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Title:
TELESCOPE WITH DE-SCANNING SECONDARY MIRROR FOR FORWARD MOTION COMPENSATION
Document Type and Number:
WIPO Patent Application WO/2023/203333
Kind Code:
A1
Abstract:
This application provides a telescope and method for performing forward motion compensation and an apparatus for performing forward motion compensation in a telescope. The telescope (100) is configured to observe an object in apparent motion having a first velocity in a first direction relative to the telescope, the telescope comprising: a primary mirror (102); a secondary mirror (104); and a detector (106); wherein the detector (106) is configured to detect light that travels from an effective target of the telescope to the detector (106), whereby: the primary mirror (102) is configured to reflect light incident from the effective target to the secondary mirror (104); and the secondary mirror (104) is configured to reflect light from the primary mirror (102) to the detector (106); wherein the secondary mirror (104) is dynamically moveable and is arranged such that movement of the secondary mirror (104) causes a position of the effective target of the telescope to move in the first direction along a track, such that the first velocity of the apparent motion of the object in the first direction is reduced.

Inventors:
REINICKE TOBIAS (GB)
BAKER ANTHONY (GB)
TUCKER SIMON (GB)
SILLS LIAM (GB)
Application Number:
PCT/GB2023/051041
Publication Date:
October 26, 2023
Filing Date:
April 20, 2023
Export Citation:
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Assignee:
GLOBAL SATELLITE VU LTD (GB)
International Classes:
G02B17/06; G02B27/64
Foreign References:
CN113189756A2021-07-30
CN103604420A2014-02-26
Other References:
LELOGLU UGUR MURAT ET AL: "A compact imager design concept for micro/nanosatellites using scanning mirrors", 2015 7TH INTERNATIONAL CONFERENCE ON RECENT ADVANCES IN SPACE TECHNOLOGIES (RAST), IEEE, 16 June 2015 (2015-06-16), pages 555 - 560, XP033196669, ISBN: 978-1-4673-7760-7, [retrieved on 20150817], DOI: 10.1109/RAST.2015.7208406
Attorney, Agent or Firm:
HILL, Justin John et al. (GB)
Download PDF:
Claims:
CLAIMS

1 . A telescope for performing forward motion compensation, the telescope configured to observe an object in apparent motion having a first velocity in a first direction relative to the telescope, the telescope comprising: a primary mirror; a secondary mirror; and a detector; wherein the detector is configured to detect light that travels from an effective target of the telescope to the detector, whereby: the primary mirror is configured to reflect light incident from the effective target to the secondary mirror; and the secondary mirror is configured to reflect light from the primary mirror to the detector; wherein the secondary mirror is dynamically moveable and is arranged such that movement of the secondary mirror causes a position of the effective target of the telescope to move in the first direction along a track, such that the first velocity of the apparent motion of the object in the first direction is reduced.

2. The telescope according to claim 1 , wherein the secondary mirror is configured to move by rotation to cause the position of the effective target of the telescope to move along the track.

3. The telescope of claim 3 wherein the secondary mirror is configured to rotate around a central axis of the secondary mirror, wherein the central axis is perpendicular to the principal axis of the secondary mirror, such that rotation of the secondary mirror causes the principal axis of the secondary mirror and the effective target of the telescope to move along the track.

4. The telescope of claim 3 or 4, wherein the secondary mirror is configured to be rotatable through a total scanning angle from a first mirror angle to a second mirror angle, wherein a normal angle of the secondary mirror is within the total scanning angle, wherein the normal angle of the secondary mirror is such that the principle axis of the secondary mirror is collinear with the principle axis of the primary mirror when the secondary mirror is arranged at the normal angle.

5. The telescope according to claim 4 wherein the secondary mirror is configured to be rotated in a scanning cycle comprising a scan and a back-scan, whereby: in the scan, the secondary mirror is configured to rotate from the first mirror angle to the second mirror angle at a first rotational velocity, such that the first velocity of the apparent motion of the object in the first direction is reduced; and in the back-scan, the secondary mirror is configured to rotate back to the first mirror angle at a second rotational velocity, wherein the second rotational velocity is greater in magnitude than the first rotational velocity.

6. The telescope of claim 5, wherein the detector is configured to capture one or more image frames during each scanning cycle.

7. The telescope of claim 5 or 6, wherein the total scanning angle is of a particular size such that rotation of the secondary mirror through the total scanning angle is configured to cause the position of the effective target of the telescope to move in the first direction along the track by a first distance, whereby the first distance is less than a second distance representing a projected field of view of the detector.

8. The telescope of claim 6 or 7, wherein the secondary mirror is configured to perform a plurality of scanning cycles, wherein the secondary mirror is configured to perform each scan of the plurality of scanning cycles such that the position of the effective target of the telescope at least partially overlaps for at least consecutive scanning cycles.

9. The telescope of claim 8, wherein the detector is configured to capture at least a first image frame in a first scanning cycle and at least a second image frame in a consecutive second scanning cycle such that the first and second image frames each include overlapping portions corresponding to the same position of the effective target of the telescope.

10. The telescope of any of claims 5 to 9, wherein the detector is configured to capture a plurality of image frames during each scan of each scanning cycle.

11 . The telescope of claim 10, wherein the detector is configured to capture each of the plurality of image frames according to a maximum exposure period for capturing each image frame, wherein the maximum exposure period is set based on a predefined pixel-drift value.

12. The telescope according any of claims 5 to 11 , wherein the first rotational velocity of the secondary mirror is dependent on the first velocity.

13. The telescope according to any of claims 5 to 12, wherein the secondary mirror is configured to rotate at the first rotational velocity to cause the position of the effective target of the telescope to move at the first velocity in the first direction along the track, such that the apparent motion of the object substantially freezes.

14. The telescope according to any preceding claim, wherein the secondary mirror is configured to be rotated by an actuator.

15. The telescope of claim 14, wherein the actuator comprises: a single axis electromagnetic voice coil actuator; a single or multi axis piezo-actuator, or a single axis direct drive brushless DC motor.

16. The telescope of any preceding claim, wherein the telescope is a Cassegrain telescope, wherein the primary mirror is concave and the secondary mirror is convex.

17. An imaging system comprising the telescope according to any preceding claim.

18. The imaging system of claim 17, wherein the imaging system includes a satellite for orbiting the Earth or a celestial body, wherein the satellite comprises the telescope.

19. The imaging system of claim 18, wherein the satellite is configured to pitch to perform forward motion compensation, such that the imaging system is configured to perform a first component of forward motion compensation by pitching the satellite and a second component of forward motion compensation by moving the secondary mirror of the telescope.

20. An apparatus for performing forward motion compensation in a telescope, the telescope having a primary mirror and a detector for observing an object in apparent motion having a first velocity in a first direction relative to the telescope, the apparatus comprising: a secondary mirror; and an actuator configured to actuate the secondary mirror; wherein the secondary mirror is configured to be positioned in an internal optical focussing pathway of the telescope to direct light to the detector of the telescope, wherein the secondary mirror is dynamically moveable by the actuator and is arranged such that movement of the secondary mirror causes a position of an effective target of the telescope to move in the first direction along a track, such that the first velocity of the apparent motion of the object in the first direction is reduced.

21 . A method of performing forward motion correction using a telescope having a primary mirror, a secondary mirror, and a detector, wherein the detector is configured to detect light that travels from an effective target of the telescope to the detector, whereby the primary mirror is configured to reflect light incident from the effective target to the secondary mirror; and the secondary mirror is configured to reflect light from the primary mirror to the detector; the method comprising: controlling the telescope to observe an object in apparent motion having a first velocity in a first direction relative to the telescope; controlling the telescope to move the secondary mirror with respect to the telescope to cause a position of the effective target of the telescope to move in the first direction along a track, such that the first velocity of the apparent motion of the object in the first direction is reduced.

22. The method of claim 21 , wherein controlling the telescope to move the secondary mirror comprises rotating the secondary mirror around a central axis of the secondary mirror, wherein the central axis is perpendicular to the principal axis of the secondary mirror, such that rotating the secondary mirror causes the principal axis of the secondary mirror and the effective target of the telescope to move along the track.

23. The method of claim 22, further comprising rotating the secondary mirror through a total scanning angle from a first mirror angle to a second mirror angle, wherein a normal angle of the secondary mirror is within the total scanning angle, wherein the normal angle of the secondary mirror is such that the principle axis of the secondary mirror is collinear with the principle axis of the primary mirror when the secondary mirror is arranged at the normal angle.

24. The method of claim 23, further comprising rotating the secondary mirror in a scanning cycle comprising a scan and a back-scan, whereby: performing the scan comprises rotating the secondary mirror from the first mirror angle to the second mirror angle at a first rotational velocity, such that the first velocity of the apparent motion of the object in the first direction is reduced; and performing the back-scan comprises rotating the secondary back to the first mirror angle at a second rotational velocity, wherein the second rotational velocity is greater in magnitude than the first rotational velocity.

25. The method of claim 24, further comprising capturing one or more image frames during each scanning cycle.

26. The method of claim 24 or 25, further comprising performing a plurality of scanning cycles, wherein consecutive scanning cycles comprise rotating the secondary mirror such that the position of the effective target of the telescope at least partially overlaps for the consecutive scanning cycles.

27. The method of claim 26, further comprising: capturing, with the detector, at least a first image frame in a first scanning cycle and at least a second image frame in a consecutive second scanning cycle such that the first and second image frames each include overlapping portions corresponding to the same position of the effective target of the telescope; and summing signal data originating from the overlapping portions of the first and second image frames to produce a higher-signal image frame.

28. The method of claim 27, further comprising: capturing a plurality of image frames during each scan of each scanning cycle; and summing signal data originating from the plurality of image frames captured during each scan cycle.

29. The method of any of claims 21 to 28, wherein the telescope is included in a satellite for orbiting the Earth or a celestial body, and wherein the method further comprises determining the first rotational velocity based at least on an orbital height of the satellite and a velocity of the satellite.

30. The method of claim 29, further comprising: performing a first component of forward motion compensation by pitching the satellite and performing a second component of forward motion compensation by moving the secondary mirror of the telescope.

31 . The method of claim 30, wherein pitching the satellite comprises cyclically pitching the satellite between a first pitching angle and a second pitching angle, such that the orientation of the telescope is pitched between the first pitching angle and the second pitching angle.

32. The method of claim 31 when dependent on at least claim 24, wherein, for each pitching cycle of the satellite, the method comprises: performing a plurality of scanning cycles.

33. A computer program, which, when executed by a processor, causes the processor to perform the method according to any of claims 21 to 32.

Description:
TELESCOPE WITH DE-SCANNING SECONDARY MIRROR FOR FORWARD MOTION COMPENSATION

TECHNICAL FIELD

[0001] The invention relates to a telescope with de-scanning secondary mirror for forward motion compensation, and in particular, a telescope, system, apparatus, method and computer program for performing Forward Motion Compensation (FMC).

BACKGROUND OF INVENTION

[0002] When an image is captured at high speed it is generally subject to image blur. This problem occurs when there is a differential in speed between the observer (camera) and a target object (subject of the captured image). In the reference frame of the observer, in which the image is captured, the target object appears to move at a velocity according to the relative motion between the observer and target object. This is a problem for image-capture devices that observe Earth from above, such as aerial digital cameras and Earth observation satellites. The differential between the velocity of these image-capture devices and a target object or scene at the Earth may be substantial, resulting in a large apparent ground motion in the reference frame of the image capture-devices. This in turn can lead to substantial image blur in resultant images captured by the image-capture devices. Image blur occurs in all types of images, including thermal images captured in infrared wavelengths. Removing image blur from images may be done using Forward Motion Compensation (FMC) techniques.

[0003] FMC techniques also allow the image capture device to observe a target object or scene for a longer period of time, which allows a longer exposure and integration time for captured images. FMC techniques thus allow for adequate signal collection whilst avoiding image blur due to ground motion.

[0004] Current satellite FMC methods may involve mechanical aspects, such as pitching an entire platform of an imaging system to slow down the apparent ground motion seen by the imaging device. In satellites in Earth orbit, this involves moving the entire satellite as it orbits Earth in order to perform FMC. This can be done such that the image seen by the satellite is effectively frozen on the focal plane, allowing longer integration times without adversely affecting modulation transfer function (MTF) through motion blur. Other systems in the past have used large mechanical scanning systems to rotate the entire imaging system independently of the satellite platform. A problem associated with this technique is that moving a satellite is a slow process. The ability of a satellite to perform FMC is thus limited by the rate at which the satellite can be rotated/moved to perform the FMC. Furthermore, at the end of one FMC scan, for a particular image capture phase, it is necessary to reset the satellite in terms of its configuration. In other words, once the satellite has performed FMC by moving in one direction, it must then back scan or move in the opposite direction to return to its initial configuration to be able to perform a further image capture phase. This back scan can take a considerable amount of time in orbit, during which it is not possible to capture images using FMC. For each image captured by the satellite during an image capture phase, there is thus a considerable blind spot thereafter before a further image can be captured. Pitching the platform to perform FMC thus limits the along track image strip length.

[0005] Alternatively, electronic, time-delay integration (TDI) sensors can be used to achieve a similar effect without mechanically pitching the platform or whole imaging system. Another method uses a flat, fast steering, de-scanning mirror, external to the imaging system. This achieves the same effect without the need for a rearward platform pitch rate. The flat mirror cyclically de-scans the ground area in steps with a fast back scan prior to subsequent imaging frames. This, as with TDI detectors, allows near-continuous along track imaging.

[0006] Electronic TDI detectors in the MWIR or long-wave infra-red (LWIR) are extremely expensive to develop, and thus make the imaging system more costly.

[0007] Furthermore, external, flat de-scanning mirrors must cover the entire aperture of the imaging system. They are also used at a 45-degree angle to the optical axis. The mirror is therefore required to be 1.414 times the aperture dimension in its long axis. In the case of some known imaging telescopes, this means relatively large mirrors (~445mm x ~315mm) are required, which must be kept optically flat while also being actuated at the required de-scanning rate. This is an engineering challenge, which has problems to be overcome including increased mass and system complexity.

This inevitably leads to increased costs and practicality constraints.

[0008] It has thus been appreciated that a better method of FMC applicable to Earth observation imaging systems is required to address the above problems.

SUMMARY OF INVENTION

[0009] This Summary is provided to introduce a selection of concepts in a simplified form that are further described below in the Detailed Description. This Summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used to determine the scope of the claimed subject matter; variants and alternative features which facilitate the working of the invention and/or serve to achieve a substantially similar technical effect should be considered as falling into the scope of the invention disclosed herein.

[0010] In a first aspect, the present disclosure provides a telescope for performing forward motion compensation, the telescope configured to observe an object in apparent motion having a first velocity in a first direction relative to the telescope, the telescope comprising: a primary mirror; a secondary mirror; and a detector; wherein the detector is configured to detect light that travels from an effective target of the telescope to the detector, whereby: the primary mirror is configured to reflect light incident from the effective target to the secondary mirror; and the secondary mirror is configured to reflect light from the primary mirror to the detector; wherein the secondary mirror is dynamically moveable and is arranged such that movement of the secondary mirror causes a position of the effective target of the telescope to move in the first direction along a track, such that the first velocity of the apparent motion of the object in the first direction is reduced.

[0011] Since the secondary mirror directs light to the detector, it is internal to the focusing optics of the telescope. This allows minor movements of the secondary mirror to be used in FMC. The secondary mirror may also be relatively small in comparison to the primary mirror. These attributes mean that the secondary mirror can be moved quickly and efficiently by a relatively small movement in order to perform adequate FMC to slow down or freeze the first velocity of the apparent motion of the object in the first direction. The object may be a ground target to be imaged by the telescope.

[0012] The effective target of the telescope may be considered the area or environment observed within the field of view of the detector.

[0013] Preferably, the secondary mirror is configured to move by rotation to cause the position of the effective target of the telescope to move along the track.

[0014] Preferably, the secondary mirror is configured to rotate around a central axis of the secondary mirror, wherein the central axis is perpendicular to the principal axis of the secondary mirror, such that rotation of the secondary mirror causes the principal axis of the secondary mirror and the effective target of the telescope to move along the track. The secondary mirror faces the detector to direct light to the detector, and rotates such that light from along the track is able to be reflected towards the detector by the secondary mirror. Rotating around the central axis of the secondary mirror allows rotation to be fast.

[0015] Preferably, the secondary mirror is configured to be rotatable through a total scanning angle from a first mirror angle to a second mirror angle, wherein a normal angle of the secondary mirror is within the total scanning angle, wherein the normal angle of the secondary mirror is such that the principle axis of the secondary mirror is collinear with the principle axis of the primary mirror when the secondary mirror is arranged at the normal angle.

[0016] The first mirror angle may translate the effective target of the telescope forwards along the track, and the second mirror angle may translate the effective target of the telescope backwards along the track. The normal angle corresponds to zero rotation of the secondary mirror, wherein the secondary mirror is aligned with the primary mirror and wherein the telescope therefore observes a position directly at which it is pointed. The first mirror angle allows the telescope to effectively observe in front of this position, whilst the second mirror angle allows the telescope to effectively observe behind this position. The first mirror scan angle may be referred to as a first scan angle whilst the second mirror angle may be referred to as a final scan angle. These angles may be limited to avoid aberrations or any other undesired effects.

[0017] Preferably, the secondary mirror is configured to be rotated in a scanning cycle comprising a scan and a back-scan, whereby: in the scan, the secondary mirror is configured to rotate from the first mirror angle to the second mirror angle at a first rotational velocity, such that the first velocity of the apparent motion of the object in the first direction is reduced; and in the back-scan, the secondary mirror is configured to rotate back to the first mirror angle at a second rotational velocity, wherein the second rotational velocity is greater in magnitude than the first rotational velocity.

[0018] The back-scan may be performed at a maximum safe velocity. Moving the secondary mirror relatively fast on the back-scan means more time is available in a scanning cycle for capturing images during the scan phase. Images are not captured during the back-scan because the direction of rotation of the back scan amplifies the apparent motion of the object rather than reducing it.

[0019] Preferably, the detector is configured to capture one or more image frames during each scanning cycle. These images are captured during the scan. There may be 1 , 2, 3, 4 or 5 or more images captured per scan. These images may correspond to the same object if the object is frozen on the focal plane of the detector, due to FMC by the secondary mirror during the scan.

[0020] Preferably, the total scanning angle is of a particular size such that rotation of the secondary mirror through the total scanning angle is configured to cause the position of the effective target of the telescope to move in the first direction along the track by a first distance, whereby the first distance is less than a second distance representing a projected field of view of the detector.

[0021] The first distance may be a view scan step distance, and effectively forms a portion of the field of view of the detector. This means that each scan of the scan cycles scans a portion of the field of view of the detector, allowing for multiple scan cycles to be made over the entire field of view of the detector. This in effect creates rolling windows corresponding to consecutive scans over the field of view of the detector.

[0022] Preferably, the secondary mirror is configured to perform a plurality of scanning cycles, wherein the secondary mirror is configured to perform each scan of the plurality of scanning cycles such that the position of the effective target of the telescope at least partially overlaps for at least consecutive scanning cycles.

[0023] Since the effective target of the telescope overlaps in consecutive scanning cycles, the rolling windows of consecutive scans overlap. This means that image frames captured during each scan overlap at least partially. Since there are multiple scans per the field of view of the detector, there are multiple overlapping portions of captured image frames for the field of view of the detector.

[0024] Preferably, the detector is configured to capture at least a first image frame in a first scanning cycle and at least a second image frame in a consecutive second scanning cycle such that the first and second image frames each include overlapping portions corresponding to the same position of the effective target of the telescope.

[0025] The sum of signal data originating from the overlapping portions of the first and second image frames are aligned and co-added in a post processing step to produce a higher-signal image frame. [0026] The overlapping portions of the captured image frames for the field of view of the detector are accumulated together to improve the SNR and effectively obtain better exposure for the images of the object. Scans may overlap in the field of view of the detector with a further 1 , 2, 3 or more scans, meaning multiple overlapping portions can be accumulated and summed to improve the SNR even more.

[0027] Preferably, the detector is configured to capture a plurality of image frames during each scan of each scanning cycle.

[0028] A summing operation may be performed in the post-processing step to sum signal data originating from the plurality of image frames captured during each scan cycle.

[0029] Where the apparent motion of the object is effectively frozen, the plurality of captured image frames for each scan cycle correspond to the same object and can thus be added to improve SNR. Where the apparent motion is reduced, the plurality of captured image frames for each scan cycle may partially overlap, in which case the portions of the captured image frames which overlap may be added to improve SNR. This may be complimented by adding to images frame that partially overlap from consecutive scan cycles as set out above. Thus, SNR can be greatly improved by accumulating overlapping image frames from the same scan cycle and from the rolling windows of consecutive scan cycles.

[0030] Preferably, the detector is configured to capture each of the plurality of image frames according to a maximum exposure period for capturing each image frame, wherein the maximum exposure period is set based on a predefined pixel-drift value.

[0031] Limiting the exposure time for capturing an individual image frame beneficially reduces pixelblur originating from random or undesired telescope movement. The predefined allowed pixel drift value may be a number of pixels or physical distance corresponding to the object observed. The predefined pixel drift value may be set by a user.

[0032] Preferably, the first rotational velocity of the secondary mirror is dependent on the first velocity.

[0033] The first rotational velocity may be considered an effective mirror de-scan rate, and is optimised based on parameters of the telescope such as orbital height, telescope velocity, back-scan velocity and the like. These parameters relate to the first velocity of the object - meaning the relative velocity between object and the telescope. By optimising the rotational velocity of the secondary mirror during the scan phase, it is possible to greatly reduce the first velocity of the apparent motion of the object.

[0034] Preferably, the secondary mirror is configured to rotate at the first rotational velocity to cause the position of the effective target of the telescope to move at the first velocity in the first direction along the track, such that the apparent motion of the object substantially freezes. Optimizing rotational velocity of the secondary mirrorthus enables the object to be frozen on the focal plane of the detector during the scan phase of the scan cycle. This allows larger exposure times and/or multiple image frames to be captured of the same object without introducing excessive blur.

[0035] Preferably, the secondary mirror is configured to be rotated by an actuator. The actuator may be controlled by a computer or a processor.

[0036] Preferably, the actuator comprises a single axis electromagnetic voice coil actuator. The actuator may alternatively be any suitable actuation mechanism for actuating the secondary mirror 104. For example, the actuator may include a voice coil (magnetic drive) actuator with a mounted Tilting Flex pivot mirror cell, a tilting piezo actuation stage with mirror cell hard mounted to the mechanically flexured piezo stage, or a small direct drive brushless motor driven mirror cell.

[0037] Preferably, the telescope is a Cassegrain telescope, wherein the primary mirror is concave and the secondary mirror is convex.

[0038] Preferably, the telescope is configured to observe medium wave infrared (MWIR) light. Thus, the detector is configured to be sensitive to MWIR light. The telescope may be configured to detect incident photons in the infrared spectrum more generally such as in long-wave infrared (LWIR) wavelengths to produce thermal imagery

[0039] According to a second aspect, there is provided an imaging system comprising the telescope according to the first aspect.

[0040] Preferably, the imaging system includes a satellite for orbiting the Earth or a celestial body, wherein the satellite comprises the telescope. The telescope may be rigidly fixed to the satellite. The telescope may observe the ground, such that the object moving with apparent motion at a first velocity is or includes the ground moving relative to the satellite and the telescope. The object is thus not required to be a singular item and may simply be the ground and all the features contained thereon. The object may be a strip of ground corresponding to the ground in the field of view of the detector of the telescope.

[0041] Preferably, the satellite is configured to pitch to perform forward motion compensation, such that the imaging system is configured to perform a first component of forward motion compensation by pitching the satellite and a second component of forward motion compensation by moving the secondary mirror of the telescope.

[0042] Performing FMC with the satellite allows the secondary mirror to perform FMC more efficiently, such that there is a greater overlap between image frames captured in consecutive scanning cycles, and such that the FMC performed by the secondary mirror allows freezing of the object for capturing image frames. Furthermore, performing a combination of satellite pitching FMC together with secondary mirror scanning FMC allows the pitching of the satellite to be done gradually, increasing the track length of overlapping image frames captured by the detector before the satellite has to be reset. This allows the track length to be extended from the region of 5km on the ground to the region of 100km or more on the ground, without any blind spots. Thus, using a combination of satellite pitching FMC and secondary mirror FMC benefits both of these FMC methods and the overall FMC and image capturing process of the telescope.

[0043] According to a third aspect, there is provided an apparatus for performing forward motion compensation in a telescope, the telescope having a primary mirror and a detector for observing an object in apparent motion having a first velocity in a first direction relative to the telescope, the apparatus comprising: a secondary mirror; and an actuator configured to actuate the secondary mirror; wherein the secondary mirror is configured to be positioned in an internal optical focussing pathway of the telescope to direct light to the detector of the telescope, wherein the secondary mirror is dynamically moveable by the actuator and is arranged such that movement of the secondary mirror causes a position of an effective target of the telescope to move in the first direction along a track, such that the first velocity of the apparent motion of the object in the first direction is reduced.

[0044] The apparatus may be fitted to an existing telescope, whereby the apparatus is substituted for an existing secondary mirror or wherein the apparatus is formed by upgrading the existing secondary mirror. The apparatus includes the secondary mirror and an actuator responsible for moving the secondary mirror. The movement of the secondary mirror may be controlled by a computer or processor for example. The secondary mirror is configured to be positioned in an internal optical focussing pathway of the telescope, such that large movements of the secondary mirror are not required to perform FMC.

[0045] According to a fourth aspect, there is provided a method of performing forward motion correction using a telescope having a primary mirror, a secondary mirror, and a detector, wherein the detector is configured to detect light that travels from an effective target of the telescope to the detector, whereby the primary mirror is configured to reflect light incident from the effective target to the secondary mirror; and the secondary mirror is configured to reflect light from the primary mirror to the detector; the method comprising: controlling the telescope to observe an object in apparent motion having a first velocity in a first direction relative to the telescope; controlling the telescope to move the secondary mirror with respect to the telescope to cause a position of the effective target of the telescope to move in the first direction along a track, such that the first velocity of the apparent motion of the object in the first direction is reduced.

[0046] Preferably, controlling the telescope to move the secondary mirror comprises rotating the secondary mirror around a central axis of the secondary mirror, wherein the central axis is perpendicular to the principal axis of the secondary mirror, such that rotating the secondary mirror causes the principal axis of the secondary mirror and the effective target of the telescope to move along the track. [0047] Preferably, the method further comprises rotating the secondary mirror through a total scanning angle from a first mirror angle to a second mirror angle, wherein a normal angle of the secondary mirror is within the total scanning angle, wherein the normal angle of the secondary mirror is such that the principle axis of the secondary mirror is collinear with the principle axis of the primary mirror when the secondary mirror is arranged at the normal angle.

[0048] Preferably, the method further comprises rotating the secondary mirror in a scanning cycle comprising a scan and a back-scan, whereby: performing the scan comprises rotating the secondary mirror from the first mirror angle to the second mirror angle at a first rotational velocity, such that the first velocity of the apparent motion of the object in the first direction is reduced; and performing the back-scan comprises rotating the secondary back to the first mirror angle at a second rotational velocity, wherein the second rotational velocity is greater in magnitude than the first rotational velocity.

[0049] Preferably, the method comprises capturing one or more image frames during each scanning cycle.

[0050] Preferably, the method comprises performing a plurality of scanning cycles, wherein consecutive scanning cycles comprise rotating the secondary mirror such that the position of the effective target of the telescope at least partially overlaps for the consecutive scanning cycles.

[0051] Preferably, the method further comprises capturing, with the detector, at least a first image frame in a first scanning cycle and at least a second image frame in a consecutive second scanning cycle such that the first and second image frames each include overlapping portions corresponding to the same position of the effective target of the telescope; and summing signal data originating from the overlapping portions of the first and second image frames to produce a higher-signal image frame. There may be more than two image frames from more than two consecutive scanning cycles that contribute to the overlapping portions and thus the higher-signal image frame.

[0052] Preferably, the method further comprises capturing a plurality of image frames during each scan of each scanning cycle; and summing signal data originating from the plurality of image frames captured during each scan cycle.

[0053] The summing operations set out above may be performed by a computer or computer system on the ground. In particular, the detector of the telescope may be configured to communicate with a ground station or base station including the computer or computer system, wherein the computer or computer system performs a post-processing step to perform the summing operations.

[0054] Preferably, the telescope is included in a satellite for orbiting the Earth or a celestial body, and wherein the method further comprises determining the first rotational velocity based at least on an orbital height of the satellite and a velocity of the satellite. The first rotational velocity is preferably optimized such that the apparent motion of the object is frozen. [0055] Preferably, the method comprises performing a first component of forward motion compensation by pitching the satellite and performing a second component of forward motion compensation by moving the secondary mirror of the telescope.

[0056] Preferably, pitching the satellite comprises cyclically pitching the satellite between a first pitching angle and a second pitching angle, such that the orientation of the telescope is pitched between the first pitching angle and the second pitching angle. Rotating between the first and second pitching angle rotates the telescope and the principle axis of the telescope along the track direction. The rotation of the satellite during pitching is thus in the same orientation and rotation plane as the rotational plane of the secondary mirror.

[0057] Preferably, for each pitching cycle of the satellite, the method comprises: performing a plurality of scanning cycles. Since consecutive scanning cycles provide overlapping image frames, and since the scanning cycle of the secondary mirror corresponds to a smaller area on the ground or object than the field of view of the detector, a plurality of overlapping image frames are captured to create a continuous series of overlapping rolling windows of image frames for the duration of the pitching cycle. This means that no blind spots are present in images captured during the pitching cycle.

[0058] The method may be performed by a computer or computing device configured to control the satellite and/or telescope. The method steps may be performed in any appropriate order.

[0059] According to a fifth aspect, there is provided a computer program, which, when executed by a processor, causes the processor to perform the method according to the fourth aspect.

[0060] The methods described herein may be performed by software in machine readable form on a tangible storage medium e.g. in the form of a computer program comprising computer program code means adapted to perform all the steps of any of the methods described herein when the program is run on a computer and where the computer program may be embodied on a computer readable medium. Examples of tangible (or non-transitory) storage media include disks, thumb drives, memory cards etc. and do not include propagated signals. The software can be suitable for execution on a parallel processor or a serial processor such that the method steps may be carried out in any suitable order, or simultaneously.

[0061] This application acknowledges that firmware and software can be valuable, separately tradable commodities. It is intended to encompass software, which runs on or controls “dumb” or standard hardware, to carry out the desired functions. It is also intended to encompass software which “describes” or defines the configuration of hardware, such as HDL (hardware description language) software, as is used for designing silicon chips, or for configuring universal programmable chips, to carry out desired functions. [0062] The preferred features may be combined in any manner, as would be apparent to a skilled person, and may be combined with any of the aspects of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Embodiments of the invention will be described, by way of example, with reference to the following drawings, in which:

[0064] Figure 1 a is a schematic diagram of a imaging system including a telescope according to the invention;

[0065] Figure 1 b is a schematic diagram of a imaging system including a telescope according to the invention;

[0066] Figure 1 c is a schematic diagram of a imaging system including a telescope according to the invention;

[0067] Figure 2 is a schematic diagram of a satellite including the imaging system according to the invention;

[0068] Figure 3 is a schematic diagram of a satellite including the imaging system according to the invention;

[0069] Figure 4 is a schematic diagram of a satellite including the imaging system according to the invention; and

[0070] Figure 5 is a vector diagram illustrating a relationship between a speed of an object and a speed of the imaging system according to the invention.

[0071] Common reference numerals are used throughout the figures to indicate similar features.

DETAILED DESCRIPTION

[0072] This application relates to a telescope, apparatus, imaging system and method for performing FMC such that images captured by the imaging system are captured with minimal blur and with an adequate exposure time. The method may be used in satellite based MWIR Cassegrain telescopes, and in particular for the purpose of measuring land surface temperature via medium wave infrared (MWIR) Earth observation.

[0073] Although referred to as an imaging system here, it is to be understood that the imaging system can be considered an imager, an imaging apparatus, or device, such as a telescope. The imaging system is configured to scan a target object, for which one or more images are to be captured, in a direction that is opposite to a direction of motion of the imaging system relative to the target object. The action of 'scanning' may be considered the same as 'de-scanning', since the direction of the scan is opposite to the direction of relative motion of the imaging system. The terms scan and de-scan are thus used interchangeably throughout.

[0074] Figures 1 a to 1 c show schematic diagrams of such an imaging system 100. The imaging system 100 comprising a primary mirror 102 and a secondary mirror 104, whereby the secondary mirror 104 is moveable or rotatable relative to the primary mirror 102. Light is directed by the mirrors to a detector 106, where it is detected over an exposure period. The detector is then read-out to produce an image or frame from photon detections over the exposure period.

[0075] In Figures 1a to 1c, the imaging system 100 is exemplified by a Cassegrain telescope. The Cassegrain telescope comprises a primary mirror 102, a secondary mirror 104, and a fixed detector 106. The primary mirror 102 is concave and the secondary mirror 104 is convex. The fixed detector 106 is configured to detect incident photons.

[0076] Generally, a Cassegrain telescope operates as follows: incoming light rays 108 (photons) are reflected by the primary mirror 102; resultant reflected light rays 110 are reflected by the secondary mirror 104; the secondary mirror 104 further reflects the light rays via an aperture 112 in the primary mirror 102 to the fixed detector 106; and photons are then detected at the fixed detector. The Cassegrain telescope as illustrated in figure 1 thus folds the optical path of the incoming light rays 108 back on itself. The convex secondary mirror 104 adds a telephoto effect creating a much longer focal length in a relatively short system. This allows the focal point of the telescope to be positioned behind the primary mirror 102 at the detector 106.

[0077] In some examples, the Cassegrain telescope is included in or otherwise located on a satellite configured to orbit the Earth in a low-earth orbit (LEO). The Cassegrain telescope is configured to look down from the satellite to a ground track (suborbital track) on the Earth. A series of images are captured by the Cassegrain telescope along this track. The direction of the track depends on the direction of motion of the satellite. The direction of motion of the satellite is denoted A in figures 1 a to 1 c, whilst the direction of apparent image motion without secondary mirror rotation is denoted B. As will be understood the Cassegrain telescope optics inverts the image of the effective target on the ground track onto the focal plane. This means that the direction of the apparent image motion also inverts. Hence, although the relative motion of the ground with respect to the motion of the satellite is in the opposite direction to the motion of the satellite A, the apparent image motion B on the focal plane of the detector is in the same direction as the motion of the satellite A.

[0078] Although the imaging system 100 is exemplified here by a Cassegrain telescope, and in particular a Cassegrain telescope included in a satellite, it is to be understood that the imaging system 100 may be any imaging device that uses a reflective telescope design including a primary and secondary mirror. For example, The imaging system 100 may be any reflective telescope design including a primary and secondary mirror 104 in the optical train, that is a distance from the image plane. For example, the imaging system 100 may be a Gregorian, Newtonian, Ritchey-Chretien, Dall- Kirkham or Nasmyth type telescope. Furthermore, the imaging system 100 may be used on vehicles other than a satellite, such as aerial vehicles, and/or at other orbits other than LEO. Thus, where reference is made to a telescope, Cassegrain telescope or satellite, it is to be understood that these features may be substituted for these other imaging systems and vehicles.

[0079] The telescope may be configured to detect incident photons in the infrared spectrum and in particular MWIR or LWIR wavelengths to produce thermal imagery. However, other bands of the electromagnetic spectrum may also be observed, such as visible light, for example. It will be understood that to detect different sources of light in different parts of the electromagnetic spectrum, different detectors may be used. The detector 106 may be a CMOS or CCD detector for example, f

[0080] The imaging system 100 additionally includes an actuator (not shown) configured to actuate the secondary mirror 104. The actuator may be any suitable actuation mechanism for actuating the secondary mirror 104. For example, the actuator may include a voice coil (magnetic drive) actuator with a mounted Tilting Flex pivot mirror cell, a tilting piezo actuation stage with mirror cell hard mounted to the mechanically flexured piezo stage, or a small direct drive brushless motor driven mirror cell.

[0081] In an example, the actuator for rotating the secondary mirror 104 is a single axis electromagnetic voice coil actuator. The voice coil actuator moves the secondary mirror 104 mounted on flex pivots. This minimizes the number of moving parts to one, while providing a frictionless mechanism with a near infinite mean time before failure (MTBF). Flex pivots are also robust in typical launch environments experienced by satellites. The voice coil actuator is mounted upon a typical secondary mirror mount spider.

[0082] A launch-lock, or hold down release mechanism can be used to ensure the mirror mount does not move during launch of the satellite. This prevents the secondary mirror 104 and actuator from resonating and failing. The secondary mirror 104 is released once in orbit, allowing the actuator to actuate the secondary mirror 104.

[0083] The actuation of the secondary mirror 104 enables it to act as an oscillating, de-scanning FMC system. The process of actuating the secondary mirror 104 and the benefits this provides as an FMC system will now be described.

[0084] The actuator rotates the secondary mirror 104 around a central axis as illustrated by the respective positions of the secondary mirror 104 in figures 1 a to 1 c. The direction of rotation is such that the plane of rotation is orthogonal with the track direction and the axis of rotation is orthogonal to the track direction. In other words, the secondary mirror 104 is configured to rotate such that the optical or principal axis of the secondary mirror points along the track direction. Although figures 1 a to 1c show three discrete positions of the imaging system 100, it is to be understood that the rotation of the secondary mirror 104 is continuous between these positions.

[0085] In figure 1a, the secondary mirror 104 is in a first rotated state, wherein the secondary mirror 104a normal vector is angled towards the direction of motion of the telescope, denoted by the arrow 'A' in figure 1a, by a first scan angle 6. In this first rotated state, the effective target object of the telescope for capture at the detector 106 is shifted forwards relative to the direction of motion A and the reference frame of the telescope, along the ground track being observed by the telescope.

[0086] From the first scan angle 0, which is noted as the FMC start angle, the secondary mirror 104 is configured to be rotated by the actuator through a normal position of the secondary mirror 104 as shown in figure 1 b, wherein the secondary mirror 104 is orthogonal to the optical axis of the telescope, such that the secondary mirror 104 is rotated and de-scans to a final scan angle -6. The final scan angle -© denotes a final rotated state of the secondary mirror 104, as shown in figure 1c.

[0087] In figure 1c, the secondary mirror 104 is in the final rotated state. In this final rotated state, the effective target object of the telescope for capture at the detector 106 is shifted backwards relative to the direction of motion and the reference frame of the telescope, along the ground track being observed by the telescope.

[0088] The effect of rotating the second mirror 104 in an arc from the first scan angle © to the final scan angle -6 is thus that the effective target object of the telescope changes or sweeps in a direction opposite to the direction of motion of the telescope A when observed in the reference frame of the telescope. This has the effect of slowing down and/or freezing the apparent ground motion in the reference frame of the telescope. Slowing down and/or freezing that apparent ground motion in this manner allows one or more images to be captured by the detector 106 for the same effective target object on the ground during one or more scan periods, increasing exposure time and thus the signal to noise ratio for the one or more images, whilst also reducing motion blur.

[0089] Once the secondary mirror 104 has been rotated through to the final rotated state at the final scan angle -6, the secondary mirror 104 is back scanned from the final rotated state to the first rotated state at the first scan angle © at a maximum safe speed to reduce dead time between FMC scans of the secondary mirror 104 and subsequent image frames. De-scanning then repeats for a next scan period from the first rotated state to the final rotated state. The maximum safe speed is selected such that the risk of causing any vibrational modes in the telescope is minimal, such that the focal plane of the telescope is not undesirably modified. The maximum safe speed of back-scanning is maximized to reduce dead time between FMC scans and subsequent image frames. [0090] The secondary mirror 104 thus repeatedly rotates from the first rotated position to the final rotated position by a total of 20, to slow down the apparent ground motion observed at the telescope, to effectively freeze the ground target object on the detector at the focal plane of the telescope.

[0091] Rotating the secondary mirror 104 during de-scanning to perform FMC may eventually degrade the point spread function (PSF) at the image plane due to focal plane tilt relative to the plane of the detector 106. In Figures 1 a and 1 c, the focal plane 1 14 appears tilted with respect to the detector 106. Higher order optical aberrations, caused by the tilt away from optimum primary mirror 102 and secondary mirror 106 alignment, will also widen the PSF. PSF degradation is minimized by using very small scan angle ranges Oto -6 and a higher number of scan periods within the detector 106 field of view.

[0092] In some embodiments, FMC by actuating the secondary mirror 104 as explained above can be combined with other FMC techniques to increase the SNR of the imaging system 100 whilst avoiding any additional motion blur.

[0093] For example, FMC by actuating the secondary mirror 140 can be combined with pitching the satellite to which the telescope is rigidly fixed. Figure 2 is a schematic diagram of the imaging system 100 showing a scenario in which FMC is performed by both pitching the vehicle or apparatus (such as a satellite), and scanning the secondary mirror 104. Figure 2 shows the imaging system 100 at three points in time during capture of an image or series of images along a ground track 120. In this example, the imaging system 100 is a telescope that is rigidly fixed or mounted to a satellite. The satellite is configured to be pitched or rotated to perform FMC between orientations or configurations 100a, 100b and 100c.

[0094] At a first configuration 100a, the satellite is pitched such that the telescope is rotated forwards relative to the direction of motion A of the satellite. This means that the effective target object of the telescope for capture at the detector 106 is shifted forwards relative to the direction of motion A and the reference frame of the telescope, along the ground track 120 being observed by the telescope. The angle of rotation of the satellite relative to the normal position is the first pitching angle Q P as illustrated in Figure 2.

[0095] At a second configuration 100b, the satellite is pitched such that the telescope is rotated backwards from the first configuration 100a, relative to the direction of motion A of the satellite. In the second configuration 100b, the satellite is orientated such that the telescope is in the normal position relative to the Earth.

[0096] At a third configuration 100c, the satellite is pitched such that the telescope is rotated backwards further from the second configuration 100b, relative to the direction of motion A of the satellite. This means that the effective target object of the telescope for capture at the detector 106 is shifted backwards relative to the direction of motion A and the reference frame of the telescope, along the ground track 120 being observed by the telescope. The angle of rotation of the satellite relative to the normal position is the final pitching angle -0 P as illustrated in Figure 2.

[0097] The satellite thus provides a similar effect to the secondary mirror 104 scanning explained above. In particular, rotating the satellite in an arc from the first pitching angle QP to the final pitching angle -Q P makes the effective target of the telescope change or sweep in a direction opposite to the direction of motion of the telescope A when observed in the reference frame of the telescope. This has the effect of slowing down or freezing the apparent ground motion in the reference frame of the telescope, thus allowing for greater SNR whilst reducing motion blur in frames captured by the detector 106. Whilst this FMC is being performed by the pitching/rotation/movement of the imaging system 100, further FMC is performed using the secondary mirror 104 as explained above.

[0098] Initially, when the satellite is in the first configuration 100a, the secondary mirror 104 of the telescope is rotated to the first rotated position as shown in figure 1 a. The scan angle is 6, which is noted as the FMC start angle. Whilst the satellite is relatively slow to pitch, the secondary mirror can be actuated much faster. This allows the secondary mirror 104 to be actuated from the first scan angle © to the final scan angle -0, completing a scan period for each satellite configuration 100a, 100b and 100c. In figure 2, four scan periods are completed at each of the configurations. The secondary mirror 104 may perform more complete scans than this, such that there are five or more scan periods per configuration. It is also to be understood that, although three configurations 100a, 100b, and 100c are shown in figure 2, platform FMC is a continuous process, meaning the platform is continuously pitching from the first pitching angle 0 P to the final pitching angle -0 P , whilst a plurality of scans of the secondary mirror 104 are performed to provide a plurality of mirror scan periods.

[0099] During each mirror scan period, the ground within the field of view of the imaging system satellite moves due to the motion of the satellite. Performing platform (satellite) pitching slows down this relative ground movement but does not stop it. As such, each scanning period is performed with respect to at least a partially translated field of view of the detector 106. Figure 2 shows the projected field of view of the detector 106, of length L, on the ground for successive mirror scan periods. At each of the first, second and third configurations 100a, 100b and 100c, four scan periods of the secondary mirror 104 are performed, corresponding to four overlapping fields of view of the detector 106. The length D2 in figure 2 represents a sub-field of view scan step distance, which is a consequence of the first and final de-scan angles © to -6. Once the field of view has completely moved on, such that there is no overlap between the field of view of the first scan period and the most recent scan period, or in other words, when the trailing edge of a most recent field of view moves past the leading edge of the first field of view, no more data can be recorded of that ground area.

[0100] The overlapping portions of the fields of view corresponding to the plurality of scan periods are used to collect data of the ground area included in such overlapping portions. Since the overlapping portions include the same ground area, images captured from each scan period may be accumulated or added together with other images captured from further scan periods for the same ground area, increasing the SNR. Throughout the slower platform FMC period from the first pitching angle 6 P to the final pitching angle -6 P , the secondary mirror 104 repeatedly scans and back-scans, such that the process of providing a plurality of overlapping fields of view for the detector to capture a plurality of images or frames occurs continuously.

[0101] During each scan period of the secondary mirror 104, a plurality of images or frames are captured, of the frozen effective target object on the ground. After each scan period of the secondary mirror, the field of view of the detector moves forward along the ground track corresponding to the sub-detector field of view distance D2 on the ground.

[0102] The next scan period commences over a shifted or translated field of view due to this movement along the ground track. The capturing of images then repeats for this shifted field of view of the detector. In Figure 2, there are four scan periods, meaning that, for example, if there are 5 images captured for each scan period, the set of four scan periods form 'rolling windows' which can be used to add together the 20 frames of each point on the ground. As the process is continuous, there are no blind spots in the final image strip formed from the addition of all the frames in all the rolling windows. At the beginning and end of the strip, there will be 5 frames that do not have the 20 frames total for a specific ground object or area as it takes 4 sets of rolling widows to build up to the 20 frames of sampling.

[0103] The combination of FMC performed by the imaging system 100 and the secondary mirror 104 can improve results by improving the SNR without increase to the apparent motion blur in images. However, it is to be understood that the combination of two sources of FMC in this manner is not essential, and that it is possible to provide sufficient FMC to increase SNR and reduce motion blur in images by using secondary mirror 104 scanning alone.

[0104] The speed of rotation of the second mirror 104 between the first rotated state and the final rotated state, between the first scan angle 6 and the final scan angle -6, is subject to control of the actuator. Preferably the actuator rotates the secondary mirror 104 at an optimal speed which results in the effect of substantial slowing down or freezing of the apparent ground motion observed at the detector. This optimal speed of rotation of the secondary mirror 104 may be determined from parameters relating to the features and use of the imaging system 100. In this example, where the imaging system 100 is a telescope included in a satellite, the optimal speed may depend on orbital parameters such as velocity and distance from the ground target object. Once the optimal speed of rotation is determined, the secondary mirror 104 rotates from the first scan angle ©to the second scan angle -6 according to a fixed scan rate, whereby the fixed scan rate scans the ground target object at the optimal speed. Determining the fixed scan rate for particular orbital parameters, and controlling the second mirror to rotate at the fixed scan rate to effectively freeze the ground target object on the detector at the focal plane of the telescope, is discussed in more detail with respect to Figures 3 and 4. [0105] Figure 3 shows a schematic diagram of the operation of the secondary scanning mirror 104 of the imaging system 100, according to example working parameters. The imaging system 100 is a telescope on a satellite, and is configured to observe a target object at the ground. The detector of the telescope has a field of view, which, when projected to the ground forms the field of view projection 120. The telescope has a secondary mirror with a maximum scan angle 6, a secondary mirror to detector distance D1, a field of view length L of the projection 120, an orbit height /-/, and a scan step shift distance D2. The arrow A denotes the satellite motion. For simplicity, the schematic of figure 3 does not take into account the pitch rate and FMC performed by the satellite.

[0106] The scan rate is set such that while scanning, the ground target area defined by the field of view projection 120 is frozen on the detector at the focal plane of the telescope. The maximum allowed scan angle 0, limited by defocus and aberrations caused by mirror misalignment, along with the angular rate condition required to freeze the ground image, sets the length of the scan step shift distance, D2. The angular rate condition is the angular rate of the mirror required to freeze the image at the detector. The scan step shift distance D2 is calculated from the maximum allowed mirror scan angle, 0, using equation 1 below. Note this is independent of platform FMC rate.

D 2 = 2H tan^^ Eq.1

Where:

• H is orbit height,

• 6sc is the maximum allowed mirror scan angle

The factor of 2 is required as the maximum scan angle can be used either side of the nominal mirror planar alignment. The exact form of this equation is particular to a given telescope design. Equation 1 was taken empirically from an existing MWIR Cassegrain telescope optical design. It is to be understood that other telescope designs would have their own specific equation.

[0107] Figure 3 further illustrates an example of five successive scan steps 122 formed from consecutive scan periods of the secondary mirror.

[0108] Figure 4 shows a schematic diagram of the imaging system 100 as it is subject to platform pitching FMC. The imaging system 100 is pitched from a first pitching angle Q P to the final pitching angle -6 P , making the effective target of the telescope change or sweep in a direction opposite to the direction of motion of the telescope. The platform velocity Vp is indicated by arrow 130, whilst the effective ground velocity Vg is indicated by arrow 132. the platform is at the orbital height H.

[0109] The platform FMC factor is defined as the ratio of Orbital velocity Vp to effective ground velocity Vg. The pitch rate (dOp/dt) of the platform for a given FMC factor relies only on the orbital height or altitude, /-/, and effective ground velocity, Vg, as orbital velocity Vp is fixed for a given orbit height. Assuming a flat Earth, the platform pitch rate for a given orbit height and FMC factor can be derived using the vector diagram 500 as shown in figure 5. Firstly, it is noted that

V„

FMC = Eq.2

V B such that when Vg tends to zero, FMC tends to infinity.

[0110] From figure 5, the pitch rate is given as:

[0111] When FMC is not infinite, the pitch rate is given as:

[0112] Rearranging equation 2 and substituting for Vp, gives pitch rate in terms of FMC and Vg

[0113] Thus, in order to record image data with zero relative motion blur, the platform pitch rate, d6p/dt, and effective mirror de-scan rate, ddesc/dt, must sum to the equivalent FMC(infinity) pitch rate. The difference between the mirror de-scan rate and the effective mirror de-scan rate is the former is the physical angular scan rate of the secondary mirror the latter is the angular de-scan rate of the ground image produced by the scanning mirror. This means that the following equation 6 must be satisfied in order to freeze the ground image at the focal plane:

[0114] Substituting equations 3 and 5 into equation 6 yields equation 7 which is used to calculate the effective secondary mirror scan rate, , for a given platform FMC rate, d0p/dt: Eq.7

[0115] The effective mirror scan rate, combined with the maximum allowed mirror scan angle 6, can be used to calculate the scan time period, Tsc, for each sub-field scan step D2 of the mirror. As mirror scan rate is constant, this is simply the maximum effective mirror scan angle, 6esc, divided by the effective scan rate. The maximum effective mirror scan angle is defined in equation 8 below, and is further expanded by substitution for D2 from equation 1 :

Eq.8

[0116] Therefore, the secondary mirror scan period, Tsc, is given by:

[0117] The above logic and equations assume that there is no time spent back-scanning the secondary mirror. This is not realistic. Therefore, the equations must account for back-scan time period, Tback, which reduces the scan period, Tsc. The back-scan period has a minimum possible time due to physical limits of mechanism, mirror inertia, and allowable torques on telescope structures that do not de-stabilise the system. As back-scan time is independent of all other factors in the equations, it can simply be subtracted from equation 9, giving the total secondary mirror scan time as:

[0118] Using these equations for the total scan time and for sub-field steps in general terms, further equations can be derived for how many of such steps are required, for a given detector field of view, to obtain continuous image strips. The number or product of scan steps acquired within the detector field of view is Nsc. To meet signal to noise requirements, the total exposure time, for a given point on the ground once all frame data from the scan steps are summed, is fixed and is defined as Texp. The total time available for the ‘N’ scan steps is dictated by the detector field of view and the platform FMC rate. This time is defined as Tfov.

[0119] Using these parameters:

T 1 exp = i N^sc T 1 sc Eq.11 and where DI is the along track detector field of view on the ground, given as:

[0120] where p is the detector pixel pitch and Npix is the number of detector pixels in the along-track direction. From equation 11 , the number of scans required can be found given Texp and Tsc. Tsc is fixed by the maximum mirror scan angle and Texp is independent and fixed by SNR requirements.

Nsc is also related to Tfov by:

Tfov Eq.14

Nsc = TSCTOTAL

[0121] Given all previously mentioned constraints, and using equations 14 and 11 , the condition shown in equation 15 must be satisfied in order to obtain continuous strip images with adequate Texp, and hence, required co-added image SNR:

T eX p _ Tf 0V Eq.15

T S c T SCT0TAL

[0122] Substituting all variables in equation 16 for the previously derived expressions gives equation 17. This gives the total added frame exposure time in terms of general system parameters. This is used to calculate the signal to noise ratio of co-added frames for given maximum mirror scan angles and platform FMC rates:

[0123] Further substitution for Di from equation 13, provides an expression to calculate the total exposure time, Te>-p, in terms of the fundamental geometric features of the proposed system. The exposure time is fixed by the desired final SNR for co-added frames. The maximum mirror scan angle is fixed by desired image Modulation Transfer Function MTF. Therefore, if the minimum back-scan time of the secondary mirror is known, the number of sub-field mirror scans can be calculated for a given platform FMC rate in general terms.

[0124] The secondary mirror 104 of the Cassegrain telescope is far smaller than any flat mirror external to the aperture of the telescope. For example, the secondary mirror 104 has a 100mm diameter, or a diameter in the range of 50 to 150mm, compared to an elliptical external flat mirror with approximately 430mm major diameter and 300mm minor diameter. As such, the secondary mirror 104 has a comparatively low moment of inertia (Mol), since Mol scales at least with the square of the mirror diameter. The secondary mirror 104 can thus be rotated and used to scan a scene to be captured along the ground track much faster than a flat external mirror.

[0125] Using the secondary mirror 104 to scan comparatively faster allows for smaller angles to be used for the first de-scan angle 6 and the final de-scan angle -6. The first and final de-scan angles may be 0.1 degrees and -0.1 degrees respectively. They may however, be 0.05 degrees and -0.05 degrees, 0.15 degrees and -0.15 degrees, or any other angle in a range of 0 to 0.5 degrees in magnitude. Using smaller angles limits the focal plane tilt at the detector 106, such that MTF, through defocus at the edge of a captured image, is only marginally affected. Small angles also limit the size of higher order optical aberrations due to primary mirror 102 and secondary mirror 104 misalignments.

[0126] Furthermore, because the secondary mirror 104 can be scanned faster, the along-track image strip length can be increased, and the time between scans can be significantly reduced to allow for continuous or near-continuous along track imaging. This allows a longer strip mapping operation of the imaging system, while minimizing motion blur and maintaining the necessary SNR and GSD. If the required exposure time for each frame is reached within the scan period of the secondary mirror, blind spots will not occur. The relatively quick scanning of the secondary mirror 104 means a contribution of satellite pitching FMC may be reduced. This allows the satellite to be pitched more gradually between the first pitching angle Q P to the final pitching angle -Q P . This means satellite pitching occurs at a lower angular rate, allowing the satellite to be pitched for a longer duration, resulting in extended or longer strip imaging. Once the satellite has pitched to the final pitching angle, it is necessary to reset the satellite to the original first pitching angle, causing the strip image to stop until the reset of the satellite is complete. Thus, using the secondary mirror to provide FMC increases the overall image strip length when compared to pitching the satellite alone.

[0127] For example, by using a combination of FMC provided by the secondary mirror of the telescope and FMC provided by pitching of the platform comprising the telescope, the continuous image strip length can be increased from lengths in the region of 5km to lengths in the region of 100km.

[0128] In embodiments wherein the telescope is housed or otherwise included in a satellite, it is technically problematic to control the attitude of the satellite and hence, it is difficult to keep the telescope pointing vector perfectly stable. There is a random residual angular drift rate about the desired pointing vector. This may translate to a relative drift at the ground target to be imaged having a magnitude of multiple metres per second. To avoid excessive image blur due to this relative motion caused by residual angular drift, the exposure time of the telescope, and hence frame period, is limited. For example, the exposure time may be limited such that there is a maximum of one pixel drift during the frame period. In this example, a pixel corresponds to 3.5m on the ground at the ground target when the telescope is pointing toward the Nadir. If the residual drift is, for example, 87.5 m/s the maximum frame period is given by the 3.5 metres on the ground (corresponding to a pixel) divided by 87.5 m/s (the residual drift). This gives a frame period of 0.04 seconds, or in other terms, a frame rate of 25 frames per second. The platform pointing stability will likely remain the same even when not performing FMC manoeuvres and may not be corrected by scans of the secondary mirror. Therefore, in the above example, 25 fps is the slowest acceptable frame rate.

[0129] Multiple frames may be co-added to obtain useable SNR values for final images. However, read noise is added during every frame read out, so there is a trade-off between read noise and SNR. Because of this, the slowest frame rate possible is selected to get the best final SNR. Thus, in the above example, the frame rate is fixed at 25 frames per second.

[0130] Since there is a fixed scan rate for the secondary mirror (to rotate at the optimal speed) required to freeze the image on the focal plane while frames are taken, and a maximum scan angle range from © to -6 . through which the mirror can be moved without blurring the imagery due to defocus and other aberrations, the number of frames exposed during a single de-scan period of the secondary mirror is limited to a fixed value. This value may however change depending on the maximum allowed tilt angle and the reduced FMC factor of the platform. Frames cannot be captured during the back scan period or the reset of the satellite from the final pitching angle to the first pitching angle, due to excessive image blur. The number of frames captured during a de-scan period are limited by acceptable defocus and other aberration increases due to the tilted focus plane 114 caused by the rotated second mirror 104.

[0131] Using the secondary mirror 104 scanning alone has the benefits of improving the image throughput of the satellite/imaging system 100, and also being more energy efficient, since pitch ing/rotating the satellite is not necessary or can be reduced.

[0132] It is to be understood that, whilst the above description is exemplified by a satellite being the imaging system 100, this is not necessary. The imaging system 100 could also be a plane, unmanned aerial vehicle (UAV), or any other platform capable of housing an aerial camera and moving relative to ground. Furthermore, although the feature being observed by the imaging system 100 has been exemplified throughout as the Earth, it is to be understood than any other body moving relative to the imaging system 100 may also be observed.

[0133] Further, it is to be understood that the moveable secondary mirror may be retrofitted to an existing telescope in order to provide the existing telescope with FMC capabilities.

[0134] In the above description, it is to be understood that description of the function of various components and features may be implemented as a method, whereby the method may be implemented in a computer program. This method may be implemented as any form of a computing and/or electronic device. Such a device may comprise one or more processors which may be microprocessors, controllers or any other suitable type of processors for processing computer executable instructions to control the operation of the device in order to gather and record routing information. In some examples, for example where a system on a chip architecture is used, the processors may include one or more fixed function blocks (also referred to as accelerators) which implement a part of the method in hardware (ratherthan software or firmware). Platform software comprising an operating system or any other suitable platform software may be provided at the computing-based device to enable application software to be executed on the device.

[0135] Various functions described herein can be implemented in hardware, software, or any combination thereof. If implemented in software, the functions can be stored on or transmitted over as one or more instructions or code on a computer-readable medium. Computer-readable media may include, for example, computer-readable storage media. Computer-readable storage media may include volatile or non-volatile, removable or non-removable media implemented in any method or technology for storage of information such as computer readable instructions, data structures, program modules or other data. A computer-readable storage media can be any available storage media that may be accessed by a computer. Byway of example, and not limitation, such computer- readable storage media may comprise RAM, ROM, EEPROM, flash memory or other memory devices, CD-ROM or other optical disc storage, magnetic disc storage or other magnetic storage devices, or any other medium that can be used to carry or store desired program code in the form of instructions or data structures and that can be accessed by a computer. Disc and disk, as used herein, include compact disc (CD), laser disc, optical disc, digital versatile disc (DVD), floppy disk, and Blu-ray (RTM) disc (BD). Further, a propagated signal is not included within the scope of computer- readable storage media. Computer-readable media also includes communication media including any medium that facilitates transfer of a computer program from one place to another. A connection, for instance, can be a communication medium. For example, if the software is transmitted from a website, server, or other remote source using a coaxial cable, fibre optic cable, twisted pair, DSL, or wireless technologies such as infrared, radio, and microwave are included in the definition of communication medium. Combinations of the above should also be included within the scope of computer-readable media.

[0136] Alternatively, or in addition, the functionality described herein can be performed, at least in part, by one or more hardware logic components. For example, and without limitation, hardware logic components that can be used may include Field-programmable Gate Arrays (FPGAs), Programspecific Integrated Circuits (ASICs), Program-specific Standard Products (ASSPs), System-on-a-chip systems (SOCs). Complex Programmable Logic Devices (CPLDs), etc.

[0137] Although illustrated as a single system, it is to be understood that a computing device for performing the method may be a distributed system. Thus, for instance, several devices may be in communication byway of a network connection and may collectively perform tasks described as being performed by the system or telescope. The telescope may communicate with one or more servers, which may be ground based, in order to provide the above described functionality.