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TELIS radiometric calibration

TELIS radiometric calibration. Arno de Lange. Planar parallel atmosphere. 55 km. 50 km. 45 km. 40 km. 45 °. 30 °. 35 km. Path length ratio 30 ° / 45 ° = √2 for all layers. Determining the 0 K line 1.

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TELIS radiometric calibration

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  1. TELIS radiometric calibration Arno de Lange

  2. Planar parallel atmosphere 55 km 50 km 45 km 40 km 45° 30° 35 km Path length ratio 30° / 45° = √2 for all layers

  3. Determining the 0 K line 1 • If you have 2 spectra corresponding to 30° and 45° upwards looking then the ratio of intensity is √2 • From this it follows that: [ y(30°) – y0 ] / [ y(45°) – y0 ] = √2, y0 = [ √2 y(45°) – y(30°) ] / [ √2 – 1 ], where: y(30°) = intensity at 30° y(45°) = intensity at 45° y0 = 0 K line All intensities are in arbitrary units, and most likely in bits from the DACS.

  4. Determining the 0 K line 2 • Two assumptions have been made: • Intensity is linear with path length (= no saturation) • DACS is linear • Note that: • No information of the profile is needed • The 0 K line is determined purely by the geometry of the viewing angles • A hot lot is still needed for the absolute calibration • Horizontal variation is not accounted for. This might be an issue at sunrise with a azimuth viewing angle not along the terminator

  5. Spherical atmosphere 55 km 50 km 45 km 40 km 45° 30° 35 km (Not to scale) Path length ratio 30° / 45° √2 for low layers Path length ratio 30° / 45° 1 for very high layers

  6. Planar vs. spherical • In a planar parallel atmosphere the ratio between two path lengths is fixed and fully determined by geometry • In a spherical atmosphere the ratio between two path lengths changes with altitude: • Flight altitude  planar parallel case • Infinite altitude  1 • The main question is how fast does this ratio change with altitude?

  7. Path length ratio vs. altitudefor a spherical atmosphere and an instrument at 35 km √2

  8. 0 K determination • The ratio changes slowly with altitude: • 35 km ratio = √2 • 100 km ratio = 1.39 • The ratio is therefore within 2% of √2 for the whole atmosphere • So, assuming a fixed ratio of √2 gives rise to an error of < 2% in the calibration • The intensity of an OH line at 45° is 12 K • 2% of 12 K = 0.24 K • With two upward looking calibration observations calibration error in zero K level reduced from 12 K down to 0.24 K.

  9. Analysis with synthetic spectra • In the following slides the analysis will be done with synthetic OH spectra • Assumptions made • Spherical atmosphere • Standard tropical atmosphere • Flight altitude of 35 km • LO = 1830 GHz • Single side band (upper side band)

  10. OH spectrum

  11. Ratio 30°/45°

  12. d = [ Ratio 30°/45° ] / √ 2 – 1

  13. Error 0 K = d intensity(45°)

  14. Conclusion • Radiometric calibration can be done by 3 reference measurements: • hot load • deep space at 45° • deep space at 30° • 0 K line can be determined within 0.2 K by this method • Angles of 30° and 45° are not exactly needed, but form a good compromise between: • contrast (factor √2 ) • deviation from geometrical ratio (< 2%)

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