@@ -3,4 +3,165 @@ short_title: Rings Spectroscopy
33author : E. Todd Bradley
44---
55(sec: rings_spec )=
6- # Rings Spectroscopy Data Reduction
6+ # RingsSpectroscopy Data Reduction
7+
8+ ``` {admonition} Conversion status: Raw
9+ Layout unfinished and no figures yet
10+ ```
11+
12+ ## Introduction <!-- 7.1 -->
13+
14+ This document describes an approach for using the Cassini UVIS spectra for analysis of
15+ Saturn’s rings. Observations of Saturn’s rings with the UVIS began at orbit insertion in 2004 and
16+ will continue throughout the extended mission. The majority of rings spectroscopic observations
17+ have been configured with the UVIS acting as the secondary instrument; thus the observational
18+ geometry and spacecraft slew rate have been driven by other instruments. As of January, 2011
19+ the UVIS had only been the primary instrument one time for making rings spectroscopic
20+ measurements. This may not be the case for the extended mission where the UVIS may be used
21+ as the primary instrument for ring spectroscopy. Nevertheless, as a secondary rider the UVIS has
22+ acquired hundreds of spectroscopic observations of the rings. Observations of the rings by the
23+ UVIS for the purpose of ring spectroscopy deals with the instrument collecting solar photons that
24+ have irradiated Saturn’s rings and either reflected back into the instrument (lit side observations)
25+ or have been transmitted through the rings into the instrument (unlit side observations). Typically
26+ both EUV and FUV spectra are collected. Table 7.1 lists parameters and typical observational
27+ aspects of the rings. For a complete description of the UVIS see Esposito et al, 2004.
28+ Rings spectroscopic data suitable for analysis requires calibration of the raw spectra and
29+ then subsequent data reduction that depends on both observational geometry and the needs of the
30+ investigator using the data. There is therefore no systematic approach that can be used for all
31+ situations. However, data reduction may be broken down into distinct categories and the
32+ importance of each determined by the investigator. This document aims to present an overview
33+ of the important data reduction categories with the goal of conveying an approach for applying
34+ different data reduction steps.
35+
36+ Wavelength range EUV (56.3-118.2 nm) FUV (111.5-191.2 nm)
37+ Integration time 60 – 600 seconds
38+ Spectral slit High resolution slit (0.75 mRad) or low resolution slit
39+ (1.5 mRad). Most pre-2007 observations are high
40+ resolution and most 2007-2010 are low resolution slit
41+ Spectral binning Either 1 or 2 with the majority of the observations being
42+ a 2
43+ Spatial binning Usually always set to 1
44+ Lit / Unlit side observations 80% lit side
45+ Typical pixel field of view < 4000 km
46+
47+ Table 7.1. Parameters and observational aspects used for ring observations from orbit insertion through 2010. With
48+ the exception of the wavelength range, all of these parameters may be varied. The values listed in this table represent
49+ the majority of all observations made so far.
50+
51+ ## Calibration of raw spectra <!-- 7.2 -->
52+
53+
54+ Calibration consists of first subtracting a background from the raw counts. The
55+ background arises primarily from detector dark counts introduced by Cassini’s three radioisotope
56+ thermoelectric generators (RTGs). There are other backgrounds that may or may not contribute
57+ to the total raw counts; however the RTG background is internal to the spacecraft and must
58+ always be dealt with. The other backgrounds will be discussed in the next section. We then
59+ multiply the data by a calibration factor that includes flat fielding and converts raw spectra in
60+ counts per integration time to radiance in kilo-Rayleights/Å, where 1 kilo-Rayleigh = 10^9
61+ photons sec-^1 cm-^2 emitted over 4π steradians. Details of the UVIS instrument and calibration are
62+ given in Chapters 3 and 4. Figure 7.1 shows typical radiance from the B ring on the lit side.
63+ Lyman- α is clearly present as well as the solar continuum. This data was acquired using a
64+ spectral binning of 2 with the low resolution slit. Software developed by the UVIS team is
65+ publicly available that will convert raw data downloaded from the PDS to calibrated data. This
66+ software, called Cube Generator, is described in Chapter 12.
67+
68+ Figure 7.1 An example of radiance from the B ring measured from the lit side of the rings. Lyman- α is clearly
69+ present. The spectra longward of 160 nm is due to solar irradiance reflecting from the rings.
70+
71+ ## Data reduction <!-- 7.3 -->
72+
73+ This section describes other data reduction steps that may be taken depending on the
74+ observational geometry and the needs of the investigator. Most of these steps depend on
75+ observing geometry, which may be determined using Cube Generator that is described in
76+ Chapter 12. Investigators are strongly encouraged to look at the geometrical configuration of
77+ observations being used for analysis. Special attention should be given to the location and size of
78+ pixels projected onto the ring plane and the angle of the line of sight with respect to the dayside
79+ of the planet. The importance of these provisions is explained in the following subsections.
80+
81+
82+ ** _ 7.3.1 Saturn shine_ **
83+
84+ Solar irradiance reflected from the atmosphere of Saturn may contribute to the signal by
85+ either reflecting off of Saturn’s rings and entering into the instrument or by entering the
86+ instrument when the Saturn-spacecraft-boresight angle is sufficiently small, also known as off-
87+ axis light. The magnitude of Saturn shine varies on a number of factors. Presumably the peak
88+ Saturn shine reflected from the rings is for regions extending radially outward from local noon,
89+ with the magnitude decreasing for both increasing ring plane radius and solar hour angles away
90+ from local noon. Similarly off-axis light peaks for small off-axis angles on the dayside
91+ hemisphere and decreases for both increasing off-axis angle and observations away from local
92+ noon. Furthermore, Saturn shine that reflects off of the rings and into the instrument is spectrally
93+ modified by the reflectance properties of Saturn’s rings whereas off-axis light presumably bears
94+ the same spectral shape as that of Saturn’s atmosphere. An expression for the reflectance of the
95+ rings with both cases of Saturn shine included may be written as:
96+
97+ :::{math}
98+ (7.1)
99+ :::
100+
101+ where Fsun is the flux from the Sun divided by π, FSat is the flux from Saturn’s atmosphere
102+ divided by π, and a, b, and c are constants. The first term on the right is due to solar radiation
103+ being reflected/transmitted after only interacting with the rings, the second term on the right is
104+ due to solar radiation first reflected off of Saturn’s atmosphere and then reflecting from the rings
105+ into the instrument, and the last term on the right is due to solar radiation reflecting from
106+ Saturn’s atmosphere and then into the instrument. Figure 7.2 shows the radiance measured from
107+ Saturn’s atmosphere for observations that looked directly at the atmosphere. This corresponds to
108+ FSat given in Equation 7.1. For non-negligible Saturn shine analysis code will have to be written
109+ to solve for the constants in Equation 1. There may be situations where Saturn shine reflected
110+ from the rings is negligible or off-axis light is negligible; in which case the constants b and c,
111+ respectively, will be zero.
112+
113+ ```
114+ I = aFSunr + bFSatr + cFSat
115+ ```
116+ ```
117+ r = I − cFSat
118+ aFSun + bFSat
119+ ```
120+
121+ Figure 7.2. Normalized radiance measured from Saturn’s atmosphere. For small off-axis angles above the dayside
122+ this spectra may contribute to the total signal from the UVIS for rings observations. Also, for observations of the
123+ rings near local noon, a radiance such as this may reflect from the rings and contribute to the measured radiance
124+ from the instrument.
125+
126+ ### Skewed field of view
127+
128+ The optical system of the FUV and EUV channels images an extended source to
129+ an entrance slit and is then spectrally dispersed onto a 64 spatial X 1024 spectral detector, where
130+ the spatial direction is co-aligned along the length of the slit. The projected size of a pixel is ~ 1
131+ mrad in the direction along the length of the slit and 0.75 mrad or 1.5 mrad in the cross slit
132+ direction for either the high resolution or low resolution slit, respectively. Depending on the
133+ position and orientation of the spacecraft with respect to the ring plane, the shape of a pixel may
134+ be either rectangular or non-rectangular when projected onto the ring plane. Furthermore, the
135+ relative motion between the spacecraft and ring plane during an integration period results in the
136+ projected field of view being different than the instantaneous field of view. Figure 7.3 shows the
137+ projected field of view of a pixel at the initial, middle, and final times for a three hundred second
138+ integration period. The pixel begins in the outer B ring and moves into the Cassini Division.
139+ Thus the data for that pixel has contributions from both rings regions. This complicates analysis
140+ of ring observations and has led to procedures for binning the data and interpolating to evenly
141+ spaced grids as will be discussed in the next section.
142+
143+
144+ Figure 7.3. The projected pixel begins in the outer B ring and drifts into the Cassini Division. Contributions to the
145+ signal arise from both the outer B ring and the Cassini Division. Cube generator (Chapter 12) now returns the
146+ coordinates of the corner of the pixel at the initial, middle, and final integration period
147+
148+ ### Binning the data
149+
150+ During an observation the field of view of a pixel projected onto the ring plane is affected
151+ by the spacecraft motion and the angle and orientation at which the line of sight intersects the
152+ ring plane. This results in pixels that are non-uniform both in size and distribution in the ring
153+ plane. Azimuthally binning pixels within relatively large radial bins may bias the result towards
154+ regions within bins where there is a higher concentration of pixels. Figure 7.4 shows how pixels
155+ may be unevenly distributed within a ten thousand km radial bin in the outer B ring, denoted by
156+ the heavy lines. In this simple example there are two pixels that lie at the outer edge of the radial
157+ bin with other pixels overlapping one another radially for decreasing radius. Simply averaging
158+ the spectra from all of the pixels within the ten thousand km radial bin will weight the average
159+ towards the outer most portion of the radial bin since there are more pixels in the outer region of
160+ the bin than in the inner region. However, notice that there are pixels outside of the radial bin on
161+ both sides, which allows for a technique to deal with uneven sampling of the rings. An example
162+ is taken from Bradley et al (2010) for resampling the data into an evenly spaced grid. In
163+ anticipation of data being azimuthally binned over some radial increment, we only consider the
164+ radial direction when resampling the data. We divide the rings into a 100 km radial grid and for
165+ each grid element, we select all pixels that intersect that element. The size of the pixels takes into
166+ account the skewed pixel size as described in Section 7.3.2.
167+
0 commit comments