quickbird technote raduse v1

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Release Date: 07 November 2005 Revision 1.0

Radiometric Use of QuickBird Imagery

Technical Note

Date: 2005-11-07 Prepared by: Keith Krause

This technical note discusses the radiometric use of QuickBird imagery. The first four sections describe the QuickBird instrument and general radiometric performance including the QuickBird relative spectral radiance response, solar spectral irradiance, gain settings, and radiometric correction of QuickBird products. Sections 5-7 cover more advanced topics: conversion to top-of-atmosphere spectral radiance, radiometric balancing for multiple scene mosaics, and conversion to top-of-atmosphere spectral reflectance. QuickBird imagery MUST be converted to spectral radiance at a minimum before radiometric/spectral analysis or comparison with imagery from other sensors in a radiometric/spectral manner. The information contained in this technical note applies to the raw QuickBird sensor performance and linearly scaled top-of-atmosphere spectral radiance products. Caution is advised when applying the equations provided here to pan-sharpened products, dynamic range adjusted (DRA) products, or QuickBird mosaics with radiometric balancing because the generation of these products may apply non-linear transformations to the pixel DN values.

1 QuickBird Instrument Description The QuickBird high-resolution commercial imaging satellite was launched on October 18, 2001. QuickBird acquires 11-bit data in five spectral bands covering panchromatic (525-924 nm), blue (447-512 nm), green (499-594 nm), red (620-688 nm), and near-infrared (755-874 nm) wavelengths. At nadir, the nominal ground sample distance is 0.61 m (panchromatic) and 2.44 m (multispectral) with a nominal swath width of 16.5 km (Basic products are delivered at the native sensor resolution and swath width of the image acquisition and Standard or Ortho products are typically resampled to a panchromatic ground resolution of 0.6 or 0.7 m and cropped to a user defined geographic polygon). The QuickBird instrument is a pushbroom imager, which constructs an image one row at a time as the focused image of the Earth through the telescope moves across the linear detector arrays, which are on the focal plane.

1.1 QuickBird Focal Plane The QuickBird focal plane, is comprised of six panchromatic and six multispectral, staggered detector chip assemblies (DCAs) as shown in Figure 1. The MS DCAs contain four rows of detectors, each with a different spectral filter covering the blue, green, red, and near-infrared portions of the electromagnetic spectrum. As seen in the figure, the bands are not co-located on the focal plane. Therefore, they do not simultaneously view the same area on the ground. Adjacent DCAs contain overlap detectors that view the same area on the ground but at different times. The focal plane contains 27888 pan and 6972 detectors per MS band that must be calibrated (ignoring the overlap detectors this comes to 27568 and 6892 detectors respectively). Each MS DCA and band has its own electronic readout register. Pan DCAs are broken up into eight readout registers. Each readout register has its own analog-to-digital converter and therefore has its own gain and offset. The MS bands only have one integration time. However, Pan DCAs have 32 rows of detectors for time-delayed integration (TDI) partitioned into five different exposure levels, each of which must be calibrated. During product generation, the six DCAs are blended to form one seamless image.

©Copyright 2005, DigitalGlobe®, Inc. 1



Figure 1: The QuickBird Focal Plane Layout (not drawn to scale)

1 row per band

’

MS DCA 1

+X

+Y

27,568 Panchromatic Detectors4 x 6,892 Multi-Spectral Detectors

PAN DCA 2 PAN DCA 3

PAN DCA 4

PAN DCA 5

PAN DCA 6

MS DCA 2

MS DCA 3

MS DCA 4

MS DCA 5

MS DCA 6

Side 0 Side 1

32 rows of TDI sites.

PAN DCA 1

}

}

1.2 QuickBird Relative Spectral Radiance Response The system spectral radiance response is defined as the ratio of the number of photo-electrons measured by the system to the spectral radiance [W-m-2-sr-1-µm-1] at a particular wavelength required to enter the telescope aperture to produce them. It includes not only raw detector quantum efficiency, but also transmission losses due to the telescope optics and multispectral filters. The spectral radiance response for each band is normalized by dividing by the maximum response value for that band to arrive at a relative spectral radiance response. These curves for the QuickBird panchromatic and multispectral bands are shown in Figure 2.

Figure 2: QuickBird Relative Spectral Radiance Response




Various band passes for the QuickBird system are listed in Table 1. The nominal band passes are the instrument design wavelengths chosen to match the Landsat bands. The 50% and 5% (of peak) band passes are found from the actual system response curves from Figure 2. Comparing the nominal and actual 50% band passes in the table, the actual QuickBird bands don’t quite match the nominal bands, especially in the green band where the response overlaps the blue band with a lower 50% point at 499 nm rather than the nominal design at 520 nm.

Table 1: QuickBird Band Passes [µm] Spectral Band Nominal Band Pass 50% Band Pass 5% Band Pass

Pan 0.450-0.900 0.5252-0.9245 0.4048-1.0533 Blue 0.450-0.520 0.4467-0.5119 0.4277-0.5441

Green 0.520-0.600 0.4987-0.5945 0.4674-0.6215 Red 0.630-0.690 0.6201-0.6878 0.5911-0.7107 NIR 0.760-0.900 0.7552-0.8740 0.7155-0.9183

The effective bandwidth for each band of the QuickBird system is defined as:

∫∞

⋅′=∆0

BandBand d)(R λλλ

where ∆λBand is the effective bandwidth [µm] for a given band and R′(λ)Band is the relative spectral radiance response for a given band shown in Figure 2. The effective bandwidths should be used in the conversion to top-of-atmosphere spectral radiance for each QuickBird band and are listed in Table 2:

Table 2: QuickBird Effective Bandwidths Spectral Band Effective Bandwidth [µm]

Pan 0.398 Blue 0.068

Green 0.099 Red 0.071 NIR 0.114

2 Solar Spectral Irradiance The QuickBird instrument is sensitive to wavelengths of light in the visible through near-infrared portions of the electromagnetic spectrum as shown in Figure 2. In this region, top-of-atmosphere radiance measured by QuickBird is dominated by reflected solar radiation. Spectral irradiance is defined as the energy per unit area falling on a surface as a function of wavelength. The sun acts like a blackbody radiator so the solar spectral irradiance can be approximated using a Planck blackbody curve at 5900 degrees Kelvin corrected for the solar disk area and the distance between the Earth and the sun (Schowengerdt, pp. 36-37, 1997). However, a model of the solar spectral irradiance was created by the World Radiation Center (WRC) from a series of solar measurements (Wherli, 1985) and will be used for QuickBird conversions to surface reflectance and radiometric balancing of multiple scene mosaics. As shown in Figure 3, the WRC solar spectral irradiance curve peaks around 450 nm in the Blue band and slowly decreases at longer wavelengths. NOTE: the WRC curve is for an Earth-sun distance of 1 Astronomical Unit (AU) normal to the surface being illuminated.




Figure 3: WRC Solar Spectral Irradiance Curve

In general, band-averaged solar spectral irradiance is defined as the weighted average of the peak normalized effective irradiance value over the detector bandpass as shown in the following equation:

∫

∫∞

∞

⋅′

⋅′⋅=

0Band

0Band

Band

d)(R

d)(R)Esun(Esun

λλ

λλλ

λ

where EsunλBand is the band-averaged solar spectral irradiance [W-m-2-µm-1] for a given band, Esun(λ) is the WRC solar spectral irradiance curve [W-m-2-µm-1] shown in Figure 3, and R′(λ)Band is the relative spectral radiance response for a given band. The QuickBird band-averaged solar spectral irradiance values for an Earth-sun distance of 1 AU, normal to the surface being illuminated, are listed in Table 3:

Table 3: QuickBird Band-Averaged Solar Spectral Irradiance Spectral Band Spectral Irradiance [W-m-2-µm-1]

Pan 1381.79 Blue 1924.59

Green 1843.08 Red 1574.77 NIR 1113.71




3 Gain Settings Assuming the detectors have a linear response as a function of input radiance, the equation of a straight line can be used for the camera equation:

BandDet,BandDet,BandDet,BandDet, OffsetGainLDN +⋅= where DNDet,Band is the raw image [counts], LDet,Band is the target spectral radiance [W-m-2-sr-1-µm-1], GainDet,Band is the absolute gain [counts / W-m-2-sr-1-µm-1], and OffsetDet,Band is the instrument offset [counts]. Rather than calibrate an absolute gain for each individual detector, a single gain is determined for each band and each detector is scaled relative to the other detectors in the same band:

BandDet,BandDet,BandBandDet,BandDet, OffsetBGainLDN +⋅⋅= where GainBand is the absolute gain [counts / W-m-2-sr-1-µm-1] for each band and BDet,Band is the relative detector gain [unitless]. By definition, the average relative gain equals one. To conform to the nomenclature carried out through the rest of this technical note, DNDet,Band will be redefined as pDet,Band, LDet,Band*GainBand will be redefined as qDet,Band, and OffsetDet,Band will be redefined as ADet,Band :

BandDet,BandDet,BandDet,BandDet, ABqp +⋅= where pDet,Band are raw detector data [counts], qDet,Band are radiometrically corrected detector data [counts] which are linearly scaled to spectral radiance, BDet,Band is the detector relative gain, and ADet,Band is the dark offset [counts]. The QuickBird multispectral bands only have one gain setting. However, the panchromatic band has five possible exposure levels using time-delayed integration (TDI). These values are 10, 13, 18, 24, and 32 and correspond to the number of detector rows used for TDI. The pan TDI setting for a given image is selected using a look-up table based on the estimated solar elevation angle for the image acquisition. No land cover information is taken into account in setting the TDI level. The values in the look-up table were chosen to maximize the radiometric resolution of QuickBird while minimizing the number of saturated pixels in an image. Table 4 lists the minimum saturation values for each band and TDI setting (pan only):

Table 4: QuickBird Minimum Saturation Values Spectral Band TDI Level Minimum Saturation

Radiance [W-m-2-sr-1-µm-1] Minimum Saturation

% Reflectance Pan 10 379.08 91.72 Pan 13 291.60 70.55 Pan 18 210.60 50.95 Pan 24 158.04 38.24 Pan 32 118.44 28.66 Blue NA 424.62 73.76

Green NA 261.54 47.44 Red NA 321.30 68.21 NIR NA 243.54 73.11

The minimum saturation radiances [W-m-2-sr-1-µm-1] are calculated using the revised QuickBird absolute calibration factors (K factors) listed in Table 5, the effective bandwidths (∆λ) listed in Table 2, and a dynamic range of 1800 counts. QuickBird is an 11-bit system (0-2047 counts). 1800 counts of dynamic range are chosen to allow a zero-




radiance offset of approximately 100 counts (different for each readout register and varies as a function focal plane temperature) and a margin of approximately 100 counts at the upper end of the radiance scale. The minimum saturation % reflectances are calculated using the minimum saturation radiance, the solar spectral irradiances (Esunλ) listed in Table 3, and a solar zenith angle of 20 degrees. These values correspond to the reflectance of a Lambetian surface required to create the minimum saturation radiance when illuminated by the sun at the mean Earth-sun distance (1 AU) and a zenith angle of 20 degrees assuming no atmosphere. As seen in Table 4, the minimum saturation value for both the blue and NIR bands is around 73% reflectance with the red band close at 68%. The green band saturates before the other bands with a minimum saturation value of 47% reflectance. The gain settings were designed based on the nominal bandwidths. However, the actual green bandwidth is wider than the design allowing more photons to reach the detectors and causing the green band to saturate on lower reflectance targets than the other MS bands.

4 Radiometric Correction of QuickBird Products Relative radiometric calibration and correction are necessary because a uniform scene does not create a uniform image in terms of raw DNs. Major causes of non-uniformity include variability in detector response, variability in electronic gain and offset, lens falloff, and particulate contamination on the focal plane. These causes manifest themselves in the form of streaks and banding in imagery. In the case of a pushbroom system, the focal plane contains linear arrays so the data from every pixel in a given image column comes from the same detector. Any differences in gain or offset for a single detector show up as a vertical streak in raw imagery. Differences in gain and offset for a single readout register show up as vertical bands as wide as the number of detectors read out by the register. Relative radiometric correction minimizes these image artifacts in QuickBird products. A relative radiometric correction is performed on raw data from all detectors in all bands during the early stages of QuickBird product generation. This correction includes a dark offset subtraction and a non-uniformity correction (detector-to-detector relative gain) using the following equation:

BandDet,

BandDet,BandDet,BandDet, B

A(t)pq

−=

where qDet,Band are radiometrically corrected detector data [counts], pDet,Band are raw detector data [counts], A(t)Det,Band is the dark offset [counts] for a specific image acquisition, and BDet,Band is the detector relative gain.

Figure 4: Raw desert image (this image has been stretched so the darkest streak is black and the brightest streak is white to make the streaking easy to see in the figure)

Figure 4 is a raw desert image from the NIR band DCA 4 (only one readout register but includes the masked and invalid detectors-seen as black bands on the left and right edges of the image). Non-uniformities can be seen as both dark and light vertical streaks in the image. When radiometric correction is applied, the streaks disappear as shown in Figure 5. Figures 4 and 5 each have a different visual stretch based on the minimum and maximum brightness of




the pixels (not including masked and invalid detectors). The raw image’s stretch is set by the streaks so the detail of the desert has less contrast in the figure and the streaks are exaggerated.

Figure 5: Radiometrically corrected desert image (with the streaks corrected, the display stretch has been set to increase the contrast of the desert scene)

As seen in Figure 6, color banding is visible when the six detector chip arrays are blended into a single image without radiometric correction (image on the left):

Figure 6: Raw image (left) and radiometrically corrected image (right) of Mount St. Helens

After radiometric correction, the corrected detector data (qDet,Band) are spatially resampled to create a specific QuickBird product that has radiometrically corrected image pixels (qPixel,Band). Once spatial resampling is performed, the radiometric corrections are NOT reversible. Data from all QuickBird detectors are radiometrically corrected and used to generate QuickBird products. To date, no detectors have been declared as non-responsive detectors. The QuickBird instrument collects data with 11 bits of dynamic range. These 11 bits are either stored as 16 bit integers or are scaled down to 8 bits to reduce the file sizes of QuickBird products and for use with specific COTS tools that can only handle 8-bit data. Whether the final bit depth is 16 or 8 bits, the goal of the radiometric correction, other than minimize image artifacts, is to scale all image pixels to top-of-atmosphere spectral radiance so that one absolute calibration factor can be applied to all pixels in a given band.




5 Conversion to Top-of-Atmosphere Spectral Radiance QuickBird products are delivered to the customer as radiometrically corrected image pixels (qPixel,Band). Their values are a function of how much spectral radiance enters the telescope aperture and the instrument’s conversion of that radiation into a digital signal. That signal depends on the spectral transmission of the telescope and multispectral filters, the throughput of the telescope, the spectral quantum efficiency of the detectors, and the analog to digital conversion. Therefore, image pixel data are unique to QuickBird and should not be directly compared to imagery from other sensors in a radiometric/spectral sense. Instead, image pixels should be converted to top-of-atmosphere spectral radiance at a minimum. Top-of-atmosphere spectral radiance is defined as the spectral radiance entering the telescope aperture at the QuickBird altitude of 450 km. The conversion from radiometrically corrected image pixels to spectral radiance uses the following general equation for each band of a QuickBird product:

Band

BandPixel,BandBandPixel,

qKL

λλ ∆⋅

=

where LλPixel,Band are top-of-atmosphere spectral radiance image pixels [W-m-2-sr-1-µm-1], KBand is the absolute radiometric calibration factor [W-m-2-sr-1-count-1] for a given band, qPixel,Band are radiometrically corrected image pixels [counts], and ∆λBand is the effective bandwidth [µm] for a given band. Offset subtraction is unnecessary at this point because it has already been performed in the radiometric correction step during product generation. Conversion to top-of-atmosphere spectral radiance is a simple two step process that involves multiplying radiometrically corrected image pixels by the appropriate absolute radiometric calibration factor (also referred to as a K factor) to get band-integrated radiance [W-m-2-sr-1] and then dividing the result by the appropriate effective bandwidth to get spectral radiance [W-m-2-sr-1-µm-1]. Based on ground truth measurements and confirmed by analysis from the Joint Agency Commercial Imagery Evaluation (JACIE) Team (Holekamp, 2003), the QuickBird absolute radiometric calibration factors (K factors) were revised. The “revised” values are based on pre-flight estimates and should be applied to all QuickBird imagery acquired from launch up through the present date. The revised absolute radiometric calibration factors (K factors) were operationally released in the production system on June 6, 2003 at 0:00 GMT. It is important to point out that the brightness values in an image generated before June 6th are identical to the brightness values in the same product reproduced after the introduction of the new calibration factors. Customers DO NOT need to reorder QuickBird products that were generated before June 6, 2003. Absolute radiometric calibration factors (K factors) are delivered with every QuickBird product and are located in the image metadata files (extension .IMD). Products generated after June 6, 2003 at 0:00 GMT have the revised factors in the .IMD files. These values should be used to convert to band-integrated radiance or spectral radiance. However, products generated before June 6, 2003 at 0:00 GMT have been delivered with the original calibration factors. For better results, conversions to band-integrated radiance or spectral radiance should be performed using the factors listed in the tables in this tech note, instead of those delivered in the .IMD files. The next section contains a description of the proper way to convert to band-integrated radiance for both 16-bit and 8-bit products generated both before and after the revised factors were operationally released. NOTE: conversion equations are to be performed on all pixels in a given band of a QuickBird image and should use 32-bit floating point calculations. At the option of the customer, the resulting floating point values of band-integrated radiance or spectral radiance may be rescaled into a desired 16-bit or 8-bit range of brightness as may be required for handling by an image processing system. When doing this, it is recommended that the customer keep track of subsequent conversions so that there is a known relationship between any new image DNs and the band-integrated radiance or spectral radiance of the pixel for the given band.




5.1 Band-Integrated Radiance [ W-m-2-sr-1 ] In general, band-integrated radiance is defined as the peak normalized effective radiance value over the detector bandpass (Schott, p. 59, 1997) as shown in the following equation:

∫∞

⋅′⋅=0

BandBand d)(R)L(L λλλ

where LBand is the effective band-integrated radiance [W-m-2-sr-1] of a target to be imaged for a given band, L(λ) is the spectral radiance of a target to be imaged, and R′(λ)Band is the relative spectral radiance response for a given band shown in Figure 2. The K factors are in units of band-integrated radiance per count and follow the form:

BandSource

0BandSource

Band q

d)(R)L(K

∫∞

⋅′⋅=

λλλ

where KBand is the absolute radiometric calibration factor [W-m-2-sr-1-count-1] for a given band, L(λ)Source is the spectral radiance of the calibration source, R′(λ)Band is the relative spectral radiance response for a given band, and ⟨qSource⟩Band is the mean value of radiometrically corrected image data taken while viewing the calibration source for a given band. The revised QuickBird K factors are pre-launch estimates derived during calibration of the focal plane. The proper way to convert QuickBird products from radiometrically corrected image pixel values to band-integrated radiance depends on the generation time and the bit depth of the product. These values are contained in the .IMD files. Generation time uses the UTC time format and in the .IMD files looks like:

generationTime = YYYY_MM_DDThh:mm:ss:ddddddZ; The revised calibration factors were installed at 2003-06-06T00:00:00.000000Z. The product generation time should be compared to this installation time to determine if the product metadata file (.IMD) has original or revised factors. The bit depth is either 16 bits or 8 bits and in the .IMD files looks like:

bitsPerPixel = 16; Conversion to band-integrated radiance is based on the instructions in the following sections corresponding to the product generation time and bit depth. Additionally, the panchromatic band has five possible exposure levels using time-delayed integration (TDI). These values could be 10, 13, 18, 24, or 32 and each has its own calibration factor. The TDI level used during image acquisition for a given product can be found in the .IMD files and looks like:

BEGIN_GROUP = IMAGE_1 TDILevel = 10;

END_GROUP = IMAGE_1 If the product was generated after June 6, 2003 at 0:00 GMT, the absolute calibration factors in the .IMD files are the revised factors and should be used for radiance conversion. These factors look like:

BEGIN_GROUP = BAND_B absCalFactor = 1.604120e-02;

END_GROUP = BAND_B




where this is an example for the blue band (QuickBird multispectral Band 1). BAND_P, BAND_B, BAND_G, BAND_R, and BAND_N correspond to the pan, blue, green, red, and nir bands respectively. NOTE: the absolute calibration factors are in scientific notation.

5.1.1 16-Bit Products 11-bit QuickBird data is stored as 16-bit integers. Placeholders are added to account for the five extra bits, but no stretching is performed.

5.1.1.1 Products Generated Before 2003-06-06T00:00:00.000000Z In this case, the revised K factors listed in Table 5 should be used instead of the original absCalFactors contained in the .IMD files.

Table 5: Revised K Factors for 16-Bit Products Spectral Band TDI Level K(revised) [W-m-2-sr-1-count-1]

Pan 10 8.381880e-02 Pan 13 6.447600e-02 Pan 18 4.656600e-02 Pan 24 3.494440e-02 Pan 32 2.618840e-02 Blue NA 1.604120e-02

Green NA 1.438470e-02 Red NA 1.267350e-02 NIR NA 1.542420e-02

Conversion from radiometrically corrected image pixels to band-integrated radiance is performed using the following equation:

BandPixel,BandBandPixel, qK(revised)L ⋅= where LPixel,Band are top-of-atmosphere band-integrated radiance image pixels [W-m-2-sr-1], K(revised)Band is the revised absolute radiometric calibration factor [W-m-2-sr-1-count-1] for a given band and is listed in Table 5, and qPixel,Band are radiometrically corrected image pixels [counts].

5.1.1.2 Products Generated After 2003-06-06T00:00:00.000000Z For products generated after June 6, 2003 at 0:00 GMT, the revised K factors are listed in the absCalFactor line in the .IMD files. Therefore they should match the values in Table 5. Conversion to band-integrated radiance uses these absCalFactors and follows:

BandPixel,BandBandPixel, qorabsCalFactL ⋅= where LPixel,Band are top-of-atmosphere band-integrated radiance image pixels [W-m-2-sr-1], absCalFactorBand is the absolute radiometric calibration factor [W-m-2-sr-1-count-1] for a given band and is listed in the .IMD files, and qPixel,Band are radiometrically corrected image pixels [counts].




5.1.2 8-Bit Products For 8-bit products, 11-bit QuickBird data (counts range from 0 to 2047) must be rescaled to 8 bits (counts range from 0 to 255). No scaling is performed in the case where the original 11-bit image data has a dynamic range less than 8-bits. Scaling is done on a product-by-product basis before spatial resampling to maximize the dynamic range of the data stored in the 8-bit format:

Band

BandPixel,bit-8 q)max(

255qq

BandPixel,

⋅=

where q8-bitPixel,Band are scaled 8-bit radiometrically corrected image pixels [counts], qPixel,Band are 11-bit radiometrically corrected image pixels [counts], and max(q)Band is the maximum radiometrically corrected image pixel value [counts] for a given band. Subsequently, each 8-bit product has its own corresponding absolute calibration factors:

255q)max(KorabsCalFact BandBand

Band⋅

=

where absCalFactorBand is the absolute radiometric calibration factor [W-m-2-sr-1-count-1] for a given band and is listed in the .IMD files, KBand is the absolute radiometric calibration factor [W-m-2-sr-1-count-1] for a given band, and max(q)Band is the maximum radiometrically corrected image pixel value [counts] for a given band.

5.1.2.1 Products Generated Before 2003-06-06T00:00:00.000000Z Products generated before June 6, 2003 at 0:00 GMT have original absolute calibration factors that must be modified to revised calibration factors by multiplying by a k′ conversion factor listed in Table 6:

Table 6: k′ Conversion Factors for 8-Bit Products Spectral Band TDI Level k′

Pan 10 1.02681367 Pan 13 1.02848939 Pan 18 1.02794702 Pan 24 1.02989685 Pan 32 1.02739898 Blue NA 1.12097834

Green NA 1.37652632 Red NA 1.30924587 NIR NA 0.98368622

The k’ conversion factor is simply the ratio of the revised K factor to the original K factor for a given band:

Band

BandBand )K(original

K(revised)k =′

Conversion to band-integrated radiance uses the absCalFactors and the k′ conversion factors according to the following equation:



Release Date: 07 November 2005 Revision 1.0 ©Copyright 2005, DigitalGlobe®, Inc. 12

BandPixel,BandBandBandPixel, qkorabsCalFactL ⋅′⋅= where LPixel,Band are top-of-atmosphere band-integrated radiance image pixels [W-m-2-sr-1], absCalFactorBand is the original absolute radiometric calibration factor [W-m-2-sr-1-count-1] for a given band and is listed in the .IMD files, k′Band is a conversion factor to go from original absolute calibration factors to revised factors for a given band and is listed in Table 6, and qPixel,Band are radiometrically corrected image pixels [counts].

5.1.2.2 Products Generated After 2003-06-06T00:00:00.000000Z For products generated after June 6, 2003 at 0:00 GMT, the revised k factors are listed in the absCalFactor line in the .IMD files and are scaled differently for each individual product. Conversion to band-integrated radiance uses these absCalFactors and follows:

BandPixel,BandBandPixel, qorabsCalFactL ⋅= where LPixel,Band are top-of-atmosphere band-integrated radiance image pixels [W-m-2-sr-1], absCalFactorBand is the absolute radiometric calibration factor [W-m-2-sr-1-count-1] for a given band and is listed in the .IMD files, and qPixel,Band are radiometrically corrected image pixels [counts].

5.2 Band-Averaged Spectral Radiance [ W-m-2-sr-1-µm-1 ] In general, band-averaged spectral radiance is defined as the weighted average of the peak normalized effective radiance value over the detector bandpass as shown in the following equation:

∫

∫∞

∞

⋅′

⋅′⋅=

0Band

0Band

d)(R

d)(R)L(L

Band

λλ

λλλ

λ

where LλBand is the band-averaged spectral radiance [W-m-2-sr-1-µm-1] of a target to be imaged for a given band, L(λ) is the spectral radiance of a target to be imaged, and R′(λ)Band is the relative spectral radiance response for a given band shown in Figure 2. The second step in conversion to top-of-atmosphere spectral radiance is to divide the band-integrated radiance by an effective bandwidth using the following equation:

Band

BandPixel,

BandPixel, ∆LL λ=λ

where LλPixel,Band are top-of-atmosphere band-averaged spectral radiance image pixels [W-m-2-sr-1-µm-1], LPixel,Band are top-of-atmosphere band-integrated radiance image pixels [W-m-2-sr-1], and ∆λBand is the effective bandwidth [µm] for a given band and is listed in Table 2.



6 Radiometric Balancing for Multiple Scene Mosaics For many customers, it may be desirable to create large area mosaics from multiple QuickBird scenes. Ignoring geometric effects, adjacent areas might appear to have different brightness values (counts) leaving a visible seam between scenes. As stated earlier, QuickBird counts are a function of the spectral radiance entering the telescope aperture at the QuickBird altitude of 450km. This top-of-atmosphere spectral radiance varies with Earth-sun distance, solar zenith angle, topography (the solar zenith angle is calculated for flat terrain so topography adds an extra geometry factor for each spot on the ground), bi-directional reflectance distribution function (BRDF-the target reflectance varies depending on the illumination and observation geometry), and atmospheric effects (absorption and scattering). For simple radiometric balancing, topography, BRDF, and atmospheric effects can be ignored. Now the major difference between two scenes of the same area is the solar geometry. The solar spectral irradiance values listed in Table 3 correspond to the values for the mean Earth-sun distance, normal to the surface being illuminated. The actual solar spectral irradiance for a given image varies depending on the Earth-sun distance and the solar zenith angle during the individual image acquisition. This variation will cause two scenes of the same area (or adjacent areas) taken on different days to have different radiances and hence different image brightnesses. The difference can be minimized by correcting imagery for Earth-sun distance and solar zenith angle. Before applying this correction, the solar geometry must be determined for each scene to be used in the mosaic.

6.1 Determination of Solar Geometry The variations in solar spectral irradiance are dominated by the solar geometry during a specific image acquisition. The sun can be approximated as a point source since the Earth-sun distance is much greater than the diameter of the sun. The irradiance of a point source is proportional to the inverse square of the distance from the source. This means that the irradiance of a point source at any distance can be calculated if the irradiance is known at one distance (Schott, p. 64, 1997):

22

211

2 rrE

E =

where E2 is the irradiance at a given distance 2, E1 is the known irradiance at distance 1, r1 is distance 1, and r2 is distance 2. The average Earth-sun distance is 1 Astronomical Unit (AU) so the equation becomes:

22

12 r

EE =

or rewritten:

2esd

EsunEes Band

Band

λλ =

where EesλBand is the band-averaged solar spectral irradiance [W-m-2-µm-1] at a given Earth-sun distance, EsunλBand is the band-averaged solar spectral irradiance [W-m-2-µm-1] at the average Earth-sun distance as listed in Table 3, and des is the Earth-sun distance [AU] for a given image acquisition. As the Earth orbits the sun throughout the year, the variation in Earth-sun distance leads to a change of irradiance of around ± 3.4%.




The solar spectral irradiance is defined normal to the surface being illuminated. As the solar zenith angle moves away from normal, a projected area effect is introduced and the same beam of light illuminates a larger area (Schott, pp. 66-67, 1997). This effect is a function of the cosine of the illumination angle and can be written as:

)(cosEsunEBandBand sθ θλλ ⋅=

where EθλBand is the band-averaged solar spectral irradiance [W-m-2-µm-1] at a given solar zenith angle, EsunλBand is the band-averaged solar spectral irradiance [W-m-2-µm-1] normal to the surface being illuminated as listed in Table 3, and θs is the solar zenith angle. The two solar geometries can be combined to solve for EλBand, the band-averaged solar spectral irradiance for a given image acquisition:

)cos(d

EsunE 2

es

Band

Band sθλ

λ ⋅=

6.1.1 Earth-Sun Distance In order to calculate the Earth-sun distance for a given product, the customer must first use the acquisition time to calculate the Julian Day. The acquisition time for a product is contained in the image metadata (.IMD) files. Acquisition time uses the UTC time format and in the .IMD files looks like: Basic:

BEGIN_GROUP = IMAGE_1 firstLineTime = YYYY_MM_DDThh:mm:ss:ddddddZ; END_GROUP = IMAGE_1

Standard:

BEGIN_GROUP = MAP_PROJECTED_PRODUCT earliestAcqTime = YYYY_MM_DDThh:mm:ss:ddddddZ;

END_GROUP = MAP_PROJECTED_PRODUCT From the UTC time format, retrieve the year, month, day and calculate the Universal Time (UT) from the hours, minutes, and seconds:

3600.0ss.dddddd

60.0mmhhUT

DDdayMMmonth

YYYYyear

++=

==

=

If the customer has a program that can calculate the Julian Day, that value can be used. Otherwise use the equations listed below (Meeus, p. 61, 1998). The word “int” listed in the equations means to truncate the decimals and only use the integer part of the number. If the image was acquired in January or February, the year and month must be modified as follows:



Release Date: 07 November 2005 Revision 1.0 ©Copyright 2005, DigitalGlobe®, Inc. 15

12monthmonth1yearyear+=

−=

Next, calculate the Julian Day (JD):

[ ] [ ] 1524.5B24.0UTday)1month(30.6001int)4716year(365.25intJD

4AintA2B

100yearintA

−++++⋅++⋅=

⎟⎠⎞

⎜⎝⎛+−=

⎟⎠⎞

⎜⎝⎛=

As an example, the QuickBird launch date of October 18, 2001 at 18:51:26 GMT corresponds to the Julian Day 2452201.286. Once the Julian Day has been calculated, the Earth-sun distance (dES) can be calculated by the following equations (U.S. Naval Observatory):

)cos(2g0.00014cos(g)0.016711.00014dD0.98560028357.529g

2451545.0JDD

ES ⋅−⋅−=⋅+=

−=

NOTE: g is in degrees but most programs require radians for cosine calculations. Conversion may be necessary for g from degrees to radians. The Earth-sun distance will be in Astronomical Units (AU) and should have a value between 0.983 and 1.017. For the QuickBird launch date, the Earth-sun distance is 0.9961172 AU. At least six decimal places should be carried in the Earth-sun distance for use in radiometric balancing or top-of-atmosphere reflectance calculations.

6.1.2 Solar Zenith Angle The solar zenith angle does not need to be calculated for every pixel in an image because the sun angle change is very small over the 16.5 km image swath and the along-track image acquisition time. The average solar zenith angle for the image is sufficient for every pixel in the image. The sun elevation angle [degrees] for a given product is calculated for the center of the scene and can be found in the .IMD files:

BEGIN_GROUP = IMAGE_1 sunEl = 61.7; END_GROUP = IMAGE_1

Where this is an example for a sun elevation angle of 61.7 degrees (solar zenith angle of 28.3 degrees). NOTE: “sunEl” has been changed to “meanSunEl” in version AA of the metadata. The solar zenith angle is simply:

sunElS −= 0.90θ



6.2 Applying Geometry to data For both of the equations in this section, imagery from multiple dates can be scaled to remove geometry factors associated with the solar spectral irradiance during those image acquisitions. The scaling can be performed without calculating the actual solar spectral irradiance. After either equation has been applied, the solar geometry values associated with the imagery are: dES = 1 AU and θS = 0 degrees. Once the Earth-sun distance and solar zenith angle are know, QuickBird imagery from different dates can be modified to remove the scene specific solar conditions. In the case of a 16-bit product, radiometrically corrected MS image pixels or pan pixels (with the same TDI level) can be modified directly:

)cos(dq

qS

2ESBandPixel,

BandPixel, θ⋅

=′

where q′Pixel,Band are solar geometry corrected image pixels [counts] for a given band, qPixel,Band are radiometrically corrected image pixels [counts] for a given band, dES is the Earth-sun distance [AU] during the image acquisition, and θs is the solar zenith angle [degrees] during the image acquisition. The solar geometry is independent of wavelength so the same geometry factors are applied to each band.

Figure 7: Mosaic of Kauai, Hawaii with (right) and without (left) scaling of solar geometry

Figure 7 is a mosaic of two scenes of Kauai, Hawaii. The scene in the lower left was acquired in January of 2004 with a solar elevation angle of 39.7 degrees whereas the scene in the upper right was acquired in October of 2004 with a solar elevation of 56.1 degrees. The cosine area effect of the low sun angle in the January image explains why the lower scene in the mosaic on the left side of the figure is much darker than the upper scene. When the solar geometry is corrected for both scenes, their brightness matches much better as seen in the mosaic on the right side of the figure. If the pan TDI levels are different or the product has a bit depth of 8 bits, the imagery must be converted to top-of-atmosphere band-averaged spectral radiance first following the instructions in Section 5. Each 8-bit QuickBird product is scaled individually based on the maximum radiometrically corrected pixel value for that scene. This means that two area based products from the same acquisition made with different polygons will be scaled differently even though they both come from the same raw data. The absolute calibration factor is scaled accordingly so that the spectral radiance of an 8-bit product will match the spectral radiance of an 11-bit product of




the same scene (except with reduced radiometric resolution). Top-of-atmosphere spectral radiance imagery can be modified to account for solar geometry using the following equation:

)cos(dL

S

2ESBandPixel,

BandPixel,L θλ

λ ⋅=′

where L′λPixel,Band are solar geometry corrected top-of-atmosphere band-averaged spectral radiance image pixels [W-m-2-sr-1-µm-1] for a given band, LλPixel,Band are top-of-atmosphere band-averaged spectral radiance image pixels [W-m-2-sr-1-µm-1] for a given band, dES is the Earth-sun distance [AU] during the image acquisition, and θs is the solar zenith angle [degrees] during the image acquisition. Scenes scaled with these solar geometry corrections will not perfectly match due to topographic, atmospheric, BRDF, and other temporal differences.

7 Conversion to Top-of-Atmosphere Reflectance The shape of top-of-atmosphere spectral radiance curves as a function of the QuickBird wavelengths are dominated by the shape of the solar curve. For many multispectral analysis techniques such as band ratios, Normalized Difference Vegetation Index (NDVI), matrix transformations, etc. common practice is to convert multispectral data into reflectance before running the algorithm. The top-of-atmosphere spectral radiance in the solar reflected portion of the spectrum can be modeled as the sum of three major contributors of radiation (Schowengerdt, p. 38, 1997):

spsdsus LLLL λλλλ ++= where Ls

λ is the total top-of-atmosphere spectral radiance, Lsuλ is the unscattered surface-reflected radiation, Lsd

λ is the downwelling surface-reflected skylight, and Lsp

λ is the upwelling path radiance. Expanding the unscattered surface-reflected radiation and assuming a Lambertian reflecting target (Schowengerdt, p. 44, 1997):

πθττ

ρ λλλ

λλ

⋅

⋅⋅⋅⋅= 2

ES

Ssu

d)cos(E

L sv

where Lsu

λ is the unscattered surface-reflected radiation , ρλ is the target diffuse spectral reflectance, τvλ is the view path atmospheric spectral transmittance, τsλ is the solar path atmospheric spectral transmission, and Eλ is the solar spectral irradiance, θs is the solar zenith angle, and dES is the Earth-sun distance. Follow the directions in Section 6 to calculate the solar zenith angle and Earth-sun distance. The top-of-atmosphere band-averaged spectral radiance for a QuickBird image band can be defined as:

spsd2

ES

S LLd

)cos(EsunL Band

BandPixel,BandPixel, λλλ

λλ πθττ

ρ λλ ++⋅

⋅⋅⋅= sv

Ignoring atmospheric effects gives the general equation:

πθ

ρ λλλ ⋅

⋅⋅= 2

ES

S

d)cos(Esun

L Band

BandPixel,BandPixel,




Rearranging the equation to solve for the surface reflectance gives the top-of-atmosphere band-averaged reflectance equation for a QuickBird image band:

)cos(EsundL

S

2ES

Band

BandPixel,

BandPixel, θ

πρ

λ

λλ ⋅

⋅⋅=

Top-of-atmosphere reflectance does not account for topographic, atmospheric, or BRDF differences. Consult the references by Schott or Schowengerdt for further discussion on correction for topographic or atmospheric effects. Typically a dark object subtraction technique is recommended to reduce atmospheric effects due to the upwelling path radiance (Richards, p. 46, 1999 or Schowengerdt, p. 315, 1997) followed by atmospheric modeling.

8 Summary Raw QuickBird imagery undergoes a radiometric correction process to reduce visible banding and streaking in QuickBird products. The products are linearly scaled to absolute spectral radiance (Holekamp, 2003). Various types of spectral analysis can be performed on this radiometrically corrected QuickBird imagery. Depending on the application, QuickBird products may need to be converted to top-of-atmosphere spectral radiance or spectral reflectance. These transformations are performed using the equations listed in this technical note. In the case of large area mosaics, data conversions may not be necessary but radiometric balancing will help match the brightnesses of the scenes used in the mosaic. For customers interested in comparing QuickBird products with imagery from other sensors, keep in mind the spectral response curves and gain settings which are specific to QuickBird. Many of the differences in analysis results can be explained by the differences in the sensors themselves.

9 References Holekamp, K. “NASA QuickBird Radiometric Characterization,” Presented at the Joint Agency Commercial Imagery Evaluation (JACIE) Team 2003 High Spatial Resolution Commercial Imagery Workshop, Reston, VA, 2003. Meeus, Jean. “Astronomical Algorithms 2nd ed.,” Willmann-Bell, Inc., Richmond, Virginia, 1998. Richards, John A. and Xiuping Jia. “Remote Sensing Digital Image Analysis: An Introduction 3rd ed.,” Springer, Berlin, 1999. Schott, John R. “Remote Sensing: The Image Chain Approach,” Oxford University Press, New York, 1997. Schowengerdt, Robert A. “Remote Sensing: Models and Methods for Image Processing 2nd ed.,” Academic Press, San Diego, 1997. U.S. Naval Observatory, “U.S. Naval Observatory: Approximate Solar Coordinates,” http://aa.usno.navy.mil/faq/docs/SunApprox.html Wehrli, C. “Extraterrestrial Solar Spectrum,” Publication 615, Physikalisch-Metrologisches Observatorium Davos and World Radiation Center, Davos-Dorf, Switzerland, pp. 23, 1985.


http://aa.usno.navy.mil/faq/docs/SunApprox.html

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