Philpot & Philipson: Remote Sensing Fundamentals Scanners 8.1 W.D. Philpot, Cornell University, Fall 2015

Transcription

1 Philpot & Philipson: Remote Sensing Fundamentals Scanners SCANNERS 8.1 General Scanners are scanning radiometers which, when operated from an airborne or spaceborne platform, image the terrain in one or more spectral bands. Mechanical scanners are electro-opticalmechanical sensors that use a mirror or prism to focus radiation of ultraviolet, visible or infrared wavelengths, or combinations of these wavelengths, from the ground to one or more detectors. (Microwave scanners will be described in a later section.) The mirror or prism rotates or oscillates, scanning a line of incoming radiation that is usually perpendicular to the flight direction (Figure 8.1). New, adjacent lines are scanned as the platform moves ahead. Each line is typically recorded digitally and sometimes displayed directly on a monitor. Figure 8.1:Data collection pattern for a mechanical (whiskbroom) scanner. Recall that the aircraft or spacecraft is moving ahead during the time that each line is imaged. For mechanically scanning systems this means that the pixel the end of the scan line will be imaged later than the pixel at the beginning of the scan line and therefore be will displaced along the flight path. The displacement is usually rather small but not always entirely negligible. More troublesome is the geometric distortion introduced as a result of the variation in viewing angle. This geometric distortion is especially severe near the edges of the image where the sizes of the ground resolution elements are comparatively larger than those at nadir (Figure 8.2). For a square pixel at nadir, the width of a single scan line on the ground is Hω. At a viewing angle, θ, the along-scan-line width of a pixel is Hω sec 2 θ while the length along the flight line is ω sec θ. The distortion is called the panoramic effect. Panoramic distortion can be reduced to negligible amounts by restricting the total FOV in relation to the flight height.

2 Philpot & Philipson: Remote Sensing Fundamentals Scanners 8.2 Figure 8.2: Panoramic effect the increase in the GIFOV with viewing angle. 8.2 Scanning a Ground Resolution Element The spatial parameters of scanning which are of primary concern for remote sensing are the scanner's total field-of-view (FOV), its instantaneous field-of-view (IFOV or ω), and the ratio of the platform's velocity to its height above ground (V/H). The total FOV of a scanner is the scanner's lateral coverage (Figure 8.1). It is analogous to the angular coverage of an aerial camera in the direction perpendicular to the aircraft's flight direction. Unlike a camera, however, a scanner does not collect radiation over its total FOV at one instant of time. As noted, the scanner mirror covers the total FOV by "looking" sequentially at numerous ground spots, or resolution elements, along a scan line (Figure 8.1). These resolution elements are the smallest ground areas that the scanner can "see"; radiance emanating from all features within each ground resolution element are integrated and measured as a single level of radiation for each wavelength interval sensed by the scanner's detector or detectors. The ground resolution element viewed instantaneously by the scanner will be measured and recorded in the resultant image as a single picture element or "pixel". Ideally, each pixel corresponds to the ground resolution element defined by the IFOV. When expressed in terms of the ground distance covered by a single pixel, the instantaneous field of view is typically expressed in units of length and referred to as the Ground Instantaneous Field of View (GIFOV). Note that the GIFOV is dependent on look angle, while the angular IFOV is not. As shown in Figure 8.1, the size of the ground resolution element is determined by the scanner's IFOV, ω, its height above ground, H, and the scan angle b, the angle between the ground element and the nadir. To illustrate, a typical aircraft scanner might have a square IFOV of 2.5 milliradians on a side, and a total FOV of 120, or 60 to either side of the aircraft. If the length or width of the ground resolution element is approximated by the arc of a circle whose center is at the scanner, an angle of 2.5 milliradians would intercept an arch whose length is times the radius. For every 1,000 meters of aircraft height above ground, the dimensions of the ground spot viewed directly below the aircraft would increase by 2.5 meters on a side (R = H = 1,000). The corresponding increase for ground resolution elements away from the aircraft nadir would be larger because the distance between the scanner and element (i. e., the radius of the circle) is longer. For every increase of 1,000 meters above ground, other resolution elements would increase by 2.5/cos 2 θ along a scan line and by 2.5/cos θ perpendicular to the scan line.

3 Philpot & Philipson: Remote Sensing Fundamentals Scanners Detector-Scanner-Platform Velocity Relationships The usual goal of creating a digital image is to collect pixels in a square array in which adjacent pixels are contiguous, but not overlapping. Since with a scanner this is done on the fly, the specific geometry of the image depends on the rate of scanning. That rate is constrained, in turn by the detector response. While data are collected for a single pixel, there is both motion of the scanner and motion of the platform. As a consequence, single pixels do not correspond exactly to a ground resolution element defined by the IFOV. Moreover, although single pixels correspond to single ground resolution elements, there may be gaps or overlaps between adjacent pixels if the rate of detector sampling and the rate of scanner rotation are not well matched. It is instructive to examine these relationships further. Consider an aircraft scanner that scans the terrain with a rotating mirror through an IFOV of ω. Assuming that the mirror rotates through 360 degrees or 2p radians, the number of elements scanned per mirror rotation is 2p divided by ω, the IFOV in the direction of scanning (Figure 8.1). The number of resolution elements (N) scanned per second is thus equal to the number of elements scanned per mirror rotation multiplied by the rate of mirror rotation (M), or N = M(2p/ω ). Since the time required to scan a single resolution element is 1/N, 12 scan time per element = ω 2 p M (8.1) The time devoted to scanning a resolution element must be at least as long as it takes the detector to respond. The detector's dwell time refers to the time the detector must "look at," or dwell on, a resolution element before it "sees" it. In general, Detector dwell time per element = kt d (8.2) where k is a constant of 1.0 or more, and t d is the time constant for the detector (i.e., time required for the detector to respond). For each ground resolution element to be "seen," ω kt d 2π M (8.3) The remaining variables to be considered are the velocity, V, and height, H, of the aircraft. It should be clear that, if the aircraft is moving too rapidly, there will be gaps in the ground coverage. The velocity of the aircraft must therefore be linked with the rate of scanning. In the flight direction at the nadir, the width of a single scan line is H multiplied by ω, the IFOV in the flight direction (Figure 8.1); the width of the ground strip covered each second is M(Hω ). To avoid gaps or underlap between scan lines, M(Hω ) > V (8.4) or V M > (8.5) Hω The rate of mirror rotation is thus governed, in part, by the velocity to height ratio, and vice versa. (Note that overlap between adjacent scan lines produces redundant information.) The constraints can be combined by substituting for M in Equation 10.3, which results in the following:

4 Philpot & Philipson: Remote Sensing Fundamentals Scanners 8.4 ω V 2πkt H d (8.6) As indicated by Equation 8.6, the spatial resolution can be increased by decreasing t d, with no change in V or H, if the speed of the detector can be increased. Similarly, flying faster or lower requires a faster detector for the same ω. The relation between velocity and height, the V/H ratio, describes the angular rate (radians/second) that a point on the ground appears to pass beneath the aircraft. For a given scanner configuration, ω and t d are fixed, but the V/H ratio can be adjusted to some defined maximum value. 8.4 Power Considerations The level of signal received from a resolution element has obvious effects on the resultant scanner image. Irradiance at the scanner can be described by E = L tot ω (8.7) where L tot = (L emit + L ref ) t a + L a ω = instantaneous FOV L emit = total emitted radiance L ref = total reflected radiance t a = atmospheric transmissivity L a = path radiance As Ad For simple scanners, ω= = (8.8) 2 2 R f where As = area of ground resolution element of scene R = distance between scanner and ground element Ad = area of detector = (Do2)/4 Do = effective diameter of aperture f = focal length of scanner. The power received at the detector is: P = E A o t o (8.9) where E = irradiance at the detector A o = area of scanner aperture t o = transmission of the optical system The detector responds to the power received by producing a signal, V s = PR (8.10) where R = responsivity = V n D * /(A d B) V n = voltage generated by detector noise D* = D-star, a figure of merit of the detector B = electrical bandwidth

5 Philpot & Philipson: Remote Sensing Fundamentals Scanners 8.5 The signal to noise ratio is one means of assessing the information transferred by the power received. Rearranging Equation 8.10, V V s n PD = (8.11) A B d Substituting for P = L tot ω A o t o and A d = ω/f 2, assuming a square instantaneous FOV whereby ω = (ω ) (ω ), and letting F = the f-number of the scanner optics = f/d o, results in s n V ω DtDL o o = (8.12) V 4f (B ) In order for the scanner to achieve an angular resolution of ω all parts of the system must be able to accommodate an electrical bandwidth of B. A nominal value for B is 1/[2(detector dwell time)] or, from equation 8.2, B = 1/[2(kt d )]. Substituting from Equation 8.6, n oτo Vs ωd DL = V 4f π (V / H) (8.13) While equation 8.13 has many variables, for a given scanner configuration, one can define a system constant, oτo ωd DL C = 4fπ (8.14) then Vs CL = (8.15) V (V / H) n With C defined for the scanner optical system, the only variables involved in assessing a signal to noise ratio are L, the level of radiance from the ground, and the V/H ratio Designs to increase detector dwell time It should be clear from the above discussion that improving the spatial resolution of the scanning system will decrease the dwell time for a given design. Two possible designs are shown schematically in Figure 8.3. The simplest change is to simply add more detectors for adjacent scan lines (Figure 8.3a). Since a single detector is no longer required to collect every scan line, the collection time may be increase proportional to the number of lines scanned in a single pass. A difficulty with this design is that each detector will have a slightly different gain and offset and will have to be corrected separately. A second alternative is illustrated in (Figure 8.3b). In this case the detector is replaced by a linear CCD array. This removes the requirement for scanning entirely, since each detector can view a separate pixel on the scan line. It also increases the dwell time by several orders of magnitude. The disadvantage of this design is again related to the variable calibration of the individual detectors

6 Philpot & Philipson: Remote Sensing Fundamentals Scanners 8.6 in the array. However, this seems a small price to pay for eliminating the scanning mechanism and greatly increasing the dwell time. a. b. Figure 8.3: Detector designs to increase individual detector dwell time: a) Design using multiple detectors, one for each scan line; b) CCD array detector. 8.7 Color scanners Collection color information raises further issues of timing and registration. Consider again, the simple situation of a scanner that has a single detector for each spectral band. A diagram of such a scanner is shown in Figure 8.4. In this configuration, each detector looks at a separate area on the ground at one time. The areas viewed are a function of the placement of the detectors in the focal plane of the detector. Here they are in a line along the scan direction. It is clear from the figure that, for a single ground location, each band is collected sequentially and registration is a function of accurate timing. Figure 8.4: Diagram of color scanner with one detector per band. As with the single band case, multiple detectors and CCD arrays can be employed to expand the spectral range of the scanner. Two arrangements are illustrated in Figure 8.5. Both are variations on the single-band design and both have the same advantages and limitations as the single-band counterparts. Registration of spectral band is still an issue in both cases. With the CCD design, registration along the scan line is typically near perfect; any misregistration will occur in the flight direction.

7 Philpot & Philipson: Remote Sensing Fundamentals Scanners 8.7 a. b. Figure 8.5: Schematic drawings of two detector designs for sensing multiple spectral bands: a) design using separate detectors for each scan line and multiple detectors on each scan line to image in multiple spectral bands; b) design using a separate linear CCD array for each spectral band. Figure 8.6: Hyperspectral imaging using a 2-D CCD array. If the design is extended to collect full spectra (e.g., hyperspectral data) another possibility is to replace the linear CCD arrays with a 2-dimensional CCD array. This configuration is illustrated in Figure 8.6. One dimension of the array is spectral, collecting an entire spectrum for one sample in the scan; the other is spatial, collecting data for the full scan line. An advantage of this design is that spectral data truly come from a single ground resolution element. Light from a single pixel entering the optical system is dispersed across the along-track dimension of the array, usually with a diffraction grating. Lines are then collected sequentially as with the linear detector in Figure 8.3b. 8.8 Pointable Satellites The Landsat series of satellites, and most other mapping satellite systems, were designed with the intent of imaging the entire earth repeatedly with a fixed, nadir viewing optical system. The choice was typically between polar orbiting systems that would either provide repeat coverage on a 16-18

8 Philpot & Philipson: Remote Sensing Fundamentals Scanners 8.8 day cycle at a moderate resolution ( m), or with a 2-3 day repeat visit at low resolution (~1 km) or geostationary systems that would provide hourly coverage or better at 8-10 km. All of the early systems were nadir-viewing and higher resolution was incompatible with global coverage since it was not feasible to collect high resolution data over a FOV sufficiently wide to insure regular contiguous coverage. In order to insure the possibility of imaging all parts of the globe at high resolution, it was necessary that the system be pointable. Initially the pointing capability was limited to cross-track pointing with the SPOT satellite. More recent systems (IKONOS, GeoEye, QuickBird, Worldview, Pleiades) allow pointing in both the along-track and cross-track directions. The systems are quite agile, being capable of pointing rapidly enough to take multiple images of the same site in one orbit, or to collect multiple sites cross-track within relatively short distances. Figure 8.7: Illustration of the pointing capability of the IKONOS satellite. From Grodecki and Dial, Space Imaging. Such dynamic pointing capability means that it is possible to collect stereo imagery or to collect data of the same location on earth every 1-2 days, as needed. This is an enormous advantage for monitoring disaster sites or any rapidly developing situation. The system must be tasked to collect the imagery, however, and past data for may be quite sparse. Another issue that arises as a result of the pointing capability is the distortion introduced by the pointing. Although the high resolution systems are typically pushbroom scanners, when the system is pointed the pixels suffer the same panoramic distortion that is characteristic of whiskbroom scanners. The difference is that the entire array suffers the same distortion. An important consequence of this is that the native resolution of the image is dependent on the system viewing angle. Standard practice is to report system resolution as the nadir pixel size the

9 Philpot & Philipson: Remote Sensing Fundamentals Scanners 8.9 minimum possible resolution. For example, the nadir ground sampling distance (GSD) the pixel size for the IKONOS sensor is 0.82 m for panchromatic images. At 30 degrees, the GSD is 1 m for panchromatic images. Image products are typically resampled to a standard value (for IKONOS, this is 1 m). The resampling insures consistency among images, standardizes geometric registration and makes it possible to create mosaics and more easily compare images collected at different times, but there is some loss in fidelity that occurs as a result of the resampling. 8.9 Orbital Mechanics The flight path of a satellite is predetermined by its orbit, and one can classify satellites systems broadly based entirely on the choices made for their orbits. The orbital speed of a body, in our case, a satellite, is the speed at which it orbits around the earth. For simplicity, we consider: circular orbits Newton's laws (nothing about energy or momentum) only two objects (the earth and the satellite) need to be considered the mass of the satellite is negligible relative to the mass of the earth In order for a satellite to maintain a stable orbit, the centripetal force, F c, acting to drive the satellite away from the earth, and the gravitational force, F g, attracting the satellite toward the earth, must balance exactly. Given the above simplifying assumptions, the gravitational force is described by the equation: Gmsme Fg = (8.16) 2 r where: m s is the mass of the satellite, m e, is the mass of the earth [ x kg], G is the universal gravitational constant [ m 3 kg -1 s -2 ], and r is the distance from the center of the earth to the satellite = R e + h (radius of the earth plus the altitude of the satellite) R e = 6378 km (average value) Under the same assumptions, the centripetal force, is described by the equation: 2 mv s Fc = (8.17) r Setting F c equal to F g one may then solve for a relationship between the velocity of the satellite in a circular orbit, v c, and its distance from the earth: v Gm r e c = The ground-track velocity is related very simply to the orbital circular velocity by the ratio v g Re = v R + h e c (8.18) (8.19)

10 Philpot & Philipson: Remote Sensing Fundamentals Scanners 8.10 This ground-track velocity, combined with a desired ground-sampling distance (GSD), provides an upper limit for the amount of time available to collect a single scan line worth of data. This maximum dwell time is simply: t = GSD / v (8.20) maxdwell As an example, the Landsat satellites which fly at an altitude of h ~ 800 km (r = R e + h = 7178 km) have an on-orbit velocity of ~7,450 km/s. This corresponds to a ground speed of ~6,620 km/s and a maximum dwell time of ~1 ms for a scan line worth of data. The next issue is to choose a convenient orbital period. For example, it is often useful to require that satellites in a polar orbit pass over the same latitude at the same local time every day. This helps to minimize changes in the sun illumination angle. Another option would be to adjust the orbital period to match the earth's rotation so that a satellite at the equator could be stationary relative to the earth. The orbital period of a satellite can be determined using Kepler's 3rd Law. Johannes Kepler ( ) was concerned with the basic question of describing the motion of the earth about the sun, but his laws apply generally to all satellites. The 3rd law states that the square of the period, T, of satellite about the earth is proportional to the cube of the satellite s mean distance from the earth, or: T r 2 2 Rearranging to solve for the period, T, we have: 3 g 4π = (8.21) Gm e 3 r T = 2π (8.22) Gm As an example, the international space station has an orbital period of 92 minutes (5,520 s). Knowing the period we may then solve for the distance of the satellite from the center of the earth: e 2 1/3 2 1/ s T r = Gm = ( )( ) = 6, 750 e m kg s kg km 2π 2π making the altitude, h, of the space station: h = r - R e = 6770km 6378km h = 372km There are only a few orbits that are consistently used for the bulk of the earth-viewing satellites. The most important of these for remote sensing are the geosynchronous and sun synchronous orbits. A description of these and closely related orbits is provided below. (Adapted from Geosynchronous orbits (GEO) are circular orbits around the Earth having a period of 24 hours. A geosynchronous orbit with an inclination of zero degrees is called a geostationary orbit since a spacecraft in a geostationary orbit appears to hang motionless above one position on the Earth's equator. They are ideal for some types of communication and meteorological satellites, having a field of view that encompasses a full half of the planet. To attain geosynchronous orbit, a spacecraft is first launched into an elliptical orbit with an apogee of 35,786 km (22,236 miles) called a

11 Philpot & Philipson: Remote Sensing Fundamentals Scanners 8.11 geosynchronous transfer orbit (GTO). The orbit is then circularized by firing the spacecraft's engine at apogee. Polar orbits (PO) are orbits with an inclination of 90 degrees. Polar orbits are useful for satellites that carry out mapping and/or surveillance operations because as the planet rotates the spacecraft has access to virtually every point on the planet's surface. There are two problems with the polar orbit. The first is that since the earth moves in its orbit around the Sun, the solar irradiance angle along the satellite varies continuously throughout the year (Figure 8.8). The second flaw is that, if all the satellites in north-south oriented orbits were polar orbiting satellites, they would tend to converge at the poles making collisions more likely. Walking orbits: An orbiting satellite is subjected to a great many gravitational influences. First, planets are not perfectly spherical and they have slightly uneven mass distribution. These fluctuations have an effect on a spacecraft's trajectory. Also, the sun, moon, and planets contribute a gravitational influence on an orbiting satellite. By carefully adjusting the orbit s inclination it is possible to design an orbit which takes advantage of these influences to induce a precession in the satellite's orbital plane. The resulting orbit is called a walking orbit, or precessing orbit. Sun synchronous orbits (SSO) are walking orbits whose orbital plane precesses with the same period as the planet's solar orbit period such that the satellite will cross the equator at about the same local time every orbit making it possible to maintain a more uniform solar irradiance angle throughout the mission s duration. (For the Earth, this is accomplished by selecting an inclination about 8 off the polar orbit.) This uniformity in the equator crossing time makes adjacent swaths as similar as possible since it reduces effects due to varying atmospheric path and BRDF. In order to maintain an exact synchronous timing, it may be necessary to conduct occasional propulsive maneuvers to adjust the orbit (a) Figure 8.8: Polar (a) and sun-synchronous (b) orbit orientations. (From l-mechanics.pdf (b)