Definition

Calibration. A set of operations that establish, under specified conditions, the relationship between values indicated by a measuring instrument and the corresponding known values of a standard. For remote sensors, this typically implies the radiometric, spectral, and geometric characterization of an instrument as needed to understand the impact of the instrument’s performance on the data or the derived data products.

Calibration factors are determined by comparison with a standard whose output is known in accepted physical units as part of the Système International d’Unités (abbreviated SI). Units are based on the metric-kilogram-second (mks) system and include the Kelvin, for temperature, and Watt, for power. Derived radiometric parameters are listed in Table 1.

Table 1 Common radiometric parameters
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The calibration parameters derived for a sensor must be reported with the associated uncertainty and confidence level. The uncertainty analysis needs to establish both the precision and absolute uncertainty. The precision of the calibration is the consistency with repeated measurements. The absolute calibration is determined by the sensor’s response to stable standards. These should be related to international or national standards through an unbroken chain of comparisons. The confidence level is an interval about the result of a measurement within which the true value is expected to lie, as determined from an uncertainty analysis with a specified probability. A 3σ (sigma) confidence level implies that the stated uncertainty is achieved with 99 % probability.

Introduction

During the sensor development phase, the science and engineering teams first agree to set calibration requirements and a calibration approach. Absolute calibration requirements of 3–5 % (1σ) uncertainty are considered state of the art. Higher accuracy is typically specified for channel-relative or pixel-relative measurements. The accuracy is limited due to instrument-specific attributes, such as stray-light, out-of-field response, polarization sensitivity, scan-mirror sensitivity, linearity, signal-to-noise, temperature sensitivity, dark offset, and long-term stability. Radiometric uncertainty is increased when these effects alter the imagery and recorded signals in unpredictable ways.

Testing is conducted throughout the lifetime of the sensor. Characterizations of the filter and detector components provide early assurance that design requirements will be met. Preflight testing at the instrument level, before assembly onto the spacecraft, allows many parameters to be determined, which cannot be established on-orbit. This testing period is crucial to understanding the as-built performance. Following this, the program must commit to an on-orbit calibration plan. This allows response degradation, due to the browning of the optical elements or throughput change due to radiation damage, to be monitored. An adequate on-orbit calibration program will allow accurate radiance products to be reported even in the presence of sensor degradation. Both preflight and on-orbit calibrations are essential. An overview of the preflight testing for the Multi-angle Imaging SpectroRadiometer (MISR) is given by Bruegge et al. (2002).

Spectral response function

Most remote sensing systems measure incident light using several channels, where each channel is designed with a specified color sensitivity. That is, the instrument’s per-channel output is designed to be a function of both the amount of incident light, as well as its wavelength. The color selection may be achieved by using spectral filters within the instrument, or may be accomplished by use of a grating that disperses light according to the wavelength. In either case, the spectral response function (SRF) must be determined for each channel. This is a measure of the instrument’s output as a function of the incident wavelength of light. The distribution only needs to be known in a relative sense, and is typically normalized to unity at the wavelength of peak response.

The SRF is measured using a test setup that can illuminate an instrument with monochromatic light, and where the wavelength of light can be varied during the test. The characterization should measure both the in-band response, near the region of peak sensitivity, and also the far-wing response. The hardware used is most commonly a monochromator. For instruments with very narrow spectral response functions, a tunable diode laser can be used, or Fourier Transform Interferometer (Strow et al., 2003). In either case, it is imperative that the system response be measured. It is insufficient to substitute the filter transmittance for this response, as all optical components, as well as the detector itself, contribute to the SRF.

It is common practice to summarize a sensor’s spectral properties by tabulating the center wavelength and spectral width. This has been done by quoting the wavelength-of-peak response and full-width at half-maximum (FWHM). The latter is the wavelength at which the response falls to half of its peak value. These parameters can be misleading in cases where the SRF may be double peaked, asymmetric, or have a large out-of-band response. A better representation can be obtained from an equivalent square-band response analysis (Palmer, 1984). Here the sensor spectral response function is replaced with a function of equivalent area, but with an effective amplitude Rn and a throughput of 0 at wavelengths less than a computed minimum wavelength or greater than a computed maximum wavelength. Figure 1 gives an example of an SRF and square-band equivalent. The example is of Landsat-4, TM band 2 channel.

Figure 1
figure 1

Spectral response function and moments-derived center wavelength and width for a typical detector.

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Radiometric calibration

Band-averaged radiances

Typically, raw data (digital numbers, or DN) from a sensor are converted to radiance units by knowledge of the gain coefficient. An example might be

$$ DN-D{N_0}={{\bar{L}}_{\lambda }}\cdot G $$
(1)

where

  • DN is the sensor output count

  • DN0 is the dark-scene output count

  • \( {{\bar{L}}_{\lambda }} \) is the band-weighted spectral radiance incident onto the sensor (W m−2 sr−1 μm−1)

  • and G is the radiometric response coefficient (DN/[W m−2 sr−1 μm−1])

A precise determination of the band-weighted radiance would require knowledge of both the spectral content of the incident light as well as the sensor spectral response function, Rλ. The band-weighted incident radiance is as follows:

$$ {{\bar{L}}_{\lambda }}=\frac{{\int {{L_{\lambda }}{R_{\lambda }}\partial \lambda } }}{{\int {{R_{\lambda }}\partial \lambda } }} $$
(2)

For calibration, the gain, G, is computed with complete knowledge of the SRF and source spectral radiance. For radiance retrieval and science product generation, where output digital numbers are converted into radiances, the spectral content of the scene is not retrieved, rather only a band-weighted average.

Standards

The test equipment associated with a radiometric calibration requires an extended, spatially uniform, and spectrally smooth light source. A blackbody radiator is the most widely used source for infrared calibration. Its use in the visible, UV, and near-IR is limited. For these wavelengths, an integrating sphere or lamp and diffuse reflector fixture is more typical. The source must be larger than the geometric field of view of the sensor to be tested. This is to capture stray and diffracted light that will contribute to the output. Point sources of light are suitable for measuring a system’s point spread function response, but are not suitable as radiometric targets.

If the source is an integrating sphere, its output needs to be calibrated by use of a transfer detector. The detector is, in turn, calibrated against a source standard. Standard filament lamps are commercially available. The manufacturer typically seasons them by operating for 30 h. Lamps with output fluctuations are discarded. Suitable lamps are calibrated against a working standard that has a calibration traceable to national standards. These lamps can have accuracies approaching 1 % (2σ). Schneider and Goebel (1984) provide a review of standards.

On-orbit calibration

In-flight calibration is best accomplished using multiple technologies. Data from an on-board calibrator (OBC), for one, can provide the most frequent verification of sensor performance and stability. These systems can be used to make frequent checks on performance. Sampling dark current or the response to an attenuated view of the sun, for example, can be made once per orbit. As the OBC can itself degrade on-orbit, scene-viewing techniques are also required. Although considered the definitive validation of sensor performance, measurements are less frequent due to constraints associated with imagery collection. Scene studies can be as simple as observations of an un-instrumented desert site, or a highly accurate measurement of a site’s in situ observations, and involving a field team or a network. Coastlines and contrasts edges can be used to confirm channel geo-location and co-registration. The SeaWiFs sensor makes use of lunar observations to track relative degradation changes (Eplee et al., 2001). Finally, cross-comparisons with sensors of similar footprints and bandpasses provide convincing error estimations. The comparison of radiances as determined from all techniques allows radiance uncertainty to be determined.

On-board calibrators

Examples of on-board calibrators can be found on EOS/Terra spacecraft sensors. The Multi-angle Imaging SpectroRadiometer (MISR) makes use of two deployable Spectralon diffuse targets. These are used to reflect sunlight into the earth-observing cameras. The panels have proven to be radiometrically stable on-orbit (Chrien et al., 2002). This is attributed to cleanliness and proper handling procedures that avoid exposure to contaminants (Stiegman et al., 1993). The panels are monitored by detector standards. Both radiation-resistant and high-quantum efficient detectors are utilized. The latter are intended to provide a measure of the incident light based upon physical principles, rather than transfer calibration using a standard source. In practice, detector stability has proven to be the driving criteria for detector selection.

The MODerate resolution Imaging SpectroRadiometer (MODIS), also on the Terra spacecraft, makes use of several on-board calibrator systems. These include a blackbody (BB) radiator, solar diffuser (SD), a solar-diffuse stability monitor, and the spectroradiometric calibration assembly (SRCA). The BB is the prime calibration source for the thermal bands located from 3.5 to 14.4 μm, while the SD provides a diffuse, solar-illuminated calibration source or the visible, near-infrared, and shortwave infrared bands (0.4 μm ≤ λ < 2.2 μm). The SDSM tracks changes in the reflectance of the SD via reference to the sun so that potential instrument changes are not incorrectly attributed to changes in this calibration source. The SRCA is a very complex, multifunction calibration instrument that provides in-flight spectral, radiometric, and spatial calibration.

Unattended desert sites

The Sahara desert sites are considered stable with time. These sites have only small amounts of vegetation, are sparsely populated, and are typically found with clear-sky and low-aerosol conditions. Many instrument teams use these targets to monitor sensor degradation with time (Cosnefroy et al., 1996). Routine observations of sites such as Egypt_1 (26.10 East longitude, 27.12 North latitude) can be trended in order to determine the response degradation for a channel with time. Data are normalized by cosine of the solar zenith angle and the Earth–Sun distance. Observations are trended that are acquired at a fixed observation angle. This reduces error due to surface bidirectional reflectance factor (BRF) differences with view angle.

Vicarious calibration

Vicarious calibration (VC) is a process that is based upon in situ measurements acquired over a large, homogeneous desert site. With these data, the top-of-atmosphere spectral radiance can be computed and compared to those reported by the sensor as it simultaneously images the test site. Agreement constitutes validation of the sensor’s calibration. The in situ observations determine aerosol optical depths, surface spectral reflectance and BRF, and water vapor column amount. The top-of-atmosphere radiances are computed using a radiative transfer code such as MODTRAN. Vicarious calibrations can have uncertainties as small as 3 % (1σ). Key to the success of these measurements is the site selection. Western US desert sites, such as Railroad Valley, Nevada, are typically cloud-free and low in aerosols, minimizing errors in the radiative transfer calculation (Thome et al., 2003). It is for this reason that the vicarious calibration data is considered the radiometric standard for MISR, with the on-board calibrator adjusted to provide consistent calibrations (Bruegge et al., 2004).

Vicarious calibration requires visits by a field team to collect surface and atmospheric measurements at times necessarily coincident with a sensor over-flight. With the creation of an autonomous calibration facility, vicarious calibration data can be made available to the sensor community without the need for each research group to deploy its own field team. One example of an autonomous site is the LSpec (LED Spectrometer) automatic facility (Kerola et al., 2009). The facility is located at Frenchman Flat, within the Nevada Test Site. An array of eight LED spectrometers perform the autonomous function of recording surface reflectances at 5 min intervals, thereby permitting accurate and continual real-time scaling to a high-resolution characterization of the surface. Also resident at the LSpec site is a Cimel sun photometer, used to make atmospheric transmittance measurements. The Cimel is part of the Aerosol Robotic Network (AERONET; http://aeronet.gsfc.nasa.gov/index.html). Measurements made by the LSpec Cimel are used by AERONET to derive values of aerosol optical depths. From continuous in situ measurement of spectral reflectance of the playa surface, along with acquired aerosol optical depths and ozone optical depths (obtained from the Ozone Mapping Instrument OMI; http://jwocky.nasa.gov), the LSpec database provides all physical measurements needed to compute top-of-radiance with the same accuracy as traditional vicarious experiments. Data products are available to the public, and are available via a web-based interface at (http://LSpec.Jpl.Nasa.Gov).

Cross-calibration

The comparison of radiances from two or more sensors having similar passbands, acquired over a common target at near-coincident times can be a powerful validation exercise. In reality, the constraints on the measurements can be relaxed by making use of a radiance model for the site. That is, if the top-of-atmosphere spectral radiance can be determined, these data can be used to estimate the band-averaged radiance for a given sensor, at its SRF and for its time of observation. This is repeated for one or more sensors. The comparison of the first sensor differenced to its model with the second sensor differenced to its model constitutes the cross-calibration (Thome et al., 2003).

Summary

There is an increasing demand for higher accuracy calibration. This is driven by the desire to have long-term data records that span multiple satellite programs. In an effort to establish best practices and minimize sensor-to-sensor biases, many international working groups and national standard laboratories are in collaboration. Information on the Committee on Earth Observation Satellites (CEOS) calibration/validation group can be obtained at http://wgcv.ceos.org/.

Cross-references

Calibration and Validation

Remote Sensing, Physics and Techniques