Visible Infrared Imaging Radiometer Suite solar diffuser calibration and its challenges using a solar diffuser stability monitor Junqiang Sun1,2,* and Menghua Wang1 1

NOAA National Environmental Satellite, Data, and Information Service, Center for Satellite Applications and Research, E/RA3, 5830 University Research Court, College Park, Maryland 20740, USA 2

Global Science and Technology, 7855 Walker Drive, Suite 200, Maryland 20770, USA *Corresponding author: [email protected]

Received 1 September 2014; revised 10 November 2014; accepted 12 November 2014; posted 14 November 2014 (Doc. ID 222080); published 19 December 2014

The reflective solar bands (RSB) of the Visible Infrared Imaging Radiometer Suite (VIIRS) on board the Suomi National Polar-orbiting Partnership (SNPP) satellite is calibrated by a solar diffuser (SD) whose performance is itself monitored by a solar diffuser stability monitor (SDSM). In this study, we describe the calibration algorithm of the SDSM, analyze the current two and a half years of calibration data, and derive the performance result for the SD, commonly called SD degradation or H-factors. The application of the newly derived vignetting functions for both the SD screen and the SDSM sun-view screen effectively removes the seasonal oscillations in the derived SD degradation and significantly improves the quality of the H-factors. The full illumination region, the so-called “sweet spot,” for both SD view and SDSM sun view is carefully examined and selected to ensure a consistent and an optimal number of valid data samples to reduce the sample noise owing to inconsistent or lack of samples. The result shows that SD degrades much faster at short wavelength as expected, about 28.5% at 412 nm but only 1.2% at 935 nm up to date. The performance of the SD degrades exponentially with time until 7 November 2013 but has since become flat. This sudden flattening of the SD degradation is a new phenomenon never previously observed for the degradations of the SD on VIIRS or other satellite sensors. The overall result shows that SDSM is essentially functioning without flaws in catching the on-orbit degradation of the SD. The most significant and direct impact of this work would be on the quality of the ocean color products that depend sensitively on moderate RSB (RSB) (M1–M8, M10, and M11). Two very important and key questions on the performance of the SD are also raised. One pertains to the directional dependence of the SD degradation result, and it is shown that the SD does not degrade uniformly in all directions as has been assumed by all SD calibration analyses. This has a definitive impact on the RSB calibration. Another is on the degradation of the SD at the shortwave infrared (SWIR) wavelengths, and it is shown that the zero degradation input for the RSB calibration would be erroneous. Last, the impact of the stray light on the SD since “first light” is cleanly exhibited in the improved SD degradation result. © 2014 Optical Society of America OCIS codes: (120.0120) Instrumentation, measurement, and metrology; (120.0280) Remote sensing and sensors; (120.5630) Radiometry; (280.0280) Remote sensing and sensors; (280.4788) Optical sensing and sensors. http://dx.doi.org/10.1364/AO.53.008571

1. Introduction 1559-128X/14/368571-14$15.00/0 © 2014 Optical Society of America

The Visible Infrared Imaging Radiometer Suite (VIIRS) is one of the five instruments on-board the Suomi National Polar-orbiting Partnership (SNPP) 20 December 2014 / Vol. 53, No. 36 / APPLIED OPTICS

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satellite making global observations of earth scenes [1,2]. VIIRS has 22 spectral bands, among which are 14 reflective solar bands (RSB). The RSB are calibrated on orbit using an on-board solar diffuser (SD) [3,4] with its degradation tracked by a solar diffuser stability monitor (SDSM) [5,6]. They are also monitored by well-planned monthly lunar observations [7,8], the same as for the Moderate Resolution Imaging Spectroradiometer (MODIS) [9]. The SDSM has eight detectors covering a spectral range from 412 to 935 nm and is a ratio radiometer using views of direct solar illumination and solar illumination reflected off the SD to track relative change in the SD reflectance over time. The SDSM performs measurements during planned calibration operations, in which it observes the Sun through a sun-view port, a dark scene inside the SDSM, and the SD successively in a three-scan cycle [5,10]. The SD is fully illuminated by sunlight through an SD port only in a very short period of time when the instrument approaches the terminator from the night side to day side of the Earth at the southern pole [10]. The SDSM also views a full sun in a similarly short period of time, albeit with a shorter interval than the full illumination time period of the SD [5]. The SDSM has been used to track the SD degradation since the SNPP VIIRS launch [5,6], and then the derived SD degradation from the SDSM measurements is used as an input for RSB calibration using SD. In the first two and a half months on orbit, calibration was performed in every orbit. Then the frequency was reduced to once per day for the subsequent two years and four months. It was further reduced to about once per two days after 16 May 2014 to preserve the lifetime of the instrument. For clarification it shall be pointed out that “calibration” in the context of this paper will be used to refer to the SD degradation measurements and tracking by SDSM during planned on-orbit operations. “RSB calibration” will be explicitly stated as so. For SNPP VIIRS, there is no door installed in the front of the SD port due to the consideration of the cost, weight, and design complexity. This is different from MODIS. Both Terra and Aqua MODIS have a door, called an SD door, in the front of the SD port to provide the capability to reduce the calibration frequency and solar illumination through the SD port. Since SNPP has no SD door, the SD is fully illuminated by sunlight through the SD port whenever the instrument approaches the terminator from the night side to the day side of the Earth. Because of this, an RSB calibration coefficient using SD can be calculated every orbit, but the calibration of the SD itself via SDSM is measured only during the planned operations. The reported SD degradations up to date have exhibited large artificial noises such as sudden jumps and seasonal oscillations [5,6]. There are several important aspects in achieving an accurate SD calibration being undertaken for this study. One is the selection of a time period for the optimal SDSM response to sunlight exposure for both the SD view 8572

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and the direct sun view. Operationally, the SDSM is turned on for a calibration event for a short window of time. As the SD surface and the SDSM aperture stops are fully illuminated by the direct sunlight only in a very short period of time when the instrument passes through the southern pole area [10], the SDSM measurements can only be performed during this short time window. Selecting the proper optimal time period, the “sweet spot,” during calibration operation is a critical step of the calibration methodology. Another important factor is the effect of the attenuation screens in front of both the sun-view port and the SD port. The attenuation screens are placed in the front wall of the instrument to reduce the radiance of the passing sunlight that could otherwise saturate instrument response. However, the optical effect due to the pinholes on the screen, known as the vignetting effect, generates one more complication for calibration. The characterization of the transmittances of each screen is described by a vignetting function (VF), and the effect was measured prelaunch [11] and also was determined from on-orbit measurements using yaw maneuvers [10,12]. The accuracy of the two VFs are critical for tracking the SD degradation using the SDSM observations, and a careful analysis was carried out and described in a separate work [10]. With carefully selected “sweet spot,” the properly derived new VFs and additional treatments of the noise we can derive the SD degradation with much smaller noise and much higher accuracy. This is a significant improvement over current and standard analysis [1,5,6]. There are more challenges beyond SDSM and the standard methodology mainly due to physical limitations setting the calibration constraints. One crucial caveat in the current calibration methodology is that the SD is assumed to degrade uniformly for all incident and outgoing directions. Although the longterm SD degradation was investigated in laboratory, no experimental results prove or disprove the assumption [13]. For the VIIRS RSB calibration, the needed SD degradation should be performed for the outgoing direction toward the rotating telescope assembly (RTA) through which the RSB view the SD and all other targets. The SDSM actually measures the SD degradation for the outgoing direction not toward the RTA but toward the SDSM view. The “degradation uniformity” condition is what permits the use of the measured SD degradation to be the official SD calibration result used for RSB calibration. This assumption, although never proven by any hard evidence, has been the standard tenet under which all analyses have been carried out for all sensors employing an SD, including the twin MODIS instruments currently running onboard NASA Terra and Aqua satellites. There is otherwise no capability on orbit to make independent measurements of the SD degradation toward the direction of the RTA. The performance of the MODIS SD over time sheds some light on this issue. During early mission when MODIS SD is not yet fraught with

degradation, its performance result does not reveal any obvious evidence to disprove this assumption. This does not necessarily indicate that the assumption is valid in early mission but that the effect is small enough not to be easily observed. However, recent performance of Terra MODIS SD may be signaling that the rate of degradation for the SDSM view direction and the RSB view direction could be different for short-wavelength bands [14,15]. Another limitation is set by the fact that the SD degradation at the SWIR wavelengths is beyond the spectral coverage of the SDSM to measure. The standard analysis simply assumes zero SD degradation input when deriving RSB calibration coefficients but this is unlikely to be valid. The SD degradation within the covered range of the SDSM is already measured to be significant, thus for SWIR wavelengths sufficiently close to 935 nm the degradation could also be, in principle, measurable. This paper is organized as follows. In Section 2, the calibration algorithms are described and the approximations used in the calibration are reviewed. In Section 3, the SDSM data features are analyzed, the details of data processing are described, and the degradations of the SDSM detectors are analyzed. In Section 4, the SD degradation is calculated at eight wavelengths from the eight detectors of the SDSM. The wavelength- and time-dependence of the SD degradation is analyzed. Section 5 discusses key challenges and the lessons learned about the SD and the impact on RSB calibration. The degradation uniformity assumption as well as the zero degradation input for the SWIR wavelengths is examined. Section 6 summarizes and concludes the work. 2. Calibration Algorithms

The SNPP VIIRS SDSM is a ratio radiometer that consists of a spherical integrating sphere (SIS) with a single input aperture and eight filtered detectors. Each of the detectors has a narrow bandpass. Table 1 lists the center wavelengths of the eight SDSM detectors. A fold mirror inside the SDSM enables the SDSM to view different directions as it rotates. For each scan, the SDSM views one direction and takes 5 successive samples. A schematic diagram for the SD and SDSM calibration is shown in Fig. 1. The SDSM fold mirror has three positions, each of which corresponds to one of three views in succession as the mirror rotates: the SD view, the sun view through the sun-view port, and the dark scene inside the SDSM. The screens in the front of the SD port and the sun-view port reduce the intensity of the sunlight to avoid the saturation of the SDSM detectors. The dark scene response provides the background response of the SDSM. In the calibration methodology, a linear approximation is applied to establish the relationship between the incident sunlight and the SDSM response as LD
dcD ∕GD;

(1)

Table 1.

Center Wavelength of SNPP VIIRS SDSM Detectors and Reflective Solar Bands

SDSM Detector D1 D2 D3 D4 NA D5 D6 D7 D8 NA NA NA NA

CWa (nm)

VIIRS Bands

CWb (nm)

412 450 488 555 NA 672 746 865 935 NA NA NA NA

M1 M2 M3 M4 I1 M5 M6 M7, I2 NA M8 M9 M10, I3 M11

410 443 486 551 640 671 745 862 NA 1238 1378 1610 2250

a b

Specified Center Wavelength (CW). Nominal CW.

where LD is the incident radiance at the wavelength of the detector D, GD is the gain of SDSM detector D, and dcD is the background-subtracted digital count from the detector. SDSM is usually turned off except during a calibration event. Since the SNPP satellite housing VIIRS has a sun-synchronized ascending orbit, both the SD through the SD port and the SDSM entrance aperture through the SDSM sun-view port are illuminated during a short window of time when the satellite approaches the South Pole from the night side of the Earth. This short window of time is when an SDSM measurement must be implemented. For SNPP VIIRS SDSM, a calibration event lasts about 7.75 min (the SDSM is turned on during this time period) while the duration of the full illumination of the SD and of the SDSM entrance aperture is much shorter. For the SDSM sun view when the SDSM aperture is fully illuminated during calibration, the sunlight radiance reaching the aperture can be written in various physical parameters as LSun D


ρf m τSVS LSun;D ; d2ES

(2)

Fig. 1. Schematic diagram for SD/SDSM calibration. 20 December 2014 / Vol. 53, No. 36 / APPLIED OPTICS

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where ρf m is the reflectance of the fold mirror, dES is the Earth–Sun distance in astronomical unit (AU), and τSVS is the VF of the SDSM sun-view screen (SVS), placed in front of the sun-view port. The VF of the SDSM sun-view screen was measured prelaunch and also on orbit with 14 yaw maneuvers in 14 orbits [10,12]. The newly derived VF of the SDSM sun-view screen is applied in this analysis, but its derivation is a separate topic presented elsewhere. In Eq. (2), LSun;D is the relative spectral response (RSR) adjusted solar radiance of the SDSM detector D at the Earth–Sun distance of 1 AU, which can be expressed as Z LSun;D


Z LSun λRSRD λdλ∕ RSRD λdλ;

(3)

where LSun λ is the solar radiance at the Earth–Sun distance of 1 AU, and RSRD λ is the RSR of the detector D. The wavelength of the detector, shown in Table 1, is defined by Z λD


Z RSRD λλdλ∕ RSRD λdλ:

(4)

Given the linear relation between the radiance and the SDSM response described in Eq. (1), we can obtain GDρf m

dcSun;D d2ES
τSVS LSun;D

  d2ES dcSun;D ; τSVS Scan;Sample LSun;D

(5)

R ρf m τSDS cosθSD  LSun λRSRD λBRFSD;SDSM λdλ R
; RSRD λdλ d2ES (7)

where τSDS is the VF of the SD screen (SDS) placed in the front of the SD port, θSD is the solar-zenith angle to the SD, and BRFSD;SDSM λ is the bidirectional reflectance factor (BRF) of the SD for the view direction from the SDSM to the SD at the wavelength λ. The VF of the SDS, τSDS , was measured prelaunch [11] but we have reanalyzed the function using the onorbit measurements from the planned yaw maneuvers [10], same as for the VF of the SDSM sun-view screen. The newly derived SDS VF with the much improved result is applied in the analysis in this paper. If the SDSM detector D has a narrow bandpass, Eq. (7) can be approximated as ρf m τSDS cosθSD  BRFSD;SDSM λD LSun;D : d2ES (8)

(6)

where h…iScan;Sample indicates the average over the five samples in each scan and the selected scans corresponding to full illumination of the SDSM input aperture by the sunlight through the sun-view screen. For each sample and scan, the solar angles are computed first, the SVS VF for the solar angles are calculated second, and then the ratio of the SDSM detector D background subtracted sun-view response over the computed value of the SVS VF 8574

LSD D

LSD D


from Eq. (2), where dcSun;D is background-subtracted sun-view response of the SDSM detector D. From this we can monitor the gain change of SDSM instrument and the fold mirror using the SDSM sun-view response during full illumination of the SDSM entrance aperture. GDρf m can be calculated from each scan for as long as the SDSM entrance aperture is fully illuminated at the scan. The VF of the sunview screen, τSVS , should correct the dependence of the SDSM response, dcSun;D , on the solar angles. There are multiple scans at which the entrance aperture is fully illuminated and from them a certain number of the scans will be selected to calculate GDρf m . The detail of the selection will be discussed in the next section. An average can be taken to reduce the impact of random noise in Eq. (5) GDρf m


is evaluated. Equation (6) characterizes the degradation of the SDSM. For the SD view when the SD is fully illuminated during a calibration event, the SD scattered sunlight radiance which reaches the SDSM aperture can be expressed as

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The BRF, BRFSD;SDSM λD , changes with time and its on-orbit performance is to be derived from the SDSM calibration. It is impossible to derive the full BRF as a two-dimensional function of the incidental direction described by two solar angles as well as time, thus the role of the “degradation uniformity” assumption is here reemphasized—that the on-orbit change of the BRF is not incident angle dependent or that the dependence is negligible. With this assumption, we can write BRFSD;SDSM λD 
ρSD;SDSM λD HλD ;

(9)

where ρSD;SDSM λD  is the measured prelaunch BRF with outgoing direction toward the SDSM for the detector, HλD  is SD degradation factor at the center wavelength of detector D since prelaunch BRF measurement, and it is assumed that the degradation of the SD during the time period from the prelaunch measurements to the launch is negligible. According to Eqs. (1), (8), and (9), we can get HλD GDρf m


dcSD;D d2ES ; ρSD;SDSM λD τSDS LSun;D cosθSD  (10)

where dcSD;D is background-subtracted SD view response of the SDSM detector D. Thus, the SDSM

SD view response contains the information of the SD degradation as well as the SDSM degradation. Same as for the sun view, there are multiple scans, at which the view spot of the SDSM on the SD surface is fully illuminated by the sunlight and each of which can be used to calculate HλD GDρf m . The BRF of the SD, ρSD;SDSM λD , the VF of the SDS, τSDS , and cosθSD  should remove the dependence of dcSD;D on the solar angles. To reduce the random noise, a certain amount of scans with full illumination of the view spot on the SD surface will be selected to calculate HλD GDρf m as will be discussed later in the next section. Then Eq. (10) can be written as HλD GDρf m   d2ES dcSD;D
; (11) ρSD;SDSM λD τSDS cosθSD  Scan;Sample LSun;D where h…iScan;Sample indicates the average over the five samples in each scan and selected scans corresponding to the full illumination of the SDSM view spot on the SD surface. For each sample and scan, the solar angles are computed first, then the SD BRF, the SDS VF, and cosθSD  for the solar angles are calculated, and the quantity inside the triangles is finally evaluated with SDSM detector D background subtracted SD view response and the computed values of the SD BRF, the SDS VF, and cosθSD . Combining Eqs. (6) and (11), we obtain the degradation factor 

dcSD;D ρSD;SDSM λD τSDS cosθSD    dcSV;D ∕ : τSVS Scan;Sample



HλD 


Scan;Sample

(12)

The SD degradation then can be tracked via Eq. (12) from the SDSM measurements. It is pointed out again that HλD  in Eq. (12) arrives from using the SD degradation for the outgoing direction toward the SDSM taken to be the same as that toward the RTA. A subtle numerical and procedural difference to be made explicit is that the factor HλD  calculated here is the ratio of the averages and not the standard average of the ratios carried out by other work [5,6]. The impact of this difference is particularly illuminated for the case of VIIRS and will be discussed in the following section.

day for 2 plus years until 16 May 2014. The operational rate was then reduced to about once per two days. So far, the calibration operation has been performed for more than 1750 times since launch. Considering that the operational rates of the two MODIS instruments were weekly early in mission, then biweekly, and currently triweekly [16,17], VIIRS calibration operations are occurring at a very high frequency and may need to be reduced further to preserve the lifetime of the SDSM. A. SDSM Profile

The calibration event on 1 January 2014 is shown in Fig. 2 displaying the raw voltage of the SNPP VIIRS SDSM detector 1. The voltage is the response of the SDSM detector to the scenes which it observes and the voltage has a linear relationship with the dc of the SDSM response. Diamonds, squares, and stars represent the response to the sun view, the SD view, and the dark scene, respectively. All values of the raw response are negative. The solar declination angle is taken to be in the instrument coordinate system defined at nominal attitude by the z and x axis in the nadir and the track directions, respectively. In this event, the SDSM observation lasted about 7.7 min. The SDSM was turned off just before and after the actual observation time period. During the event, the solar declination angle changed from about 32.5° to 4.8°, at a decreasing rate of about 3.6° per minute. The response of the detector to the dark scene was about the same during the event, indicating that the detector was stable during observation. At the beginning, both the SD and the SDSM entrance aperture were not illuminated by the sunlight. The responses of the detector to them were about the same as to the dark scene, indicating that the detector performed correctly. The sunlight passing through the sun-view port started to illuminate the SDSM aperture when the declination angle approached 30°. The aperture was partially illuminated by the sunlight for about the following 2 min until at about 22.8° declination angle, the aperture became fully illuminated. About

3. SDSM Observations and Analysis

SNPP VIIRS was turned on after being on orbit for 11 days on 8 November 2011. Calibration was performed in every orbit through 19 January 2012 generating about 14 events every day. Between 19 and 24 January 2012, calibration was carried out once per day. From 25 January to 27 February 2012, calibration was again carried out in every orbit. Since then, the calibration was operating once per

Fig. 2. Raw response of SNPP VIIRS SDSM detector 1 on 1 January 2014. 20 December 2014 / Vol. 53, No. 36 / APPLIED OPTICS

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3 min. later, the declination angle decreased to be about 12.5° and the aperture became partially illuminated. The sunlight through the sun-view port moved away from the aperture when the declination angle became smaller than 6°. The VIIRS SDSM consists of a spherical integrating source (SIS) with a single input aperture as mentioned previously. The sunlight passing through the sun-view screen and the input aperture reaches the detectors inside the SDSM. The input aperture was designed to allow only the sunlight passing 16 pinholes of the SDSM sun-view screen to go to the SIS. In that ideal case, the radiance of the sunlight should be a very smooth function of the incident direction of the sunlight on the SDSM sun-view screen and the maximum response of the SDSM should occur at the center of the plateau of the full illumination. In Fig. 2, the maximum response of the detector for the sun view indeed occurs at the center of the full illumination region. The response varies with the declination angle in the region but with a very distinctive small up-and-down stepping pattern. This pattern suggests that there is a slight imperfection in the arrangement of the pinholes of the SDSM sun-view screen, resulting in the sunlight passing through more or less than 16 pinholes to reach the SDSM SIS. The four steps in the declination angle range from 30° to 22.8° correspond to the projection of one, two, three, and four rows of pinholes onto the aperture, respectively. The SDSM initially “sees” one row of pinholes on the SDSM sun-view screen near the beginning of the illumination, then two rows, three rows, and finally four rows entering the full view. The view maintains the four-row projection of pinholes, with one row moving out of its scope while another comes into its view. The four steps in the declination angle range from 12.5° to 6° correspond to the phase out of the final four rows of pinholes one by one. The spot viewed by the SDSM on the SD started to be illuminated when the declination angle is 25.2°, 4.8° smaller than the declination angle and 1.5 min. later at which the SDSM aperture was started to be illuminated by the sunlight from the sun-view port. The spot was partially illuminated until the declination angle decreased to 19°. The spot was fully illuminated since then and became partially illuminated again just before the SDSM was turned off. Unlike the response to the sun view, the response to the SD view decreases significantly with the decrease of the declination angle even if the view spot on the SD is still fully illuminated. This is caused by the change of the solar-zenith angle to the SD surface as well as the change of the BRF of the SD and the VF of the SDS with respect to the change of solar angles as described by Eq. (6). For the sun view, the response is only affected by the VF of the sun-view screen, which is symmetric with respect to the center of the calibration as shown in Fig. 2 and is to be explained later. It is clearly seen in Fig. 2 that the full-illumination range for the SD view 8576

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and that for the sun view do not fully coincide. For both the SD view and the sun view, only the data in the fully illuminated ranges can be used to derive the SD degradation as required by Eqs. (6), (11), and (12) in Section 2. B. Selection of the “Sweet Spot”

The mismatch of the SD view and the sun view brings to light a step in the data processing procedure that is not optimal for SNPP VIIRS. The mismatch is due to the misalignment of the SDSM SD view and sun view resulting from a design error [11]. Subsequently, the common middle interval of the full-illumination is restrictively narrow, which will be discussed in detail later. The low number of available data samples to calculate the ratios of SD view to sun-view measurements has the effect of generating noisy H-factors. The different order of numerical processing by Eq. (12), taking an average of each view before taking the ratio, averts the need for the two views to match, and gives in addition a statistically more robust result due to having more samples. The responses of other SDSM detectors have similar behaviors as that of detector 1. The detail of the patterns of the responses may change with seasons by a couple of degrees. The range of the solar angles should be selected to ensure full illumination of the SD by the sunlight from the SD port and of the SDSM aperture by the sunlight from the sun-view port in all seasons. It is not necessary that the range for the SD view and that for the sun view identically match for as long as the measured data are properly processed [18]. The selected range will be called the “sweet spot” and the selection will be shown for both SD and the sun view. Figure 3 shows the backgroundsubtracted SD view and sun-view response for SDSM detector 1, derived from the raw data shown in Fig. 2, with diamonds and squares, respectively. To achieve a higher signal-to-noise ratio, it is better to keep the signal as large as possible. There also should be a margin of safety to ensure that the selected range is within the full-illumination range at any time of the year and that there are enough scans to provide high-quality samples. In order to accurately describe the variation of solar radiance at a given wavelength with solar angles using a smooth function, the size of the range should not be too large but should be large enough to have adequate scans. Based on the MODIS SD/SDSM calibration experience, a size of 4° for the range is a reasonable choice. Then according to the SD view response in Fig. 3 and the concerns mentioned above, it is reasonable to select a declination angle range from 13° to 17° as the “sweet spot” for the SD view. The two vertical dashed lines correspond to the declination angle of 13° and 17° mark the “sweet spot” boundary for the SD view. In this “sweet spot,” there are about 38 scans and about 13 of them are for the SD view. The “sweet spot” range selected here is consistent with that for the data selection in the RSB calibration using the SD observations. For the sun

Fig. 3. Background-subtracted response of SNPP VIIRS SDSM detector 1 to the SD view on 1 January 2014 and the “sweet spot” for the SDSM SD and the sun view.

view, the SDSM response is mainly impacted by the VF of the SDSM sun-view screen as expressed in Eq. (2). Since the VF is a geometrical effect of the pinholes on the screen, it is better to show the sun-view response and the “sweet spot” for the sun view according to the solar angles in the coordinate system of the screen which is defined as the z axis in the normal direction of the screen and the x axis toward the center of the Earth. The background-subtracted sunview response of detector 1, denoted with squares in Fig. 3, is displayed in Fig. 4 as a function of solar elevation angle in the sun-view screen coordinate system. With the same reasons and concerns for the selection of the “sweet spot” for the SD view as discussed previously, it looks reasonable to select the range of elevation angles from −2° to 2° as the “sweet spot,” defined by the two vertical dashed lines in Fig. 4, for the sun view. There are about 38 scans in the “sweet spot,” in which there are about 13 scans for the sun view. The “sweet spot,” corresponding to that defined in Fig. 4, for the sun view is shown in Fig. 3 by the dashed-dotted lines with declination angles of 15.7° and 20.1°. It is clearly seen that the “sweet spot” for the SD view and that for the sun view are quite different and their common range is less than 1.5°. In fact, the size of the common range changes with seasons and can become smaller in other seasons. In the literature [5,6,18], the common range has been used as the “sweet spot” for both views, but the restrictively narrow range in the case of VIIRS can result in insufficient valid scans. In such case, due to the lack of data samples the derived SD degradations at the eight wavelengths of the 8 SDSM detectors can have larger uncertainties as demonstrated by unexpected wiggles and noises in the derived SD degradation trending [5,6]. With two independent “sweet spots,” one for the SD view and

Fig. 4. Background-subtracted response of SNPP VIIRS SDSM detector 1 to the sun view on 1 January 2014.

the other for the sun view, the numbers of the data samples for all calibration events are about the same and are sufficient for calibration calculations [18]. For the dark scene, the selection of the “sweet spot” appears to have no detectable impact. However, for consistency, we select the joint range of the “sweet spot” for the SD view and that for the sun view, which is the range of the declination angle from 13° to 20.1° for the event on 1 January 2014, as the “sweet spot” for the dark scene. The “sweet spot” for the dark scene may change slightly with seasons. C.

SDSM Degradation

The gain change of the SDSM system is tracked by using Eq. (6). Figure 5 displays the gains of the 8 SDSM detectors including the contributions of the fold mirror from the sun view normalized at the first point. It is clearly demonstrated that the gains of detectors change with time and the change rate is detector or wavelength dependent. It is interesting to note that the detector with longer wavelength has larger gain degradation. In other words, the detector with the longest wavelength (935 nm) has the largest gain degradation. In the past two plus years, the gains of detectors 7 (865 nm) and 8 (935 nm) have decreased about 18.5% and 32.7%, respectively, while those of all other detectors have decreased less than ∼6%. The gain change rate for all detectors smoothly decreases with time except for detector 4 (555 nm), which shows a sudden increase around day 815. Nevertheless, a closer look of the apparently smooth trend reveals the presence of minor wiggles due to the fact that the VF of the sun-view screen cannot be fully characterized by a smooth function [19]. A comparison with the SD view response trending below will illuminate this point. D.

SD View Response Trending

As previously mentioned in Section 2, the solar angle and Earth–Sun distance effect-corrected SDSM SD 20 December 2014 / Vol. 53, No. 36 / APPLIED OPTICS

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fluctuation in Fig. 6 should be induced by the irregular change of the SD degradation, which will be discussed more in the next section. In comparison with Fig. 5, the SD view trending in Fig. 6 shows a remarkable smoothness devoid of minor wiggles. The clear inference is that the SDSM is performing very well and that the vignetting effect of the SD screen in front of the SD port is well-captured by the smooth VF used to characterize the effect. On the other hand, the minor wiggles in Fig. 5 are mainly due to the small imperfection of the VF as the smooth function used for the vignetting effect of the screen in front of the sun-view port cannot fully characterize the screen effect [19]. Fig. 5. Degradation trend of the SDSM detectors including the effect of the fold mirror.

4. SD Degradation and Performance

view response defined on the right-hand side of Eq. (11) contains both the gains of the SDSM and the degradation of the SD or represents the product of the SDSM gain and the SD degradation. Figure 6 shows the trending of the SDSM gain and SD degradation products for all the 8 SDSM detectors. It is clearly seen that they decrease with time and the rates of decrease are strongly detector or wavelength dependent. But the rate of change cannot be aligned according to the wavelength of the detectors. This indicates that the SD degradation and the SDSM gain have different wavelength dependencies. In fact, the products for detector 1 with the shortest wavelength of 412 nm and detector 8 with the longest wavelength of 935 nm have largest degradations. The degradation of the former is mainly induced by the SD degradation, while the latter is mainly due to the degradation of the detector according to Eqs. (5) and (11). The sudden increase in the corrected response for detector 4 around day 815 is mainly due to the sudden increase in the detector as discussed above. It is also worth mentioning that the rate of change of the corrected response fluctuates in the last half-year. Since no fluctuation has been seen in the gains of the SDSM detectors, the

The symbols in Fig. 7 show the on-orbit SD degradation derived from SDSM measurements via Eq. (12) at the wavelengths of the SDSM detectors. The first set of SDSM measurements was made on 8 November 2011 when the SNPP VIIRS was turned on after 11 days on orbit. However, the SDSM measurements for the first two days were noisy and hence the data for 10 November 2011 and on are shown instead. It is clearly seen that the SD started to degrade the very first day on orbit by the solar illumination through the SD screen placed in the front of the SD port. Thus, the SD degradation in Fig. 7 is normalized to 28 October 2011. The SD degradation shows the expected result that the degree of degradation is greater at lower wavelengths. In the past two plus years since the VIIRS has gone on orbit, the SD has degraded about 28.4%, 22.2%, 17.0%, 11.0%, 4.3%, 2.8%, 1.5%, and 1.2% at wavelengths of 412, 450, 488, 555, 672, 746, 865, and 935 nm, respectively. There are also three time periods: from the day on which the instrument was turned on to day 24 when the nadir door opened, from day 24 to day 740 (7 November 2013), and finally after day 740, in which the SD degrades very differently. It is well-known that the SD degradation is caused by ultraviolet (UV) exposure [13]. The UV illuminated on the SD can come from direct solar illumination through the SD port as well as from the sunlight

Fig. 6. SDSM gain and SD degradation product trending.

Fig. 7. SD degradation derived from the SDSM measurements.

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scattered from the earth’s surface. To illustrate the SD degradation differences between the first two time periods of different solar exposures, we redraw the SD degradation in the time period of first 75 days since launch in Fig. 8. The opening of the nadir door on 21 November 2011 at day 24 marks a new and clearly worsening trend for the SD degradation due to additional UV exposure coming through the nadir door. By comparing the SD degradation rates before and after the opening of the nadir door, one can estimate the impact of the UV from the scattered sunlight is about twice the impact of that coming from the SD port. The relative contributions of the UV from the two sources may slightly change with seasons. In the first and the second time regions, the SD degrades smoothly at all wavelengths and the degradation in each region can be described by an exponential function. In the third time region, the SD reflectance started to increase on 7 November 2014 and this trend lasted for about 75 days before reverting back, but no longer following an exponential pattern. This is an unexpected behavior not previously observed for VIIRS or other remote sensors. For Terra and Aqua MODIS, the SD has almost stopped degrading after being on orbit for 14 and 12 years, respectively, while the degradation rate gradually reaches zero. Although the increase of the SD reflectance after 7 November 2013 is unexpected, it is a true performance of the SD. The RSB calibration coefficients, F-factors, are derived from SD observations but they should not depend on the degradation of the SD as long as the SD degradation is accurately determined. In other words, RSB F-factors should continue to be smooth functions of time after 7 November 2014 regardless of SD degradation. It is actually found that the Ffactors have remarkable variations if any fitting to smooth out the SD degradation abnormality is applied. On the other hand, the F-factors become smooth if the actual measured SD degradation including the abnormality is used in the calculation of the F-factors. In fact, the VIIRS ocean color

EDR products also demonstrate that the SDR calculated with the F-factors derived using the actual measured SD degradation has correct features. The recent unexpected SD reflectance change for VIIRS signals a different physical or chemical change of the SD surface that shortly dominated the degradation of the SD surface and this factor may continue to compete further as demonstrated by the fact that the reflectance started to decrease again but to a different pattern after day 915, 21 May 2014. The intensities of both sunlight sources impacting the SD, through the SD port or from the scattered light from the earth scenes, depend on the Earth– Sun distance. Meanwhile, the former depends on the solar azimuth angle, θSD , on the SD surface during the “sweet spot” time period, while the latter depends on the solar beta angle, β, the angle between the vector from the Earth to the Sun and the orbital plane of the SNPP satellite. The solar beta angle changes smoothly with season but effectively remains constant throughout one day. Although the scattered light from the earth’s surface is geolocation dependent, but because VIIRS observations approximately cover the entire earth’s surface every day (although its orbit repeat cycle is 16 days), then on a daily basis, the earth surface reflectance is about the same when considering the scattered sunlight from the earth’s surface to the SD surface. A good approximation to characterize the total UV illuminated on the SD surface per day, EUV , then can be expressed as EUV ∝ cosθSD   qβ∕d2ES ;

where qβ is a smooth function of β and d2ES is the Earth–Sun distance. One can derive the dependence of qβ on β by analyzing the dependence of the total visible scattered sunlight from the earth’s surface and the global averaged ratio of the earth surface reflectance for the UV to that for the visible sunlight. The detailed analysis of the solar UV exposure on the SD surface is beyond the scope of this paper but is not necessary for this analysis. It is adequate to use cosβ as a first approximation to establish the dependence of the scattered sunlight on the solar beta angle. With this approximation Eq. (13) then takes on a simple form EUV ∝ cosθSD   R cosβ∕d2ES ;

Fig. 8. SD degradation derived from the SDSM measurements shown for the first 75 days. The opening of the nadir door is on day 24.

(13)

(14)

where R can be determined from the SD degradation rates just before and after 8 November 2011 and is set to zero before the opening of the nadir door. Since θSD , β, and d2ES all have annual repeatability, EUV also exhibits a seasonal oscillation pattern. A smoothing fitting function of time actually will not represent the SD degradation trend with enough fidelity because of the seasonally varying UV exposure on the SD on top of the multiyear degradation trend. In doing so, the seasonal effect not captured by 20 December 2014 / Vol. 53, No. 36 / APPLIED OPTICS

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the simple fitting scheme will eventually propagate its way into the RSB calibration coefficients, the F-factors. To capture also the annual effect induced by the variation of solar exposure in the fitting of the measured SD degradation, we define a solar exposure adjusted time as Z ta
s

t

0

EUV t0 dt0 ;

(15)

where s is a scaling constant such that the solar exposure adjusted time for a year with the nadir door kept in the open position equals 365.25. This transform preserves the one-to-one correspondence between the adjusted time, ta , and the real time, t, counted from launch. In the new adjusted time domain, the corresponding third time period is further divided into two segments, one for day 740 to day 915 and other for days after 915. This choice is made for fitting improvement. For each of the two segments in the third time period, a linear function can be chosen to describe the degradation. For the first time region from first day to day 24, a linear function or the exponential function in Eq. (16) can be used. For the second time period from day 24 to day 740, an exponential function of a quadratic form of the adjusted time f t
expa0  a1 ta  a2 t2a 

(16)

can be used. One can even combine the first two time periods if R in Eq. (14) is accurately determined. The fitted analytic functions of all segments for a given wavelength need to be smoothly connected across the joining points of the segments. The solid lines in Figs. 7 and 8 show the fitted SD degradation at the eight wavelengths. It is seen that the fitted smooth functions describe the measured data quite well except for the third time period where the SD degrades unusually. For the third time period, it seems that more time segments for the fitting are needed for the improved fitting but having fewer data points in each segment could render the fitting infeasible. In a real application, one does not have to fit the measured SD degradation results to smooth functions and can directly apply the measured H-factors in the RSB calibration using the SD observations. The measured SD degradation results shown in Figs. 7 and 8 with symbols are much more stable and less noisy compared to those reported in the literature [5,6]. As previously mentioned, several key improvements are used for this analysis: better selection of the “sweet spots,” carefully rederived BRF for the SD, VF for SD screen, VF for SDSM sun-view screen, and finally improved numerical treatments. The results in Figs. 7 and 8 demonstrate that the SD performed as expected except after the day 740. The unexpected increase of the SD reflectance after the day 750 to day 915 has been shown to be a real SD degradation from results in the 8580

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Fig. 9. Wavelength dependence of the SD degradation derived from the SDSM measurements for selected dates.

calculated RSB calibration coefficients, the F-factors, using the SD calibration and the VIIRS ocean color products, which will be discussed elsewhere later. All these indicate that the SDSM accurately catches the performance of SD, multiyear trend or sudden changes alike. In principle, it catches the SD degradation for the outgoing direction toward the SDSM view direction. To obtain the SD degradation at other wavelengths within the SDSM spectral coverage, we can use the results at the eight wavelengths and interpolate between adjacent pairs. Figure 9 displays the constructed SD degradation surface for six different times with wavelength as the variable. The symbols are the degradation values at the wavelength of the eight detectors and the segments are the interpolations. It provides the SD degradation information for VIIRS visible bands I1, I2, and M1–M7 and can be applied to derive their calibration coefficients using SD. The SD degradation cannot be derived for the SWIR bands, I3 and M8–M11. Currently, it is assumed that the SD has no degradation at the SWIR wavelengths when the SD result is applied to calibrate the SWIR bands. 5. Challenges

It is shown in the previous section that the SDSM can accurately catch the SD degradation. However, there are two issues worth drawing attention to. One is the SD degradation beyond 935 nm, outside the coverage of SDSM, and the other is the assumption that the SD degrades uniformly for all incident and outgoing directions. The challenge for each is discussed in detail. Part A will discuss the evidence of the SD degradation at the SWIR wavelengths. Part B will take a close examination of dc versus inclination angle to show that the degradation uniformity assumption indeed does not hold for VIIRS short wavelength bands. Part C will discuss the impact on the RSB calibration coefficients. Some suggestions are also provided.

A.

SD Degradation at SWIR Wavelengths

The wavelengths of the SWIR bands (M8–M11 and I3), shown in Table 1, are longer than 935 nm and therefore not within the spectral coverage of the SDSM. In the current VIIRS calibration methodology, it is assumed that the SD has no degradation for wavelengths longer than 935 nm in the derivation of the RSB calibration coefficients. MODIS also has a similar situation. From both Figs. 7 and 9, it is seen that the SD has clearly degraded about 1.2% at the wavelength of 935 nm since launch. To justify that the SD is without degradation at the SWIR wavelengths, especially for band M8 (1238 nm), would be contrived at best. In fact, one may conclude from the curves in Fig. 9 that the SD degradation at the wavelength of band M8 could have degraded by as much as 0.5% or more. This can induce a 0.5% error in the calibration coefficients derived from the SD calibration and then bring on a 0.5% error in the Science Data Record (SDR) of the band M8. Since band M8 is a critical band for ocean color products [20], a 0.5% error in the SDR could have significantly impacted the ocean color products. In addition, as SD degrades further at all wavelengths the error from neglecting SD degradation beyond 935 nm in the VIIRS SDR and the ocean color Environmental Data Record (EDR) products will become even more significant [21,22]. One interesting suggestion is to extend the SDSM spectral coverage into the SWIR region provided that it is feasible. This may be done, for example, by adding an additional detector at a longer wavelength or simply by increasing the spectral spacing while keeping the same number of detectors. Likely over the mission life of the instrument like MODIS or VIIRS, the SD will exhibit measureable degradation at the tail end, at longer wavelengths beyond 935 nm as shown in Fig. 9. Having a greater spectral coverage can provide valuable statistical and numerical leverage to improve fitting, to gain more insight into the longer wavelength regime, and to achieve more accurate calibration. If there are technical difficulties to extend the SDSM spectral coverage in the SWIR region, then alternative approaches to calibrate the SWIR bands will be required. Lunar calibration can play an important role in this issue [8,9].

follow. Since the reflectance of the SD degrades much more at short wavelengths while it almost has no change at long wavelengths, the “corrected dc” of detector 1, which has the shortest wavelength among all 8 SDSM detectors, will be examined first in detail in the following. Figure 10 shows the corrected dc of SDSM detector 1 with respect to solar declination angle for 15 November 2011, 15 March 2012, 15 July 2012, and 15 July 2013. The corrected dc for each SDSM event is fitted to a linear function and then both the corrected dc and the function are normalized to the fitted value at the declination of 13° for ease of plotting and comparison. If SD degradation uniformity is indeed true for all angles, then all linear functions should be constant with a value of one as explained above. This is because the uniform degradation condition will preserve the shape of the dc with respect to the declination angle, thus making corrected dc be flat and the normalized curves of unity. Of course, an important caveat is that the denominator in the corrected dc, expressed in Eq. (10) with BRF and VF, is accurately determined. The linear curves in Fig. 9 demonstrate that the corrected dc does not stay flat, and in fact shows a clear divergence with passing time. The 15 March 2012 case shows a near-flat line but this is expected since the SD BRF and SD screen VF were derived from the yaw measurements that were implemented on 15 and 16 February 2012. Whether or not the SD BRF degrades uniformly, the corrected dc for time close to the yaw measurement event should be flat because the BRF and the VF should catch the solar dependency of the SDSM response to the SD view at the time of the yaw measurements. The VF, in principle, should not change with time and the BRF should not change much in a short period of time. The near flatness of the curve for 15 March 2012 gives great credence and one more supporting fact that the BRF and the VF were properly derived. The other three functions demonstrate that the dc

B. Nonuniformity of SD degradation and Its Impact on RSB Calibration

Embedded within each SDSM measurement is how dc of each scan varies with solar declination angle in the instrument coordinate system. During the short time interval of a calibration event, as the incident angle of light on the SD varies over a few degrees, the scan reading then records the responses over a range of angles. The key, then, is to look for divergent patterns of responses in the SDSM records over time to disprove degradation uniformity. One direct way is to examine the right-hand side of Eq. (10), which will be referred to as the “corrected dc” for the analysis and the explanations that immediately

Fig. 10. Symbols are corrected dc of SDSM detector 1 for the SD view, calculated by the formula expressed on the right-hand side of Eq. (10). Solid lines are linear functions fitted to the corrected dc. All data for each event are normalized to the linear function of the event at a declination angle of 13°. 20 December 2014 / Vol. 53, No. 36 / APPLIED OPTICS

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decreases with rising declination angle before yaw measurements, but increases with rising declination angle after the yaw measurements and that the rate of increase becomes larger with time passing. The azimuth angles on the four dates may be quite different. However, the effect of the solar azimuth angle on the corrected dc has been corrected by the SD BRF and SDS VF if the BRF degrades uniformly with respect to the incident solar angles. Thus, the curves in Fig. 10 essentially show that the BRF degradation depends on the incident angle at the wavelength of 412 nm and disproves the uniformity assumption of SD degradation. To further investigate the nonuniformity of the SD degradation, we fit the corrected dc for all events and for all SDSM detectors to linear functions and normalize at a 13° declination angle. The slopes of the normalized fitted linear functions are displayed in Fig. 11. It is clearly seen that the slopes for detectors 1 (412 nm), 2 (450 nm), 3 (488 nm), and 4 (555 nm) increase with time until about day 475 (15 February 2013) and then remain mostly constant in the last one and a half years. The rate of increase of the slopes before day 475 and the maximum value of the slopes after day 475 are clearly decreasing with increasing wavelength. For other detectors with longer wavelengths, the slopes remain more or less constant. This indicates that the degree of the nonuniformity decreases with the wavelength for incident declination angle. Since the SD degradation also decreases with the wavelength, the insensitivity of the SD degradation at long wavelengths to the nonuniformity may be due to the smaller degradation of the SD at those wavelengths. In other words, the degree of the nonuniformity of the SD degradation with respect to the incident angles increases with the degradation of the SD. If the outgoing direction toward the SDSM is the same as that toward the RTA, the SDSM would still be able to catch the SD degradation correctly regardless of the nonuniformity problem. However, the two outgoing directions are quite different, one in the forward direction and the other in the backward direction for the sunlight coming from the SD port.

Fig. 11. Slopes of the normalized fitted linear functions for all SDSM eight detectors. 8582

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If the SD degradation is not uniform for the incident angle, there is no reason that it must be uniform for the outgoing direction. Since the difference between the two outgoing directions is much larger than the range of the incident direction, the differences between the SD degradation for the two outgoing directions could be much larger than those shown in Figs. 10 and 11. The same level of errors as the SD degradation percentage differences would propagate into the derived RSB calibration coefficients and eventually into VIIRS SDR and EDR products. C.

Concerns and Suggestions

It is known that both Terra and Aqua MODIS SD calibration has lost the capability to provide accurate calibration coefficients for 412 nm and other short wavelength bands after the designed 6-year lifetime has passed [14,15]. The error for the 412 nm band can be as large as ∼10% for Terra MODIS and ∼1% for Aqua MODIS [14,15]. One possibility is thought to be the failure of the SDSM measurements to accurately catch the SD degradation or the SD degradation for the outgoing direction of the RSB view, but no conclusion has ever been reached. Both Terra and Aqua MODIS have an SD door in the front of the SD port as mentioned previously. The door has two positions, open and close. When the SD door is in the open position, the sunlight can pass through the SD port to reach the SD, while in the closed position the sunlight is blocked from reaching the SD. This provides the capability for a MODIS instrument to reduce the amount of the UV to illuminate the SD. Terra MODIS SD has degraded about 50% at 412 nm since launch in December of 1999 [14–16], but it has ceased to degrade since the beginning of 2012 and even has started to raise its reflectance after January of 2014 [23]. In its early mission, the SD door was kept closed except during weekly calibration events [17]. However, an SD door open failure in May of 2003 prompted a decision to keep the SD door open since 2 July 2003 [16,23]. Consequently, the SD degraded at a much faster pace afterward [16]. On the other hand, the Aqua MODIS SD door is usually kept close except when there is a calibration event, which occurs once every three weeks late in the mission [17,23]. For its entire mission since launch in May of 2002, the Aqua MODIS SD has degraded only about 20% at the wavelength of 412 nm. However, the SNPP VIIRS SD in a little less than 3 years has already degraded ∼28.5% at 412 nm, significantly surpassing the 20% Aqua MODIS SD degradation result in its entire mission at the same wavelength. Terra MODIS SD degradation reached the current degradation level of VIIRS SD at the wavelength of 412 nm by late 2005, which by then Terra MODIS SDSM has already lost its accuracy to catch the degradation of the SD for the 412 nm and other short wavelength bands. Thus, the VIIRS SD degradation derived from the SDSM measurements may have already introduced nonnegligible errors into the RSB calibration coefficients

for short wavelength bands. Base on the performance of the Aqua MODIS SD, the errors of the calibration coefficients due to the nonuniformity of the SD degradation for outgoing directions for the VIIRS 410 nm band can be estimated to be as large as ∼1.4%. If Terra MODIS is instead used as a reference, the estimated errors for the band would be much larger. This error for VIIRS is likely to become very significant as SD degradation worsens further. Considering the requirement of high accuracy on the SDR [24] from the EDR [21,22,25–20], especially ocean color EDR, a few percent of error in the calibration coefficients, F-factors, of the short wavelength bands, derived from the SD/SDSM calibration, will not satisfy the required accuracy of the ocean color products for the bands. A similar issue is likely to occur for the follow-up VIIRS instruments or other instruments on future missions if there is no door in the front of the SD port to provide the capability to reduce the illumination of sunlight on the SD surface as is currently done for SNPP VIIRS. Therefore, a recommendation for future missions is to minimize UV exposure, most primarily by installing a door in the front of the SD port and keeping the SD door in close position except during calibration events, and also by reducing the calibration operational frequency. For SNPP VIIRS and the follow-up instruments, which have already been built without an SD door, a strategy to mitigate the calibration error is desired and needed. Lunar calibration can be used for a useful mitigation strategy [8,9]. One other suggestion for future design is to include a blocking mechanism of stray light from the nadir door to reach the SD. A final one that may warrant consideration is to layout the instruments such that the SDSM view and the RTA view are as close as possible. 6. Conclusions

A careful examination of the calibration and the performance of VIIRS SD has revealed many insights. The derived SD degradation or H-factors show that degree of degradation is the greatest for the shortest wavelength bands, about 28.5% at 412 nm since launch but only 1.2% at 935 nm. The “sweet spot” for the full illumination of the SD for the SD view and of the SDSM entrance aperture for the sun view is properly selected, and the applied BRF and VFs are shown to be properly derived. The very clean results lend support that the SDSM instrument, apart from extraneous effects, performs very well. The very clean results also help to illuminate other issues affecting the performance of the SD. It is shown that SD degradation at the SWIR wavelengths should not be zero and even more importantly that the SD degradation is not uniform for all angles. Given the substantial SD degradation brought about by excessive UV exposure and the error induced by degradation nonuniformity, RSB calibration is likely already affected by a few percent errors at short wavelengths. It is therefore recommended to take measures to minimize light exposure. The gain

changes of the SDSM detectors including the fold mirror are derived from the SDSM sun-view responses in SD/SDSM calibration events for the last two plus years since VIIRS launch. It is shown that the gain degradation is greater for an SDSM detector with longer wavelengths. The derived SD degradation results at the 8 wavelengths are fitted to smooth functions and a two-dimensional surface with both time and wavelength as variables are constructed from the measured SD degradation. This work significantly improves older and other results, and the approach and the arguments presented here are relevant and applicable to other satellite sensors. An immediate impact is on the quality improvement of the ocean color products, but a longer-term implication is on the future operation and design of SD and SDSM for the VIIRS and other satellite sensors. The work was supported by Joint Polar Satellite System (JPSS) funding. We would like to thank Mike Chu for insightful suggestions. We thank two anonymous reviewers for their useful comments. The views, opinions, and findings contained in this paper are those of the authors and should not be construed as an official NOAA or US Government position, policy, or decision. References 1. C. Cao, F. DeLuccia, X. Xiong, R. Wolfe, and F. Weng, “Early on-orbit performance of the Visible Infrared Imaging Radiometer Suite (VIIRS) onboard the Suomi National Polar-orbiting Partnership (S-NPP) satellite,” IEEE Trans. Geosci. Remote Sens. 52, 1142–1156 (2014). 2. X. Xiong, J. Butler, K. Chiang, B. Efremova, J. Fulbright, N. Lei, J. McIntire, H. Oudrari, J. Sun, Z. Wang, and A. Wu, “VIIRS on-orbit calibration methodology and performance,” J. Geophys. Res. Atmos. 119, 5065–5078 (2014). 3. N. Lei, Z. Wang, J. Fulbright, S. Lee, J. McIntire, K. Chiang, and X. Xiong, “Initial on-orbit radiometric calibration of the Suomi NPP VIIRS reflective solar bands,” Proc. SPIE 8510, 851018 (2012). 4. J. C. Cardema, K. Rausch, N. Lei, D. I. Moyer, and F. DeLuccia, “Operational calibration of VIIRS reflective solar band sensor data records,” Proc. SPIE 8510, 851019 (2012). 5. J. Fulbright, N. Lei, K. Chiang, and X. Xiong, “Characterization and performance of the Suomi-NPP VIIRS solar diffuser stability monitor,” Proc. SPIE 8510, 851015 (2012). 6. E. Hass, D. Moyer, F. DeLuccia, K. Rausch, and J. Fulbright, “VIIRS solar diffuser bidirectional reflectance distribution function (BRDF) degradation factor operational trending and update,” Proc. SPIE 8510, 851016 (2012). 7. J. Sun and X. Xiong, “Solar and lunar observation planning for Earth-observing sensor,” Proc. SPIE 8176, 817610 (2011). 8. J. Sun, X. Xiong, and J. Butler, “NPP VIIRS on-orbit calibration and characterization using the moon,” Proc. SPIE 8510, 85101I (2012). 9. J. Sun, X. Xiong, W. L. Barnes, and B. Guenther, “MODIS reflective solar bands on-orbit lunar calibration,” IEEE Trans. Geosci. Remote Sens. 45, 2383–2393 (2007). 10. J. Sun and M. Wang, “On-orbit characterization of the VIIRS solar diffuser and solar diffuser screen,” Apt. Opt. (in press). 11. JPSS, “Joint Polar Satellite System (JPSS) VIIRS reflective solar bands-performance verification report (PVR)” (NASA Goddard Space Flight Center, 2011). 12. J. McIntire, B. Efremova, D. Moyer, S. Lee, and X. Xiong, “Analysis of Suomi-NPP VIIRS vignetting functions based on yaw maneuver data,” Proc. SPIE 8510, 851011K (2012). 20 December 2014 / Vol. 53, No. 36 / APPLIED OPTICS

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