Radiometric Calibration Methodology of the Landsat 8 Thermal Infrared Sensor

1.1. Instrument Overview

The TIRS instrument is designed to detect and record long-wave infrared radiance emitted from the Earth. It consists of an optical system, focal plane, onboard calibration sources and the associated electronics and structures. The optical system is made up of a four-element refracting telescope, which produces an f/1.64 beam onto the focal plane. A flat mirror, known as the Scene Select Mechanism (SSM), attached to the front of the telescope is able to rotate through three preset positions. This mechanism allows the telescope to switch between viewing the Earth (nadir), a deep space calibration port or a variable temperature blackbody, known as the on-board calibrator (OBC). A mechanical cryocooler cools the focal plane detectors to less than 40 K. Excess heat from the focal plane is dissipated through a radiator attached to the side of the instrument structure. The telescope optics are held at approximately 186 K by heating elements and a passive radiator [4].

The focal plane is comprised of three Quantum Well Infrared Photodetector (QWIP) arrays, each having 512 by 640 detectors [5]. The imaging arrays are sometimes referred to as sensor chip assemblies (SCAs). Specially designed spectral interference filters are placed over two regions on each array to produce two spectral channels when combined with the QWIP spectral response. Areas of the arrays not containing a filter are masked, so that radiance from the telescope does not reach the detectors. There are approximately 30 rows of detectors in each spectral region. One spectral channel is centered at 10.9 μm with a bandwidth of 0.6 μm and is referred to as Landsat 8 Band 10 (sometimes called the 10.8 band or the 10.9 band). The other channel is centered at 12.0 μm with a bandwidth of 1.0 μm and is referred to as Landsat 8 Band 11 (sometimes called the 12.0 band).

For normal science imaging, a primary and redundant row of detectors from each filtered region and from the masked region are read off the arrays (six rows total per array) and transmitted to the ground for assembly into the final image product. The placement of the arrays and the spectral filters produce a 15° field-of-view in the across-track direction for each spectral channel. The layout of the focal plane is illustrated in Figure 1.

The focal plane also has a diagnostic mode in which nearly all rows from each array are read out instead of the usual six rows. The diagnostic mode is especially useful for the characterization and trending of the rows of detectors in each spectral region that are not used in the final science product. The performance of these detectors are tracked should the need arise to swap the primary row of detectors with another row in the spectral region.

1.2. Overview of the Detected Signal

In order to understand the TIRS radiometric calibration process, an understanding of the way a signal from the Earth is detected by TIRS is needed. The top-of-atmosphere (TOA) radiance from the Earth scene enters the aperture of the instrument and passes through the optical system. The radiance is reflected off the flat SSM mirror and then passes through the telescope, which focuses the incoming photons onto the focal plane. Radiance passes through one of the two spectral interference filters that transmit only photon wavelengths between roughly 10.6–11.2 μm for the Band 10 filter and 11.5–12.5 μm for the Band 11 filter. The filtered radiance then strikes the QWIP detector material, where electrons are produced and captured.

The instrument optics and structure will also emit photons according to the Planck function, since they have a non-zero temperature. The self-emitted radiance of the optical path impinges on the detectors and produces a measureable signal in the arrays. This represents a background signal that will always be detected, even when the at-aperture radiance is zero. In addition, the thermal energy of the detector and electronics will produce electrons in the detector material. This signal, known as the dark signal or dark current, is greatly mitigated by actively cooling the focal plane. The telescope optics are also thermally controlled in order to keep the background signal stable. The stability of the background and dark signals are essential to the calibration process.

The electrons generated in the detector material from all three energy paths (Figure 2) are recorded by the read-out electronics of the detectors. The analog-to-digital converter and downstream electronics then condition and digitize the signal to produce 12-bit digital numbers to represent the recorded signal on each detector. Header information, such as acquisition time, integration time, etc., is added to each line of raw image data after which ancillary data is interleaved with the image data by the observatory. Ancillary data includes instrument temperatures, voltages, ephemeris data, attitude data and other instrument and observatory telemetry. TIRS science data, as this dataset is known as, is saved onboard the observatory and transmitted to Earth when in view of ground stations. Ground processing takes place at the USGS Earth Resources Observation Systems (EROS) Data Center [6]. Using the developed calibration algorithms, the image data from the arrays are combined and the raw digital values converted into spectral radiance for each detector. Image data are then geo-located to produce Worldwide Reference System 2 (WRS2) Earth scenes of an approximately 185 by 180-km area on the ground per scene [7]. The data product available to users is rescaled to 16-bit integers that can be converted back into spectral radiance using the coefficients available in the image metadata [8].

2.1. Linearization

The raw signal in terms of digital numbers is produced by electronics that have a non-linear response. This means that there is not a strictly linear relationship between the electrons in the detector and the output signal. The gain of the read-out electronics is dependent on how many electrons have been produced in the detector material. For TIRS, there are essentially two separate regimes where the gain is linear (i.e., the read-out response is piece-wise linear), as illustrated with the integration time sweep data in Figure 3. As electrons are produced in the detector, the output signal is the result of a particular linear gain. Then, as the number of electrons in the detector material reach a certain point (about 10% of detector well capacity), the resulting output signal is produced by a different linear gain (roughly ⅓ to ¼ of the original gain). In order to correctly compare two different signals detected from the two different gain regimes, the digital counts produced from one gain regime must be translated into counts that would have been produced by the other gain regime.

In the integration time sweep data from the instrument shown in Figure 3, the detector was integrated in time steps of 0.1 milliseconds. As time increases, background photons and dark current produce an increasing amount of electrons in the detector material. The time axis on the figure (representing electrons) is linear, while the digital number axis (representing the output signal) is roughly piece-wise linear. The change in response around the 1000 count level is due to the transition from the lower gain regime to the upper gain regime.

A linearization algorithm is necessary to transform the raw digital counts into “linearized counts” in which the ratio of a change in electron level to a change in output counts (i.e., the gain) is constant over the dynamic range of the detector. All TIRS data must be linearized before any further processing.

2.2. Background Removal

As described previously, the recorded digital number from the detectors represents the signal, not only from the desired Earth scene, but also the signal from the self-emitted radiance of the instrument and the signal from the thermal energy of the detectors and electronics. The background and dark current are undesirable signals that must be removed in order to isolate the signal produced by the at-aperture radiance.

The characterization of the background and dark responses can be accomplished by viewing a zero-radiance source. In such a configuration, the only signal recorded by the detector is the background signal from the instrument optical path and the dark current from the detector and electronics. If the instrument is thermally and electrically stable between the collection of the zero-radiance frame, known as the “background frame”, and the source (Earth) image, then the change in the background and dark responses are zero, and the subtraction of the background frame is sufficient to remove the self-emitted signal from the instrument. The result of the background-subtraction calibration step will be digital counts that represent the source only. This can be expressed as,

Operationally, the stability of the background signal between the collection of background frames is checked periodically on-orbit through special calibration collections and through instrument temperature telemetry. In addition, a dark band line is read off the arrays for every image line from TIRS. This band is monitored for changes on a line-by-line basis in between collections of the background frames. A change in the dark band (i.e., the dark signal) would be an indication of a similar change in the spectral bands. Should this be the case, the change in counts from the dark band may be subtracted from the counts in the spectral bands to remove the fluctuation in the dark signal from the spectral bands. For analyses on the stability of the background and dark signals, refer to [2].

2.3. Relation to Radiance

The result of the linearization and background removal steps is the at-aperture source signal represented as “linearized, background-subtracted counts”. These counts must now be related to the absolute spectral radiance entering the instrument aperture. To develop such a relationship, the counts are recorded for a range of known spectral radiance entering the TIRS aperture. The counts-radiance dataset is a look-up table (LUT) that can be used to convert counts into the expected at-aperture radiance. A uniform blackbody-like source at a well-known temperature is sufficient to calculate a known spectral radiance to illuminate the instrument aperture. The spectral radiance of the source is calculated from the recorded temperature of the source (from temperature sensors on the source) along with the Planck blackbody function and known source emissivity to generate a spectral radiance curve for the given source temperature. The incident radiance on the detector is then given by the Planck radiance multiplied by the emissivity and then multiplied per wavelength by the relative spectral response (RSR) of the detector and integrated over the wavelength. This is expressed as,

The process of recording the detector counts (at a fixed integration time and detector bias voltage) for a given input radiance is repeated for a range of source temperatures. The result is an integrated incident spectral radiance per detector for each source temperature along with the associated measured linearized, background-subtracted count. This LUT is stored for every detector, and a linear interpolation may be used between the measured points in the table to convert the detected counts into the expected spectral radiance.

3.1. Radiometric Calibration Data

The raw signal from the detectors is a function of the integration time and the bias and offset voltages for the focal plane arrays. The integration time and voltages were set to values, such that the detectors would provide a sufficient signal without saturating for the required range of source temperatures (240 K–360 K) [9]. The nominal integration time for TIRS is approximately 3.4 ms.

The first required dataset in the calibration process is a set of parameters required for linearization. The goal of the linearization process is to convert the two detector gain regimes into a single regime in which the gain (or change in digital number with change in signal) is the same regardless of the source signal. Integration time sweep data provides the necessary dataset for the linearization process. Data observed from a low radiance source (the CGSE background) was sufficient to observe the change from the lower gain regime to the upper gain regime in both TIRS spectral channels.

The linearization algorithm accepts raw digital counts for a detector and transforms the data, such that a change in count value is constant over the dynamic range of the detector. The integration time sweep data has three distinct regions: a lower linear region, an upper linear region and a transition region between the lower and upper regions. The data points in each region are fit with a quadratic function that relates raw counts into the new linearized count space. The linearization algorithm will determine the appropriate quadratic function to use based on the value of the raw count to be linearized. The application of the algorithm to integration time sweep data for one detector is shown in Figure 4.

The lower gain region was chosen as the regime to be held fixed in the linearization process, since it is the region that is common across the two spectral bands and the dark band. The low signal in the dark band only produces counts in the lower gain region. Should it become necessary to use the dark band counts to correct the two spectral bands (recall Section 2.2), the counts from all bands must be in the same gain regime. As such, all raw data from the detectors are linearized before any further processing utilizing a set of quadratic coefficients.

The second half of the calibration process involves the removal of the instrument background and the development of the radiance LUT. The deep space view port serves as the near-zero radiance source to characterize the background signal. While operating on-orbit, the SSM mirror turns so the instrument views deep space, which has a temperature of approximately 0 K. The signal on the detectors is therefore only the background and dark signal. In the TVAC chamber, a liquid nitrogen-cooled plate served as a substitute for deep space. The cold plate, with a temperature of less than 100 K, produces a signal that is less than 0.005% of the signal of a 300-K blackbody source in the TIRS spectral channels. This signal is negligible for TIRS.

The CGSE Flood source served as the known at-aperture radiance for TIRS. A typical data collection would involve obtaining a deep space collection followed by an acquisition of the Flood source at a specified temperature. All image data of the Flood source is linearized and then background-subtracted with the associated deep space frame (nearest in time to the Flood source collection). These linearized, background-subtracted counts exist for ten Flood source temperatures of 240 K, 250 K, 270 K, 290 K, 300 K, 310 K, 320 K, 330 K, 345 K and 360 K, which span the required sensitivity range of TIRS [9].

To obtain a relationship between counts and spectral radiance, the expected spectral radiance of each of these Flood source measurements must be calculated for every detector. The Flood source was subsequently calibrated to a National Institute of Standards and Technology (NIST) standard at the Space Dynamics Laboratory (SDL) in Logan, UT, in the fall of 2012. The results of that calibration campaign revealed that the Flood source behaved as a blackbody with a 0.992 emissivity that was spatially and spectrally invariant over the spectral range of the two TIRS bands (approximately 9.0 μm to 13.0 μm). The calculated uncertainty in the radiance output of the Flood source at a given temperature is 0.3% [10].

The expected radiance is calculated by computing the spectral radiance of the Flood source at the given temperature through the Planck blackbody function. The temperature sensors on the Flood source give the temperature of the source. The emissivity of the Flood source (as measured by SDL) is taken as 0.992 for all wavelengths. The band relative spectral response (see Section 3.2) is then multiplied per wavelength and integrated to arrive at the expected radiance for the band for the given source temperature. The appropriate values are inserted into Equation (2) and are expressed as,

3.2. Spectral Response

For Equation (3), the band average relative spectral response (RSR) is needed to calculate the predicted integrated radiance from the blackbody calibration source. The RSR for TIRS was constructed from component-level measurements of the various elements of the optical system and the focal plane arrays and verified during instrument-level testing on a small sample of detectors. This section focuses on the combined spectral responses of the science row detectors.

The relative conversion efficiency of each QWIP array was measured by the Detector Characterization Laboratory at NASA/GSFC. The in-band response of every detector was measured over a wavelength range of 7–15 μm at operational cryogenic temperature. The out-of-band response was measured for the average of all detectors on each array over a wavelength range of 1.8 μm to 20 μm. For the RSR measurements needed for the TIRS calibration process, the in-band responses of the detectors that make up the primary and redundant science detectors in the image product are taken from the measured dataset.

The filter spectral transmissions were designed to produce the desired band shape for the two TIRS spectral channels when combined with the QWIP spectral response. The filter vendor then constructed the transmission of the filters to match the desired design as close as possible. Iterations between the manufacturer and the TIRS project continued until the transmission spectrum was agreed upon. The design of the filter was based on only the QWIP response and did not take the telescope transmission into account.

The transmission of the spectral interference filters were measured and provided by the filter vendor. The spectral transmission at five locations on the wafer from which the individual filters were cut were measured at ambient temperature. These measurements were scaled to the spectral transmissions at the operational cryogenic temperature based on measurements from a witness sample at ambient and cryogenic temperatures. Subsequent measurements at NASA/GSFC of the witness sample at ambient and cryogenic temperatures confirmed the vendor measurements.

The spectral transmission of the separate telescope lenses were measured at NASA/GSFC at their operational temperature of approximately 185 K. The product of the measurements from the three germanium (Ge) lenses and the one zinc selenide (ZnSe) lens yields the combined transmission of the telescope.

The spectral responses of the various elements in the optical system are shown in Figure 6. The QWIP response curve is the average response for all detectors. The QWIP and filter responses have been normalized to the peak response. The telescope transmission is the combined product of the transmissions of the four lenses. Finally, the average combined response of the two TIRS channels are shown. These combined band responses are used as the relative spectral responses for the two TIRS channels in the radiometric calibration calculations (Equation (3)) and are also made available to the user community [11].

The relative spectral response varies slightly from detector to detector. The RSR of all detectors in both bands are shown in Figure 7. The average peak-normalized response of the bands is also illustrated in the figure. The variation of band shape for each detector can be quantified by calculating the integrated radiance of each band shape from a blackbody at a typical Earth temperature. The radiance can be compared to the integrated radiance calculated by using the band average response. From a 300 K blackbody, the maximum variation of an individual detector from the band average response is approximately 0.05% in Band 10 and 0.2% in Band 11.

3.3. Radiometric Calibration Uncertainties

The uncertainty in the conversion process can be estimated from the uncertainties of several components of the radiometric process. Performing a linear interpolation between counts in the counts-to-radiance LUT will produce radiance accuracy of approximately 0.4% in the worst case. The NIST traceability of the Flood source radiance is accurate to within 0.3%. The count data in the look-up table is slightly sensitive to the temperature of the focal plane electronics. Over the maximum temperature range expected on-orbit, the counts may change by 0.4%. The error introduced by the slightly different spectral band shapes for each detector produces an uncertainty of about 0.2% in the worst case. Combining these uncertainties yields an overall radiometric uncertainty for the ground-based measurements of approximately 0.7%.

3.4. Implementation of Calibration Method

The calibration process is implemented in the USGS/EROS ground processing system. All raw image data is first linearized. The average of the deep space data collected before and after an Earth collection interval is used as the background frame for that interval. To facilitate processing, the aforementioned LUT is separated out into separate processes. A linear function is fit to each detector’s LUT. The slope, intercept, and residuals of this fit are known as the gain, the gain-offset, and the second-linearization, respectively. The second-linearization is a LUT of linearized counts; the gain-offset is in units of linearized counts, and the gain is in units of radiance per linearized count. In the processing flow, the linearized counts from the background frame (deep space) are subtracted from the linearized counts from the Earth scene. The gain-offset is then added, followed by the counts from the second linearization LUT. Finally, the gain is applied to convert the adjusted counts into radiance. The radiance data is then geo-located and rectified to the WRS2 grid [12]. The standard Landsat Earth scene images available to users are expressed as 16-bit integer numbers and must be rescaled to spectral radiance using the provided coefficients in the image metadata.

5.1. Uniformity

The relative calibration adjustment discussed previously has removed large striping artifacts in most TIRS Earth scenes. However, other Earth scenes have exhibited a particular artifact, known as banding, which refers to low frequency variation in the across-track direction from scenes that are expected to be uniform. Prime examples of Earth scenes expected to be essentially uniform are open water scenes in which the water near the overlap between adjacent focal plane arrays should have nearly the same temperature and should therefore report the same radiance on both arrays if properly calibrated. A representative Earth scene where this is not true is the Red Sea in the Middle East (WRS2 Path 173, Row 41), as shown in Figure 11.

The non-uniform effect across the field-of-view (FOV) is 2.5% or greater and also varies in the along-track direction. This variation is not caused by any internal instability within TIRS, since all indications are that the noise and radiometric stability is well behaved. Furthermore, no relative adjustment to the calibration would successfully remove the varying banding in the along-track direction.

It has been determined that stray light is the cause of the banding issues. Unwanted signals from outside the FOV are entering the optical system and add to the direct line-of-sight signal recorded by the focal plane arrays. The stray light produces a non-uniform signal across the arrays depending on the strength of the source from outside the FOV. The investigation of the stray light issue is ongoing, and possible correction strategies are being explored. For a detailed description of this issue, see [1].

5.2. Absolute Radiometric Response

The absolute radiometric response of TIRS is assessed through the use of in situ temperature measurements of water bodies. The top-of-atmosphere (TOA) radiance from the water bodies is calculated from the temperature measurements and from atmosphere profile knowledge at the time of data acquisition along with radiative transfer models [14]. The calculated TOA radiance from the water bodies is compared with the TIRS-derived image radiance of the water bodies. An overall difference between the TIRS data and the ’ground truth’ is considered an error in the absolute TIRS radiometric calibration.

From data over the first year on-orbit, a varying bias error of approximately 0.29 W/m²/sr/μm in Band 10 and 0.51 W/m²/sr/μm in Band 11 has been observed. The source of the absolute calibration error is now understood to be the same stray light issue mentioned previously. The extra stray light radiance is adding a varying signal to the focal plane. Until a complete correction has been devised, an interim adjustment to the absolute calibration has been implemented to partially correct for this bias error for typical Earth scenes during the mid-latitude growing season. For a detailed treatment of the absolute calibration for TIRS, refer to [3].