data from said two or more A-scans. The invention also extends to 2-dimensinal imaging where the resolution is better than the spot size of the imaging beam. The OCT A-scans may be obtained simultaneously from collectors located at different off-axis locations or sequentially by moving a collector over the target while keeping it pointed at the same spot so as to obtain said A-scans from different angles.

A collector as used herein refers to the aperture receiving a beam returned from the target in an OCT setup.

Off-axis means that the collector is located such that the return beam lies at an oblique angle to the normal to the surface of the target. In a conventional OCT setup the image beam and return beam lie typically along the normal to the surface of the target. A feature of the invention is that the return beams lie at an angle to this normal.

As used herein OCT includes any interferometric method of determining depth information including FMCW (frequency modulated continuous wave).

The invention also extends to computer readable storage medium, such as a disk drive, flash drive etc, having stored thereon instructions which when executed on a computer combine data from two or more OCT A-scans of an illuminated spot on a target taken at different off- axis angles to compute the topography of the target within the illuminated spot.

According to another aspect of the present invention there is provided a high resolution remote imaging system, comprising an OCT apparatus for generating an image beam and a reference beam ; at least two off-axis collectors for receiving light returned from an image spot remote object illuminated by the image beam, said collectors being for placement in a spaced relationship; a reference path for returning the reference beam to said respective collectors; optical combiners at said respective collectors for combining the returned reference beam with light returned from the remote object; and detectors at said respective collectors for producing OCT image signals.

The image beam may lie along the normal to the surface of the target as in the case of conventional OCT, or alternatively it may be coincident with the or one of the return beams to the collectors. In this case the OCT apparatus for generating the image beam could be co- located with the collector.

The separate OCT image signals can be processed in a processor to obtain the enhanced image. One technique is to take into account the phase relationships between the OCT image signals received at the respective detectors, although other synthetic aperture techniques can be employed to increase the lateral resolution.

The reference path may include a reference mirror, but since it is in effect a delay line, other techniques, for example, using fiber optics can be employed. For example, if the imaging system was installed on an aircraft, a fiber optic delay line could be employed to create the reference path.

It will be understood that the term "light" as herein defined is not restricted only visible wavelengths, but also includes near infrared and ultraviolet wavelengths. In the preferred embodiment, it is envisaged that the light source will operate at 1550nm because this wavelength has good atmospheric transmission characteristics, but it will be appreciated that other wavelengths can also be employed. For example, the invention can be used to image underwater objects, in which case it may be desirable to employ visible wavelengths for which water is transparent.

Moreover the processor can be distributed over the various components as sub- processors or mounted at a central location with communication channels between them taking into account signal delays.

It should be also understood that the phase referred to above relates to the phase of the OCT signals, not the phase of the light, as will be explained in more detail below.

Embodiments of the present invention make use of a combination of synthetic aperture techniques employing a long base line to increase transverse resolution and optical coherence tomography techniques to obtain depth information.

The collectors can be located on separate satellites orbiting in a low earth orbit (LEO) constellation with a fixed relationship relative to each other. The reference mirror would need to be separated from the source by a distance approximately equal to the distance of the satellite above the ground, typically about 300kms. Alternatively, the collectors could be arranged on an aircraft. In this case, the required optical separation could be achieved with the aid of a wound optical fiber.

It is known from basic optics that the resolving power of a telescope is inversely proportional to the diameter of the objective lens. Synthetic aperture techniques rely on the fact that the same resolution can be achieved by collecting light at various different locations on a notional objective lens and combining the received light, knowing its amplitude and phase, to obtain an image. With appropriate processing the effective resolution is that of a large lens having a diameter equal to the separation of the collectors.

Optical Coherence tomography (OCT) is a technique for obtaining depth information in a semi- transparent medium such as the eye. Originally, OCT was performed in the time domain (TD) using a modified form of Michelson interferometer. Incident monochromatic light of limited spatial coherence was split into a reference beam and an object beam that was reflected off the object of interest. In TD interferometry, at the point where the optical path difference between the reference beam and object beam is zero ± 512, where δ is the coherence length of the light interference fringes are be formed. By modulating the light, a signal is created whose amplitude represents the reflectivity at that point. As the path length of the reference beam is changed, by moving the reflective m irror, the point where the OPD is changed can be moved in the axial direction. As a result, moving the mirror results in an A-scan wherein information can be obtained about the reflectivity in the depth direction. The depth resolution depends on the coherence length, which in the case of ophthalmic equipment is typically in the order of 10 microns.

A variant of TD OCT is spectral OCT, wherein instead of moving a mirror to change the point where the OPD is zero, the OPD is fixed and the object is scanned with light of multiple wavelengths. By performing a Fourier analysis it is possible to extract a full A-scan, i.e. a line of depth information, without changing the point where the OPD is zero. It is also possible to extract the information without performing a Fourier analysis using correlation techniques.

A related technique is to use a swept-frequency source (time-encoded Fourier domain), wherein a tunable laser is used as the source, and the wavelength is swept over a broad range of wavelengths. The results obtained by swept-source OCT are similar to those obtained using spectral OCT. A single A-scan can be obtained by sweeping the source over a range of wavelengths without changing the point where the OPD is zero. Swept source OCT is described, for example, in the paper Swept-Wavelength Source for Optical Coherence Tomography in the Ιμ Range, F.F Nielsen, L.Thrane, J. Black, K. Hsu, A. Bjarklev, and P.E. Andersen. Optical coherence tomography and coherence techniques 2. ed. / W. Drexler. Bellingham, WA : The International Society for Optical Engineering, 2005. (SPIE Proceedings Series, 5861 ; Progress in Biomedical Optics and Imaging, v. 6, no. 30).

In the prior art OCT is used to obtain tomographic information. By scanning horizontally and vertically, and combining the results with the depth information obtain from the A-scans, it is possible to build up a complete three-dimensional image of the object in question.

Typically, the arms of the Michelson interferometer have lengths in the order of centimeters. Embodiments of the invention take advantage of the fact that it is possible to scale up an OCT set up, such that the length of the arms of the Michelson interferometer have arms in the order of 300km long. Such an arrangement can be achieved by placing a constellation of satellites in low earth orbit (LEO) that are stationary relative to each other.

LEO satellites typically have an orbital height of about 300kms above the earth surface. If a source of coherent light is placed on a first satellite, and the resulting beam split into a reference beam and an object beam, with a mirror for the reference beam placed on a second satellite stationary relative and space from it by the same distance as the first satellite is spaced from the ground, the object beam can be pointed at the ground at the point in the object beam where the optical path difference is zero can be arranged to be located just above the ground. With this arrangement employing swept source OCT the depth resolution with a tuning range in the order of 50 picometers would typically in the order of 5 cms. The actual depth resolution depends on the tuning range and other physical parameters.

The diameter of the object beam striking the earth would typically be in the order of 1 meter, which would limit the lateral resolution. However, by taking advantage of synthetic aperture techniques, it is anticipated that the lateral resolution can be reduced significantly, for example, to the order of 10 cms. According to another aspect of the invention there is provided a method of performing high resolution remote imaging to obtain depth information, comprising: generating an image beam and a reference beam ; collecting, at two off-axis locations in fixed spatial relationship with each other, light returned from an image spot on a remote object illuminated by the image beam ; returning a reference beam to said respective collectors; combining the returned reference beam with light returned from the remote object at each collector; producing OCT image signals at each collector; and processing the OCT signals received at the respective detectors to create a two or three dimensional image of the remote object with enhanced resolution.

In one embodiment the processing takes into account the phase relationships between the OCT signals at the two collectors.

In yet another aspect the invention provides a high resolution remote imaging system providing depth information, comprising: a constellation of at least three satellites in fixed relationship to each other; an OCT unit for generating an image beam and a reference beam one of the satellites; at least two off-axis collectors for receiving light returned from an image spot on a remote object illuminated by the image beam, said collectors being on the respective other satellites; a reference path for returning the reference beam to said respective collectors; optical combiners at said respective collectors for combining the returned reference beam with light returned from the remote object; detectors at said respective collectors for producing OCT image signals; and a processor for processing the OCT signals received at the respective detectors to create a two or three dimensional image of the remote object with enhanced resolution.

If the surface within the spot can be assumed to be flat, the resolution can be enhanced with a single off-axis collector, and the invention expressly extends to such a configuration.

Yet another aspect of the invention provides a high resolution remote imaging system providing depth information, comprising: an OCT unit for generating an image beam and a reference beam; an off-axis collector for receiving light returned from an image spot on a remote object illuminated by the image beam ; a reference path for returning the reference beam to said collector; an optical combiner at said collector for combining the returned reference beam with light returned from the remote object; and a detector at said the collectors for producing an OCT image signal with enhance lateral resolution.

The invention is particularly suited for mounting on CubeSats, i.e. miniaturized satellites that are mode up of cubic units.

Brief Description of the Drawings

The invention will now be described in more detail, by way of example only, with reference to the accompanying drawings, which:

Figure 1 is a general overview of the satellite setup; Figure 2 is more detailed view of the interferometer setup;

Figure 3 is a diagram showing the interferometer scheme;

Figure 4 is a diagram illustrating the difference in path length between different beams for a flat surface within the spot;

Figure 5 is a diagram illustrating the difference in path length between different beams for a surface of varying height within the spot;

Figures 6a to 6c show the detector signals in a swept-source arrangement;

Figure 7 is a further illustration of an embodiment of the invention with a target having different reflectivities over the beam spot;

Figures 8a to 8c show the results of performing an A-scan on the illustrated target as seen by the different collectors;

Figure 9 is an illustration of an illuminated spot on a target;

Figure 10 is a block diagram of the electronics unit;

Figure 1 1 is a flow chart showing the processing steps carried out by the processing unit; Figure 12 is a schematic diagram of a system similar to the one shown in Figure 1 ;

Figure 13 is a schematic view showing a spot trace a path over the ground;

Figure 14 is a side view of a system with a common single source OCT and collector mounted on the same satellite and in the same plane as Figure 2, but with a tilting beam;

Figure 15 is a schematic diagram of an experimental setup illustrating the present invention; Figure 16 is a diagrammatic representation of a spotlight mode system ;

Figure 17 shows the set-up assuming that the source is moving along a straight line in the y- direction;

Figure 18 shows a basic "generic" swept-source OCT set-up in schematic form ;

Figure 19 shows the outgoing signals (positive gradient) and the returning signals;

Figure 20 shows the section of the Fourier (X, Y) plane in which samples are available; and Figure 21 is a diagram helpful in understanding the theory.

Detailed Description of the Preferred Embodiments

In Figure 1 , the system in accordance with one embodiment of the invention comprises an OCT apparatus mounted on a main satellite 10 producing an image beam 1 1 directed at the earth 12, a reference beam 13 directed at a mirror mounted on a second satellitel 4 and spaced from the OCT apparatus by approximately the height of the first satellite 10 above the ground, typically about 300kms for a low-earth orbit satellite. The reference mirror 14 returns the reference beam 13 to the OCT apparatus on satellite 10, and first and second collectors mounted on third and fourth collector satellites 16, 18 respectively, also located in orbit at the same height above the ground and distance from the reference mirror as the OCT apparatus. The satellites 10, 12, 18 move together in a constellation in a low earth orbit such that they remain stationary relative to each other.

It will be appreciated that it is also possible to dispense with the main satellite 10 and mount the OCT source on one of the off-axis collectors 16, 18. The OCT source does not have to be normal to the surface of the target as illustrated.

The system is shown in more detail in Figure 2. In this non-limiting example the collector satellites 16, 18 are stationed about 50m from the main satellite 10. The length of the object beam is about 300kms. The point 9 in the main beam where the optical path difference between the reference beam and object beam is zero is located at a known point above the ground, in this example about 50 meters above ground. Advantageously, the satellites can have greater separation, for example, 3 or 6kms as discussed below. The system will return a signal when the reflecting point lies within a distance from the point where OPD=0 up to a maximum theoretical range of approximately the instantaneous coherence length of the source. A typical source might have an instantaneous coherence length of 200 meters, but in practice only about half that range is likely to be useful, making the effective range 100 meters. The system will also return mirror image signal on the opposite side of OPD=0 at the same distance as the actual object, so it is desirable to have OPD=0 at a point above the highest point that is likely to be imaged to eliminate any ambiguity in the results.

Light scattered off an object on the ground within the illuminated spot 15 is returned to satellite 10 and some light is also returned to the collector satellites 16, 18.

In this exemplary embodiment the OCT apparatus carried by the satellite 10 and shown in more detail in Figure 3 comprises a light source 20 in the form of a swept source tunable laser with a center frequency of 1550nm, a beam splitter/combiner 22 dividing the light into an object beam 24 that is scanned over a ground-based target 28 by scanner 26 and directed through lens 48 on the main satellite 10. With the aid of adaptive optics, it is expected the collimated object beam 24 will have a spot size of about 1 meter where it strikes the ground, although the spot size may be greater than this.

The splitter/combiner 22 also outputs a reference beam 30 that is reflected by mirror 45 to splitter/combiner 34, which in turn directs one portion of the reference beam to splitter/combiner 38 via splitter/combiner 36 and mirror 40 and another portion of the reference beam 32 to splitter/combiner 42 via mirror 44.

A portion of the light striking the target 26 is reflected and collected by lens 48 and directed via splitter/combiner 22 and mirror 44 to splitter/combiner 42, where mixes with the portion of the reference beam 32 and provides output beams split 55/50 to photo-detectors 64 that provide a balanced output to differential amplifier 65. The light returned from the target is also on the ground is also collected by lenses 46, 50 located on collector satellites 14, 18 respectively.

The collector beam from lens 46 is returned via mirror 52 and splitter/combiner 54, where it mixes with the first collector reference beam for detection in balanced photo-detectors 56 that provided an output to differential amplifier 63. The output from lens 50 is returned via mirror 58 to splitter/combiner 38, where it mixes with light from the second collector reference beam to provide an output to balanced photo-detectors 60 that provide an output to differential amplifier 61 .

In Figure 3, the mirror 45 and splitter/combiners 34, 36 are mounted on the reference satellite 14. The lens 46, splitter/combiner 54, photo-detectors 56, and differential amplifier 63 are mounted on one of the collector satellites 16, while the lens 50, mirror 58, splitter/combiner 38, photo-detectors 60, and differential amplifier 61 are mounted on the other collector satellite 18. The remaining components are mounted on the main satellite 10.

Referring again to Figure 3, the main channel functions in a similar manner to a conventional swept-source OCT instrument except that it is scaled up to kilometers and centimeters instead of microns. As shown the OCT apparatus on the main satellite 10 is 300km above the ground, where it creates an illuminated spot 15 of about 1 meter in diameter.

The axial resolution Azof a swept source OCT system is given by the expression

where n is the refractive index of the medium, A₀\s the center wavelength of the light source, and Α is the swept wavelength.

In the present example the source 20 is a tunable laser with a center wavelength of 1550nm, but very different parameters from conventional OCT. The coherence length of the light source defined by the instantaneous line-width is in the order of 100s meters, and at least 100 meters. The tuning range is in the order of picometers. Such a source would provide remote depth information over a range of 100s meters within the point where OPD = 0 to an axial resolution in the order of 5 cms, the precise value depending on the laser parameters and atmospheric properties. In order to ensure that the point where OPD=0 is close to the ground, the reference beam needs to be approximately the same distance from the OCT source as the height of the OCT source above the ground.

The frequency sweep speed should be in the order of tens or hundreds of kilohertz (where 10 kHz implies 10,000 sweeps per second). Such a sweep frequency is required in order to maintain sensitivity, which is affected by the speed of the satellite over the ground.

Each sweep produces an A-scan over the measurement range (100s meters) in the axial direction of the beam from the point where OPD=zero over the measurement range, which as noted is determined by the coherence length of the source. It should be noted that unlike conventional OCT, the object is not assumed to be transparent, so the reflected light is returned only from a single point in the depth direction. This means that the OCT acts to provide topographic information, rather than tomographic information as is the case in conventional OCT where the target is assumed to be at least partially transparent to the light.

In order to build up an image on the ground, the spot needs to be moved in translation, both in the x-y directions. The scanning in one direction can be achieved by the motion of the satellite constellation over the ground. The motion in the perpendicular direction can be achieved by the scanner 26 tilting the object beam 1 1 in a direction perpendicular to the direction of the motion of the satellite. With the single beam described so far, the lateral resolution will not be better than the spot size, which as noted is typically in the order of 1 meter. However, the resolution can be dramatically improved by making use from the off-axis collectors 16, 18, which act to create a synthetic aperture that results in a effective spot size much smaller than can be achieved by a single beam alone. In alternative arrangement, it is possible to replace the scanner 26 by a line array of detectors so as to effectively complete a line scan in one operation.

A typical OCT signal produced at the output of amplifier 65 forming the main channel is shown in Figure 6a. A signal is returned within the instantaneous coherence length of the source about OPD=0. The spatial frequency within the signal shown in Figure 6a represents the distance from OPD=0. The higher the spatial frequency, the further the reflective point from OPD=0 . The Fourier transform of the OCT signal gives the distance of the reflective point from OPD=0. It is worth mentioning at this point that as with any interferometer instrument, the coherence length of the source only has to be at least equal to the measurement range. It does not have be coherent over the distance to the object.

If we turn now again to Figure 2, and look at a sub spot 15a on the target within the spot 15, the optical path length for the beams 17, 19 will not quite be the same. In this example, the beam 17 will have approximately an extra 4mm optical path length relative to the beam 19. The extra path length for other sub spots within the spot 15 will vary.

If the signal shown in Figure 6a is considered to be the signal output by collector 18 and the signal shown in Figure 6, the signal output by collector 16, the two signals will be offset by a small phase difference dependent on the extra path length as shown in Figure 6c. As will be explained in more detail below, this path difference will vary across the spot 15, but two signals generated at the two collectors emanating from the same sub spot on the spot 15 will always have the same phase difference. Consequently, by comparing signals from the two collectors 16, 18 having a constant phase difference as the spot 15 moves over the ground, the effective spot size on the target can be reduced to the detectable size of the sub spot 15a, which very much less than the size of the spot 15, and may be in the order of 10cms depending on many setup parameters. OCT in effect measures the reflectivity of a point at different OPDs. The basic principle of the combination of OCT with a synthetic aperture is illustrated in Figure 4, which shows the computation of the change in path difference for the left and right beams 17, 19 for the simple case where the object is flat with varying reflectivity across the spot 15. Regions 15c are assumed to have lower reflectivity and region 15b is assumed to define a sub-spot 15c of higher reflectivity. In Figure 4:

x represents the diameter of the spot 15.

δζ represents the difference in optical path difference as seen by each collector from one side of the spot 15 to the other.

c represents the height of the reflecting point relative to some arbitrary reference; in this example c is constant because the surface is assumed to be flat.

x, represents the position of the point 15b within the distance x; the mid-point of the spot is defined as x, = 0.

Zj represents the depth position of a point x, on the OPD scale, i.e. relative to the point where OPD=0, as seen by the collectors 18, 16;

RHz_j and LHz_j are the reflectivity values obtained from an OCT measurement as seen by the collectors 18, 16 pointx, as if the beams 19, 17 were single rays. In reality, the beams 19, 17 have a finite width so that the collectors 16, 18 actually create an aggregate signal from all the points x, across the illuminated spot 15 as shown below.

Θ is the known off-axis angle of the beam.

Using the small angle approximation it will be seen that

from which it follows, assuming that the surface of the target illuminated by the spot is flat that:

RH₇ = c + x£

LH = c - x£ where RH and LH represent the axial depth for the respective right and left beams, 19, 17 of the point at position x_i along a ray extending from the point at position x, to the respective collectors.

The OCT signal that each collector 16, 18 actually generates is an aggregate of the OPDs from all the points x, from -x/2 to + x/2 across the width of the illuminated spot. Different positions of x, contribute different amounts to the aggregate OCT signal received at the collector. The instantaneous reflectivity RH recorded by collector 19 is given by the expression:

In a conventional OCT system no fine detail is available within the spot 15 since only the aggregate signal RH is available. Looking at Figure 4, it will be seen that as soon as the spot 15 begins to move, the values of ¾ which are measured relative to the spot 15, change even while the new position of the spot overlaps with the previous position. For example, when the spot 15 has moved half a spot width to the right, the central higher reflectivity sub-spot 15b will be located on the left side of where the spot was in the previous position, thus changing the values of ¾. The net result of this effect is to increase the lateral resolution to a value that is greater than would be the case if it were dependent only on the spot size as in a conventional OCT system. In the case of the above example, where it is assumed that the object is flat across the width of the beam, an improvement in resolution is obtained with a single collector 18 or 16.

In the above illustration, it was assumed that the target was flat. In practice, the height h will vary across the width of the spot 15 so the actual OPD on one side of the spot could be the same as on the other if the height difference 8h exactly matches the difference in OPD. However, with two or more beams as described, the ambiguity is resolved.

Figure 5 shows an example where the height of the surface is assumed to vary across the width of the spot 15.

In this case

h(x) is the height of the point as a function of x.

Using a similar analysis that the one above, it follows that

or

RH + LH = 2h x. )

As in the case of Figure 4, an increase in lateral resolution is obtained but without making the assumption that the surface is flat.

By way of non-limiting example, if the satellite separation is 6kms and the distance to the ground is the ground is 300km, Θ ~ 0.01 and the spot size is about 1 m. In a conventional OCT system with a reflected beam normal to the target, the axial resolution would be not greater than 1 m, namely the width of the spot 15. Taking the case where the surface is flat but R, (Where R is reflectivity at the position x,) varies, the resolution of reflectivity differences in in the example shown in Figure 4 x, is ~ 2cm/axial resolution.

If the axial resolution is 2mm (approximately 500pm or 60GHz sweep range at 1550nm), the transversal resolution would be expected increase to ~ 10cm from 1 m.

This difference manifests itself among other things in the phase difference between the OCT signals noted in Figures 6b, 6c.

A further illustration of the invention can be seen with reference to Figures 7 and 8a to 8c. In Figure 7 the illuminated spot 15 is assumed to have a central region 15d of zero reflectivity (R=0 and outer regions 15e, 15f of reflectivity R = 2/3 and R=1 /3 of the overall reflectivity R of the spot 15.

Figures 8a to 8c are Fast Fourier transforms of the swept wavelength signals shown in Figures 6a to 6c and plot amplitude of the returned signal against distance measured on the OPD scale. This means that the position of the peaks is the distance from the point where OPD = 0 as set by the reference path to the OCT system.

The height of the peak is measure of the reflectivity of the returned light. In the case of Figure 8a, which relates to the light collected by the central collector 10, the height of the peak is a measure of the total reflectivity of all the regions 15d, 15e, 15f within the illuminated area because their optical path difference are equal as shown. The height of the peak in Figure 8a is a summation of the reflectivity from the different regions. The central collector 10 acts in a similar manner to a conventional OCT apparatus, except of course with path lengths in the order of 100's kms instead of a few centimeters as is the case in a conventional OCT apparatus, used for example to examine the eye. No extra information of the reflectivity variation within the illuminated area can be obtained from this single A-scan alone.

The additional information from the A-scans produced using the left and right collectors 18, 16 is shown in the Figures 8b and 8c. The left hand collector 16 'sees' the right hand region 15f (R=1 /3) as further away than the left hand region 15e (R=2/3) and therefore can differentiate the regions in the A-scan. The right and left hand regions in this example show up as separate peaks with different heights corresponding to their different reflectivities. The right hand collector 18 sees the left hand region 15e (R=2/3) as further away, so the peak with the greater reflectivity appears further along the x-axis. The left hand collector 16 sees the left hand region 15e (R=2/3) as further away, so the peak with the greater reflectivity appears nearer along the x-axis.

In the example shown in Figure 7 the surface of the target is assumed to be flat so the peaks give the locations of the regions with different reflectivity on the OPD scale as well as the amount of reflectivity of the regions. In practice the surface is not flat so that, for example, the extra path length that displaces the peak corresponding to the region 15f to the right of the peak corresponding to the region 15e could be completely or partially cancelled out by the increase in height of the region 15f resulting in the peak corresponding to the region 15f being shifted to the left. With a single A-scan there is thus an ambiguity as to whether the apparent location of a peak of particular reflectivity results from a lateral or vertical displacement within the illuminated spot. It is this ambiguity that is resolved by taking multiple A-scans of the same spot in accordance with the teachings of the invention.

In the case of Figure 8b the extra path length to the region 1 5f results in it being shifted to the right as seen by collector 16. However, for collector 18 it is closer so it is shifted to the left as seen by that collector.

However, if the surface was not flat and the extra path length as seen by collector 16 resulted from a depression in the surface of the target, the peak would still be shifted to the right as seen by collector 16. On the other hand as seen by collector 18 the depression would be even further away. As a result instead of appearing shifted to the left for the collector 18 this peak would be shifted even further to the right.

By correlating the data the ambiguities can be resolved to provide topographical information about the surface of the target within the illuminated spot. In some respects the methodology can be compared to the way in which the density ambiguities are resolved along successive radial scans in a CT scanner.

It can be seen from the A-scans shown that the combination of A-scans from the LH and RH apertures can be used to effectively 'triangulate' sub-areas within the illuminated area and differentiate their reflectivity. This explained in more detail with reference to Figure 9.

Consider a target that has a spot 52 illuminated by the OCT image beam. The spot is shown exaggerated for the purposes of illustration. Assume that the spot is non-reflective (black) except for a small sub-spot 58 of reflectivity Ft whose position within the spot is unknown. Assume also that the spot is flat except for a small depression 60 at some arbitrary location within the spot.

The Fourier transform of the signal generated by the collector 54 will show a peak whose height represents the reflectivity R of the sub- spot whose position on the x axis represents the distance of the sub-spot 58 from the collector 54 on the OPD scale. If this distance is Xi , it will be seen from Figure X that the sub-spot 58 could be located in the depression 60 or at position 62 on the flat portion of the spot where the distance to the collector 54 is the same as to the point on the surface of the target in the depression 60. Both locations would return the same signal to the collector 54.

However, if we now look at the signal returned by the collector 56, if the sub-spot were located at position 62 on the flat portion of the spot it would appear at a shorter distance x₂ from the collector 56 than if it were located in the depression, where it would appear at distance x₃. By knowing x, and x₃ from the respective A-scans taken from the collectors 54, 56, it is possible to triangulate the position of the sub-spot 58 within the spot 52.

In practice of course the target surface is not smooth and multiple overlapping signals different reflectivities are obtained. However, by correlating and mathematically processing the signals in a manner similar to the way in which CT scan signals are processed, it is possible to obtain a topographical map of the surface within the spot 52 at a greater resolution than can be obtained with a single beam.

In an OCT system, the lateral resolution is dependent on the optics. Another way at looking at the system is to consider the collectors as creating a synthetic aperture that effectively increases the lateral resolution of the optical system.

During the lateral scanning process, the beam should be moved a minimum distance equal to the theoretical sub spot size produced by the synthetic aperture of the imaging system (i.e. a smaller distance than that of the case for a single aperture.

Figure 10 is a diagram of the system showing the main functional components. The target 28 is scanning by the imaging system forming part of the OCT apparatus connected by an optical fiber network 82 to the tunable source 20, which is in turn controlled by central processing unit or processor 86. The low speed DCA and ADC sends control signals to the tunable source 20 and imaging system 80. The fiber network is also connected to the high speed ADC card, which generates digitizes the signals generated by the differential amplifiers. The instructions controlling the processor may be stored in a suitable storage medium such as a hard disk, flash drive etc.

Figure 1 1 outlines the steps involved in generating a 3D image. In a first step 100, the object beam 1 1 is pointed at a target. At step 102, the wavelength is swept for each location before the beam is moved to the next location, wherein each location is defined by a sub-spot. At step 104, light collected at each aperture is mixed with a portion of the reference beam taking into account the time delay time delay from the source down to the object and back. At step 106 an A-scan is produced for each collector, and at step 108, the different A-scans from the different apertures are collated to produce a composite A-scan of increased resolution for that location, in this example using the relative phase information of the signals. It will be appreciated that it is also possible to collate the A-scans based on the path length information. At step 1 10, an A- scan is produced for each location, and at step 1 12 the composite A-scans are collated to produce a 3D topographical image.

Typically, the scanner 26 will scan the target laterally moving from location to location after each A-scan has been taken, and then the movement of the satellite constellation over the ground can be used to effect the longitudinal scan. This creates a raster scan of the area of interest. Alternatively, it is possible to dispense with the scanner by using one or two dimensional detectors arrays. For example, if the image is focused onto a line of detectors, it is possible to obtain a complete horizontal line of information at once. This coupled with the A-scan will give a B-scan, i.e a sectional scan (although in this case, the information is likely to be only topographical as opposed to tomographical since unlike conventional OCT the wavelength does not penetrate the object) . Usually, this will be sufficient since the motion of the satellite will effectively perform the scan in the orthogonal direction. However, in the case of a vehicle- mounted system, especially if it is a slow-moving or stationary vehicle, it may be desirable to have a two-dimensional detector array to create a complete X-Y raster scan at once.

It will be appreciated that resolution can be improved by employing more than two collectors and also of course making use of the signal returned to the main OCT source.

Moreover, in the embodiments described so far simultaneous A-scans have been obtained of the same illuminated spot on the target from different angles by the off-axis collectors 16, 18. As explained above by aggregating the information from the different off-axis A-scans of the same spot it is possible to increase the lateral resolution to a level greater than the resolution that can be achieved by a single A-scan alone.

It will be appreciated that a similar result can be achieved by obtaining the different A-scans of the target with the same collector by rotating the collector as it moves over the target so that it points at the same spot on the target. In this embodiment successive A-scans from different positions of the collector, and thus at different off-axis angles, are recorded for subsequent post-processing. The successive A-scans are then aggregated in the same manner as described above in the case of simultaneous scanning to obtain an image of greater lateral resolution than can be achieved with a single A-scan. In this embodiment the synthetic aperture is obtained by moving the collector and retaining the obtained A-scans for subsequent post processing.

Figure 12 provides a further illustration of the improvement in resolution achieved with embodiments in accordance with the invention. It is assumed for illustrative purposes that satellites 210, 213, 214 and spot 212 on the ground 1 lie in the plane of the paper with satellite 219 out of the plane of the paper. In this, the increase in resolution occurs in the plane of the paper, i.e. in the x-direction as shown. The array of satellites moves over the surface of the earth in a direction normal to the plane of the paper, or y-direction. The use of collectors at different angles in the x-direction does not improve the resolution in the y-direction.

As shown in Figure 13, as the array of satellites moves relative to the surface of the earth, if the imaging beam 21 1 remains fixed relative to the satellite 210, the imaging beam 21 1 traces out a series of spots 212, 212¹ , 212² etc. However, as the satellite moves if the imaging beam is slightly tilted so that the spot remains in the same position as the OCT satellite 210 moves a defined distance, a measurement can be taken from the same collector of the same spot at one or more different angles. The OCT signals obtained at different angles in the y-direction from the collectors 213, 214, which can also include tilting mirrors 251 , 252 to enable them to point at the same spot, enable the resolution to be improved to better than the spot size in the y-direction in a similar manner to the way it is improved in the x-direction.

This point can be better illustrated with reference to Figure 14, which shows an embodiment wherein only a single OCT satellite 20 containing the both source and collector illuminates a spot 2 on the ground with spotlight beam 22. Satellite 23 moving in fixed relationship to the satellite 20 returns a reference beam 24. The satellites 20 works like a scaled up version of an ophthalmic OCT. The satellite 20 contains a tilting mirror 50, such as a galvo scanner, which as the satellite moves over the range r, tilts to keep the beam 22 on the same spot 21 on the ground. This process is repeated for a succession of spots. If OCT measurements are taken when the satellite 20 is at positions 20¹ , 20², it will be seen the signals can be combined to obtain an imaging resolution better than the width of the spot in the y-direction.

Thus, by taking measurements at different angles in the y-z plane due to the motion of the satellite over the ground, and tilting the mirror, it is possible to increase the resolution in the y- direction. By combining the two techniques, multiple satellites in the x-direction, and motion of satellites in the y-direction, couple with a tilting mirror, it is possible to increase the resolution in both the x-y directions to a level better than dictated by the spot size. In this example, the collectors lie in the x-z plane, i.e. in a plane whose normal is the direction of movement. It will be appreciated that the plane containing the collectors could lie at an angle to direction of movement since there would still be a component in the x-z plane.

In another embodiment, particularly useful for marine applications, it possible to replace the reflector satellite with a reflector on the surface of the earth, on the ground, or possible on the water. In the case of marine applications, it may be possible to use the water-air interface itself as a reflector, in which case a single satellite could be used for imaging underwater objects. An advantage of using a surface-based reflector is that both the imaging beam and reference beam travel essentially the same path through the atmosphere. The closer the reflector is to the target the more this is the case. A wavelength of 1 .5 microns could be used to image objects on the surface and 532 nm for subsurface objects down to a depth of around 40 m.

Although the increase in resolution obtained by taking OCT measurements of the same spot at different angles has been described in geometric terms, the essence of the OCT technique is that it provides both amplitude and phase information about the target. Unlike synthetic aperture radar systems, where it is possible to track the phase directly, optical frequencies have periods in the order of 10^~14 seconds. Optical detectors cannot respond this fast, so it is not possible to generate in-phase and quadrature channels directly. OCT in effect uses an optical technique to recover the phase of the light interferometrically.

As noted previously, the OCT signal received by a collector from an illuminated spot is effectively a composite signal derived from all the individual reflector points within the illuminated spot. Combining the OCT signals containing amplitude and phase information obtained at different angles from the same spot allows the information from the individual reflector points to be obtained in a manner that may be compared to the way in which multiple X-ray line scans through an object at different angles may be combined to create a map of the reflectivity of the points within the area scanned. The output of each line scan is a composite result of the absorption along the line, but by combining the results from line scans at different angles it is possible to compute mathematically the absorption of each point. Another way of looking at the system is that the OCT signals provide the phase information required by a synthetic aperture system similar to that available at radar wavelengths. The system is an optical analogy of a synthetic aperture radar system. A similar improvement to that obtained by synthetic aperture radar over conventional radar can be seen.

In order to demonstrate the concept and experimental setup was established as shown in Figure 15. Light from tunable source 330 is split at directional coupler 331 . This was a Purespectrum LM, from Teraxion Inc, Canada. Measurements were made at 10GHz with a 1 kHz sweep rate. A portion of the light is sent to the k-clock network 332 whose output is sent to a high speed balanced detector 334. The output of the balanced detector 334 is passed to high speed analog-to-digital converter (ADC) 335. The k-clock network is a Mack-Zender interferometer with a fixed path difference. The k-clock has is common in swept source OCT designs for resampling of data to take into account non-linearity and variation of frequency sweeps. The k-clock channel is used for both timing of sweep start and linearization.

The main portion of the light is sent to the target 336 through the directional coupler 337. Light returned from the target 336 returns through the directional coupler 337 and mixes with the reference light from reference path 339 in the directional coupler 338. The output is sent to balanced detector 340 and then to analog-to-digital convert (ADC) 341 . The ADCs 341 and 344 are connected to processor 344, which extracts the image data from the composite OCT signals.

Light from the directional coupler 337 is directed as a beam 343 from collimating lens 342 via termination 345. The target 336 is mounted for angular movement in the x-plane (the plane of the paper) and tilt movement in the y-plane. It will be observed that the beam or spot size is comparable to the size of the target so in a conventional OCT, the system would not be able to resolve an image on the target. This demonstrates the ability to resolve images greater than the spot size by taking measurements from different angles using the principles of the invention.

In practice, two targets 336 were employed. One consists of a small rectangular black card with a pair of parallel white stripes approximately 2 mm. apart. The other consists of a card with a single white stripe. The card is mounted on a 6210 Cambridge Technology galvo- scanner.

Using the test setup we have measured a sensitivity of ~100dB for a 1 millisecond measurement time (a 20mW input power). This means that for every 10¹⁰ photons sent out, a signal can be detected if at least 1 is returned to the receiver. At this wavelength (1550nm) 1 mW equals ~ 8 x 10¹⁵ photons per second, therefore we are currently needing 16000 photons each millisecond (noise equivalent power is 2 picowatts).

The resolution measurements were consistent with a value of ~50mm, expected for a source modulation bandwidth of 10GHz.

The above experiment demonstrates how using an OCT signal it is possible to resolve distances less than the width of the beam by obtaining signals at different angles. In a space environment, rotation of the mirror would be co-ordinated with movement of the satellite over the ground so as to keep the spot in the same place on the ground while the set of measurements are taken. Alternatively, rotating the mirror to different angular positions is equivalent to taking measurements from collectors receiving returned beams at an angle to each other.

It should be noted that the use of interferometric optical techniques from space to look at the ground would normally be limited by the coherence length of the source needed to cover the distances involved. While it is not impossible to build a source with several hundred kilometres of coherence length, it is expensive and subject to difficulties such as the need for a high power output. Using a reference path delay rather than mixing with a local oscillator, a much shorter coherence length can be used. This shorter coherence length means high power and compact sources could be exploited for low earth orbit use. The coherence length only needs to cover a range of 100 meters or so, which is achievable with current technology.

While the above demonstration used a target of several millimetres across and captured data from this at angles spanning hundreds of milliradians, this requirement is a function of wavelength. If the target was meters across the required number of angles would be measured in tens of microradians or less. This would equate to a satellite only moving a matter of meters.

It is important to establish that a demonstration that works over a short distance in the lab will also be viable in a real-world situation, imaging from a satellite at, say, 300km. In order to examine this, we need to determine that the atmospheric effects will not interfere with the ability of the spotlight-mode optical SAR system to synthesize images of sub beam-width transverse resolution. One place to look for the required formalism is the astronomy literature, and we note several key results from this area. Turbulence, air currents etc. will produce random fluctuations of refractive index. The main effect of these is to introduce a random phase shift in the wave fronts passing through the medium. An analysis of this is covered in the appendices, but our analysis suggests that a 10cm resolution from a measurement time of < 1 milliseond will not be limited by atmospheric effects.

In the above embodiments only two dimensions have been considered. In the case of simultaneous collection of A-scans the enhanced resolution is obtained in the plane containing the collectors. In the case is sequential scanning the enhanced resolution is obtained in the plane (X-Z) defined by the beam and the motion of the collector. It is also possible to enhance the resolution in the orthogonal direction (Y-Z plane). In the case of simultaneous scanning an array, for example a triangular array, of collectors not in the same vertical plane can be arranged above the target so as to give enhanced resolution in the Y direction. In the case of sequential scanning the collector can be set to look sideways relative to its direction of motion at a specific angle. Since the angle is known, enhanced resolution can be obtained in the X-Y plane in a similar manner to the embodiment with an array of collectors above the target.

It is also possible to make the system polarization sensitive as can be done with conventional OCT to take advantage of different polarization properties of the target. The invention also extends to a system operating in different polarizations.

Additionally phase information can be used to further enhance the sensitivity of the system.

The system can be scaled down for terrestrial use, or use, for example, on a vehicle such as an aircraft, boat or truck. In the case of an aircraft the collectors could be conveniently mounted at the wingtips. In these, cases the necessary path length for the reference beam, which needs to be roughly the same as the distance to the target, can be obtained by using an optical fiber delay line.

A more rigorous analysis of the underlying theory will be now presented with reference to Figures 16 to 21 . The set-up is basically that of an OCT system, but with rather different parameters to those normally encountered. The general idea for the is to combine data sets collected from multiple angles from the same patch of ground, so as to overcome the transverse resolution lower limit of classical OCT, which, being a probe technique, is limited by the beam spot size.

The situation can be formalized in a manner analogous to the processing in a CAT scanner, where a series of projections of an unknown inhomogeneous solid object (the patient) are combined so as to provide a 2D slice of that object. The signal processing rests on the so- called Fourier slice theorem, which says that the Fourier transform of the projection taken through the object at angle <9 is equal to a slice at angle Θ through the 2D Fourier transform of the (unknown) object. Thus a series of projections at a set of angles {<¾ can be used to produce a polar sampling of the 2D Fourier representation of the unknown object, which can then be used to recover an estimate of the true physical object by an inverse Fourier transform (IFT). After obtaining the polar sampling, one can then either interpolate to get samples on a Cartesian grid, before performing the 2D-IFT to get the range and cross-range information, or one can use the "filtered back-projection" algorithm, or some variant of it . The main difference between the CAT data and the SAR data is that the SAR data is available only over a limited range of angles, while the CAT data is available over the full [0, π] range. This puts a limit in the spatial resolution in the cross-range direction. In any case, the spatial resolution in the range direction (conventional OCT "A" -scans) are largely determined by the chirp range of the swept laser source, as in conventional OCT. Figure 17 shows the set-up assuming that the source is moving along a straight line in the y- direction and looking at a patch on the ground defined by a circle of radius L. Of course, the source will probably be a Gaussian beam, but we can define L as the region where a useful S/N ratio is obtainable for practical purposes, and leave the exact details of the formulation until later

The illuminated ground patch is at a mean distance R (in conventional terminology, the "Range"), and Y is the direction of travel. X is the (conventionally-called) "Range" direction, while Y is the transverse, or "cross-Range" direction. The source is assumed to be flying at constant speed along the Y-axis, at a height h. We will initially set the height to h=0_t and ignore the logical contradiction this causes, as it does not affect the basic principle of operation and keeps the mathematics as simple as possible. It is possible to add the necessary refinement of h>0 later, and accommodate it by simple co-ordinate scaling. Other details such as the locus of constant range fi=constant being actually arcs of circles and not straight lines of constant X, we will also gloss over, as these refinements can be applied later without greatly affecting the results.

The object of the exercise is to find the ground reflectivity function g(x,y). Referring to Figure 17, the lack of resolution in the cross-field direction can be interpreted as the received signal being simply the line integral of the complex ground reflectivity function g(x,y) along a line of constant v in the (u,v) rotated local co-ordinate system. This local system is adjusted so that u coincides with the projection of the radius vector R onto the ground, v is orthogonal to it, and u=x, v=y when 6=0 (and R is a minimum).

Figure 18 shows a basic "generic" swept-source OCT set-up in schematic form.

The source has constant amplitude ^o^ . d and C₂ are fused couplers, assumed 50:50 for now. The signal and reference fields on the output side of 0_Λ are given by

(1 )

Paralleling the notation of [5], we define the input field as the linearly chirped signal of amplitude

E₀ = Aexp [ί^' ( ί¾ί + at² )}

(2)

Where a is the chirp rate, and the signal lasts from t=-T/2 to t=+T/2, i.e. a length of time T. Define ¾ as the round-trip time from the center of the observed patch, as a distance R, we have

2R

c (3) Where c is the speed of light. The distinguishing feature of this application, in contrast to conventional (short range) OCT, is that the chirp time is generally small compared to the transit time given by equation (3). In OCT, the reference and the signal strongly overlap in time, and so it has more in common with FMCW.

Thus, the reference electric field is described by

E_R = A exp {i [e¾ (i - T₀ ) + a(t - r₀† ]}

(4)

And the returning signal field is described by

Where p (0, u) = j g (M COs (#) - vsin(#) , M sin(#) + vcos(#)) iiv

(6) is the line integral of the ground reflectivity function along the line u=constant, in the rotated (u,v) co-ordinate system. The constants A and a are real quantities denoting strength of the reference field (A) and system losses in the signal arm (a), and can be found by calibration.

Equation (6) gives the projection of the unknown function g(x,y) onto the u-axis, which is (for the f^h measurement) inclined at <9=<¾ to the x-axis.

In conventional SAR using microwave radar, the returning signal is multiplied by the real and imaginary parts of the chirped, delayed, reference signal given by (2) to generate the in-phase and quadrature channels. This is the point of departure with the optical version, in which this multiplication is not possible, and interferometric signal processing schemes are used instead.

Referring again to figure 18, the fields after the second coupler are represented by

(7)

Where E_R and E_sare given by equations (4) and (5) respectively.

Assuming a detector responsivity of unity, the two detector currents Ι_Ί and l₂ are given by ~ ( ⁺ l¾l

= (_iiE_R + E_S

After a little algebra, we get Ι, ^Ε^ + \E_S - ΑαΕ (ρ Χ , θ) + Ρ (Χ, θ))

Where

Ρ(Χ , Θ) = j^" p (0, u)exp{-iuX}du

-L

Which is proportional to the Fourier transform of the quantity ρ(θ,υ) the projection of the reflectivity function g along the v-direction, inclined at Θ to the x-axis.

In order to get to equation 10, we have ignored the (dimensionless) term

Which is quadratic in u. Keeping this term spoils the simple Fourier transform relationship expressed in (10), this quantity can be ignored compared to other terms in the exponential for a wide range of cases of practical use, the same applies in the optical domain, although care is needed. The quantities Ρ(Χ,Θ) are only available for a limited range of X and t. We can derive the permissible range of X, from causality and the fact that the chirp is only on from - 772 to +T/2. Figure 19 shows the passage of the various signals on a "space-time" diagram.

Figure 19 shows the outgoing signals (positive gradient) and the returning signals (negative gradient), and it can be seen that the first valid signal resulting from the chirp pulse in [- T/2 , +T/2] arrives back at the source at time t_start = +T/2 +2(R-L)/c , while the last valid signal arrives at time -T/2+2(R-L)/c. From this, X_mi„ and X_max can be calculated using equation 10.

Figure 20 shows the section of the Fourier (X, Y) plane in which samples are available. It can be seen that this region is very limited. By considering a single ^-function reflector at location (x₀, y₀), we find that the 2D Fourier representation of this is proportional to exp{-i[x₀X + y_QY]}

And by considering the inverse FT of this sampled by integrating A^" from X_m,„to X_max, and Y from -zlVto +ΔΥ, with AY= (2fi¾ c)sin(0_max) , the spatial resolution is given by

c. 2π nc

ox -

AX 2ατ

c 2π 7Tc

oy =

AY 2<y_o sin (0_max ) _{(1 3)} Note that the axial (range) resolution, δχ, is inversely proportional to the sweep offset independent of the angle scanned (as per conventional A-scan resolution in OCT), and the cross-range resolution, dy, is dependent on the total angular scan range and independent of the sweep parameters. Our proof of principle experiment used a fixed range, so only the y- resolution was relevant. The y-resolution can be alternatively derived by considering a Michelson interferometer with a single point scatterer on a tilted plane, giving the same result. In order to be able to use the Fourier slice theorem to build a densely sampled Fourier-plane representation of g, we need the FT. of the p(x,u) quantities as expressed in equation (10), so we need Ρ(Χ,Θ), however, we see from (9) that only the real quantities P+P* are available.

If we temporarily forget about OCT and put P = exp(/ in equation (9), as would be the case in an "ordinary" interferometric sensor set up to measure the phase difference between the two paths, we would have the classic "1 +cos" and "1 -cos" terms.

A similar problem exists and is well-known in classical OCT, it is that of the "artifact problem". Here the full measurand range is generally unavailable, as Fourier transforming the real sampled quantity gives a folding about the origin, so a reflective feature at +u₀ (in our notation) will be associated with one at -u₀. The corresponding problem in the current context is far worse, because we are trying to reconstruct a 2D surface, and a detailed treatment shows that a feature at (x₀, yo) in the region of interest produces an artifact at (-x₀, -yo)-

As a result, the circular region gets folded twice, as in figure 21 . In figure 21 , we can see that quadrant q₁ is effectively reflected through the -axis onto q₂ and then in the y-axis to q₃. Meanwhile, q_∑ is reflected onto q and then onto q₄. If q₃ and q₄ had zero reflectivity so g=0 in those regions, then the features in the semicircle defined by q₁ and q₂ would be "flipped over" onto q₃ and q₄, and we would lose half the information. However, of course, if the quadrants are non-empty, then there will be a hopeless jumble from which nothing useful can be recovered.

In summary, embodiments of the invention are capable of detecting an object or person with a resolution less than ten centimeters and height measurement to a resolution less than 5 centimeters. The use of active infrared imaging means that the system is able to "see in the dark" . Persons or weapons concealed below the natural level of the ground such as in dug out trenches, below the tree canopy or on the surface of water would also be detectable even at night with a resolution not possible with current LIDAR or SAR techniques.

By systematically scanning known areas of activity, a detailed picture of changes to that area can be mapped. Small surface vessels can be used in coastal waters or rivers to move people, equipment or small vehicles around. Detection of these craft and identification by way of size and height in the water would be an advantage if undertaken to a high resolution. Similarly, good resolution of moving aircraft can also be achieved without risk to intelligence gathering personnel.

Claims

1 . A high resolution remote imaging apparatus comprising an OCT source for illuminating a remote object with an imaging beam; a reflector for generating a reference beam; one or more collectors for receiving light returned from the remote object and comparing the returned light with the reference beam at different angles to obtain a plurality of OCT signals; and a processor for extracting image data from the OCT signals.

2. A high resolution remote imaging apparatus as claimed in claim 1 , wherein said processor is programmed to extract said image data from amplitude and phase information provided by said OCT signals.

3. A remote imaging apparatus as claimed in claim 1 , or 2 wherein the OCT source and one or more collectors include tiltable mirrors so that the one or more collectors obtain data from the same spot as the OCT source and collectors move relative to the object.

4. A remote imaging apparatus as claimed in any one of claims 1 to 3, comprising at least two collectors moving in tandem for obtaining data at different angles in a plane lying at an angle to the direction of movement of the OCT source and one or more collectors.

5. A remote imaging apparatus as claimed in claim 1 , wherein the reflector comprises a reflective surface in fixed relation to the OCT source and remote from the object.

6. A remote imaging apparatus as claimed in claim 1 , wherein the reflector comprises a reflective surface in close proximity to the target.

7. A remote imaging apparatus as claimed in any one of claims 1 to 5, wherein the OCT source and collectors are mounted on satellites moving in a fixed relationship to each other.

8. A remote imaging apparatus as claimed in claim 6, wherein the reflective surface is mounted on a satellite moving in a fixed relationship with the OCT source and collectors.

9. A remote imaging apparatus as claimed in any one of claims 1 to 8, wherein the OCT source is a swept source laser.

10. A remote imaging apparatus as claimed in any one of claims 1 to 9, that is mounted on one or more cube satellites.

1 1 . A computer-implemented method of remote imaging comprising :

illuminating a remote object with an imaging beam from an OCT source;

generating a reference beam;

receiving light returned from the remote object and comparing the returned light with the reference beam at different angles to obtain a plurality of OCT signals; and

processing the OCT signals to extract image data.

12. A method as claimed in claim 1 1 , comprising processing phase and amplitude information provided by said OCT signals to extract said image data.

13. A method as claimed in claim 1 1 , comprising angularly displacing the imaging beam over a range of angles as the OCT source moves relative to the object to illuminate a defined spot for a sufficient period of time to permit returned light to be collected at different angles.

14. A method as claimed in any one of claims 1 1 to 13, comprising moving at least two collectors in tandem to obtain data at different angles in a plane lying at an angle to the direction of movement of the OCT source and one or more collectors.

15. A method as claimed in claim 12, wherein the reference beam is returned from a reflective surface in fixed relation to the OCT source and remote from the object.

16. A method as claimed in claim 12, wherein the reference beam is returned from a reflective surface in close proximity to the object.

17. A method as claimed in any one of claims 1 1 to 16, wherein the OCT source and collectors are mounted on satellites moving in a fixed relationship to each other.

18. A method as claimed in claim 17, wherein the reflective surface is mounted on a satellite moving in a fixed relationship with the OCT source and collectors.

19. A method as claimed in any one of claims 1 1 to 18, wherein the OCT source is a swept source laser.

20. A high resolution remote imaging system, comprising:

an OCT unit for generating an image beam and a reference beam;

at least two off-axis collectors for receiving light returned from an image spot on a remote object illuminated by the image beam, said collectors being for placement in a spaced relationship;

a reference path for returning the reference beam to said respective collectors;

optical combiners at said respective collectors for combining the returned reference beam with light returned from the remote object; and

detectors at said respective collectors for producing OCT image signals.

21 . A high resolution remote imaging system as claimed in claim 20, further comprising; a processor for processing the OCT signals received at the respective detectors by taking into account their phase relationships to create a two or three dimensional image of the remote object with enhanced resolution.

22. A high resolution remote imaging system as claimed in claim 20 or 21 , wherein the reference path includes a mirror for returning the reference beam to said respective collectors.

23. A high resolution remote imaging system as claimed in any one of claims 20 to 22, wherein the reference path is in the form of a delay line.

24. A high resolution remote imaging system as claimed in claim 23, wherein the delay line is a fiber optic delay line.

25. A high resolution remote imaging system as claimed in any one of claims 20 to 24, wherein the OCT unit comprises a swept light source.

26. A high resolution remote imaging system as claimed in claim 25, further comprising a controller for sweeping the wavelength at each of a series of sub-spots on the remote object.

27. A high-resolution remote imaging system as claimed in claim 25 or 26, wherein the swept light source is a tunable laser.

28. A high-resolution remote imaging system as claimed in claim 27, wherein the tunable laser has a coherence length of at least 100 meters.

29. A high resolution remote imaging system as claimed in claim 21 or any one of claims 22 to 27 when dependent on claim 21 , wherein the processor processes the OCT signals from each collector to produce a composite A-scan having an effective resolution less than the size of said image spot.

30. A high-resolution remote imaging system as claimed in 29, wherein the OCT unit also receives the reference beam to create OCT signals, and the processor includes an A-scan generated from the OCT unit in the composite A-scan.

31 . A high-resolution remote imaging system as claimed in any one of claims 20 to 30, further comprising a scanner for scanning the image beam laterally over an imaging area on the remote object to obtain two or three dimensional images.

32. A high-resolution remote imaging system as claimed in any one of claims 20 to 31 , further comprising an array of detectors at each collector to obtain two or three dimensional images.

33. A high-resolution remote imaging system as claimed in any one of claims 20 to 32, wherein the collectors are mounted on respective satellites for arrangement in a constellation with a fixed spatial relationship to each other.

34. A high-resolution remote imaging system as claimed in any one of claims 20 to 33, wherein the collectors are mounted on a vehicle.

35. A computer-implemented method of performing high resolution remote imaging to obtain depth information, comprising:

generating an image beam and a reference beam;

collecting, at two off-axis locations in fixed spatial relationship with each other, light returned from an image spot on a remote object illuminated by the image beam;

returning a reference beam to said respective collectors;

combining the returned reference beam with light returned from the remote object at each collector;

producing OCT image signals at each collector; and processing the OCT signals received at the respective detectors to create a two or three dimensional image of the remote object with enhanced resolution.

36. A computer-implemented method as claimed in claim 35, wherein phase and amplitude information obtained from the OCT signals is used to obtain the image.

37. A method as claimed in claim 36, wherein two or three dimensional image by taking into account phase relationships between the OCT signals generated at the different collectors.

38. A method as claimed in any one of claims 35 to 37, comprising reflecting the reference beam to said respective collectors.

39. A method as claimed in any one of claims 35 to 38, wherein the reference beam is subjected to a delay.

40. A method as claimed in any one of claims 35 to 39, comprising sweeping the wavelength of the image beam.

41 . A method as claimed in claim 40, wherein the wavelength is swept at each of a series of sub-spots within a spot illuminated by the image beam on the remote object.

42. A method as claimed in any one of claims 35 to 41 , further comprising processing the OCT signals from each collector to produce a composite A-scan having an effective resolution less than the size of said image spot.

43. A method as claimed in 42, wherein an A-scan generated from an OCT unit generating the image beam is included in the composite A-scan.

44. A method as claimed in any one of claims 35 to 43 further comprising scanning the image beam laterally over an imaging area to obtain two or three dimensional images.

45. A method as claimed in any one of claims 35 to 44, further comprising employing an array of detectors at each collector to obtain two or three dimensional images.

46. A method as claimed in any one of claims 35 to 45, wherein the collectors are mounted on respective satellites for arrangement in a constellation.

47. A method as claimed in any one of claims 35 to 46 wherein the collectors are mounted on a vehicle.

48. A high resolution remote imaging system providing depth information, comprising: a constellation of at least three satellites in fixed relationship to each other;

an OCT unit for generating an image beam and a reference beam one of the satellites; at least off-axis two collectors for receiving light returned from an image spot on a remote object illuminated by the image beam, said collectors being fon the respective other satellites;

a reference path for returning the reference beam to said respective collectors; optical combiners at said respective collectors for combining the returned reference beam with light returned from the remote object;

detectors at said respective collectors for producing OCT image signals; and a processor for processing the OCT signals received at the respective detectors by to create a two or three dimensional image of the remote object with enhanced resolution.

49. A high resolution remote imaging system, comprising:

an OCT unit for generating an image beam and a reference beam;

an off-axis collector for receiving light returned from an image spot on a remote object illuminated by the image beam ;

a reference path for returning the reference beam to said collector;

an optical combiner at said collector for combining the returned reference beam with light returned from the remote object; and

a detector at said the collectors for producing an OCT image signal with enhance lateral resolution.

50. A method of obtaining a topographical image of a remote target, comprising:

obtaining two or more OCT A-scans of an illuminated spot on the target taken at different oblique angles; and

computing the topography of the target within the illuminated spot by combining data from said two or more A-scans.

51 . A method as claimed in claim 50, wherein said OCT A-scans are obtained simultaneously from collectors located at different off-axis locations.

52. A method as claimed in claim 50, wherein said OCT A-scans are obtained sequentially by moving a collector over the target while keeping it pointed at the same spot so as to obtain said A-scans from different angles.

53. A computer readable storage medium having stored thereon instructions which when executed on a computer combine data from two or more OCT A-scans of an illuminated spot on a target taken at different off-axis angles to compute the topography of the target within the illuminated spot.

54. A computer readable storage medium as claimed in claim 53, wherein the topography is computed by triangulation.