2.2. VIIRS
The VIIRS optics has the Rotating Telescope Assembly (RTA), the Half Angle Mirror (HAM) and all of the optics past HAM called
aft. Reflected and emitted radiation from the earth enters the sensor through the RTA and is reflected from HAM into the
aft optics sub system. The HAM is a two sided mirror and derives its name as half angle mirror because it rotates at half the angular speed of RTA as both sides of the mirror become active one after another in its full revolution to reflect the radiation from the RTA via a fold mirror into the aft optics. The VIIRS ATBD Section 2.2.2 describes the Opto-Mechanical Module in full detail [
19]. The on-board calibrators are the black body (OBCBB) for TEB and the Solar Diffuser (SD) for RSB with a Solar Diffuser Stability Monitor (SDSM) to monitor SD degradation just as in MODIS. The radiometric equations are developed in Section 2.3 in Reference [
19].
The transmittance through the RTA follows Equation (4) and an assumption is made that the scan angle dependence and the wavelength dependence of the transmittance (ρ) of the optics are separable as the spectral wavelength is narrow for each band. The scan angle dependence of the response is due to the rotation of HAM presenting different angles during its scan and is denoted as Response Versus Scan (RVS (,B)). It is measured in pre-launch testing and is an important parameter in the development of calibration equation. The term in the brackets in the equation below is the product of the reflectance of HAM wavelength dependence part and the angular dependence part of HAM reflectance.
The angle independent transmittance of the system is combined as
given by
where
,
,
denote the transmittance through rotating telescope assembly, the HAM and the aft assembly respectively.
The VIIRS (RTA) has three views, the space, the blackbody and the earth. They are abbreviated as sv, obc and ev.
The measurement equation is given by Equation (8) in Section 2.3 of Reference [
18],
where
Ne is the number of photo electrons per detection,
is the solid angle of the aperture stop as seen from the field stop and
A is the area of the field stop,
is the spectral radiance at the aperture at angle
ϴ, and
is the spectral irradiance at the field stop due to the self-emissive background detected at the scan angle
ϴ.Equation (24) is in integral form to account for wavelength dependence within the band. Also, in Reference [
4] the relative spectral response, RSR is defined as in Equation (6) in
Section 1.
The following notation was used in Reference [
18] for any quantity to be band averaged. For example, the quantity
F(
λ) is band averaged as follows
Using Equations (25) and (26), the quantities in the bracket of Equation (24) are band averaged and the resulting quantity is called the band-averaged detectable radiance, .
Equation (27) is transformed into the calibration equation as shown below
where the quantity G relates
Ne to the radiance at the detector.
Equation (27) relates the radiance at the detector as due to radiance entering the aperture modified by the response vs. scan angle of the HAM and the background radiance.
The space view (sv) provides zero radiance entering the aperture. It is a calibration of zero external radiance input for the sensor output, i.e., and in the notation B representing each band can be replaced with corresponding λ for that band; i.e., .
Substituting from Equations (27) and (30), the net radiance detected, in Equation (29) is given by
Basically, we have the radiance causing the detector to respond
given by Equation (31) that excludes the space view background. The non-linearity effects and the temperature effects of the detectors in the FPA and the electronics are parameterized by coefficients
Ci and expresses
as
where
dn is the detector output signal in digital counts after subtracting the space view counts accounting for the space view background. The detector output is expressed as a second order polynomial and coefficients
Ci which are theoretically analyzed as combination of individual components
ai for the detector and
bi for the electronics and shown in Tables 11–13 in Section 2.3.1 in Reference [
19] for various possible scenarios of VIIRS performance. The
Ci determined pre-launch are changed to
Ci’ post launch and are being tracked and calibrated. A scale factor
F is introduced to account for the change quantitatively and to be dynamically calibrated on orbit. It is assumed that all three coefficients change by the same factor F and
.
Therefore,
where
, is the background subtracted counts.
2.2.1. VIIRS TEB Radiometric Calibration
The RTA views the emissive sources in all three of its views, the space, the earth and the on-board blackbody and always having the background contribution from the optics and any reflected radiation. In Reference [
19] all background sources within the solid angle of the aperture stop are analyzed and it is assumed that all components of the RTA are at same temperature T
rta and the temperature of the HAM mirror T
ham will be different.
The band averaged residual background for any view subtracting the space view is given in Reference [
19] Equation (44).
So Equation (31) transforms to the following equation which is essentially Equation (45) in Reference [
18].
The OBCBB look is used for calibration as the RTA views it in each scan. The contribution to the radiance from other possible sources that add to the OBC radiance is analyzed. Other sources are the reflections from the blackbody shield, the cavity and the telescope. The band averaged radiance at the aperture stop for OBC look is given by
So the measurement equation while viewing the OBC is given as essentially Equation (111) in Reference [
18] and can be written with the Cal factor
F in Equation (32) as below.
F can be determined as part of On Board calibration. The RVS is arbitrarily normalized to one scan angle (Space view angle) . The calibration factor F is determined from Equation (36).
The band averaged OBC blackbody reflected radiance is:
where the factors
Fsh, Fcav , Ftele represent the fraction of the reflectance off the OBC blackbody originating from the blackbody shield, cavity and telescope. Assuming the emissivity of these three sources to be 1, it follows
Fsh + Fcav + Ftele = 1. The OBC blackbody reflected radiance is routinely updated knowing the temperatures of all relevant components in Equation (38).
The scene radiance
is obtained for Earth view angle
ϴ using the Equations (34)–(37) and is given by the following calibration equation
The above equation essentially gives the radiance (Earth view) as the sum of Calibrated FPA signal converted to radiance accounting for HAM scan angle dependence and the residual background from the RTA and the HAM.
In summary, for evaluating Equation (39), the pre-launch data provide the HAM scan angle dependence of the RVS (response vs scan angle) as LUTs. The background is evaluated from the emitted radiance determined at the temperature of the optics dynamically measured on-orbit. The is determined pre-launch and stored in the LUTs. The gain Coefficient F is determined from the blackbody view and Equation (37).
2.2.2. VIIRS Radiometric RSB Calibration
The calibration equation shown below for the RSB is developed from the general calibration algorithm developed earlier i.e., Equations (31) and (32).
The calibration source for RSB is the solar diffuser (SD) for which the reflectance factor,
, is determined as discussed for MODIS sensor, by the pre-launch measurements of the SD Bi-directional Reflectance Distribution Function (BRDF) and corrected to account for the SD degradation on-orbit based on the trending of the solar diffuser stability monitor (SDSM) output. There is also a SD screen (SDS) at the entrance to the instrument aperture to attenuate the solar irradiance when pointing to the SD. The radiance at the entrance aperture viewing the SD can be written as:
where
and
are the vertical and horizontal incidence angles of solar illumination upon the SD,
θinc is the incidence angle onto the SD relative to normal,
dse is the distance from the sun to the earth,
,
, d) is the transmittance of the SDS,
d is detector index and
(
λ,
is the irradiance from the sun upon a surface with its normal pointing toward the sun. Integrating Equation (41) over the spectral band “
B” and substituting it into Equation (40), we obtain the measurement equation.
where the average denotes the averaging over the spectral band “
B”. It is further assumed that
and BRDF are invariant with wavelength within the narrow band and are taken out of the integral. All the variables on the right of Equation (42) are based on preflight measurements and on angles that can be determined from the geometry. All values on the right are known. The three
c coefficients are determined pre-launch and Equation (40) allows the scale factor
F to be determined for RSB from the solar diffuser measurements. The determination of
F for RSB resembles the case of IR bands as discussed in relation to Equation (32).
After determining the
F factor from the solar diffuser measurements, the calibrated earth view at-aperture radiance for RSB is calculated using the calibration equation
i.e., Equation (40),
where
, the band-averaged spectral radiance at the aperture for earth view scan angle
,
, is the response
versus scan function at earth view scan angle
for band
B and
, the difference between total digital output for earth view angle
and digital counts for space view.
The spectral earth-view reflectance for VIIRS RSB can be written as discussed for MODIS sensor,
Applying band-averaging for Equation (44) over spectral band “
B” and using Equation (40) to substitute for
, we obtain the band- averaged earth-view reflectance as
2.2.3. Analysis of the VIIRS Calibration Algorithm and SI Traceability
The VIIRS sensor was launched into orbit in October 2011 and much experience on its On-orbit performance is reported in literature. The calibration equations, Equation (39) for TEB and Equation (45) for RSB have been developed from first principles of Radiometry as shown in
Section 1 of this paper. The calibration algorithm differs from the simplicity of MODIS due to new Cal factor “F” introduced as a scaling factor in the calibration equations as discussed in
Section 2.2.1 and
Section 2.2.2 for monitoring on-orbit performance compared to the results of extensive pre-launch characterization and calibration of the sensor. The pre-launch test data was comprehensive over the full range of instrument operating conditions guided by stringent uncertainty requirements that provided LUTs for on-orbit data analysis. The F factor is evaluated at every scan, at every detector of every band, for every HAM mirror side which is a good practice to identify anomalies. However there is an intrinsic difficulty in determining the F factor for TEB due to the RVS variation with angle of incidence as can be seen in the Equations (37) and (39). The space view does not cancel the background because of the RVS difference between space view and the blackbody view. As such one needs accurate RVS data to evaluate F using the blackbody radiance as input in Equation (37). The other way out is to have RVS for blackbody view same as for the space view by design and provide an accurate measurement of this RVS in LUT. This will eliminate background contribution and F can be determined from Equation (37) without getting coupled to RVS and Equation (38) can be used for analyzing earth view radiances knowing the other parameters. However, at the time of this writing the long wave TEB radiances for Sea Surface Temperature (SST) Environmental data Record (EDR) for the blackbody Warm Up and Cool Down (WUCD) time periods showed anomalous values. David Moyer
et al., are analyzing the WUCD data to resolve the issue [
20].
The radiometric performance and stability of VIIRS sensor TEB during normal operations is considered excellent compared to expectations [
21]. The large degradation of the NIR and SWIR of the RSB bands soon after launch was addressed and resolved as caused by the tungsten contamination in the RTA mirror coatings. This degradation is currently reported to have considerably leveled off [
22]. As part of good practice, spacecraft maneuvers are being performed to verify and update key parameters. At the beginning of the mission yaw maneuver was performed to validate and update the transmission of the SD and SDSM screen [
23]. Roll maneuvers are performed on nearly monthly-basis for lunar observations for independent validation of RSB calibration using the SD and SDSM. Pitch maneuver was performed and the data validated the relative TEB RVS values [
24]. However, a pitch maneuver coupled to WUCD may provide independent data to address the SST EDR anomaly. The pitch maneuver will point the earth view to another space view and thus provide another zero radiance reference. The path difference background signal can be analyzed independently as a function of the temperature of the HAM mirror and the angle dependent RVS. This independent experiment could validate the parameters evaluated by Reference [
19] for SST anomaly resolution. If there are limitations of time for the complete WUCD cycle, even a part of the cycle during the useful time of the pitch maneuver may help to get TEB data for the anomaly resolution.
The SI traceability is addressed in the ATBD comprehensively as part of stringent uncertainty requirements [
19]. The Reference [
19] and published literature followed GUM to a large extent to determine uncertainty by using the calibration equations [
23,
25]. However, the usage of terminology of GUM such as “Standard uncertainty” for individual components and “Combined Standard uncertainty” for the total are yet to be introduced in to the common practice for VIIRS calibration.