IMAGE NAVIGATION AND REGISTRATION
3.1 INTRODUCTION
Geostationary imagery products are used mainly for storm surveillance, cloud drift wind calculation, and water vapor observation. In the future, closer observations to support operational mesoscale forecasting and observation will become part of the geostationary imaging mission. In all these cases, and especially for mesoscale operations, accurate location of atmospheric phenomena and measurement of their motions and positions over time (e.g., satellite-based photogrammetry) are underlying requirements for the imaging instrument that appear to transcend other requirements. To perform these missions, the imaging instrument must offer higher-quality images with higher resolution of terrestrial atmospheric and surface features, and improved accuracy in measuring spatial relationships relative to conventional imaging technology.
The desired resolution of the visible-spectrum images to be produced by the focal plane array (FPA) detector instrument being studied here is 0.5 kilometer (km) pixel dimension. There would be about half a billion pixels in such an image of the full earth disk. A high-quality image is one that has the needed resolution, and in which all pixels retain their spatial relationships with respect to the target (i.e., the earth) and to every other pixel. These spatial relationships are known as image registration and the process of maintaining the relationships is called image navigation and registration (INR).
Image navigation is the process of assigning the latitude and longitude values for each pixel of an image. Image registration is the process of maintaining pixel latitude and longitude accuracy within and among images, independently of time. A high quality of registration is required to provide high-quality images. Classically, doing this well has required the ability to know the orbit and attitude of the spacecraft bearing the imager, and to translate those parameters into the desired pixel coordinates. In addition, a spacecraft responds noticeably to the smallest disturbances, whether they are torque imbalances produced by the solar wind, stepping forces and motions of the solar array, reactions to propulsion jet firings, or reactions to changes in instrument mirror positions. Compared with the large-magnitude low-rate shifts and rapid motions that will be exhibited by spacecraft not tailored to the high-resolution remote sensing mission, the pointing resolution needs to be fine and the accuracy needs to be high to obtain the desired image quality.
Consider that geostationary spacecraft orbit at an altitude of 22,300 miles (mi) and have optical instruments that resolve 1 km on the earth in the case of current imaging systems. The FPA instrument concept is directed toward resolving half a kilometer. From an altitude of 22,300 mi, half a kilometer at the subsatellite point represents an angle of about 14 microradians (urad) or about 0.0008[[ring]]. Slow spacecraft motions that might be expected in a host spacecraft such as used for commercial geostationary communications platforms are of the order of 0.2[[ring]] [Interav92] long-term or more than 250 times larger than required if motions are to be held to the same order of magnitude as resolution. Short-term disturbances, however, are not so well characterized.
In our FPA imager concept, large groups of pixels are captured simultaneously, thereby capturing their relative positions. It is well known that motions of a geostationary spacecraft over long and short periods of time will introduce distortions in the resulting images and sequences of images that could impair their usefulness for purposes of locating and tracking atmospheric phenomena such as cloud motion. It is important, therefore, that motions of the spacecraft be considered in the design of the remote sensing instruments we propose.
We use the GOES I imager as a point of reference. We compare FPA detector approaches using step-stare and time delay and integration (TDI) scanning strategies with GOES and with each other to explore several methods and image quality issues. This section reviews the problem and presents some ideas for future study. Section 3.2 examines the GOES I implementation of geosynchronous imaging instruments, section 3.3 presents INR approaches, section 3.4 offers some observations on image spatial relationships and ways in which they can be less than perfect, section 3.5 adresses an error budget for INR, and section 3.6 presents a summary and conclusions.
3.2 GOES I INSTRUMENTS
The GOES I imager is a flying spot scanner wherein the desired images of the earth are scanned by the instrument's small instantaneous geometric field of view (IGFOV). The imager's multidetector spectral channels simultaneously view the IGFOV, which amounts to about an 8 km field of view on earth through the optical system at the subsatellite or nadir point. The area is larger away from nadir because of the earth's curvature. The optical system provides simultaneous viewing coverage for two redundant sets of detectors for a total field of view of 16 km (a circular area 17.9 km in diameter). The IGFOV is swept along east-west and west-east (latitudinal) paths at a rate of 20[[ring]]/sec by means of a two-axis gimballed mirror scan system. At the end of each scan, the scan mirror moves the IGFOV in the north-south (longitudinal) direction to be ready for the next latitudinal scan.
The GOES I sounder has operational principles similar to those of the imager. It positions its IGFOV through use of a gimballed mirror which produces mechanical disturbances in the spacecraft, due to mirror motions, similar to those produced by the imager. Each instrument is disturbed by the same spacecraft- and instrument-produced motion factors.
The imager's mirror scan system is able to position the center of the IGFOV at any point in a rectangular field of regard (FOR) with respect to the spacecraft consisting of a rectilinear array of positions measuring about 25,000 (latitudinal) by 46,000 (longitudinal) positions. This corresponds with an angular FOR of 23[[ring]] by 21[[ring]] which is the imager's full viewing range. The positioning resolution is about 8 urad in the longitudinal direction and 16 urad in the latitudinal direction. The resulting visible spectrum image has 1 km pixel resolution, with about 0.29 km positioning resolution in the longitudinal direction and about 0.57 km in the latitudinal direction. The GOES imager provides an oversampled image in the latitudinal dimension with 1 km square pixels on 16 urad (0.57 km) centers for the visible channel, and 4 and 8 km square pixels on 64 urad (2.29 km) centers for the IR channels. Scan lines are separated nominally by 8 km center-to-center without oversampling (in the longitudinal direction).
Variations in the spacecraft's motions and orbit that would alter the resulting image in undesirable ways are compensated through use of image motion compensation (IMC) and mirror motion compensation (MMC). For a rectilinear scan, the longitudinal position of the IGFOV stays at a constant latitudinal coordinate value in its FOR for the entire latitudinal motion of the scan mirror. For a motion-compensated scan, the system alters the mirror coordinates during the course of scanning, departing from the rectilinear mirror positioning to track and counteract undesirable motions, position, and attitude of the spacecraft in addition to scanner and other instrument errors. INR for the GOES I system is very complex and we have chosen to represent it here in a greatly simplified way to avoid very detailed and lengthy descriptions which would not contribute to the presentation of FPA INR.
For slower, predictable spacecraft displacements, IMC corrective mirror motions are predetermined by the GOES ground system; they are communicated to the spacecraft by way of the telemetry and command system and then to the imager through the attitude and orbit control system (AOCS), where departures from a strictly rectilinear scan are programmed into the mirror motion. Orbit inclinations and latitudinal drifts may be compensated in this way, as may thermal distortions of the spacecraft and instrument and drifts due to solar wind-induced torques on the solar array panels.
For motions of the imager and sounder instrument mirrors, which also cause predictable spacecraft disturbances, the AOCS calculates MMC corrections onboard and provides them in real time directly to the imager, along with IMC corrections.
For the GOES spacecraft, part of the spectrum of motions to be compensated is indicated in figure 3-1. Note that the figure does not include long-term orbital effects or the effects of propulsion system firings. The orbit inclinations of +/-0.5[[ring]] are off the scale of the figure to the left, and propulsion system firings produce such large disturbances as to render dynamic correction impossible. Fortunately, IMC can compensate for orbital effects. Propulsion system firings are used infrequently to perform orbit adjustments. Instrument performance requirements may be suspended during and for a period immediately after those maneuvers.
Figure 3-2 shows, for reference, definitions used to describe geostationary communications spacecraft motions. With respect to image motions, yaw produces latitudinal shifts of the image in the instrument FOR, pitch produces longitudinal shifts, and roll produces image rotation about the earth-spacecraft line.
3.3 APPROACHES TO IMAGE NAVIGATION AND REGISTRATION
For GOES I, INR is intended to produce images having a fixed earth-projection, that is, images that appear to have been captured from a zero-inclination geostationary orbit at all times. This is done through the IMC feature, whereby pixel shifts due to orbit inclination and other slow factors can be compensated by driving the flying spot through nonrectilinear scans, thereby straightening the equator and adjusting for apparent rotation of the earth in the instrument's FOR.
In the FPA imaging concept, IMC cannot be performed the same way because large blocks of pixels will be captured simultaneously, and individual pixel locations and scan line trajectories cannot be altered. Images, therefore, must be captured without the beneficial distortion afforded by a GOES-like IMC system. This is one of the prices paid for the simultaneity offered by the FPA detector approach. Another price paid is that of having longer image pixel exposure times, which is discussed below.
However, it must be noted that there is no more information offered by the GOES IMC-based instrument than by the FPA concept, other than the possible benefits of oversampling. This is the case since both images will have been made from the exact same orbital position with the exact same field of regard and the exact same ability to "see" the features and extent of the target, the earth. The major differences are the amount of time taken to capture the image--about 30 minutes for GOES versus about 3 minutes projected for the FPA concept--and the enhanced coregistration, hence spatial accuracy, offered by an image composed of large blocks of perfectly coregistered pixels.
The approach to INR for the FPA instrument includes features that, taken together, would provide an accurate image set capable of fulfilling the accuracy requirements needed to support present and future primary image uses. Note that the approach outlined in the following addresses mainly the step-stare imaging method; time did not permit development of an approach for for the TDI imaging method. The step-stare approach, here termed the "overlap" approach, requires three features to provide accurately registered and located images:
* Acquisition of overlapping image blocks or frames
* Application of image processing to creating a mosaic of adjacent frames
* Creation of a collateral data set consisting of information that links together all visible landmarks, and provides a basis for spatial location and measurements in the image
Acquisition of overlapping frames is discussed below. The creation of mosaics of frames and of collateral data sets are discussed in section 4 on ground-based processing.
3.3.1 Acquisition of Overlapping Image Frames
The FPA imaging instrument produces an image of the earth or a segment of the earth using a FPA detector as described in section 2 of this report. An image frame is produced by the array detector instrument using the step-stare method in a single exposure time; that is, all pixels in the frame are exposed simultaneously.
An image of an area larger than an image frame is a mosaic of adjacent image frames "stitched together" through ground-based image processing, as in figure 3-3. Spacecraft motions will not permit accurate enough positioning of the IGFOV of the instrument to abut adjacent frames such that pixel relationships between the two frames are maintained. The effects of motions on the use and content of the image frame are shown in figure 3-4.
Consequently, it is better to overlap adjacent frames and allow the spacecraft motions to expand and contract the overlap. In this way, the relationship between adjacent frames can be retained despite spacecraft motion, and spacecraft motion bounds need only be understood and not mitigated to retain spatial relationships. The adjacent frame relationship is retained by virtue of the fact that both frames will capture an image of the same area, the overlap. This feature obviates the need for the predictor-corrector approach to INR, as used in the GOES system, or for a real-time feedback system.1 This is done at the expense of collecting and carrying redundant image information.
Table 3-1 shows the results of a calculation of overlap for the case of a variety of motions of the spacecraft. In these cases, the basic FOR covered was 17.4 degrees latitudinally and longitudinally. This is the minimum angle measured at the spacecraft subtended by a full earth disk across the equator.
Given a detector array having 512 x 1024 pixels for the visible channel at 0.5 km resolution, as in the FPA instrument design, 43 frames would be required to cover the 17.4 degree FOR in the latitudinal direction using the 512 pixel dimension. Likewise, it would require 22 frames in the longitudinal direction using the 1024 pixel dimension. In this case, there would be no overlap and since a discrete number of frames must be used, the FOR would be somewhat bigger than 17.4 degrees.
The table shows the number of pixels overlapped around the edges of each interior frame, given the addition of one or more frames to each FOR image dimension and overlapping them to yield the FOR angle indicated in the five center table columns. The FOR angle dimension of the table indicates the displacement of the spacecraft added to the 17.4 degrees. That is, the 17.6 degrees column implies that the spacecraft displacement is 0.2 degrees (or +/-0.1 degrees) and the imager FOR is increased by the displacement amount to accomodate the pointing error and still record the entire earth disk in the FOR. That number of frames is given in the first column of the table.
The overlap length (the last column of the table) is the other dimension of the overlap region; together with the overlap width, it forms an overlap or "stitching" vector that appears in both adjacent frames. For example, the table entry for a latitudinal direction of 45 frames and a 17.6 degrees FOR angle indicates a stitching vector with dimensions of 24 x 1024 pixels.
Although the stitching vector sizes are substantial in terms of the size of the pixel array available for image matching, the added frames represent no more than about 21 percent overhead in terms of data volume for a full earth disk in any of the cases in the table. A description of stitching vector processing is given in section 4.
Most commercial communications spacecraft attitude control systems can point the spacecraft toward the earth and at the subsatellite point within a half-cone angle of 0.2 degrees. The table and the column for a FOR angle of 17.8 degrees then describe the instrument overlap parameters. An image composed of 45 latitudinal frames x 23 longitudinal frames would be able to capture the full earth disk under all normal circumstances of attitude and orbit shift.
The preceding, however, does not account for pointing errors within the instrument, such as effects due to the diurnal heating cycle. Nor does it account for more dynamic factors, such as vibrations due to other subsystems on the spacecraft. See figure 3-1 for several examples of the types of disturbances that can occur.
If we view these other disturbances as being additive to the spacecraft pointing error in the worst case, it is conceivable that overlap permitting relative frame displacement would be one of the solutions. For the 17.8 degree column and 45 latitudinal frames, the table shows an overlap of 18 pixels. Each pixel represents 0.5 km on earth or 14 urad at the spacecraft; 18 pixels represents 252 urad for these additional phenomena. Using an additional latitudinal frame (46 total) would permit increasing overlap to 29 pixels, giving 406 urad in the latitudinal direction and retaining the 23 frames in the longitudinal direction, which gives 59 pixels or 826 urad. Based upon the preceding discussion, this is about 9 percent data volume overhead.
The discussion of scanning in section 2 of this report notes that overlap might be a good way to compensate for dead pixels, and that doing so might require that each earth pixel be viewed by four detector pixels. The subject of scanning strategy could take considerable time and yet not be treated exhaustively. Perhaps the best approach is to make it possible to take any or all approaches and to make overlap a dynamically programmable feature, a dynamically programmed overlap method for INR.
FOR Angle
Latitudinal
Direction 17.4 degrees 17.5 degrees 17.6 degrees 17.7 degrees 17.8 degrees Overlap
Length
(frames) Overlap Width (pixels) (pixels)
44 19 16 13 (a) (a) 1024
45 29 27 24 21 18 1024
46 40 37 35 32 29 1024
47 42 39 1024
Longitudinal Direction
(frames)
23 80 75 70 64 59 512
24 120 115 109 104 99 512
25 156 151 146 141 136 512
(a) Indicates that more than 44 frames are required to cover the FOR angle with overlap.
Step-stare scanning could be implemented as it is for the GOES I sounder. The sounder scan mechanism has a gimballed mirror similar to that of the GOES I imager. The scanner is capable of stepping the IGFOV 17.5 urad in the longitudinal direction and 35 urad in the latitudinal direction within a total FOR of 21 degrees longitudinally x 23 degrees latitudinally. Latitudinal mirror scan motions of 280 urad require 25 milliseconds (msec) to accelerate, step in 35 urad steps at 10,000 steps/sec, and settle prior to beginning a detector exposure. The sounder then performs a 75 msec detector exposure cycle prior to repeating the mirror stepping operation for a total cycle time of 0.1 sec.
Using these performance parameters as a guide, the FPA imager needs to step about 17.8 degrees/46 = 0.387 degrees per step (about 6755 urad). At 7.2 sec per 20 degrees latitudinal scan, the time alloted for 17.8 degrees is 6.4 sec or 139 msec for each frame. The exposure cycle would require 19 msec to finish considering the longest required exposure time (channel 2). This would leave 120 msec for scanner motion. A GOES-like scanner stepping rate is fast enough to move the IGFOV 6755 urad latitudinally in about 20 msec, leaving 100 msec for acceleration and settling.
3.4 IMAGE SPATIAL RELATIONSHIPS
The quality of an image produced from geostationary orbit is related to the spatial and temporal synopticity2 of the image components (i.e., pixels, frames, and/or lines), and the ability to maintain spatial relationships between and within images. In the FPA imaging concept, synopticity is improved over current technology by having the same viewing range and an order-of-magnitude improved temporal performance.
Spatial relationship effects examined include pixel location, spread, smear, and rotation. Location refers to the ability to determine in absolute terms the earth latitude and longitude of an image pixel, and is addressed in section 4. Spread is the enlargement in scene dimension represented by a detector pixel due to spacecraft motions during pixel exposure; smear is distortion of the representation of objects in the image due to their motion during image exposure; and rotation is image distortion due to scan mirror effects.
The current, GOES I, technology differs significantly from FPA detector technology. The approaches are discussed below.
3.4.1 GOES I Technology
In the GOES I imager instrument, single image pixels are formed predominantly independently of other image pixels.3 The spatial relationship between any two nonsimultaneous pixels is largely indeterminate because there are no inherent physical properties fixing the location of one pixel relative to another as with FPA detectors, where multiple detectors share the same rigid mechanical mounting surface. In addition, detector pixel exposures are made at different times since the instrument needs to point the IGFOV at the next target after each image pixel exposure. Although the spatial relationships among image pixels can be bounded by carefully controlling the motions of the spacecraft and of the imaging instrument, those relationships are statistical in nature because the spacecraft motions that occur between exposures are somewhat indeterminate.
GOES I technology has pixels formed during a more or less continuous scan of the instrument IGFOV across the earth. The instrument uses single- and double-pixel imaging for IR channels and an array of eight detectors for the visible channel. The visible channel is sampled every 45.7 usec, corresponding to 0.57 km scan movement of the IGFOV at nadir. The IR channels are sampled every 183.4usec, corresponding to 2.28 km movement of the IGFOV at nadir. Sampling durations are small (estimated at about 1 usec) to form a pixel.
Over tenths of seconds to seconds, the GOES I AOCS and the instrument servo systems can respond to correct for the spacecraft motions of concern. The net result is the predicted performance of the instrument as shown in table 3-2.
3.4.2 Array Detector Instruments
The array detectors employed in the FPA concept use the same materials as in the GOES I imager, but are constructed and operated differently. The GOES I instrument detectors are operated as light energy rate-sensitive devices, in which the instantaneous detector output corresponds with the rate of arrival of photons. Array detector devices are integrators in which electrons freed by arriving photons are collected and retained for a period of time, until the total number of photons for a detector pixel is read by the device and external circuits.
Image formation times (time between start and finish of exposure) for the step-stare approach, stated in section 2 of this report extend from 160 microseconds (usec) to 19 msec, orders of magnitude larger than the formation time needed by the GOES I technology. One detector pixel exposure is made for each image pixel. TDI image pixel formation time, as defined in section 2 of this report, is 37 msec.
3.4.2.1 Time Delay and Integration (TDI)
With the TDI method, image pixel exposures are the sum of a number of detector pixel exposures. While TDI has an advantage radiometrically because of superior noise levels (see the discussion of instrument design in section 2), from the standpoint of immunity to motion, TDI image pixel exposure times can be of concern since they are so long. Detector pixel exposure intensity for the TDI approach is adjusted to make all image pixel exposure times the same.
The TDI approach improves spatial relationships with respect to current technology in one dimension because of the columnar nature of the TDI array detectors. The visible channel detector array would be 1024 pixels long, compared with 8 pixels in the GOES I instrument, and IR channels would be composed of 128 and 256 pixels compared with 1 or 2 for the GOES I. Exposure time per image pixel would be the same for all channels, and incoming light energy in some channels would have to be attenuated to make this possible.
The simultaneous image formation of the entire column of TDI detectors preserves the spatial relationships among all the target pixels in the column since no spacecraft or image motion can take place between the times of capture of the individual pixels in the column. The motions that can reduce image quality in this case are motions that can take place during column image formations, that is, during exposure of a single image pixel, which is the same as the period between the start of the first detector pixel column exposure and the end of the last.
Performance Parameter 3 [[sigma]] Performance Prediction
Image navigation accuracy 22 km at nadir
Registration within an image 74 urad in 25 minutes
Registration between repeated images 37 urad in 15 minutes
Source: [GOES91].
Compared with the flying spot, the TDI approach might offer a quality improvement related to the number of pixels captured simultaneously and related inversely to the image formation times. Image pixel formation times for the TDI approach, as described earlier, are the longest of those for all the approaches, rendering this approach the most sensitive to mechanical noise (i.e., unwanted mechanical perturbations).
3.4.2.2 Step-Stare
The step-stare approach offers an advantage over the other approaches in retention of spatial relationships. First, a large area of pixels is exposed simultaneously, compared with single pixels or one-dimensional arrays of pixels. Thus, quality improvement is related not only to the linear dimension or number of coregistered pixels, as with the TDI array, but also to the area of pixels. The exposure time is longer than that of the GOES I technology and shorter than that of the TDI approach.
The step-stare approach offers an added feature. Since it produces two-dimensional frames of pixels that are formed simultaneously, the spatial relationships among all image pixels in the scene area represented by the frame are perfectly, deterministically defined. This means any recognizable detail in the frame image can be located on earth to at least pixel-size accuracy.
Adjacent frames can be overlapped, thereby providing added features. Since image detail can be recognized in the overlapped region common to both frames, the adjacent frames can be accurately registered to one another through image processing after image formation. Without remapping of pixels, registration within about half a pixel dimension should be possible; with remapping, it may be possible to do better. See section 4 of this report for a discussion of the processing needed to register adjacent frames.
3.4.3 Pixel Spread
A detector pixel views a scene area on the earth (e.g., at nadir) that is the same shape and size as the detector pixel transformed (i.e., magnified, rotated, and perhaps distorted in other ways) by the optical system in a perfectly noise-free environment. Scene area coverage by the detector pixel increases because of the effects of mechanical noise or motions of the spacecraft during the time period of image pixel formation (i.e., exposure time).
If the motion of the spacecraft relative to the target earth were predictable and always the same, one could reduce the size of the detector pixel relative to the intended image pixel and, allowing for the detector (i.e., IGFOV) motion, represent the result as an image pixel. If the motion were random or not always the same, or not conveniently predictable, the coverage represented by the resulting image pixel would be somewhat larger than that of the desired image pixel. This excess size is referred to here as "spread." Spread is the enlargement in the coverage of an image pixel relative to that of the corresponding detector pixel, both referred to the same side of the optical system to account for optical transformations.
Spread is related to both the rate of motion and the time of exposure, and is a measure of the distance the pixel moves (rate multiplied by time = distance). In addition, spread brings with it the problem of adjacent pixel overlap, in which a pixel value is influenced by an area that contains all or part of adjacent scene pixel areas. This also can result in an apparent loss of resolution due to inadvertant exposure of more than one adjacent pixel to the same target area. The effective resolution of the step-stare FPA imager was investigated; the analysis is presented in appendix B, and shows that the RMS value of the imager-spacecraft system's effective resolution is given by the root sum square (RSS) of the full-half-width-maximum values of the point spread functions of the instrument and the spacecraft. These terms are defined in the appendix.
For a perfect spacecraft exhibiting no extraneous motions, spread would be equal to zero, and the image pixel would have the same coverage as the detector pixel. For present purposes, spread and coverage have a linear dimension, but a similar argument could be made using an area dimension.
Figure 3-5 is a display of linear spread value incurred over image pixel exposure time. Spread is produced by spacecraft rotational rates about any axis that produce image displacements during exposure, and by finite frame exposure times. Points for GOES, TDI, and step-stare approaches are displayed for spread limited to 0.1 pixel size. The figure shows spacecraft angular rates relative to earth that would incur the 0.1 pixel spread, spreads that would result because of scanning rates, and spacecraft rates that could be tolerated without exceeding 0.1 pixel spread.
For step-stare imaging, the maximum exposure time needed for the 3.8-4.0 micron near IR channel is about 19 msec and the visible channel requires 200 usec. Allowing 0.1 pixel dimension or 0.2 km movement in the near IR (channel 2) during exposure, spacecraft rates of up to 295 urad/sec could be tolerated. If Step-Stare imaging required continuous exposure during scanning, the spreads would range from about 0.3 km to 33 km as shown along the TDI/Step-Stare scan line.
TDI-based imaging, as described earlier, could tolerate only 38 urad/sec without exceeding 0.1 pixel spread. TDI imaging exposes continuously while scanning. Each detector pixel contributing to an image pixel views the same scene pixel. The spreads associated with TDI scanning operation are shown in figure 3-5 along the TDI/step-stare scan line, and are, by definition of the TDI scan, equal to the scene pixel dimensions of 0.5, 2, and 4 km.
Published GOES I simulation results [GOES91] imply rates of 50 urad/sec for more than 80 msec and lower rates for a wide range of durations. This is shown in figure 3-5. We have no data at this time on commercial spacecraft dynamic environments.
3.4.4 Image Smear
Pixel spread, discussed above, relates image pixel enlargement for given spacecraft motions. Smear is defined as image object distortion due to object motion. To illustrate, consider that the FPA imager (TDI or step-stare) requires about 7.2 sec to complete a latitudinal 20 degree scan. From the left edge of the FOR, it requires about 14.4 sec to scan to the opposite edge of the FOR and return (neglecting turnaround, which would only increase the effect) to capture the frame below the starting frame.
This is a worst case, although there is not much moving detail of interest at the earth edge. A bad case might be farther in toward nadir longitude, at which the return time would be 7.2 sec, a median value. The shortest interval occurs between the last frame in the scan and the first frame on the return scan. For a step-stare step interval, as discussed in section 3.3.1 above, the return time is 0.139 sec. A scan need not cover the width of the FOR. Figure 3-6 shows translational smear effects for a 16-frame wide scan.
The GOES I imager scans about 7 times faster than the FPA imager. Consequently, smeared images of moving scene objects that span more than one sampling period will appear smoother in GOES I images because of the higher scan rate and sampling frequency.
In assembling the total image, frames are stitched together around all edges. As the scan returns from the far edge to a point just below the starting frame, the starting frame must be stitched to the scan frame below it through the overlap on their lower and upper edges. A moving image object lying in both frames will undergo translation during the return time, with the part lying in the last frame displaced in the direction of motion and the part lying in the starting frame occupying its starting position. Displacements are shown for the FPA imager in figure 3-7. The figure accounts for a 52-frame FOR to cover the full 20 degrees. Object speeds range from 10 to 300 miles per hour (mph). The shaded area indicates displacements of half a pixel that would affect frame overlap matches.
3.4.5 Field Rotation
With a single-scan mirror, image field rotations will occur as a result of the rotation of the mirror in the longitudinal and latitudinal directions. The distortions will be manifested in apparent rotation of the image focal plane, with accompanying changes in the transform of earth dimensions to image dimensions.
The scan mirror has two axes about which it can rotate, as shown in figure 3-8: One, the latitudinal scan axis, call it V, about a line perpendicular to the orbit plane; the other, the longitudinal scan axis, call it H, about a line parallel to the orbit plane. The mirror is nominally at a 45 degree angle with respect to the orbit plane, and the V-axis is perpendicular to the earth-spacecraft line through the nadir point. In this position, the imager is viewing a frame centered on the nadir point or the TDI array is centered on the nadir point, and is viewing along a longitude meridian. In either case, the detector is located in a plane parallel to the orbit plane.
If the detector is located northward of the scan mirror, and if the scan mirror is made to rotate about its H-axis toward either pole, there will be a maximum foreshortening of features in the longitudinal dimension of about 1.3 percent at the Poles. The phenomenon is a cosine function in between the extremes.
Likewise, scanning about the V-axis will produce a rotation of the image field, with scans toward the east producing clockwise rotation and those to the left producing counterclockwise rotation for the detector located northward of the scan mirror. Equal but opposite rotations will occur if the detector is located southward of the scan mirror. This is illustrated in figure 3-9, which shows how frames in the northeast quadrant would have to be rotated in order to be stitched together for a scanner having a detector located south of the scan mirror. In addition, the figure shows rotation about the detector's center. If the optical rotation center of the frame image field were located, say, at the detector edge, rotation would be about that point, thereby altering the frame assembly stitching pattern. Scan adjustments may be required to ensure that overlap occurs at all frame edges.
For scans about the V-axis with the mirror positioned to view along a line through the nadir point, the extremes of rotation will be equal to the mirror rotation angle, since the detector does not rotate along with the mirror. Rotation of the detector is precluded by the need to attach it rigidly to its heat sink.
For compound mirror deflections about the H-axis, there also will be a foreshortening or lengthening of the field as described above, so as to alter the apparent rotation angle, as well as distort feature dimensions.
While these distortions can be accomodated and compensated with a flying spot imager, they are not so easily accomodated with a two-dimensional detector. One approach to be investigated would be to use a two-element scanner, such as a mirror-based equivalent of a Risley prism. Analysis of this option was beyond the scope of the present investigation.
3.5 ERROR BUDGET
In view of the lack of design details, an error budget cannot be stated conclusively at this time, although a rough order of magnitude (ROM) estimate for some of the error parameters is interesting to consider. Note that time dependency is not apparent in these estimates. This is due largely to the pixel spatial relationship inherent in the focal plane detector array.
For image navigation accuracy, we need to know the error implicit in the collateral data set. However, knowing the locations of landmarks with great accuracy and being able to recognize them in an image frame, it should be possible for that frame to provide a level of error well below that to be expected at the level of an integrated whole image. Allow one-third of a pixel error in locating any pixel within a landmark-bearing frame as an initial estimate, or 4.67 urad. This should be due largely to error in assigning the landmark location to specific pixels. No allocation is made for errors in pixel distribution in a FPA.
The error in assembling non-landmark-bearing frames having some image structure (see section 4) into an image is about half a pixel or 7 urad. If the typical distance to be measured from an image is assumed to be in the range of 1000-3000 km, then assume that knowledge of pixel location is required over that distance. This is a span of as many as 12 frames. In the worst case, only one frame contains any landmarks, and the potential error in locating a pixel 12 frames away from a landmark-bearing frame would be the RSS of 11 frame errors.
Additional error is incurred as a result of frame rotation; pixel spread; and other, as yet unconsidered parameters that cannot be assessed with the information on hand. Allow one-third of a pixel per frame for error due to compensation for rotation and for spread. The total error would be the RSS of 11 frame errors.
Total ROM navigation error due to the above factors would be 28.3 urad RSS. This is the error to be expected in measuring distances of the order of 3000 km from a known landmark in a two-dimensional image.
For registration within an image, there are two errors to assign--error within a frame and interframe errors. Registration error within a frame is negligiable since all frame pixels are fixed with respect to one another. Interframe errors between any two adjacent frames would consist of translational and rotational errors, or about 8.4 urad RSS. Over the 3000 km range, errors would result from translation and rotation errors for 11 frame assemblies, or a ROM error of about 27.9 urad RSS so far, with changes to come as we learn more about the errors in this system.
Registration error between repeated images should not be greater than the navigation error within an image, or 28.3 urad RSS, with the understanding that there are more factors to be defined and evaluated.
3.6 SUMMARY AND CONCLUSIONS
The above discussion can be summarized in the following conclusions:
* The use of FPA detectors precludes the use of image motion compensation and mirror motion compensation as defined for the GOES I system. This is due to the rigid spatial relationships among the pixels within a single frame of an image, and the consequent inability to alter the positions of individual pixels during image creation.
* There is as much information in the FPA-based image of the earth as there is in the GOES I image, except for the possible benefits of oversampling as achieved in the GOES I imager.
* There is greater simultaneity, hence temporal synopticity in a FPA-based image relative to a GOES I image as a result of an order-of-magnitude shorter total image formation time.
* Use of overlapping image frames in the step-stare method offers deterministic spatial relationships within and among image frames.
* The creation of overlapping image frames by the imager is necessary to provide well-coregistered images, with ground-based processing after image creation responsible for assembling the frames into a whole image. This is contrasted with the predictor-corrector approach to motion compensation used in the GOES I imaging system.
* The predictor-corrector and feedback approaches to INR place the burden of image spatial relationships on the spacecraft and the imager scan system, whereas the overlap approach uses data redundancy and image processing.
* The overlap INR approach and the feedback approach allow the imager to operate more independently of the spacecraft as compared with the GOES I predictor-corrector approach, whereas the overlap approach results in the simplest of the three space segments.
* Whole image assembly from overlapped frames after image frame exposure permits compensation for all spacecraft-earth relative motions as compared with the predictor-corrector approach, which can correct only as well as it can model the motions.
* The step-stare approach to image creation has the advantage over the TDI approach of shorter image pixel exposure times, which result in greater immunity to pixel spread due to spacecraft motion, while the GOES I/flying spot approach has still better immunity to pixel spread due to shorter effective image pixel exposure times.
* The slower frame scan rates of the proposed FPA imager would result in lower sampling rates for moving scene objects. Such objects would thereby be rendered less smoothly in scan-to-scan transitions than would be the case for the GOES I or other imager having greater scan rates, despite the FPA imager's smaller overall scan time.
* Rotational distortion of the image focal plane due to rotation from single mirror scanning could amount to as much as 1.3 percent foreshortening of earth dimensions at the earth poles, and apparent rotation of image frame fields of about 8.9[[ring]] at latitudinal scan extremes. This is not peculiar to the FPA concept.
* Scanning strategy and image frame assembly will be affected by rotational distortion, optical centering, and detector and scan optics design.
Several areas require further analysis to support design decisions and performance issues. Time and resources prevented us from examining the following areas further:
* Resolution of the TDI-step-stare tradeoff or adoption of an appropriate combination is needed to obtain the best possible radiometric vs. mechanical noise rate immunity and spatial relationship performance.
* Oversampling needs to be considered in the context of the FPA.
* Optical scanning systems need to be investigated to eliminate, or reduce to acceptable levels, the effects of image field rotation due to scanning.
* Scanner design, scan strategy, and scanning parameters need to be studied for impacts on image processing and image frame assembly.
* A comprehensive error budget needs to be developed for navigation and registration performance.
2 Synopticity here refers to the degree or faithfulness of representation by an image of an entire original scene of a wide area at a given time or over a short span of time. The notion is that an image of a very large area could be faulty and not represent meteorological events happening simultaneously. Spatial synopticity refers to the breadth of coverage at a given time, and temporal synopticity refers to the time needed to obtain a given breadth of coverage.
3 Strictly speaking, the GOES I imager creates eight simultaneous visible channel 1 image pixels and two simultaneous IR image pixels for each of channels 2, 4, and 5. Therefore, there is a degree of simultaneity. However, compared with the FPAs of 2000 to more than 500,000 detector pixels, this number of simultaneous pixels is small and offers small benefit as regards spatial relationships.