1. OMI Meeting KNMI June 2006 OMI groundpixels Bert van den Oord

2. OMI Team Meeting, KNMI, June 2006 Slide 2 Bert van den Oord, KNMI Contents OMI (Development Model) telescope IFOV Effect of the polarisation scrambler IFOV: summary Centre locations ground pixels Recipe for calculating response function

3. OMI Team Meeting, KNMI, June 2006 Slide 3 Bert van den Oord, KNMI DM Telescope FOV (1) Stray light tail Beam off secondary mirror 0.78 o OMI-DM with dummy scrambler

4. OMI Team Meeting, KNMI, June 2006 Slide 4 Bert van den Oord, KNMI DM Telescope FOV (2) Scrambler broadens FOV

5. OMI Team Meeting, KNMI, June 2006 Slide 5 Bert van den Oord, KNMI Effect of scrambler Unpolarised ray incident on scrambler is split in four rays. OMI CCD pixel measures signal from 4 footprints that are located at corners of parallelogram. Weight from releative contributions depends on polarisation state incoming radiation (s-p). Sum of four contributions gives intrinsic FOV (IFOV).

6. OMI Team Meeting, KNMI, June 2006 Slide 6 Bert van den Oord, KNMI Scrambler: Wybertje/Diamond effect 0.058 deg 0.34 deg Slit orientation S-polarised P-polarised The angular deviations of the beams in the flight direction are  0.34 ◦ and  0.058 ◦. Flight direction

7. OMI Team Meeting, KNMI, June 2006 Slide 7 Bert van den Oord, KNMI IFOV: contribution of 4 rays Scrambler increases IFOV from 0.78 ◦ to 0.98 ◦

8. OMI Team Meeting, KNMI, June 2006 Slide 8 Bert van den Oord, KNMI IFOV: summary IFOV FWHM & centre determined by polarization state incident radiation. Weighted contributions from 4 locations. Resulting telescope IFOV:  Flat-topped Gaussian with FWHM about 0.98 ◦ (variations along swath).  Exponential stray light tails up to about  2 ◦ in flight direction.  Beyond  2 ◦ beam moves off secondary mirror: signal drop Calculations show that for global ground pixel percentage out- of-FOV radiation varies between 16.8% and 31.3% depending on swath angle.

9. OMI Team Meeting, KNMI, June 2006 Slide 9 Bert van den Oord, KNMI Centre locations ground pixels For each CCD pixel the LOS has been determined in OMI coordinate system (azimuth, elevation). These are stored in Operational Parameter File (OPF). GDPS: 1. Averages CCD pixel-line-of-sights per ground pixel (both in swath and wavelength direction). 2. Applies coordinate transform OMI-to-S/C reference frame that includes OMI-S/C alignment information. 3. This gives LOS in S/C reference frame. 4. Toolkit used for geolocation calculation.

10. OMI Team Meeting, KNMI, June 2006 Slide 10 Bert van den Oord, KNMI Centre locations ground pixels Rotation around x-axis: azimuth Rotation around y-axis: elevation

11. OMI Team Meeting, KNMI, June 2006 Slide 11 Bert van den Oord, KNMI Simple model for centres ground pixels Parameterization azimuth & elevation per CCD row (from OPF):

12. OMI Team Meeting, KNMI, June 2006 Slide 12 Bert van den Oord, KNMI Simple model: CCD readout CCD row range ModeBinningUV2 & VISUV1 Global849 - 528169 – 408 Spatial4169 - 408

13. OMI Team Meeting, KNMI, June 2006 Slide 13 Bert van den Oord, KNMI Flat Earth differences = angle x 705 km Azimuth differences Elevation differences

14. OMI Team Meeting, KNMI, June 2006 Slide 14 Bert van den Oord, KNMI Recipe for OMI response function 1. Telescope response function (IFOV) in elevation direction (flat-topped Gaussian) has been measured at fixed azimuth angles. 2. Determine curves of constant azimuth on Earth surface during 2 second exposure. 3. Convolve IFOV (flat-topped Gaussian) along curves of constant azimuth to determine the Effective Response Function. 4. Set your own criterion for ground pixel size (FWHM, e- folding, 99% light, 90 % light,…….) 5. Note that for fixed point on Earth surface both elevation and azimuth change during integration!

15. OMI Team Meeting, KNMI, June 2006 Slide 15 Bert van den Oord, KNMI Some suggestions X Y Z Z’ X’ Y’ -Ω-Ω Place Earth at origin and transform to X’Y’Z’ frame.

16. OMI Team Meeting, KNMI, June 2006 Slide 16 Bert van den Oord, KNMI Some suggestions In XYZ frame:  OMI (RH cosΩ, 0, -RH sinΩ)  Point on Earth surface (A,B,C) In X’Y’Z’ frame:  OMI (RH, 0, 0)  Point on Earth surface (A’,B’,C’) (RH/R)tan az + tan az sinΩ cosθ – tan az cosΩ sinθ cosφ = sinθ sinφ Write: A=R cosφ sinθ B=R sinφ sinθ C=R cosθ RH=orbit radius R=Earth radius Ω=orbit phase

17. OMI Team Meeting, KNMI, June 2006 Slide 17 Bert van den Oord, KNMI Some suggestions R = 6371 km RH=7076 km Orbit phase: 0≤Ω≤2π Latitude: 0≤θ≤π Longitude: 0≤φ≤2π Swath: -56 ◦ ≤az≤ 56 ◦ (RH/R)tan az + tan az sinΩ cosθ – tan az cosΩ sinθ cosφ = sinθ sinφ Ω+δΩ Ω δΩ=0.0021 rad