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Unified approach to absolute radiometric calibration in the solar-reflective range
Remote Sensing of Environment 77 (2001) 293 – 303 www.elsevier.com/locate/rse
Unified approach to absolute radiometric calibration in the solar-reflective range Philip N. Slater1, Stuart F. Biggar*, James M. Palmer, Kurtis J. Thome Remote Sensing Group, Optical Sciences Center, University of Arizona, P.O. Box 210094, Tucson, AZ 85721-009, USA
Abstract The need is identified for a unified approach to the preflight and in-flight absolute radiometric calibration of satellite sensors, which does not depend on the accurate transfer of lamp and detector calibrations from the laboratory to orbit. Such an approach is described that uses the sun to provide the link between preflight solar radiation-based calibration (SRBC), in-flight solar diffuser-based calibration, and vicarious calibration. Examples are given of these methods and uncertainty estimates are provided. It is shown that an uncertainty, with respect to solar exoatmospheric irradiance, of < 3%, 1s, can be attained for each method and that each can, if needed, be accurately related to national laboratory standards. In addition to providing the link between preflight and in-flight on-board calibrations, this unified approach also fills the critical need to relate these calibrations to those of the radiometers used for vicarious calibration and data-product, field-validation measurements, by also referencing them to the same solar-irradiance scale. D 2001 Elsevier Science Inc. All rights reserved.
1. Introduction The need for a unified calibration strategy has been obvious since the idea of using a solar diffuser was generally accepted as being perhaps the best solution for on-board sensor calibration in the solar-reflective range. The problem the solar diffuser presented was that, in using the sun, it provided a calibration against an approximately 6000-K source while an approximately 3000-K source was used for preflight calibration. Not only are the color temperatures very different, resulting in different sensor responses if a small amount of integrated out-of-band response is present, but there are Fraunhofer lines in the solar spectrum that are not present in the output of a tungsten lamp. For sensors with bandpasses of about 10 nm or less, Flittner and Slater (1991) have shown that the effects of these absorption lines can be a few percent. The inappropriate output spectral distribution of lamps also creates a problem in attaining near-saturation levels for the sensor in the blue. Other problems relate to their
* Corresponding author. Tel.: +1-520-621-8168; fax: +1-520-6218292. E-mail addresses: [email protected] (P.N. Slater), [email protected] (S.F. Biggar). 1 Also corresponding author. Now retired and traveling a lot. Present address: 4051 E Bujia Primera, Tucson, AZ 85718, USA.
unreliability in transferring the preflight calibration to orbit because of the zero-g effect on gaseous convection within the lamp envelope and the vacuum conditions of orbit. Typically, lamps are only used for partial-aperture calibration and, in some cases, only illuminate the filtered focal plane. It is also difficult to check the stability of lamps in space. Finally, there are serious discrepancies, e.g., dispersions as high as 3% in the blue and 8%, in the shortwave infrared (see Fig. 1), between lamp calibrations performed by the various national laboratories. Thus, although lamps have been shown to be reliable on the SPOT and Landsat programs for relative calibration over periods in excess of 5 years, they are not appropriate sources for absolute calibration. Ideally, we need a single, stable source, available worldwide, that can be used for preflight, on-board, and vicarious calibration purposes and for data-product validation work. It should have the appropriate spectral distribution of output radiance. The choice is obviously the sun, the question is: how do we use the sun reliably and accurately for fullaperture preflight and in-flight calibration, and for the calibration of radiometers used in ground measurement campaigns and in aircraft? In Section 2, we show how solar radiation-based calibration (SRBC) can be used to unify the multiple calibration steps mentioned in the above question. We then review: (1) the use of SRBC to provide the preflight calibration of the
0034-4257/01/$ – see front matter D 2001 Elsevier Science Inc. All rights reserved. PII: S 0 0 3 4 - 4 2 5 7 ( 0 1 ) 0 0 2 1 0 - 3
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Fig. 1. Grand-mean differences from NIST of all participant’s spectral-irradiance measurements. CSIRO: Australia; ETL: Japan; INM: France; IOM: Spain; NIM: China; NIST: USA; NPL: UK; DPT: South Africa; NRC: Canada; OMH: Hungary; PTB: Germany; and VNIIOFI: Russia. Data from Walker et al. (1991).
sensor – solar – diffuser combination, (2) the simple extension of this procedure to calibrate aircraft and field radiometers, and (3) a method we have proposed for using a ratioing radiometer (RR) to check the stability of a solar diffuser for in-flight calibration. Uncertainty estimates are associated with each of these procedures.
laboratory. Note the on-board calibration is calibrated with respect to the SIS by using the sensor as a transfer radiometer (TR). It is becoming increasingly common now to cross-compare the output of SISs, used to cali-
2. Description of the unified method Fig. 2 shows how solar radiation can be used to unify preflight, on-board, and vicarious calibrations, and the calibration of radiometers used in validation campaigns. The horizontal dashed line separates calibrations conducted in space from those conducted on the ground or in the earth’s atmosphere. The vertical dashed line separates calibrations conducted with reference to the sun from those conducted with reference to lamps and detectors. It is interesting to note that the left- and right-hand sides of the diagram are entirely independent, and that the right-hand side describes the usual procedure followed to date. Until now, vicarious calibration and validation experiments have not been associated directly with preflight or in-flight calibrations or their radiometric scales. It is, of course, this important association that we are proposing to implement by the common use of the sun, as shown on the left-hand side of the diagram. The right-hand side of Fig. 2 shows the sphericalintegrating source (SIS), which creates a uniform radiance area, large enough to fill the aperture and field-of-view of the sensor and variable in its output to cover the dynamic range of the sensor. The SIS is typically calibrated by reference to a 1000-W tungsten lamp, whose calibration is traceable to a source or detector in a national standards
Fig. 2. SRBC and SIS calibration of a sensor. SD: solar diffuser; RR: ratioing radiometer; VC: vicarious calibration; TR: transfer radiometer.
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brate earth observation sensors, with other sources from other laboratories. The reason for this are the serious discrepancies, up to 8%, noted in recent years, Guenther et al. (1990) and Leroy et al. (1990). Biggar and Slater (1993) have shown that such cross-comparisons are best performed using ultra-stable, well-characterized, TRs. These provide accurate cross-comparisons as well as independent absolute calibrations by reference to standard lamps. The main limitation to their absolute accuracy is the uncertainty in the measurement of the filter transmittance. Trap detectors for the SWIR have not yet been perfected, but well-designed radiometers using liquidnitrogen cooling for the detector(s) can probably insure the necessary high stability. The two-way arrows in Fig. 2 are to indicate that a TR can be used, for example, to check the SIS calibration and also to relate it to the calibration of the vicarious calibration and validation radiometers and the SRBC of the sensor preflight. The use of the sun as the primary source does not entirely replace lamp-based, in-flight calibration. A limitation in the use of an on-board solar diffuser is that it can, at most, be used once an orbit when the sun – diffuser – sensor geometry is appropriate. This means it cannot be used to monitor intra-orbit changes induced, for example, by heating effects due to the spacecraft being alternately in the earth’s shadow and in the sun. Dinguirard et al. (this issue) and Markham et al. (1998) have shown that on-board lamps are useful for relative calibration, although not the best choice for use as sources for absolute calibration, for the reasons mentioned above. Lamps can be used very effectively for monitoring intra-orbit response changes, including the linearity (using multiple lamps) of the sensor.
3. Use of SRBC in the preflight calibration of a space sensor The radiance level of a diffuser panel above the atmosphere can be approximated at ground level in a simple manner. The radiance due to direct solar irradiance is given by Ldir sun = Lglobal Ldiffuse where Lglobal is the radiance due to irradiance directly from the sun plus the diffuse sky irradiance, and Ldiffuse is the diffuse sky irradiance, i.e., with the sun occulted. The direct solar irradiance Edir sun is determined using a solar radiometer to measure the atmospheric spectral transmittance along the path to the sun and by reference to the solar exoatmospheric irradiance as provided, e.g., by Neckel and Labs (1984). A correction, described later, has to be made in the determination of Ldir sun for the central small region of the solar aureole that is occulted unavoidably in the measurement of Ldiffuse. In the calibration, the radiances mentioned above are recorded as digital counts (DCs) by the instrument being calibrated. The top-of-the-atmosphere (TOA)
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DCs generated by the sensor under the same geometrical conditions is given by (Eq. (1)): DCTOA ðlÞ ¼ ¼
DCglobal ðlÞ DCdiffuse ðlÞ T ðlÞ DCdir sun ðlÞ T ðlÞ
ð1Þ
where T(l) is the transmittance along the slant path to the sun. An SRBC of a space sensor can be performed in several ways. One is to take the sensor outside, mounted in a fixture, that allows the solar diffuser to be aligned correctly with the sun, that is, in the same geometry to be used on orbit. The fixture is moved to track the sun during the calibration. The sensor is enclosed in a portable clean room with positive pressure and an opening just large enough to allow correct solar illumination of the diffuser. This procedure was followed successfully for SeaWiFS by Biggar, Slater, Thome, Holmes, and Barnes (1993). A different calibration procedure, but one using solar radiation, was used for the preflight calibration of ScaRaB. Dinguirard et al. (1998) estimate the uncertainty in the calibration of the 500– 700-nm channel to be about 5%. A proposed modification to the SeaWiFS procedure brings the solar beam into the laboratory using one or more mirrors, for example, a heliostat. In this case, the solar radiometer would be used to measure the total path transmittance including the mirrors. This would reduce the possibility of contamination of the sensor. An SRBC could be conducted with the sensor in a large vacuum tank if a suitable window was found and the sensor could be correctly positioned in the tank. An important characteristic of the SRBC is that it is unaffected by the presence of stray light on the diffuser reflected from surrounding structures and the instrument itself. Such stray light is usually present in both the DCglobal and DCdiffuse measurements and is therefore subtracted out. However, care must be taken to ensure that light reflected from the diffuser is not strongly reflected back on to the diffuser. Such a problem is only likely to exist due to the presence of a specular or large area, highly reflecting diffuse surfaces in proximity to the diffuser. This is an unlikely problem and stray reflections should be easy to baffle. The spectral transmittance of the atmosphere can be measured with satisfactory accuracy using a solar radiometer. Such instruments typically include about ten 10-nm spectral filters covering the range from about 400 to about 1000 nm. The conventional method for measuring the atmospheric transmittance involves using an uncalibrated radiometer and recording voltage measurements during a cloud-free morning. The slope of the resulting Langley plot of log voltage vs. air mass yields the spectral optical depth from which the spectral transmittance is immediately available. A limitation of this procedure is that it depends on cloud-free and stable atmospheric conditions for the entire
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morning of the sensor calibration. The use of a wellcalibrated radiometer reduces this dependancy. Then an instantaneous, or two-point, Langley plot can be constructed in which one point corresponds to a measurement made at the time that the diffuse and global measurements are being made and the other point is the zero intercept voltage obtained from the calibration of the instrument. The uncertainty of this approach depends primarily on the uncertainty in the calibration of the solar radiometer. In addition to the accuracy of calibration of the solar radiometer, the accuracy of the SRBC depends on the wavelength, the atmospheric conditions during the calibration, the error in measuring the solid angle subtended by the small occulting plate, and the errors in the correction for the blocked solar aureole. The spectral transmittance T(l) along the slant path to the sun is (Eq. (2)): T ðlÞ ¼ expðdðlÞ=ms Þ
ð2Þ
where d(l) is the spectral optical depth and ms cosqs where qs is the solar zenith angle. The fractional uncertainty in the transmittance is: DT ðlÞ DdðlÞ dðlÞsinqs Dqs þ T ðlÞ ms m2s
ð3Þ
where Dd(l) is the absolute uncertainty in the optical depth and Dqs is the uncertainty (in radians) in the knowledge of the solar zenith angle. The second term on the right of Eq. (3) is negligible compared to the first. The spectral extinction optical depth is the addition of the following component optical depths due to molecular scattering, aerosol scattering, ozone absorption, water vapor absorption, and absorption by other gases such as oxygen. The molecular optical depth is approximated by Rayleigh scattering and known from the barometric pressure. The extinction spectral optical depth is measured. The uncertainty is in the aerosol optical depth and extinction due to absorption. From previous analysis, it can be shown that the uncertainty is less than 3% of the difference between the extinction and molecular optical depth. For a nominal 23km visibility US standard atmosphere, this corresponds to a transmittance uncertainty of ± 2.7% to ± 1.4% for a solar zenith angle of 60 for wavelengths of about 400 and 900 nm, respectively. This uncertainty is reduced to ± 1.9% to ± 1.1% when the measurement is made at a solar zenith angle of 39. (A solar zenith angle of nearly 60 was used mid-morning in early March 1993 for a SeaWiFS calibration at Santa Barbara Research Center, California. Solar noon there on that day corresponded to a solar zenith angle of 39.) In general, the uncertainty is smaller the cleaner the atmosphere and the shorter the atmospheric path, i.e., the smaller the solar zenith angle and the higher the elevation. The uncertainties in the calibration attributable to the small occulting plate are smaller than those caused by the transmittance measurement. These uncertainties cannot be accurately forecast without details on the geometry of the
sensor’s diffuser and the size of the occulting plate. The size of the latter depends on the entrance aperture. For SeaWiFS, the estimated uncertainties were ± 0.8% after correction for the DCglobal DCdiffuse measurement, and ± 0.4% corresponding to the uncertainty of ± 0.25 for the angle of incidence on the diffuser. Summarizing, using the calibrated solar radiometer approach, the uncertainty is primarily due to the uncertainty in the calibration of the radiometer. In the Langley plot method, the total uncertainty is ± 2.8% to ± 1.4% at a solar zenith angle of 60 and ± 1.9% to 1.1% for a zenith angle of 39. These uncertainties are 1s with respect to the sun. The uncertainty of the exoatmospheric solar irradiance has to be accounted for if there is a need to convert the calibration and its uncertainty into physical units, e.g., of spectral radiance. Neckel and Labs (1984) claim an uncertainty of < ± 1% in the range 400 to 1250 nm; unfortunately this is difficult to verify. As for all calibration activities, it is prudent to validate results by reference to results derived from an independent method. For the SRBC, a recommended independent method is to measure the radiance of the diffuser panel using a TR immediately before and after the SRBC measurements. This will allow a correction to be made for the small change in the angle of incidence on the diffuser between measurements. Such validation measurements will help ensure that there are no systematic errors introduced in the SRBC, e.g., due to sensor geometry effects. A further discussion of this subject can be found in Section 5.3. However, because these effects are sensor design-specific, they are only discussed briefly.
4. Extension of the method to calibrate other radiometers The extension of the above method to aircraft and field radiometers is conceptually straightforward. In these cases, the solar diffuser, which was integral with the space sensor in the above example, is replaced by a diffuse reflecting panel whose BRDF has been accurately measured in the laboratory. The sun-illuminated diffuser is accurately leveled beneath the radiometer of interest. In the aircraft case, this will involve correctly positioning the aircraft so the diffuser is sun-illuminated when placed beneath the sensor. There may be the possibility of light from the diffuser being specularly reflected off the fuselage to be incident on the diffuser for the Lglobal but not the Ldiffuse measurements. Masking the reflection or blackening the appropriate area of the fuselage may then be necessary. A precise laboratory TR was calibrated to test this concept. The test procedure is shown on the right-hand side of Fig. 3. The TR is a seven-band, interference-filter-based radiometer with a silicon ‘‘trap’’ detector assembly (Biggar & Slater, 1993). The filter bandpasses are between 10 and 15 nm. The TR has no imaging optics and the throughput is
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297
Fig. 3. Procedure to compare the exo-atmospheric spectral irradiance measurements of Biggar (1998) and Thuillier et al. (1998).
determined by two apertures spaced by invar rods. The second aperture is at the detector assembly and the first (front) aperture is removable to allow calibration and use in the irradiance mode. With the front aperture in place, the TR measures in a radiance mode. The TR detector, electronics, and filters are temperature-stabilized at about 303 K. The TR was calibrated in the laboratory by reference to a National Institute of Standards and Technology (NIST)supplied standard of spectral irradiance, F-330 (a 1-kW FEL-type halogen lamp operated at 7.9-A DC). The spectral irradiance calibration of the lamp was interpolated to the TR wavelengths by use of a ‘‘Wien’’ type distribution with a polynomial correction term as suggested by the NIST. The front aperture was removed for the irradiance calibration and the aperture was reinstalled for the SRBC. The laboratory irradiance calibration was used with knowledge of the geometry to calculate a radiance mode calibration. The calibration was then compared to the radiance mode calibration derived from a solar calibration. The experiment was done outside our laboratory in Tucson, AZ on 1996 March 19 in the late morning. Sky conditions were clear. The TR was positioned such that the optical axis was normal to, and centered on, a 0.61-m2, painted barium sulphate reflectance panel, leveled with respect to the local horizontal. A solar radiometer, with 10 filters of width approximately 10 nm, was used during the
morning to determine extinction optical depth at the solar radiometer wavelengths. These data were used along with atmospheric pressure to estimate the optical depth components (Rayleigh, aerosol, and ozone) at the laboratory TR wavelengths. From the optical depth components, an inband transmittance was computed for each of the TR bands. Measurements of the TR output voltage were made for each band with the panel illuminated by the direct sun and diffuse skylight and then with the direct beam of the sun blocked by a ‘‘parasol’’ consisting of a blackened aluminum plate about 0.6 m2 mounted on the end of a pole at an angle adjusted so that the panel was perpendicular to the direct beam from the sun. These two measurements, each corrected for ‘‘dark’’ current, were subtracted to give the attenuated direct-solar irradiance. The in-band transmittance determined from the solar extinction measurements was applied to the bandaveraged exoatmospheric solar irradiance to calculate the solar irradiance on the panel. The panel directional reflectance was previously determined in the laboratory and these values spectrally interpolated to TR wavelengths. From the irradiance, the solar zenith angle at the time of measurement, and the directional reflectance, the in-band radiance from the panel was calculated and used to determine a radiance calibration coefficient. Sources of uncertainty greater than or equal to 0.5% are tabulated in Table 1. The values in parentheses show the
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extent of expected reductions in the uncertainties in the near future. For example, the atmospheric transmittance uncertainties can be reduced by the use of an improved solar radiometer, the BRDF measurements can be made more accurately with a better current control of the source and a better amplifier for the radiometer, and the Optronic transmittance uncertainties can be reduced with a more precise amplifier. Note also in Table 1 that each source estimated or known to be less than 0.5% has been omitted, however, each contribution is included in the final root-sum-square value. (Omitted quantities are: Optronic source stability; source error due to 0.05% wavelength uncertainty and 0.01% wavelength repeatability; filter shift due to measurement geometry; filter nonuniformity; finite spectrometer bandwidth; angular sensitivity of TR; amplifier gain settings; voltmeter uncertainties; and spectral out-of band errors. Together they have a negligible effect on the final RSS value.) Many of these uncertainties are wavelength dependent, however, the largest error source (amplifier uncertainty in an Optronic 750M used for filter measurement) is not. A similar table for the laboratory calibration is given as Table 2. (With the exception of the spectral out-of-band errors, all the < 0.5% errors mentioned above have also been omitted from Table 2. In this case, there are also small unlisted errors due to lamp current uncertainty and stability, lamp distance, and lamp angular alignment. Again these unlisted errors have been included in the final RSS value.) For a radiance calibration, using a diffuser, the total uncertainties increase by 0.8% at both wavelengths. Table 3 lists differences between radiances measured from a reflectance panel using the TR and two sets of solar irradiance values (Biggar, 1998). The agreement is excellent, exceeding what we might expect as a result of the uncertainties listed in Table 1, and this in spite of the use of two completely independent calibration paths: Biggar (1998) used a lamp calibrated by the NIST for his reference, while Thuillier et al. (1998) used a blackbody source whose temperature was referenced to Physikalisch – Technische Table 1 Uncertainty estimate for the radiance mode calibration of the laboratory TR with reference to the sun Wavelength (nm)
412.8
666.6
Solar spectral irradiance uncertainty (Neckel and Labs quoted uncertainty) Transmittance errors (based on solar radiometer intercept history) BRDF of diffuser panel (estimated for our laboratory-referenced to pressed polytetraflouroethylene) Filter transmittance (terms included) Optronic 750 M amplifier inaccuracy (1% spec.) Filter temperature stability/uniformity(estimate) Stray light (in the TR-estimate) Out of field-of-view (measurement) Total RSS (RSS with improvements)
1.0
1.0
2.0 (1.0)
1.1 (0.6)
2.0 (1.0)
2.0 (1.0)
1.4 (0.1) 0.5 0.5 0.5 3.5 (2.0)
1.4 (0.1) 0.5 0.5 0.5 3.0 (1.8)
Uncertainties are given in percent (1s if stated in the manufacturer’s data). Items with a second figure in parentheses are values with improvements (see text for mention of other sources of uncertainty).
Table 2 Uncertainty estimate for the radiance mode calibration of the laboratory TR with reference to an NIST standard of spectral irradiance Wavelength (nm) Lamp uncertainties (NIST FEL irradiance standard, F-330) Irradiance calibration uncertainty Spectral interpolation uncertainty Uncertainty in lamp-distance scaling (1/r2) Lamp ageing and drift (estimate) Filter transmittance (terms included) Optronic 750 M amplifier inaccuracy (1% spec.) Filter temperature stability/uniformity (estimate) Front aperture area (5 mm diameter uncertainty) Stray light (in the TR-estimate) Out of field-of-view (measurement) Spectral out-of-band (out-of-band response to lamp vs. sun) Total RSS (RSS with improvements)
412.8
666.6
0.5 0.5 0.6
0.5 0.5 0.6
0.5
0.2
1.4 (0.1)
1.4 (0.1)
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.1
0.9
2.1 (1.6)
2.2 (1.7)
Uncertainties are given in percent (1s if stated in the manufacturer’s data). Items with a second figure in parentheses are values with improvements (see text for mention of other sources of uncertainty).
Bundesanstalt (PTB) (see the left-hand side of Fig. 3). It should be noted that the lamp-derived results listed in Table 3 used the irradiance calibration results. This was because the irradiance method is of smaller uncertainty, not involving a BRDF characterization. It is interesting to note that Biggar agrees better with Thuillier et al. than with Neckel and Labs over the radiometer’s spectral range. In summary, the component uncertainties associated with the SRBC of field and aircraft-mounted radiometers are similar to those mentioned in Section 3. The total uncertainties may be about the same or even smaller, making the technique generally applicable for remote sensing work. It is of interest to note that for field and aircraft-mounted radiometers, the additional uncertainty of about ± 1% associated with the knowledge of the reflectance of the diffuser, may be offset by a reduction in the uncertainty in the atmospheric transmittance. This can be achieved by conducting the calibration at high elevation and near solar noon during the summer. As with SeaWiFS, neither of these may be possible in the general case of the preflight calibration of a space sensor.
5. On-board calibration using a solar diffuser and RR The desirable characteristics of an on-board calibration system are that it should:
Provide a complete system, or end-to-end, calibration Make use of the full aperture of the system
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Table 3 Percent differences between measured radiances from a reflectance panel and those predicted from solar irradiance tables of Neckel and Labs (1984) and Thuillier et al. (1998) Percent differences for the given wavelength (nm) Source of values for exoatmospheric solar spectral irradiance
413
442
488
550
667
747
868
Neckel and Labs values in (SRBC lamp)/lamp Thuillier et al. values in (SRBC lamp)/lamp
0.46 1.17
2.26 0.48
3.17 0.01
0.73 0.35
0.28 0.41
2.00 0.69
1.94 2.10
Make use of the full field-of-view of the system Provide at least one value near the top and the bottom of the sensor’s dynamic range
Preferably the on-board system should be complemented by one or more independent in-flight methods to attempt to identify systematic errors which would otherwise be impossible to detect.
period was not described, but it is the first discussion found that proposes a ratioing method. The method proposed here uses a radiometer in a ratioing mode (Slater & Palmer, 1991) to view the sun and the diffuser alternately during the calibration of the sensor of interest, as shown in Fig. 4. The same basic principle is being used for the Moderate Resolution Imaging Spectroradiometer (MODIS) (Guenther et al., 1996), however, in this case, a metal plate containing an array of small apertures is placed in front of the monitor to attenuate the direct solar beam.
5.1. Characteristics of a solar diffuser 5.2. The RR concept A method which has often been suggested to meet the above-listed characteristics involves the use of a solardiffuser panel. Simply, a flat plate with high, near-lambertian reflectance over the spectral range of interest is located at an appropriate angle to the solar direction (usually between 45 and 60 to obtain a full-scale calibration) and at a smaller angle, preferably 0, to the optical axis of the sensor during the calibration period. It should be at least a little larger than the projected area of the sensor’s aperture to fill the field-of-view of the sensor. Ideally, a knowledge of the spectral bidirectional reflectance of the diffuser, the solar incidence angle, and the exoatmospheric spectral irradiance is all that is needed for the spectral radiance of the diffuser to be calculated. By changing the angle of incidence to the diffuser, a number of different radiance levels can be obtained. A look at deep space, or an on-board black surface, is also required to provide a zero radiance level. The graph of radiance levels vs. sensor-output DCs allows the gains and offsets for the sensor’s calibration equation to be determined. The drawback to using a solar-diffuser panel is that we cannot accurately predict the changes in radiance of the diffuser with conditions on orbit. In particular, effects of reflectance loss with proton and high-UV irradiance, stray reflections falling on the diffuser from other illuminated surfaces on the instrument or spacecraft, and UV-induced luminescence effects cannot be accurately predicted. The simplest solution to the problem is to monitor the diffuser radiance directly with a radiometer. However, the stability of the radiometer will always be in question. A conceptual solution, suggested by O’Mongain et al. (1983), to the problem uses an integrating sphere, externally baffled to define the field-of-view, to view alternately the diffuser and the sun. Differently filtered detectors sample the radiance within the sphere. The implementation of this arrangement to monitor diffuser radiance during the sensor calibration
A simple radiometer that images the surface of interest on a detector with a single lens is not a suitable design, mainly because the ratio of irradiances on the detector will be about 10,000:1, creating an extraordinary demand for instrument linearity. To avoid this problem, the radiometer can follow the design originally due to Ko¨hler for substage microscope condensers. A field lens is located at the focus of the objective lens to image the uniformly illuminated aperture of the objective onto the detector plane (Fig. 5). This arrangement provides uniform irradiance over the radiometer’s field-of-view, even though a source of small angular extent, the sun, is viewed in one case. When the acceptance angle of the radiometer is sufficient to nearly fill the area of the diffuser, Palmer and Slater (1991) showed the ratio of the signal output from the radiometer viewing the sun to that when viewing the diffuser, RRR, is: RRR ¼
p rP VcosqP
ð4Þ
where rP is the diffuser panel directional – hemispherical reflectance, V is the solid angle field-of-view or acceptance
Fig. 4. Layout of solar-diffuser panel and RR for in-flight calibration.
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Fig. 5. Ko¨hler layout of the RR.
angle of the radiometer, and qP is the angle between the sun and the normal to the solar diffuser. To reduce the ratio of about 10,000:1, mentioned above, to a more manageable ratio of about 20:1, the full field-of-view should be about 30 for a 45 solar incidence angle and a high reflectance diffuser. Because of the near-lambertian characteristics of the diffuser panel, its bidirectional reflectance, rP, can be written: rP ¼
pLP d 2 EcosqP
ð5Þ
where LP is the panel radiance and d is the Earth –Sun distance in Astronomical Units. The quantity of interest in many remote sensing investigations is the bidirectional spectral albedo, A(q, f; l), of the Earth – Atmosphere (EA) system. This is also sometimes referred to as the apparent reflectance r*. If, for simplicity, the albedo is assumed to be close to lambertian, then Eq. (5) can be written: Aðqz ; f; lÞ ¼
pLEA d 2 Ecosqz
ð6Þ
where LEA is the radiance of the EA system, and Ecosqz is the solar exoatmospheric irradiance on the EA system at a solar zenith angle of qz. If we assume that DCEA = kLEA, and DCP = kLP, where DCEA and DCP are the DCs recorded by the sensor when observing the EA system and the solardiffuser panel, respectively, and k is the calibration coefficient for the sensor, then by the use of these equations, together with Eqs. (4), (5), and (6) we can determine the following relationship: Aðqz ; f; lÞ ¼
p DCEA RRR Vcosqz DCP
to be illuminated only by direct sunlight or by stray light off the sensor or other parts of the spacecraft as well. In the no-stray-light mode, the diffuser radiance can be calculated from the knowledge of the exoatmospheric solar irradiance, the BRDF of the diffuser, and the angle of incidence on the diffuser. A change in the diffuser reflectance is detected from a change in the ratio of diffuser-to-sun signals and the new value for the diffuser radiance is calculated. In the mode when stray light is anticipated, the diffuser radiance can be calculated by reference to a preflight calibration of the sun-to-diffuser ratio. This ratio may be determined by accurately measuring the solid angle of the radiometer’s field-of-view and the diffuser reflectance and, if possible, conducting an SRBC as described earlier. For both modes the assumptions are mentioned below. (1) Stray light must not enter the field-of-view of the radiometer when it observes either the sun or diffuser. (2) During the sensor’s lifetime, either the loss in reflectance of the diffuser is not accompanied by a change in the shape of its BRDF, or the angles of incidence of the radiometer and the sensor at the diffuser are equal. For the no-stray-light mode only, the assumption is: (3) The diffuser does not change in reflectance from its preflight measured value during the first calibration on orbit. Subsequent calibrations are all done with respect to this calibration. A result of this assumption is that no preflight calibration or determination of the sun-to-diffuser ratio is needed. An important advantage of the above design is that several differently filtered detectors can be placed in the uniformly irradiated focal plane, thus allowing for the monitoring of the spectral radiance of the diffuser, Biggar (1998). The selection of the spectral channels for the RR is based on the need to maximize the science return from the multi- or hyper-spectral sensor consistent with minimizing the complexity, cost, and data quantity from the RR. We need:
ð7Þ
where qz and f are the solar zenith and view angles for the area of the EA system being observed. Eq. (7) is the basic equation for determining bidirectional spectral albedo from a sensor using a RR and diffuser panel. Note that it is only valid for observations made in time intervals that are short compared to changes in the calibration of the system and the reflectance of the solar-diffuser panel. RR measurements have to be made periodically to update the calibration of the sensor. Note that, because of the ratioing measurement that is made, neither Eq. (4) nor Eq. (7) is a function of the solar exoatmospheric irradiance or the Earth –Sun distance. 5.3. Operating modes and design considerations The RR – solar diffuser system can be used in two operational modes depending on whether the diffuser is expected
Continuous coverage, 400 –2500 nm. Ability to monitor slowly changing solar diffuser spectral reflectance with wavelength. Ability to monitor rapidly changing solar diffuser spectral reflectance with time.
Inspection of selected data on the emission spectrum of typical organic dyes indicates that they usually emit over the visible range from 400 to about 700 nm with a half-width of about 50 nm. This means that 50-nm bandwidth coverage of the detectors will be sufficient over this range. Initial measurements of the spectral reflectance of solar diffuser material candidates made by Bruegge et al. (1993) and Guzman et al. (1991), show relatively slow changes in spectral reflectance with wavelength, the most noticeable changes occurring at short wavelengths. As a result, the bandwidths tentatively proposed are 50-nm wide from 400–
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700 nm, 100-nm wide from 700 – 1000 nm, and 500-nm wide above 1000 nm. It will be necessary to place 12 detectors in relatively close quarters such that all are irradiated uniformly. A focal plane 22 mm in diameter can accommodate nine silicon detectors, each 3 mm2, for the first nine spectral channels, covering the range 400– 1000 nm, and three infrared detectors up to 5 mm2. Candidate detectors include germanium (Ge), indium gallium arsenide (InGaAs), indium arsenide (InAs), and mercury – cadmium – telluride (MCT). Bandpass interference filters would be installed on each detector to provide the desired spectral band coverage. Cooling will also be mandatory for the IR detectors and desirable for the Si detectors as well. A thermoelectric cooler is the best choice, as the cooling requirements are not stringent. An analysis of the signal-to-noise ratio (SNR) expected from an RR built to these tentative specifications was made. Assumptions were made regarding RR size (aperture area), the band-limited solar spectrum, the solar diffuser spectral reflectance, typical detector areas and NEPs, and the RR field-of-view. The SNR is greater than 104 for all bands in the solar view and greater than 103 for all bands in the solar diffuser view. The positioning of the RR is of importance. It must be in a location such that it can see the solar diffuser simultaneously with the sensor and not obstruct the sensor’s view. It must also be able to look at the sun with an unobstructed view. A suitable location may be found, on the leading edge of the unit containing the sensor. From this position, the internal optics can be scanned with a single, simple motor drive to look in three directions: (1) stowed for dark calibration (2) out front for direct solar view, and (3) toward the solar diffuser. Positions (1) and (3) are fixed with hard, mechanical stops for repeatable positioning. Position (2) must be variable to adjust the solar view to exclude platform reflections and earthshine.
5.4. Other operational considerations and estimated uncertainties Since the RR is always operated in a ratioing mode, calibrating itself against the sun and then transferring that calibration to the diffuser, the stability requirements are modest. It is essential that the RR field-of-view remain constant with time, temperature, etc., and that the field-ofview is uniform for solar viewing. Degradations that one might encounter in orbit will not affect the RR results. It should be stable in the presence of the solar UV; stable UV blockers can prevent the UV from degrading the interference filters used to define the spectral bandwidths. The only problem that is apparent from contamination is if a contaminant, which exhibits solar-induced luminescence, is deposited on the optics. Its influence will be much greater during solar view than during solar diffuser view, rendering
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the ratio incorrect. The RR has a duty cycle of 0.0007, based on an average of one calibration, of 5-min duration, every 5 days through a 5-year mission lifetime. The total exposure is thus about 35 h, when the initial data, described below, are included. The optics will be stowed the rest of the time, minimizing the possibility of platform contaminants reaching the optics. The RR should be used frequently during the first few weeks of sensor operation. It is suggested that a calibration be performed twice per day, or once every eight orbits, for the first week to track degradations in the solar diffuser and in the sensor. For the next several weeks, a calibration is suggested once per day. When sufficient experience has been obtained, the rate can be reduced to the abovementioned once per 5 days for the mission duration. Careful planning is required to determine when the first calibration should take place. It is desirable that the entire platform undergo an initial stabilization period, when most of the component and system outgassing occurs, to minimize contamination of the RR, the sensor, and the solar diffuser. The calibration cycle should not start until after this initial period. Whenever the RR is not in operation, the optics should be protected from the surrounding environment. Similarly, the solar diffuser should be stowed when not in use to protect it from contamination and solar radiation. Palmer (1991) has demonstrated that stray light effects from both the platform and earthshine can significantly change the irradiance on the solar diffuser, often unpredictably. The RR is also subject to some stray light effects, but inasmuch as the field-of-view is restricted, the effects are different. In the solar diffuser view, baffling should prevent the RR from being subject to out-of-field stray light effects. The solar diffuser fills the field-of-view, and there are no other in-field sources available to irradiate the focal plane of the RR. Of course, the RR measures the solar diffuser radiance from the sun and all the stray sources, but so does the sensor. We need to know the solar diffuser radiance during the sensor’s calibration, including that due to stray light and luminescence, and the RR does just that. During the solar view, the RR is subject to stray radiation due to reflections from the platform and due to earthshine. The location and timing of the operation of the sensor must be such that for any calibration angle, from before the terminator to the end of the calibration window, the RR can be pointed to avoid both earthshine and reflections from the platform. This may mean that the RR look angle must be set for each calibration, coordinated with the calibration angle. Estimates of the uncertainties introduced by the RR and the solar diffuser are hard to make because they are certain to differ for specific sensors depending on the location of the solar diffuser and RR with respect to sources of stray light, and other variables such as contamination types and concentrations. Palmer estimated that, if no RR were used, the uncertainty in the calibration
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could be about 15% and the use of an RR could reduce this figure to about 2%.
6. Concluding remarks There is a compelling need in quantitative remote sensing to use a unified approach to radiometric calibration, one that uses a universally available, single, stable source, for preflight, on-board, and vicarious calibration, and also for the calibration of radiometers used in data validation campaigns. The sun is the obvious choice in the solarreflective spectral range, perhaps most importantly because it is also the source used predominantly in remote sensing in that range. This paper has described some calibration procedures that can unify the various calibrations mentioned above. In all cases, the methods are at least as simple as older established methods and yield uncertainties which are less than 3%, 1s, with respect to the sun. The use of the sun allows international comparisons of remote sensing results on a more reliable basis than otherwise, particularly in the blue and the range from 1 to 2.5 mm where different national laboratories can differ by as much as 3% and 8%, 1s, respectively. The main limitations of this approach are that it: (1) only provides one point on the dynamic range of the instrument being calibrated, unless some known attenuator is used in the solar beam, as is the case for MODIS, and (2) the sun has to be conveniently available, which is not always the case, for example, in the space-sensor case. For these reasons, the use of lamps is still important but more in a relative than an absolute calibration sense: for monitoring intra-orbit response drifts and determining the BRDFs of diffusers to be used in space. In the case of absolute calibration in radiance units, Biggar (1998) shows an average relative difference between an irradiance calibration, using a 1-kW tungsten – halogen lamp calibrated by the NIST, in the USA, in irradiance, and a SRBC, of less than 0.75%. For four of the seven wavelengths, the differences are less than 0.5%. New values were used for exoatmospheric spectral irradiance from Thuillier et al. (1998). The latter were obtained using an entirely independent calibration path: a blackbody source whose temperature calibration was traced to the PTB, in Germany, by the use of a portable pyrometer. Older sets of exoatmospheric spectral irradiance values gave significantly larger differences. Thus, SRBC seems to hold the promise of providing high accuracy for preflight and in-flight satellite-sensor calibration, and for ground-based radiometer and aircraftsensor calibration.
Acknowledgments The authors wish to acknowledge continued support from NASA contract NAS5-31717, and support from
NASA grant NAGW-896. Other activities contributed substantially to this research including the SeaWiFS program, for which we thank Robert Barnes representing the SeaWiFS project office, and Alan Holmes of Santa Barbara Research Center, now Santa Barbara Remote Sensing (SBRS). John LaMarr is thanked for collecting the solar radiometer data mentioned in Section 4. Some of the early ratioing radiometer concepts were developed during the MODIS Phase-B and HIRIS programs and we wish to thank James Young and Stillman Chase (SBRS) and Edward Miller and David Norris of the Jet Propulsion Laboratory for their enthusiastic interest and support.
References Biggar, S. F. (1998). Calibration of a visible and near-infrared portable transfer radiometer (Special NEWRAD’97 issue). Metrologia, 35, 701 – 706. Biggar, S. F., & Slater, P. N. (1993). Preflight cross-calibration radiometer for EOS AM-1 platform visible and near-IR sources. Proceedings of SPIE-The International Society for Optical Engineering, 1939-24, 243 – 249. Biggar, S. F., Slater, P. N., Thome, K. J., Holmes, A. W., & Barnes, R.A (1993). Preflight solar-based calibration of SeaWiFS. Proceedings of SPIE-The International Society for Optical Engineering, 1939-23, 233 – 242. Bruegge, C. J., Stiegman, A. E., Rainen, R. A., & Springsteen, A. W. (1993). Use of Spectralon as a diffuse reflectance standard for in-flight calibration of earth-orbiting sensors. Optical Engineering, 32 (4), 805 – 814. Dinguirard, M., Briottet, X., Henry, P., Meygret, A., Slater, P. N., Santer, R., & Deuze, J. L. (this issue). Calibration of the SPOT HRV cameras. Personal Communication. Dinguirard, M., Mueller, J., Sirou, F., & Tremas, T. (1998). Comparison of ScaRaB ground calibration in the short-wave and long-wave spectral domains (Special NEWRAD’97 issue). Metrologia, 35, 597 – 601. Flittner, D. E., & Slater, P. N. (1991). Stability of narrow-band filter radiometers in the solar-reflective range. Photogrammetric Engineering and Remote Sensing, 57, 165 – 171. Guenther, B., Barnes, W., Knight, E., Barker, J., Harnden, J., Weber, R., Roberto, M., Godden, G., Montgomery, H., & Abel, P. (1996). MODIS calibration: A brief review of the strategy for the at-launch calibration approach. Journal of Atmospheric and Oceanic Technology, 13, 274 – 285. Guenther, B., McLean, J., Leroy, M., & Henry, P. (1990). Comparison of CNES spherical and NASA hemispherical large aperture integrating sources: I. Using a laboratory transfer radiometer. Remote Sensing of Environment, 31, 97 – 104. Guzman, C. T., Palmer, J. M., Slater, P. N., Bruegge, C. J., & Miller, E.A (1991). Requirements of a solar diffuser and measurements of some candidate materials. Proceedings of SPIE-The International Society for Optical Engineering, 1493-14, 120 – 131. Leroy, M., Henry, P., Guenther, B., & McLean, J. (1990). Comparison of CNES spherical and NASA hemispherical large aperture integrating sources: II. Using the SPOT-2 satellite instruments. Remote Sensing of Environment, 31, 97 – 104. Markham, B. L., Seifert, J. C., Smid, J., & Barker, J. L. (1998). Lifetime responsivity behavior of the Landsat-5 Thematic Mapper. Proceedings of SPIE-The International Society for Optical Engineering, 3427, 420 – 431. Neckel, H., & Labs, D. (1984). The solar radiation between 3300 and ˚ . Solar Physics, 90, 205 – 258. 12,500 A O’Mongain, E., Goodman, M., Reynolds, M., & Connor, C. B. (1983).
P.N. Slater et al. / Remote Sensing of Environment 77 (2001) 293–303 High accuracy calibration of optical imaging instruments in space. ESA Journal, 7, 299 – 309. Palmer, J. M. (1991). Stray light effects on calibrations using a solar diffuser. Proceedings of SPIE-The International Society for Optical Engineering, 1493-16, 143 – 154. Palmer, J. M., & Slater, P. N. (1991). A ratioing radiometer for use with a solar diffuser. Proceedings of SPIE-The International Society for Optical Engineering, 1493-13, 106 – 117. Slater, P. N., & Palmer, J. M. (1991). Solar-diffuser panel and ratioing radiometer approach to satellite sensor on-board calibration. Proceed-
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ings of SPIE-The International Society for Optical Engineering, 149312, 100 – 105. Thuillier, G., Herse´, M., Simon, P. C., Labs, D., Mandel, H., & Gillotay, D. (1998). Observation of the solar spectral irradiance from 200 to 870 nm during the Atlas 1 and Atlas 2 missions by the SOLSPEC spectrometer (Special NEWRAD’97). Metrologia, 35, 689 – 695. Walker, J. H., Saunders, R. D., Jackson, J. K., & Mielenz, K. D. (1991). Results of a CCPR intercomparison of spectral irradiance measurements by national laboratories. Journal of Research of the National Institute of Standards and Technology, 96-6, 647 – 668.
Unified approach to absolute radiometric calibration in the solar-reflective range Philip N. Slater1, Stuart F. Biggar*, James M. Palmer, Kurtis J. Thome Remote Sensing Group, Optical Sciences Center, University of Arizona, P.O. Box 210094, Tucson, AZ 85721-009, USA
Abstract The need is identified for a unified approach to the preflight and in-flight absolute radiometric calibration of satellite sensors, which does not depend on the accurate transfer of lamp and detector calibrations from the laboratory to orbit. Such an approach is described that uses the sun to provide the link between preflight solar radiation-based calibration (SRBC), in-flight solar diffuser-based calibration, and vicarious calibration. Examples are given of these methods and uncertainty estimates are provided. It is shown that an uncertainty, with respect to solar exoatmospheric irradiance, of < 3%, 1s, can be attained for each method and that each can, if needed, be accurately related to national laboratory standards. In addition to providing the link between preflight and in-flight on-board calibrations, this unified approach also fills the critical need to relate these calibrations to those of the radiometers used for vicarious calibration and data-product, field-validation measurements, by also referencing them to the same solar-irradiance scale. D 2001 Elsevier Science Inc. All rights reserved.
1. Introduction The need for a unified calibration strategy has been obvious since the idea of using a solar diffuser was generally accepted as being perhaps the best solution for on-board sensor calibration in the solar-reflective range. The problem the solar diffuser presented was that, in using the sun, it provided a calibration against an approximately 6000-K source while an approximately 3000-K source was used for preflight calibration. Not only are the color temperatures very different, resulting in different sensor responses if a small amount of integrated out-of-band response is present, but there are Fraunhofer lines in the solar spectrum that are not present in the output of a tungsten lamp. For sensors with bandpasses of about 10 nm or less, Flittner and Slater (1991) have shown that the effects of these absorption lines can be a few percent. The inappropriate output spectral distribution of lamps also creates a problem in attaining near-saturation levels for the sensor in the blue. Other problems relate to their
* Corresponding author. Tel.: +1-520-621-8168; fax: +1-520-6218292. E-mail addresses: [email protected] (P.N. Slater), [email protected] (S.F. Biggar). 1 Also corresponding author. Now retired and traveling a lot. Present address: 4051 E Bujia Primera, Tucson, AZ 85718, USA.
unreliability in transferring the preflight calibration to orbit because of the zero-g effect on gaseous convection within the lamp envelope and the vacuum conditions of orbit. Typically, lamps are only used for partial-aperture calibration and, in some cases, only illuminate the filtered focal plane. It is also difficult to check the stability of lamps in space. Finally, there are serious discrepancies, e.g., dispersions as high as 3% in the blue and 8%, in the shortwave infrared (see Fig. 1), between lamp calibrations performed by the various national laboratories. Thus, although lamps have been shown to be reliable on the SPOT and Landsat programs for relative calibration over periods in excess of 5 years, they are not appropriate sources for absolute calibration. Ideally, we need a single, stable source, available worldwide, that can be used for preflight, on-board, and vicarious calibration purposes and for data-product validation work. It should have the appropriate spectral distribution of output radiance. The choice is obviously the sun, the question is: how do we use the sun reliably and accurately for fullaperture preflight and in-flight calibration, and for the calibration of radiometers used in ground measurement campaigns and in aircraft? In Section 2, we show how solar radiation-based calibration (SRBC) can be used to unify the multiple calibration steps mentioned in the above question. We then review: (1) the use of SRBC to provide the preflight calibration of the
0034-4257/01/$ – see front matter D 2001 Elsevier Science Inc. All rights reserved. PII: S 0 0 3 4 - 4 2 5 7 ( 0 1 ) 0 0 2 1 0 - 3
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Fig. 1. Grand-mean differences from NIST of all participant’s spectral-irradiance measurements. CSIRO: Australia; ETL: Japan; INM: France; IOM: Spain; NIM: China; NIST: USA; NPL: UK; DPT: South Africa; NRC: Canada; OMH: Hungary; PTB: Germany; and VNIIOFI: Russia. Data from Walker et al. (1991).
sensor – solar – diffuser combination, (2) the simple extension of this procedure to calibrate aircraft and field radiometers, and (3) a method we have proposed for using a ratioing radiometer (RR) to check the stability of a solar diffuser for in-flight calibration. Uncertainty estimates are associated with each of these procedures.
laboratory. Note the on-board calibration is calibrated with respect to the SIS by using the sensor as a transfer radiometer (TR). It is becoming increasingly common now to cross-compare the output of SISs, used to cali-
2. Description of the unified method Fig. 2 shows how solar radiation can be used to unify preflight, on-board, and vicarious calibrations, and the calibration of radiometers used in validation campaigns. The horizontal dashed line separates calibrations conducted in space from those conducted on the ground or in the earth’s atmosphere. The vertical dashed line separates calibrations conducted with reference to the sun from those conducted with reference to lamps and detectors. It is interesting to note that the left- and right-hand sides of the diagram are entirely independent, and that the right-hand side describes the usual procedure followed to date. Until now, vicarious calibration and validation experiments have not been associated directly with preflight or in-flight calibrations or their radiometric scales. It is, of course, this important association that we are proposing to implement by the common use of the sun, as shown on the left-hand side of the diagram. The right-hand side of Fig. 2 shows the sphericalintegrating source (SIS), which creates a uniform radiance area, large enough to fill the aperture and field-of-view of the sensor and variable in its output to cover the dynamic range of the sensor. The SIS is typically calibrated by reference to a 1000-W tungsten lamp, whose calibration is traceable to a source or detector in a national standards
Fig. 2. SRBC and SIS calibration of a sensor. SD: solar diffuser; RR: ratioing radiometer; VC: vicarious calibration; TR: transfer radiometer.
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brate earth observation sensors, with other sources from other laboratories. The reason for this are the serious discrepancies, up to 8%, noted in recent years, Guenther et al. (1990) and Leroy et al. (1990). Biggar and Slater (1993) have shown that such cross-comparisons are best performed using ultra-stable, well-characterized, TRs. These provide accurate cross-comparisons as well as independent absolute calibrations by reference to standard lamps. The main limitation to their absolute accuracy is the uncertainty in the measurement of the filter transmittance. Trap detectors for the SWIR have not yet been perfected, but well-designed radiometers using liquidnitrogen cooling for the detector(s) can probably insure the necessary high stability. The two-way arrows in Fig. 2 are to indicate that a TR can be used, for example, to check the SIS calibration and also to relate it to the calibration of the vicarious calibration and validation radiometers and the SRBC of the sensor preflight. The use of the sun as the primary source does not entirely replace lamp-based, in-flight calibration. A limitation in the use of an on-board solar diffuser is that it can, at most, be used once an orbit when the sun – diffuser – sensor geometry is appropriate. This means it cannot be used to monitor intra-orbit changes induced, for example, by heating effects due to the spacecraft being alternately in the earth’s shadow and in the sun. Dinguirard et al. (this issue) and Markham et al. (1998) have shown that on-board lamps are useful for relative calibration, although not the best choice for use as sources for absolute calibration, for the reasons mentioned above. Lamps can be used very effectively for monitoring intra-orbit response changes, including the linearity (using multiple lamps) of the sensor.
3. Use of SRBC in the preflight calibration of a space sensor The radiance level of a diffuser panel above the atmosphere can be approximated at ground level in a simple manner. The radiance due to direct solar irradiance is given by Ldir sun = Lglobal Ldiffuse where Lglobal is the radiance due to irradiance directly from the sun plus the diffuse sky irradiance, and Ldiffuse is the diffuse sky irradiance, i.e., with the sun occulted. The direct solar irradiance Edir sun is determined using a solar radiometer to measure the atmospheric spectral transmittance along the path to the sun and by reference to the solar exoatmospheric irradiance as provided, e.g., by Neckel and Labs (1984). A correction, described later, has to be made in the determination of Ldir sun for the central small region of the solar aureole that is occulted unavoidably in the measurement of Ldiffuse. In the calibration, the radiances mentioned above are recorded as digital counts (DCs) by the instrument being calibrated. The top-of-the-atmosphere (TOA)
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DCs generated by the sensor under the same geometrical conditions is given by (Eq. (1)): DCTOA ðlÞ ¼ ¼
DCglobal ðlÞ DCdiffuse ðlÞ T ðlÞ DCdir sun ðlÞ T ðlÞ
ð1Þ
where T(l) is the transmittance along the slant path to the sun. An SRBC of a space sensor can be performed in several ways. One is to take the sensor outside, mounted in a fixture, that allows the solar diffuser to be aligned correctly with the sun, that is, in the same geometry to be used on orbit. The fixture is moved to track the sun during the calibration. The sensor is enclosed in a portable clean room with positive pressure and an opening just large enough to allow correct solar illumination of the diffuser. This procedure was followed successfully for SeaWiFS by Biggar, Slater, Thome, Holmes, and Barnes (1993). A different calibration procedure, but one using solar radiation, was used for the preflight calibration of ScaRaB. Dinguirard et al. (1998) estimate the uncertainty in the calibration of the 500– 700-nm channel to be about 5%. A proposed modification to the SeaWiFS procedure brings the solar beam into the laboratory using one or more mirrors, for example, a heliostat. In this case, the solar radiometer would be used to measure the total path transmittance including the mirrors. This would reduce the possibility of contamination of the sensor. An SRBC could be conducted with the sensor in a large vacuum tank if a suitable window was found and the sensor could be correctly positioned in the tank. An important characteristic of the SRBC is that it is unaffected by the presence of stray light on the diffuser reflected from surrounding structures and the instrument itself. Such stray light is usually present in both the DCglobal and DCdiffuse measurements and is therefore subtracted out. However, care must be taken to ensure that light reflected from the diffuser is not strongly reflected back on to the diffuser. Such a problem is only likely to exist due to the presence of a specular or large area, highly reflecting diffuse surfaces in proximity to the diffuser. This is an unlikely problem and stray reflections should be easy to baffle. The spectral transmittance of the atmosphere can be measured with satisfactory accuracy using a solar radiometer. Such instruments typically include about ten 10-nm spectral filters covering the range from about 400 to about 1000 nm. The conventional method for measuring the atmospheric transmittance involves using an uncalibrated radiometer and recording voltage measurements during a cloud-free morning. The slope of the resulting Langley plot of log voltage vs. air mass yields the spectral optical depth from which the spectral transmittance is immediately available. A limitation of this procedure is that it depends on cloud-free and stable atmospheric conditions for the entire
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morning of the sensor calibration. The use of a wellcalibrated radiometer reduces this dependancy. Then an instantaneous, or two-point, Langley plot can be constructed in which one point corresponds to a measurement made at the time that the diffuse and global measurements are being made and the other point is the zero intercept voltage obtained from the calibration of the instrument. The uncertainty of this approach depends primarily on the uncertainty in the calibration of the solar radiometer. In addition to the accuracy of calibration of the solar radiometer, the accuracy of the SRBC depends on the wavelength, the atmospheric conditions during the calibration, the error in measuring the solid angle subtended by the small occulting plate, and the errors in the correction for the blocked solar aureole. The spectral transmittance T(l) along the slant path to the sun is (Eq. (2)): T ðlÞ ¼ expðdðlÞ=ms Þ
ð2Þ
where d(l) is the spectral optical depth and ms cosqs where qs is the solar zenith angle. The fractional uncertainty in the transmittance is: DT ðlÞ DdðlÞ dðlÞsinqs Dqs þ T ðlÞ ms m2s
ð3Þ
where Dd(l) is the absolute uncertainty in the optical depth and Dqs is the uncertainty (in radians) in the knowledge of the solar zenith angle. The second term on the right of Eq. (3) is negligible compared to the first. The spectral extinction optical depth is the addition of the following component optical depths due to molecular scattering, aerosol scattering, ozone absorption, water vapor absorption, and absorption by other gases such as oxygen. The molecular optical depth is approximated by Rayleigh scattering and known from the barometric pressure. The extinction spectral optical depth is measured. The uncertainty is in the aerosol optical depth and extinction due to absorption. From previous analysis, it can be shown that the uncertainty is less than 3% of the difference between the extinction and molecular optical depth. For a nominal 23km visibility US standard atmosphere, this corresponds to a transmittance uncertainty of ± 2.7% to ± 1.4% for a solar zenith angle of 60 for wavelengths of about 400 and 900 nm, respectively. This uncertainty is reduced to ± 1.9% to ± 1.1% when the measurement is made at a solar zenith angle of 39. (A solar zenith angle of nearly 60 was used mid-morning in early March 1993 for a SeaWiFS calibration at Santa Barbara Research Center, California. Solar noon there on that day corresponded to a solar zenith angle of 39.) In general, the uncertainty is smaller the cleaner the atmosphere and the shorter the atmospheric path, i.e., the smaller the solar zenith angle and the higher the elevation. The uncertainties in the calibration attributable to the small occulting plate are smaller than those caused by the transmittance measurement. These uncertainties cannot be accurately forecast without details on the geometry of the
sensor’s diffuser and the size of the occulting plate. The size of the latter depends on the entrance aperture. For SeaWiFS, the estimated uncertainties were ± 0.8% after correction for the DCglobal DCdiffuse measurement, and ± 0.4% corresponding to the uncertainty of ± 0.25 for the angle of incidence on the diffuser. Summarizing, using the calibrated solar radiometer approach, the uncertainty is primarily due to the uncertainty in the calibration of the radiometer. In the Langley plot method, the total uncertainty is ± 2.8% to ± 1.4% at a solar zenith angle of 60 and ± 1.9% to 1.1% for a zenith angle of 39. These uncertainties are 1s with respect to the sun. The uncertainty of the exoatmospheric solar irradiance has to be accounted for if there is a need to convert the calibration and its uncertainty into physical units, e.g., of spectral radiance. Neckel and Labs (1984) claim an uncertainty of < ± 1% in the range 400 to 1250 nm; unfortunately this is difficult to verify. As for all calibration activities, it is prudent to validate results by reference to results derived from an independent method. For the SRBC, a recommended independent method is to measure the radiance of the diffuser panel using a TR immediately before and after the SRBC measurements. This will allow a correction to be made for the small change in the angle of incidence on the diffuser between measurements. Such validation measurements will help ensure that there are no systematic errors introduced in the SRBC, e.g., due to sensor geometry effects. A further discussion of this subject can be found in Section 5.3. However, because these effects are sensor design-specific, they are only discussed briefly.
4. Extension of the method to calibrate other radiometers The extension of the above method to aircraft and field radiometers is conceptually straightforward. In these cases, the solar diffuser, which was integral with the space sensor in the above example, is replaced by a diffuse reflecting panel whose BRDF has been accurately measured in the laboratory. The sun-illuminated diffuser is accurately leveled beneath the radiometer of interest. In the aircraft case, this will involve correctly positioning the aircraft so the diffuser is sun-illuminated when placed beneath the sensor. There may be the possibility of light from the diffuser being specularly reflected off the fuselage to be incident on the diffuser for the Lglobal but not the Ldiffuse measurements. Masking the reflection or blackening the appropriate area of the fuselage may then be necessary. A precise laboratory TR was calibrated to test this concept. The test procedure is shown on the right-hand side of Fig. 3. The TR is a seven-band, interference-filter-based radiometer with a silicon ‘‘trap’’ detector assembly (Biggar & Slater, 1993). The filter bandpasses are between 10 and 15 nm. The TR has no imaging optics and the throughput is
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Fig. 3. Procedure to compare the exo-atmospheric spectral irradiance measurements of Biggar (1998) and Thuillier et al. (1998).
determined by two apertures spaced by invar rods. The second aperture is at the detector assembly and the first (front) aperture is removable to allow calibration and use in the irradiance mode. With the front aperture in place, the TR measures in a radiance mode. The TR detector, electronics, and filters are temperature-stabilized at about 303 K. The TR was calibrated in the laboratory by reference to a National Institute of Standards and Technology (NIST)supplied standard of spectral irradiance, F-330 (a 1-kW FEL-type halogen lamp operated at 7.9-A DC). The spectral irradiance calibration of the lamp was interpolated to the TR wavelengths by use of a ‘‘Wien’’ type distribution with a polynomial correction term as suggested by the NIST. The front aperture was removed for the irradiance calibration and the aperture was reinstalled for the SRBC. The laboratory irradiance calibration was used with knowledge of the geometry to calculate a radiance mode calibration. The calibration was then compared to the radiance mode calibration derived from a solar calibration. The experiment was done outside our laboratory in Tucson, AZ on 1996 March 19 in the late morning. Sky conditions were clear. The TR was positioned such that the optical axis was normal to, and centered on, a 0.61-m2, painted barium sulphate reflectance panel, leveled with respect to the local horizontal. A solar radiometer, with 10 filters of width approximately 10 nm, was used during the
morning to determine extinction optical depth at the solar radiometer wavelengths. These data were used along with atmospheric pressure to estimate the optical depth components (Rayleigh, aerosol, and ozone) at the laboratory TR wavelengths. From the optical depth components, an inband transmittance was computed for each of the TR bands. Measurements of the TR output voltage were made for each band with the panel illuminated by the direct sun and diffuse skylight and then with the direct beam of the sun blocked by a ‘‘parasol’’ consisting of a blackened aluminum plate about 0.6 m2 mounted on the end of a pole at an angle adjusted so that the panel was perpendicular to the direct beam from the sun. These two measurements, each corrected for ‘‘dark’’ current, were subtracted to give the attenuated direct-solar irradiance. The in-band transmittance determined from the solar extinction measurements was applied to the bandaveraged exoatmospheric solar irradiance to calculate the solar irradiance on the panel. The panel directional reflectance was previously determined in the laboratory and these values spectrally interpolated to TR wavelengths. From the irradiance, the solar zenith angle at the time of measurement, and the directional reflectance, the in-band radiance from the panel was calculated and used to determine a radiance calibration coefficient. Sources of uncertainty greater than or equal to 0.5% are tabulated in Table 1. The values in parentheses show the
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extent of expected reductions in the uncertainties in the near future. For example, the atmospheric transmittance uncertainties can be reduced by the use of an improved solar radiometer, the BRDF measurements can be made more accurately with a better current control of the source and a better amplifier for the radiometer, and the Optronic transmittance uncertainties can be reduced with a more precise amplifier. Note also in Table 1 that each source estimated or known to be less than 0.5% has been omitted, however, each contribution is included in the final root-sum-square value. (Omitted quantities are: Optronic source stability; source error due to 0.05% wavelength uncertainty and 0.01% wavelength repeatability; filter shift due to measurement geometry; filter nonuniformity; finite spectrometer bandwidth; angular sensitivity of TR; amplifier gain settings; voltmeter uncertainties; and spectral out-of band errors. Together they have a negligible effect on the final RSS value.) Many of these uncertainties are wavelength dependent, however, the largest error source (amplifier uncertainty in an Optronic 750M used for filter measurement) is not. A similar table for the laboratory calibration is given as Table 2. (With the exception of the spectral out-of-band errors, all the < 0.5% errors mentioned above have also been omitted from Table 2. In this case, there are also small unlisted errors due to lamp current uncertainty and stability, lamp distance, and lamp angular alignment. Again these unlisted errors have been included in the final RSS value.) For a radiance calibration, using a diffuser, the total uncertainties increase by 0.8% at both wavelengths. Table 3 lists differences between radiances measured from a reflectance panel using the TR and two sets of solar irradiance values (Biggar, 1998). The agreement is excellent, exceeding what we might expect as a result of the uncertainties listed in Table 1, and this in spite of the use of two completely independent calibration paths: Biggar (1998) used a lamp calibrated by the NIST for his reference, while Thuillier et al. (1998) used a blackbody source whose temperature was referenced to Physikalisch – Technische Table 1 Uncertainty estimate for the radiance mode calibration of the laboratory TR with reference to the sun Wavelength (nm)
412.8
666.6
Solar spectral irradiance uncertainty (Neckel and Labs quoted uncertainty) Transmittance errors (based on solar radiometer intercept history) BRDF of diffuser panel (estimated for our laboratory-referenced to pressed polytetraflouroethylene) Filter transmittance (terms included) Optronic 750 M amplifier inaccuracy (1% spec.) Filter temperature stability/uniformity(estimate) Stray light (in the TR-estimate) Out of field-of-view (measurement) Total RSS (RSS with improvements)
1.0
1.0
2.0 (1.0)
1.1 (0.6)
2.0 (1.0)
2.0 (1.0)
1.4 (0.1) 0.5 0.5 0.5 3.5 (2.0)
1.4 (0.1) 0.5 0.5 0.5 3.0 (1.8)
Uncertainties are given in percent (1s if stated in the manufacturer’s data). Items with a second figure in parentheses are values with improvements (see text for mention of other sources of uncertainty).
Table 2 Uncertainty estimate for the radiance mode calibration of the laboratory TR with reference to an NIST standard of spectral irradiance Wavelength (nm) Lamp uncertainties (NIST FEL irradiance standard, F-330) Irradiance calibration uncertainty Spectral interpolation uncertainty Uncertainty in lamp-distance scaling (1/r2) Lamp ageing and drift (estimate) Filter transmittance (terms included) Optronic 750 M amplifier inaccuracy (1% spec.) Filter temperature stability/uniformity (estimate) Front aperture area (5 mm diameter uncertainty) Stray light (in the TR-estimate) Out of field-of-view (measurement) Spectral out-of-band (out-of-band response to lamp vs. sun) Total RSS (RSS with improvements)
412.8
666.6
0.5 0.5 0.6
0.5 0.5 0.6
0.5
0.2
1.4 (0.1)
1.4 (0.1)
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.1
0.9
2.1 (1.6)
2.2 (1.7)
Uncertainties are given in percent (1s if stated in the manufacturer’s data). Items with a second figure in parentheses are values with improvements (see text for mention of other sources of uncertainty).
Bundesanstalt (PTB) (see the left-hand side of Fig. 3). It should be noted that the lamp-derived results listed in Table 3 used the irradiance calibration results. This was because the irradiance method is of smaller uncertainty, not involving a BRDF characterization. It is interesting to note that Biggar agrees better with Thuillier et al. than with Neckel and Labs over the radiometer’s spectral range. In summary, the component uncertainties associated with the SRBC of field and aircraft-mounted radiometers are similar to those mentioned in Section 3. The total uncertainties may be about the same or even smaller, making the technique generally applicable for remote sensing work. It is of interest to note that for field and aircraft-mounted radiometers, the additional uncertainty of about ± 1% associated with the knowledge of the reflectance of the diffuser, may be offset by a reduction in the uncertainty in the atmospheric transmittance. This can be achieved by conducting the calibration at high elevation and near solar noon during the summer. As with SeaWiFS, neither of these may be possible in the general case of the preflight calibration of a space sensor.
5. On-board calibration using a solar diffuser and RR The desirable characteristics of an on-board calibration system are that it should:
Provide a complete system, or end-to-end, calibration Make use of the full aperture of the system
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Table 3 Percent differences between measured radiances from a reflectance panel and those predicted from solar irradiance tables of Neckel and Labs (1984) and Thuillier et al. (1998) Percent differences for the given wavelength (nm) Source of values for exoatmospheric solar spectral irradiance
413
442
488
550
667
747
868
Neckel and Labs values in (SRBC lamp)/lamp Thuillier et al. values in (SRBC lamp)/lamp
0.46 1.17
2.26 0.48
3.17 0.01
0.73 0.35
0.28 0.41
2.00 0.69
1.94 2.10
Make use of the full field-of-view of the system Provide at least one value near the top and the bottom of the sensor’s dynamic range
Preferably the on-board system should be complemented by one or more independent in-flight methods to attempt to identify systematic errors which would otherwise be impossible to detect.
period was not described, but it is the first discussion found that proposes a ratioing method. The method proposed here uses a radiometer in a ratioing mode (Slater & Palmer, 1991) to view the sun and the diffuser alternately during the calibration of the sensor of interest, as shown in Fig. 4. The same basic principle is being used for the Moderate Resolution Imaging Spectroradiometer (MODIS) (Guenther et al., 1996), however, in this case, a metal plate containing an array of small apertures is placed in front of the monitor to attenuate the direct solar beam.
5.1. Characteristics of a solar diffuser 5.2. The RR concept A method which has often been suggested to meet the above-listed characteristics involves the use of a solardiffuser panel. Simply, a flat plate with high, near-lambertian reflectance over the spectral range of interest is located at an appropriate angle to the solar direction (usually between 45 and 60 to obtain a full-scale calibration) and at a smaller angle, preferably 0, to the optical axis of the sensor during the calibration period. It should be at least a little larger than the projected area of the sensor’s aperture to fill the field-of-view of the sensor. Ideally, a knowledge of the spectral bidirectional reflectance of the diffuser, the solar incidence angle, and the exoatmospheric spectral irradiance is all that is needed for the spectral radiance of the diffuser to be calculated. By changing the angle of incidence to the diffuser, a number of different radiance levels can be obtained. A look at deep space, or an on-board black surface, is also required to provide a zero radiance level. The graph of radiance levels vs. sensor-output DCs allows the gains and offsets for the sensor’s calibration equation to be determined. The drawback to using a solar-diffuser panel is that we cannot accurately predict the changes in radiance of the diffuser with conditions on orbit. In particular, effects of reflectance loss with proton and high-UV irradiance, stray reflections falling on the diffuser from other illuminated surfaces on the instrument or spacecraft, and UV-induced luminescence effects cannot be accurately predicted. The simplest solution to the problem is to monitor the diffuser radiance directly with a radiometer. However, the stability of the radiometer will always be in question. A conceptual solution, suggested by O’Mongain et al. (1983), to the problem uses an integrating sphere, externally baffled to define the field-of-view, to view alternately the diffuser and the sun. Differently filtered detectors sample the radiance within the sphere. The implementation of this arrangement to monitor diffuser radiance during the sensor calibration
A simple radiometer that images the surface of interest on a detector with a single lens is not a suitable design, mainly because the ratio of irradiances on the detector will be about 10,000:1, creating an extraordinary demand for instrument linearity. To avoid this problem, the radiometer can follow the design originally due to Ko¨hler for substage microscope condensers. A field lens is located at the focus of the objective lens to image the uniformly illuminated aperture of the objective onto the detector plane (Fig. 5). This arrangement provides uniform irradiance over the radiometer’s field-of-view, even though a source of small angular extent, the sun, is viewed in one case. When the acceptance angle of the radiometer is sufficient to nearly fill the area of the diffuser, Palmer and Slater (1991) showed the ratio of the signal output from the radiometer viewing the sun to that when viewing the diffuser, RRR, is: RRR ¼
p rP VcosqP
ð4Þ
where rP is the diffuser panel directional – hemispherical reflectance, V is the solid angle field-of-view or acceptance
Fig. 4. Layout of solar-diffuser panel and RR for in-flight calibration.
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Fig. 5. Ko¨hler layout of the RR.
angle of the radiometer, and qP is the angle between the sun and the normal to the solar diffuser. To reduce the ratio of about 10,000:1, mentioned above, to a more manageable ratio of about 20:1, the full field-of-view should be about 30 for a 45 solar incidence angle and a high reflectance diffuser. Because of the near-lambertian characteristics of the diffuser panel, its bidirectional reflectance, rP, can be written: rP ¼
pLP d 2 EcosqP
ð5Þ
where LP is the panel radiance and d is the Earth –Sun distance in Astronomical Units. The quantity of interest in many remote sensing investigations is the bidirectional spectral albedo, A(q, f; l), of the Earth – Atmosphere (EA) system. This is also sometimes referred to as the apparent reflectance r*. If, for simplicity, the albedo is assumed to be close to lambertian, then Eq. (5) can be written: Aðqz ; f; lÞ ¼
pLEA d 2 Ecosqz
ð6Þ
where LEA is the radiance of the EA system, and Ecosqz is the solar exoatmospheric irradiance on the EA system at a solar zenith angle of qz. If we assume that DCEA = kLEA, and DCP = kLP, where DCEA and DCP are the DCs recorded by the sensor when observing the EA system and the solardiffuser panel, respectively, and k is the calibration coefficient for the sensor, then by the use of these equations, together with Eqs. (4), (5), and (6) we can determine the following relationship: Aðqz ; f; lÞ ¼
p DCEA RRR Vcosqz DCP
to be illuminated only by direct sunlight or by stray light off the sensor or other parts of the spacecraft as well. In the no-stray-light mode, the diffuser radiance can be calculated from the knowledge of the exoatmospheric solar irradiance, the BRDF of the diffuser, and the angle of incidence on the diffuser. A change in the diffuser reflectance is detected from a change in the ratio of diffuser-to-sun signals and the new value for the diffuser radiance is calculated. In the mode when stray light is anticipated, the diffuser radiance can be calculated by reference to a preflight calibration of the sun-to-diffuser ratio. This ratio may be determined by accurately measuring the solid angle of the radiometer’s field-of-view and the diffuser reflectance and, if possible, conducting an SRBC as described earlier. For both modes the assumptions are mentioned below. (1) Stray light must not enter the field-of-view of the radiometer when it observes either the sun or diffuser. (2) During the sensor’s lifetime, either the loss in reflectance of the diffuser is not accompanied by a change in the shape of its BRDF, or the angles of incidence of the radiometer and the sensor at the diffuser are equal. For the no-stray-light mode only, the assumption is: (3) The diffuser does not change in reflectance from its preflight measured value during the first calibration on orbit. Subsequent calibrations are all done with respect to this calibration. A result of this assumption is that no preflight calibration or determination of the sun-to-diffuser ratio is needed. An important advantage of the above design is that several differently filtered detectors can be placed in the uniformly irradiated focal plane, thus allowing for the monitoring of the spectral radiance of the diffuser, Biggar (1998). The selection of the spectral channels for the RR is based on the need to maximize the science return from the multi- or hyper-spectral sensor consistent with minimizing the complexity, cost, and data quantity from the RR. We need:
ð7Þ
where qz and f are the solar zenith and view angles for the area of the EA system being observed. Eq. (7) is the basic equation for determining bidirectional spectral albedo from a sensor using a RR and diffuser panel. Note that it is only valid for observations made in time intervals that are short compared to changes in the calibration of the system and the reflectance of the solar-diffuser panel. RR measurements have to be made periodically to update the calibration of the sensor. Note that, because of the ratioing measurement that is made, neither Eq. (4) nor Eq. (7) is a function of the solar exoatmospheric irradiance or the Earth –Sun distance. 5.3. Operating modes and design considerations The RR – solar diffuser system can be used in two operational modes depending on whether the diffuser is expected
Continuous coverage, 400 –2500 nm. Ability to monitor slowly changing solar diffuser spectral reflectance with wavelength. Ability to monitor rapidly changing solar diffuser spectral reflectance with time.
Inspection of selected data on the emission spectrum of typical organic dyes indicates that they usually emit over the visible range from 400 to about 700 nm with a half-width of about 50 nm. This means that 50-nm bandwidth coverage of the detectors will be sufficient over this range. Initial measurements of the spectral reflectance of solar diffuser material candidates made by Bruegge et al. (1993) and Guzman et al. (1991), show relatively slow changes in spectral reflectance with wavelength, the most noticeable changes occurring at short wavelengths. As a result, the bandwidths tentatively proposed are 50-nm wide from 400–
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700 nm, 100-nm wide from 700 – 1000 nm, and 500-nm wide above 1000 nm. It will be necessary to place 12 detectors in relatively close quarters such that all are irradiated uniformly. A focal plane 22 mm in diameter can accommodate nine silicon detectors, each 3 mm2, for the first nine spectral channels, covering the range 400– 1000 nm, and three infrared detectors up to 5 mm2. Candidate detectors include germanium (Ge), indium gallium arsenide (InGaAs), indium arsenide (InAs), and mercury – cadmium – telluride (MCT). Bandpass interference filters would be installed on each detector to provide the desired spectral band coverage. Cooling will also be mandatory for the IR detectors and desirable for the Si detectors as well. A thermoelectric cooler is the best choice, as the cooling requirements are not stringent. An analysis of the signal-to-noise ratio (SNR) expected from an RR built to these tentative specifications was made. Assumptions were made regarding RR size (aperture area), the band-limited solar spectrum, the solar diffuser spectral reflectance, typical detector areas and NEPs, and the RR field-of-view. The SNR is greater than 104 for all bands in the solar view and greater than 103 for all bands in the solar diffuser view. The positioning of the RR is of importance. It must be in a location such that it can see the solar diffuser simultaneously with the sensor and not obstruct the sensor’s view. It must also be able to look at the sun with an unobstructed view. A suitable location may be found, on the leading edge of the unit containing the sensor. From this position, the internal optics can be scanned with a single, simple motor drive to look in three directions: (1) stowed for dark calibration (2) out front for direct solar view, and (3) toward the solar diffuser. Positions (1) and (3) are fixed with hard, mechanical stops for repeatable positioning. Position (2) must be variable to adjust the solar view to exclude platform reflections and earthshine.
5.4. Other operational considerations and estimated uncertainties Since the RR is always operated in a ratioing mode, calibrating itself against the sun and then transferring that calibration to the diffuser, the stability requirements are modest. It is essential that the RR field-of-view remain constant with time, temperature, etc., and that the field-ofview is uniform for solar viewing. Degradations that one might encounter in orbit will not affect the RR results. It should be stable in the presence of the solar UV; stable UV blockers can prevent the UV from degrading the interference filters used to define the spectral bandwidths. The only problem that is apparent from contamination is if a contaminant, which exhibits solar-induced luminescence, is deposited on the optics. Its influence will be much greater during solar view than during solar diffuser view, rendering
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the ratio incorrect. The RR has a duty cycle of 0.0007, based on an average of one calibration, of 5-min duration, every 5 days through a 5-year mission lifetime. The total exposure is thus about 35 h, when the initial data, described below, are included. The optics will be stowed the rest of the time, minimizing the possibility of platform contaminants reaching the optics. The RR should be used frequently during the first few weeks of sensor operation. It is suggested that a calibration be performed twice per day, or once every eight orbits, for the first week to track degradations in the solar diffuser and in the sensor. For the next several weeks, a calibration is suggested once per day. When sufficient experience has been obtained, the rate can be reduced to the abovementioned once per 5 days for the mission duration. Careful planning is required to determine when the first calibration should take place. It is desirable that the entire platform undergo an initial stabilization period, when most of the component and system outgassing occurs, to minimize contamination of the RR, the sensor, and the solar diffuser. The calibration cycle should not start until after this initial period. Whenever the RR is not in operation, the optics should be protected from the surrounding environment. Similarly, the solar diffuser should be stowed when not in use to protect it from contamination and solar radiation. Palmer (1991) has demonstrated that stray light effects from both the platform and earthshine can significantly change the irradiance on the solar diffuser, often unpredictably. The RR is also subject to some stray light effects, but inasmuch as the field-of-view is restricted, the effects are different. In the solar diffuser view, baffling should prevent the RR from being subject to out-of-field stray light effects. The solar diffuser fills the field-of-view, and there are no other in-field sources available to irradiate the focal plane of the RR. Of course, the RR measures the solar diffuser radiance from the sun and all the stray sources, but so does the sensor. We need to know the solar diffuser radiance during the sensor’s calibration, including that due to stray light and luminescence, and the RR does just that. During the solar view, the RR is subject to stray radiation due to reflections from the platform and due to earthshine. The location and timing of the operation of the sensor must be such that for any calibration angle, from before the terminator to the end of the calibration window, the RR can be pointed to avoid both earthshine and reflections from the platform. This may mean that the RR look angle must be set for each calibration, coordinated with the calibration angle. Estimates of the uncertainties introduced by the RR and the solar diffuser are hard to make because they are certain to differ for specific sensors depending on the location of the solar diffuser and RR with respect to sources of stray light, and other variables such as contamination types and concentrations. Palmer estimated that, if no RR were used, the uncertainty in the calibration
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could be about 15% and the use of an RR could reduce this figure to about 2%.
6. Concluding remarks There is a compelling need in quantitative remote sensing to use a unified approach to radiometric calibration, one that uses a universally available, single, stable source, for preflight, on-board, and vicarious calibration, and also for the calibration of radiometers used in data validation campaigns. The sun is the obvious choice in the solarreflective spectral range, perhaps most importantly because it is also the source used predominantly in remote sensing in that range. This paper has described some calibration procedures that can unify the various calibrations mentioned above. In all cases, the methods are at least as simple as older established methods and yield uncertainties which are less than 3%, 1s, with respect to the sun. The use of the sun allows international comparisons of remote sensing results on a more reliable basis than otherwise, particularly in the blue and the range from 1 to 2.5 mm where different national laboratories can differ by as much as 3% and 8%, 1s, respectively. The main limitations of this approach are that it: (1) only provides one point on the dynamic range of the instrument being calibrated, unless some known attenuator is used in the solar beam, as is the case for MODIS, and (2) the sun has to be conveniently available, which is not always the case, for example, in the space-sensor case. For these reasons, the use of lamps is still important but more in a relative than an absolute calibration sense: for monitoring intra-orbit response drifts and determining the BRDFs of diffusers to be used in space. In the case of absolute calibration in radiance units, Biggar (1998) shows an average relative difference between an irradiance calibration, using a 1-kW tungsten – halogen lamp calibrated by the NIST, in the USA, in irradiance, and a SRBC, of less than 0.75%. For four of the seven wavelengths, the differences are less than 0.5%. New values were used for exoatmospheric spectral irradiance from Thuillier et al. (1998). The latter were obtained using an entirely independent calibration path: a blackbody source whose temperature calibration was traced to the PTB, in Germany, by the use of a portable pyrometer. Older sets of exoatmospheric spectral irradiance values gave significantly larger differences. Thus, SRBC seems to hold the promise of providing high accuracy for preflight and in-flight satellite-sensor calibration, and for ground-based radiometer and aircraftsensor calibration.
Acknowledgments The authors wish to acknowledge continued support from NASA contract NAS5-31717, and support from
NASA grant NAGW-896. Other activities contributed substantially to this research including the SeaWiFS program, for which we thank Robert Barnes representing the SeaWiFS project office, and Alan Holmes of Santa Barbara Research Center, now Santa Barbara Remote Sensing (SBRS). John LaMarr is thanked for collecting the solar radiometer data mentioned in Section 4. Some of the early ratioing radiometer concepts were developed during the MODIS Phase-B and HIRIS programs and we wish to thank James Young and Stillman Chase (SBRS) and Edward Miller and David Norris of the Jet Propulsion Laboratory for their enthusiastic interest and support.
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