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1 LA-UR V I Approved for public release; distribution is unlimited. Title : Relative radiometric correction of QuickBird imagery using the side-slither technique on orbit Author(s) : Bradley G. enderson and Keith S. Krause Submitted to: Proceedings of the SPI E Los Alamos NATIONAL LABORATOR Y Los Alamos National Laborato ry, an affirmative action/ equal opportunity employer, is operated by the University of alifornia for the U.S. Department of Energy under contract W-7405-ENG-36. By acceptance of this article, the publisher recognizes that the U. S. Government retains a nonexclusive, royalty-free license to publish or reproduce the published form of this contribution, or to allow others to do so, for U.S. Government purposes. Los Alamos National Laboratory requests that the publisher identify this article as work performed under the auspices of the U.S. Department of Energy. Los Alamos National Laboratory strongly suppo rt s academic freedom and a researcher's right to publish; as an institution, however, the Laboratory does not endorse the viewpoint of a publication or guarantee its technical correctness. Form 836 (8/00)

2 Relative radiometric correction of QuickBird imagery using the sideslither technique on-orbit Bradley G. enderson*a and Keith S. Krauseb alos Alamos National Laboratory, MS B244, ISR-2, Los Alamos, NM, USA bdigitalglobe, Inc., 1900 Pike Rd, Longmont, O, USA ABSTRA T The QuickBird commercial imaging satellite is a pushbroom system with four multispectral bands covering the visible through near-infrared region of the spectrum and a panchromatic band detectors in each MS band and detectors in the pan band must be calibrated. In an ideal sensor, a uniform radiance target will produce a uniform image. Unfortunately, raw imagery generated from a pushbroom sensor contains vertical streaks caused by variability in detector response, variability in electronic gain and offset, lens falloff, and particulate contamination on the focal plane. Relative radiometric correction is necessary to account for the detector-to-detector non-uniformity seen in raw imagery. A relative gain is calculated for each detector while looking at a uniform target such as an integrating sphere during ground calibrations, diffuser panel, or large desert target on-orbit. A special maneuver developed for QuickBird called the "Side-Slither" technique is discussed. This technique improves the statistics of a desert target and achieves superior non-uniformity correction in imagery. The "Side-Slither" technique is compared to standard techniques for calculation of relative gain and shows a reduction in the streaking seen in imagery. Keywords : Relative, radiometric, calibration, QuickBird 1.1. Radiometric calibration and correctio n 1. INTRODUTION The focal planes of modem digital imaging satellites contain thousands of electronic detectors that collect focused light for reconstructing an image of the Earth's surface. In general, every detector is electronically unique and will thus produce a different output signal (referred to as "counts") when illuminated by the same uniform light source. This difference in detector response will create image artifacts referred to as "fixed pattern noise" (Fig. 1, top). Removing fixed pattern noise and other image artifacts is accomplished by radiometric calibration of the sensor, followed by radiometric correction of the imagery. Radiometric calibration is the process by which all detectors' response to a known light source is quantified, whereas radiometric correction is the process by which the measured calibration is used to normalize the response of each detector (i.e., adjust raw pixel values) in order to remove image artifacts (Fig. 1, bottom). During radiometric calibration, a response function is computed for each detector on the focal plane ; e.g., DN=L x g+a, (1) where DN is the detector response in digital counts, L is the radiance of the calibration source in units of W/m2/ster/µm, g is the gain (i.e., the slope of the response function of a given detector), and A is the "offset ;" i.e., the signal level for 0 radiance. In practice, the offset A is given by the DN level in the absence of light: A = DNdark, (2) and the gain g is computed by solving equation (1) after measuring the detector response to one or more known radiance levels : g _ DN-A L (3 ) henders(a)lanl.gov ; phone ; fax

3 Figure 1. Top: A raw pushbroom image showing characteristic streaking. Bottom: The same image with relative radiometric correction applied. In effect, Eq. (1) is the mathematical function, computed for each detector, which gives the predicted response in DN (or "counts" ) for any input radiance L. Once this calibration function is known for each detector, a raw image can he radiometrically corrected by applying the calibration coefficients to each pixel in the image : q A (5 ) where ga,5 is the band-averaged gain. B is close to I and is computed for every detector. The operation described by Eq. (4) in effect is a relative radiometric correction by which the individual pixel counts are adjusted relative to an average response in order to remove the effects of fixed pattern noise. The conversion to absolute radiance, i.e., the ah.soluic radiometric correction, is done by the following : L=Kq, (6) where L is the absolute radiance in units of NV m'isterr,cem, and K is a constant computed for each hand. Multiplying the corrected counts q by K gives the absolute radiance at the telescope aperture for the given detector Flat fielding and relative radiometric calibratio n Often during radiometric calibration, the absolute radiance level L is not known, and thus it is not possible to compute the absolute gain g that is inherent to an absolute calibration. owever, it is still possible to compute a relative radiometric calibration by flat fielding. During flat-field calibration, the focal plane of the imaging satellite is illuminated by a uniform light source, termed a "flat field." Although the absolute radiance level of that field may not he known, it is uniform, and thus the gain of each detector can be computed relative to the gain all other detectors, so that

4 the relative gain B can still be computed and used to apply a relative radiometric correction (also called a flat-field correction) to the image using Eq. (4). Although satellite imaging sensors are usually calibrated on the ground prior to launch, they must be recalibrated on orbit as a result of calibration drift, particulate contamination, etc. Since these calibration changes are more or less independent from detector to detector, performing a new flat-field calibration on-orbit is essential. Producing a flat field in the laboratory is usually straightforward. owever, flat fielding on orbit can be difficult because there are not many targets on the ground that are radiometrically flat over the size of a typical imaging footprint (tens to hundreds of kilometers). Deep space is a good flat field but only for measuring the dark level ; computing the relative gain requires a finite radiance. Oceans are fairly flat radiometrically but typically are not bright enough in the solar reflective region to get a good calibration over the entire dynamic range of the instrument. There are a number of fairly uniform desert targets in N. Africa,"2 but for most flat-field applications they simply are not uniform enough. One standard option for flat fielding is an on-board calibration source such as a reflecting panel or solar diffuser. owever, these add to the cost of the satellite, and the radiometric uniformity typically changes with time. In this paper, we introduce the concept of a "side-slither" scan in order to generate a flat field for a pushbroom imager looking at the Earth's surface from orbit. (This type of imaging has been mentioned before by other names (e.g., 90 maneuveri), but to our knowledge, detailed results have not been presented in the remote sensing literature.) Keep in mind that the goal in flat fielding is to have every detector "see" the same total radiance. In side-slither imaging, this is accomplished by rotating the satellite to force every detector to integrate over the same stretch of ground. In the next section, we will, review pushbroom imaging and describe how to perform side-slither imaging for construction of a flat field on orbit. In section 3, we will describe the QuickBird satellite and sensor followed by the results in section 4 and the conclusion in section PUSBROOM IM AGING 2.1. Normal pushbroom sca n The basic pushbroom imager is a linear detector array that constructs an image one row at a time by using mechanical motion to sweep a focused image across the focal plane in a direction perpendicular to the array (Fig. 2, left). (It is often easier in concept to reverse the situation and consider the image of the linear array sweeping across the ground.) The readout rate of the detector array is usually set so that it matches the speed of the image on the focal plane in units of lines per second. Given perfect optics and a uniform sweep during the duration of the imaging event, an undistorted image of the scene can be reconstructed. For pushbroom imagers, a column in an image corresponds to a single detector on the focal plane. As long as the calibration is not a function of time, the coefficients computed for a given detector will be applied to an entire image column. An example of normal pushbroom imaging of an "alphabet" scene is shown in Fig. 3. The scanning motion is perpendicular to the linear array, and the detectors are read out at a rate equal to the ground-track speed divided by the GSD (or, equivalently, the sensor scan rate is set so that the image of a point on the ground moves the width of one detector element during one line time). The image is reconstructed, in simple terms, by "stacking" the individual rows on top of each other in time-sequential order so that the final image looks like the scene (Fig. 3) Side-slither sca n In side-slither imaging, the focal plane is rotated 90, and the scanning is done parallel rather than perpendicular to the linear array (Fig. 2, right). Each detector thus passes over the same stretch of ground and sees the same amount of light. Given an ideal scan (perfectly parallel to the array, no optical distortion, etc.) and by picking appropriate starting and ending times for each detector, all detectors will see the same strip of ground and therefore will have been exposed to the same amount of light. By averaging over "common ground," we have in effect created a flat field. Fig. 4 shows the same alphabet scene being imaged by a side-slither scan. The linear array has been rotated by 90, and the scanning motion is parallel to the linear array. Rather than image the entire scene, the array sees just a thin slice of it. At time = 1, the array is just about to enter the scene, and at time = 2, the detector 1 has imaged the letter. At time = 3, detector 1 has moved to the second row of letters while the detector 2 has imaged the letter, one time step behind its neighbor

5 Normal scan Side-Slither" Sca n 4 Pushbroom linear array Figure 2. Normal pushbroom imaging (left), and side-slither imaging (right). Scan Sca n Direction Direction Scan Sca n Directio n Direction A B O D E B D E A B D E A B O D E L N 1 Time = 1 1 Time =2 Time = 3 1 Time = 4 Scan Directio n Scan Scan Direction Direction A B D E A B D E Y A B D E A F K P U B L Q V D E I M N 0 R S W X Y 1 Time = 5, Time = 6 Time 7 Resulting Imag e Figure 3. A normal pushbroom scan through an "alphabet" scene. detector 1. The process repeats itself until the array has passed through the entire scene. Note that a given point on the ground is imaged in successive time steps by neighboring detectors. As a result, when the image is reconstructed, a given point on the ground (in this example a given letter) is translated over and down from one row to the next, making a 45 angle across the image. To make a flat field, starting and ending times are selected, corresponding to a section of image bounded above and below by 45 diagonal lines. For a given column, which corresponds to a single detector, the DN values are column averaged for every detector, which gives each detector's response to the same brightness level. Next, all the column-averaged responses are averaged for a given band, and then finally the relative gain B is computed for each detector by taking the ratio of the column-averaged response to the band-averaged response.

6 Scan Scan Scan Scan Scan Scan Direction Direction Direction Direction Direction Directio n A 8 D E A 8 U D E A 8D E A 8 D E A 8 D E A 8 0 E F G I J F G I J F G I J K L M N D K L M N D P Q RR S T K L P Q U V M R W N D S T X Y Time =1 Time = 2 Time = 3 Time = 4 Time = 5 Time = 6 Scan Scan Scan Scan Scan Direction Direction Direction Direction Directio n A 8 D E F G K L I J N D A 8 D E A B D E K LAM N D A 0 D E K L M N D A 8 0 E K L M N D M W M R M P Q U V S T x Y P Q U V R W S T x Y P QIRIS T U V W x Y U VR x Y W R W M R w M R w Time =7 Time =8 Time = 9 Time = 10 Time = 11 Resulting Image Figure 4. A side-slither scan through the same alphabet scene. aving introduced side-slither imaging, we will now describe the QuickBird satellite and sensor, data from which were used for the results presented in section QUIKBIRD For this work, we performed side-slither imaging using the QuickBird satellite. QuickBird is a multispectral pushbroom imager owned and operated by DigitalGlobe. It was launched in October 2001 into a 450-km altitude, 98-degree

7 27,568 Panchromatic Detector s 4 x Multi- Spectral Detectors 32 rows of TDI sites. PAN DA 2 1 PAN DA 3 PAN DA 5 PANDA4 PAN DA 6 1 row per band } MS DA 1 MS DA 2 MS DA 3 MS DA 5 MS DA 4 MS DA 6 +X Side 0 Side 1 +Y E Figure 5. The QuickBird focal plane. inclination, sun-synchronous orbit. The imager has 5 bands: a panchromatic band with 0.61-meter ground sample distance (GSD), and four multispectral bands (red, green, blue, and near-infrared) with 2.44-meter GSD. The swath width is approximately 16.5 km. The focal plane is composed of 12 staggered detector chip assemblies, or DAs, 6 for the panchromatic band and 6 for the multispectral bands (see Fig. 5). Each MS DA has four linear arrays, one for each of the four multispectral bands. The panchromatic Ds have TDI (Time-Delayed Integration) capability with 32 rows of detectors. Each DA is a D array of 4736 (pan) or 1184 (per MS array) detectors, including masked, invalid, and overlap detectors pan and 6972 detectors per MS band must be calibrated. General radiometric performance of QuickBird is discussed in this volume.5 4. RESULTS A raw side-slither image is shown in Fig. 6. This image and all others discussed in this paper utilized desert targets in N. Africa. 1,2 This particular image is a strip of the blue band from one MS DA. The left side shows the entire image strip, whereas the right side shows a close-up view. Note the 45 linearities visible in both images. These features represent a particular spot on the ground imaged by neighboring detectors in successive time steps. When the image is reconstructed, any given feature thus moves down and across-down one step and over one GSD. The left-hand image shows 45 black bars indicating example starting and ending times for processing the image in order to construct a flat field. Each column of pixels between the black bars is summed and averaged to produce a mean response (DN) for each detector. The column-averaged responses for all detectors in a band are then averaged to produce a band-averaged response. The relative gain B is then computed for each detector by taking the ratio of the column-averaged response to the band-averaged response, as in Eq. 5. Relative gains computed for the panchromatic band (13 TDI) from two independent side-slither images are shown in Fig. 7. To reiterate, this plot shows the side-slither-computed relative gain for each panchromatic detector on the focal plane. We emphasize that these two plots were computed from side-slither images of completely different sites. They have been offset for clarity. The structure in each plot represents variations in detector gain. Note that the structure in the two plots is nearly identical. In Fig. 8, we plot the difference in percent between the two relative gain calculations. With the exception of one spike around 0.65%, all the values are less than 0.5%, with the vast majority being less than 0.2%. Since the two relative gain calculations were performed on different sites, we can conclude that the side-slither technique is able to produce extremely flat fields. Fig. 9 shows the percent difference between side-slither relative gain, and relative gains computed using different methods, including an on-board calibration lamp (green), pre-launch calibration coefficients (red), and a flat field computed from a normal pushbroom desert image (blue). This last flat field was computed by taking column averages of

8 12 km PAN rows MS rows Figure 6. Left : a raw side slither image from one D!\ of the blue hand. Right : a closer view of the image strip on the left 1.2 Side-slither, Pan 13 TD I ,0x x X104 2,0x10 ` 2.5x104 Detector 3.0x10 4 Figure 7. Relative gain computed from two independent images for all detectors of the panchromatic band. 13 I'I)I.

9 0.4, SSL variation. Pon 13 TD l " x x x104 Detector 2;0x x x10 4 Figure 8. The percent difference between the two relative gains shown in the previous figure. a normal pushbroom image over a desert scene. The side-slither relative was used as the reference for differencing and is therefore all zeros. Notice that there are significant variations between the side-slither flat field and the others. The largest difference is with the pre-launch flat field, which is not surprising since a large amount of time elapsed between ground calibration and launch. The on-board calibration lamp (labeled "stim") also shows a fair amount of deviation and also a trend across the focal plane. There is also a noticeable difference (1%-2%) between the side-slither flat field and the normal pushbroom flat field. We cannot say definitively that the side-slither is necessarily better since we do not know a priori which of the flat fields is the best. We can only say that the difference between them is within a couple of percent, and that in principle, we believe the side-slither flat to be better since it is constrained to a smaller part of the desert scene and should therefore sample less spatial variability than the normal desert flat field, which will see all the scene variability in the swath, which is about 16.5 km at nadir. In Fig. 10, we present the difference between side-slither streaking and normal desert streaking. That is, we first applied a side-slither flat field to an image and computed the streaking, then applied a normal desert flat field to the same image and computed the streaking, then took the difference. Note that there are both "ups" and "downs," which means that sometimes the regular pushbroom desert flat field was better than the side-slither flat field. owever, a histogram (not shown here) demonstrates that in general the side-slither does a better job Problems DA offse t Ideal side-slither imaging requires a perfectly linear array and perfectly linear scanning motion. The QuickBird focal plane and others like it have staggered DAs (see Fig. 5), which means that the linear arrays on adjacent DAs will not pass over the same stretch of ground. With QuickBird for example, DAs 1, 3, and 5 will see the same linear strip of ground, which will be offset from that seen by DAs 2, 4, and 6. If the scene is not completely uniform (guaranteed), then this offset will result in a different radiance seen by the fore and aft DAs. If not all the detectors see the same total radiance, then the created radiance field is not flat. In practice, this problem can be minimized by taking a longer image

10 ti Difference of MS Rekative Gain % Difference of MS Relative ai n 4 60< tlu0 j ui, l 8000 Z Difference of MS Relative Gain fi Difference of MS F,elative Gain _ ` r3j Figure 9. The percent difference between side-slither relative gain and 3 other relative gains computed from the following : normal puslibroom desert image (blue), pre-launch ground calibration (red). and on-board calibration lamp (green). strip in order to get better statistics. Also, if the offset of the linear arrays on adjacent DAs is small relative to the decorrelation length of the scene, then the problem will likely be small. For perfect side-slither imaging (perfectly linear array, no optical distortion, etc.), a side-slither flat field could be acquired over any target, since every detector will pass over the same line of ground. Since any real side-slither imaging event is not perfect, the errors can be minimised b\ starting with a scene that is as flat as possible Optical Jistortion A similar problem is created by optical distortion. If the focal length varies across the focal plane, then the image on the ground of a single linear array will be a curved line. A side-slither scan will result in detectors seeing slightly different portions of the scene. As before, this problem can be minimized by taking longer scans and starting with a fairly uniform scene.

11 0. 3 r Desert Minus Side-slither Streakin g I I E I I I I I I I I I I I I I I I I I I I I I 1 I I I I 1 5.0x x x x x x10' Figure 10. The percent difference between side-slither streaking and normal desert streaking TDI A D array with TDI has multiple rows of detectors. The charge is transferred from one row to the next at the same rate that a point in the image moves perpendicular to the array, thus allowing longer integration periods. The- impact of TDI on a side-slither image is that the integration path on the ground is not linear, but rather diagonal. owever, it turns out that all detectors integrate over the same diagonal patch of ground, so that TDI does not create much of a problem for side-slither imaging. 5. ONLUSION In this paper, we have introduced the concept of a side-slither scan, by which a pushbroom imager is rotated 90, and scanning is done parallel to the linear array. A side-slither scan forces all detectors to pass over the same stretch of ground and thereby see the same total radiance. As such, the image from a side-slither scan can be used to generate a flat field on orbit for improved relative radiometric calibration and correction. We performed side-slither imaging using the QuickBird satellite and showed that the flat fields produced by side-slither imaging are flat to within less than 0.5%. We also showed that side-slither flat fields do better relative radiometric correction than other techniques including ground calibration, an on-board calibration lamp, and a flat field generated from a normal pushbroom scan over a uniform desert scene. Side-slither imaging should thus provide an alternate means for relative radiometric calibration of pushbroom imagers on orbit. omplications such as optical distortion and staggered arrays can be minimized by starting with a ground scene that is as radiometrically flat as possible.

12 REFERENE S 1. osnefroy,., X. Briottet, and M. Leroy, "haracterization of desert areas with Meteosat-4 data for the calibration of optical satellite sensors," Proc. SPIE 1938, , enry, P. J., M.. Dinguirard, and M. Bodilis, "SPOT multitemporal calibration over stable desert areas," Proc. SPIE 1938, 67-76, Bender, S.., W.. Atkins, W. lodius,. Little, and W. hristensen, "LANL MTI calibration team experience," Proc. SPIE 5159, , osnefroy,., M. Leroy, and X. Briottet, "Selection and haracterization of Saharan and Arabian desert sites for the calibration of optical satellite sensors", Remote Sens. Environ. 58, , Krause, K., "Relative radiometric characterization and performance of the QuickBird high -resolution commercial imaging satellite," Proc. SPIE 5542, 2004.