Derivation of the MODIS Aqua Point-Spread Function for Ocean Color Bands

1. Derivation of the MODIS Aqua Point-Spread Function for Ocean Color Bands Gerhard Meistera, Yuqin Zongb, Charles McClainc a: OBPG (Ocean Biology Processing Group; Futuretech) b: National Institute of Standards and Technology, Gaithersburg c: OBPG (Ocean Biology Processing Group; NASA) August 11, 2008 Earth Observing Systems XIII, SPIE Optonics + Photonics 2008, San Diego

2. Background • Ocean color products (e.g. chlorophyll) are derived from water-leaving radiances • Ocean color remote sensing imposes very stringent requirements on radiometric precision (typically only 10% or less of the TOA signal is of interest) • Oceans scenes are typically a mixture of cloud and ocean pixels • Radiometric quality reduced near high contrast ratio for any imaging sensor

3. MODIS Optical Path Page 3

4. PSF definition: Lm (i0,j0) = Sij PSF(i- i0,j- j0)*LT(i,j) Lm = Measured radiance LT = True radiance PSF = Point Spread Function i = line index j = column index PSF kernel 25x25: i= i0-12, i0 -11,..., i0+11, i0+12 j= j0-12, j0 -11,..., j0+11, j0+12

5. Available from SBRS: • LSF (Line Spread Functions): smaller slit, 1 pixel from either side of slit, dynamic range 1-10-3, scan and (simulated) track direction • NFR (Near Field Response) measurements: scans of 1x10 slit (slit in track direction), up to 100 pixels to either side of peak, dynamic range 1-10-7 • NFR modeling: scatter model, certain shape parameters, no absolute scale for PSF Acknowledgement: NFR data provided by Roger Drake (SBRS/Raytheon), NFR model taken from James Young (SBRS/Raytheon) memo

6. Creation of PSF: Assume that PSF of adjacent pixel in scan direction is given by 0.125/0.75 (theoretical value from Geolocation ATBD) of center value, adjacent pixel in track direction is 5% (from LSF) Adjust center value and scale parameter from SBRS model (Harvey-Shack) so that NFR measure- ments are reproduced

7. NFR measurements and model: Band 11

8. NFR measurements and model: All bands

9. PSF model in track direction Solid line: track direction, dashed line: scan direction

10. PSF detector dependence Left: Band 16, detector 1 Right: Band 16, detector 10

11. PSF effect: Large cloud, band 11 Contamination of TOA radiance over ocean due to semi-infinite cloud

12. PSF effect: Large cloud, all ocean bands Contamination of TOA radiance over ocean due to semi-infinite cloud

13. PSF effect: Small cloud, all ocean bands Contamination of TOA radiance over ocean due to 10x10 pixel cloud

14. Straylight effects in ocean color images (preliminary) 3 Aqua granules, one coastal, 2 open ocean A20031271435 A20030702305 A20030701810

15. Definition of ‘Distance to Cloud’ C = cloud pixel, number = distance to cloud Approach: Average ocean color products for each ‘Distance to Cloud’ from 1-40

16. Histogram of ‘Distance to Cloud’ • Black, blue, red lines for Aqua granules • 3 green lines for SeaWiFS granules • Logarithmic scale, not much data beyond ‘Distance to cloud’ 20

17. TOA ocean radiances versus ‘Distance to Cloud’

18. Ocean color products versus ‘Distance to Cloud’

19. PSF correction algorithm • Traditional algorithms calculate stray light contribution to receiver assuming measured sender radiance is the true radiance • Calculation can be done iteratively • Matrix inversion approach: YIF = Cspat Ymeas YIF = column vector of straylight corrected image Cspat = straylight correction matrix Ymeas = column vector of measured image

20. Summary • MODIS has been characterized for stray light in scan direction only • PSF was developed assuming symmetry in scan and track direction • Modeled PSF predicts significant stray light contamination of ocean radiances for large clouds • MODIS Aqua image analysis suggests dependence of ocean products on distance to nearest cloud • Future: apply matrix inversion algorithm to MODIS Aqua images