The Solar Source and SOFIE Measurements         

Characteristics of the sun are an important consideration in solar occultation measurements.   Solar intensity is measured above the Earth's atmosphere (exoatmospheric) and through the atmosphere (endoatmospheric) during spacecraft sunset or sunrise.  The ratio of endoatmospheric to exoatmospheric intensity (Iendo/ Iexo) yields transmission,  which is the quantity used to determine atmospheric properties.   Since the same optical-electrical path is used to measure Iendo and Iexo,  solar occultation measurements are essentially self calibrating.   Complications arise,  however,  due to spatial and spectral variability in solar intensity.  

The impact of solar source variability on SOFIE measurements was examined using a description of solar intensity based on theory and measurements ["Allen curves"].  The Allen relationship describes solar limb darkening (SLD) as a function of wavelength and distance from the sun's center.   The resulting SLD curves are radially symmetric and do not account for real solar features such as sun spots.   These results indicate that movement of the FOV from its desired position on the sun ("lockdown" position") will induce false signals.   Keeping these movement-induced signals below the measurement noise (or at least well below expected signal levels) places requirements on telescope pointing accuracy.  

Solar intensity decreases from sun center to the solar edge,   at a rate that increases with decreasing wavelength (Figure 1).  Measured solar intensities are affected by averaging over the instrument field of view (FOV).   Solar intensities were averaged over a theoretical SOFIE FOV (Figure 2) for the calculations presented here.   The SOFIE FOV center will be pointed at sun center ("zero lockdown") during a limb scan.  Since solar intensity decreases away from sun center,  FOV drift from lockdown will result in a decrease in the background solar intensity.  This decrease will induce a false transmission signal,  as demonstrated in Figure 3 for one SOFIE wavelength.  Induced transmissions were calculated as the ratio of solar intensity at some distance from lockdown to the value at lockdown.  These results indicate that an unwanted FOV drift of roughly 5 arcsec will induce a false signal of 1e-6 at 2.6 microns wavelength.  Drift induced signals are larger at shorter wavelengths,  because the SLD curves are steeper at shorter wavelengths (Figure 1).  This effect is demonstrated in Figure 4.
   
 
 
The effects of FOV movement from lockdown also impact the SOFIE band pair difference (BPD) signal measurements.  Because SLD is wavelength dependent,  the same amount of FOV drift will induce a different signal in each SOFIE channel.  Induced BPD signals were calculated as the difference in induced transmission for each SOFIE channel pair.  Figure 5 shows the induced BPD signal versus wavelength,  for the FOV straying 10 arcsec from zero lockdown.   The effect on BPD measurements is driven by the spectral dependence of solar intensity and the wavelength separation between band pairs.   Drift induced BPD signals are greatest where the solar intensity is strongly dependent on wavelength (short wavelengths) and where band pairs are widely spaced.  Figure 6 shows the induced band pair difference signal versus distance moved from zero lockdown for three wavelengths.  To keep the drift-induced BPD signal below the measurement noise (about 1e-6) for the 1 micron particle channel,  the FOV cannot drift more than about 5 arcsec from lockdown.  

The effect of FOV drift from lockdown depends on the lockdown position.  Figure 7 shows the induced 2.6 micron (H2O) difference signal vs. distance moved from lockdown,  for 3 lockdown positions.   When lockdown is off-center,  drift towards sun center induces a negative difference signal.  If FOV drift were known to occur in one direction (up or down),  then the drift induced difference signal could actually be minimized by using an off-center lockdown.  However,  for random FOV drift (up or down relative to lockdown),  the effects of drift are minimized at zero lockdown.  Figure 8 shows the induced H2O channel difference signal vs. lockdown position,  for drifting 10 arcsec from lockdown.  These results further demonstrate the benefits of sun-center lockdown.   In addition,   these results elude to the effects of lockdown uncertainty.   If lockdown is known to better than 25 arcsec,  the induced difference signal is less than about 1e-6 if FOV drift remains less than 10 arcsec.  

 

The effects of FOV drift are summarized by showing the amount of drift (from zero lockdown) that will induce a difference signal equal to the measurement noise (1e-6) (Figure 9).  The ozone channel (0.3 microns) represents the worst case scenario for drift induced noise,  where roughly 3 arcsec FOV drift will induce a difference signal of 1e-6 .  The IR channels can tolerate about 25 arcsec FOV drift.

Another issue for pointing requirements is how well the lockdown position must be known.  For example,  what is the result of a 5 arcsec lockdown when 0 arcsec is expected?  If FOV drift does not occur,  then lockdown errors have no effect.  However,  if FOV drift occurs,  then induced signals occur at a rate determined by the SLD curves.  If we know exoatmospheric FOV position exactly,  then a known drift can be corrected using the SLD curve.  If we do not know the exoatmospheric FOV position,  then a known drift cannot be corrected.  The question then,  is how will uncertainty in the exoatmospheric FOV position affect our ability to remove known drift?  Figure 10 shows how lockdown uncertainty can affect drift induced difference signals.   For example,  if the FOV drifts 10 arcsec from zero lockdown,  then the lockdown must be known to within about 30 arcsec to keep the induced difference signal below 1e-6 for the IR channels (the induced signal is always greater than 1e-6 in the short wavelength channels for 10 arcsec FOV drift).  For 1 arcsec FOV drift,  the lockdown uncertainty is relaxed to nearly 300 arcsec for the IR channels,   but remains less than 20 arcsec for the short wavelength channels.  



The above analysis used an idealized description of the sun ("Allen curves").  Here we consider real solar variability by using HALOE measurements of solar limb darkening.   HALOE scans across the solar disc outside the atmosphere before or after each occultation event.   These data offer SLD measurements at 8 wavelengths covering the past 12 years.  The example below shows HALOE SLD measurements that encountered a sunspot.  The measured SLD curves at 2.45 and 5.26 microns wavelength are compared to Allen curves in Figures 11 and 12.  A sunspot is evident near -8 arcmin,  as a sharp decrease in solar intensity.  The SLD spectra from HALOE and the Allen relationship are compared in Figures 13 and 14.   HALOE SLD spectra at -8 arcmin are compared to the Allen results for -8 arcmin.   Because the sun is considered radially symmetric,  the HALOE SLD spectra at 8 arcmin is shown for reference.   While the HALOE SLD at 8 arcmin and the Allen SLD spectra are close in magnitude (Figure 13),  the relative wavelength dependence of the HALOE measurements deviates from the Allen predictions (Figure 14).  The HALOE SLD measured under sunspot conditions exhibits an even steeper slope than the quiescent HALOE measurement or the Allen curve.  Our next step is to determine the effects of sunspots on SOFIE measurements using real SLD curves measured by HALOE.