Radiometer Considerations And Cal/Val Lectures in Bertinoro 23 Aug – 2 Sep 2004 Paul Menzel NOAA/NESDIS/ORA Examples from MODIS MODIS NEdR Estimate

Radiometer Considerations And Cal/Val Lectures in Bertinoro 23 Aug – 2 Sep 2004 Paul Menzel NOAA/NESDIS/ORA Examples from MODIS MODIS NEdR Estimate www.phwiki.com

Radiometer Considerations And Cal/Val Lectures in Bertinoro 23 Aug – 2 Sep 2004 Paul Menzel NOAA/NESDIS/ORA Examples from MODIS MODIS NEdR Estimate

Chase, Jodie, Food Correspondent has reference to this Academic Journal, PHwiki organized this Journal Radiometer Considerations And Cal/Val Lectures in Bertinoro 23 Aug – 2 Sep 2004 Paul Menzel NOAA/NESDIS/ORA Comparison of geostationary (geo) in addition to low earth orbiting (leo) satellite capabilities Geo Leo observes process itself observes effects of process (motion in addition to targets of opportunity) repeat coverage in minutes repeat coverage twice daily (t 30 minutes) (t = 12 hours) full earth disk only global coverage best viewing of tropics best viewing of poles same viewing angle varying viewing angle differing solar illumination same solar illumination visible, IR imager visible, IR imager (1, 4 km resolution) (1, 1 km resolution) one visible b in addition to multispectral in visible (veggie index) IR only sounder IR in addition to microwave sounder (8 km resolution) (17, 50 km resolution) filter radiometer filter radiometer, interferometer, in addition to grating spectrometer diffraction more than leo diffraction less than geo

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Relevant Material in Applications of Meteorological Satellites CHAPTER 12 – RADIOMETER DESIGN CONSIDERATIONS 12.3 Design Considerations 12-1 12.3.1 Diffraction 12-1 12.3.2 The Impulse Response Function 12-2 12.3.3 Detector Signal to Noise 12-2 12.3.4 Infrared Calibration 12-3 12.3.5 Bit Depth 12-5 Remote Sensing Instrument Considerations Radiometer Components Optics collect incoming radiation separate or disperse the spectral components (dichroics, grating spectrometer, interferometer, prism, ) focus the radiation to field stop Detectors respond to the photons with a voltage signal Electronics voltage signal is amplified by the electronics A/D converts into digital counts. Per as long as mance Characteristics Responsivity measure of the output per input Detectivity ratio of the responsivity per noise voltage Calibration attempts to reference the output to known inputs. Design Considerations Diffraction function of the mirror size Impulse Response determines how sharp edges appear Signal to Noise how clean is the image Infrared Calibration enables quantitative use of measurements Bit Depth truncation error can limit precision of data Satellite Orbits Geostationary vs Polar orbiting vs Other Telescope Radiative Power Capture proportional to throughput A Spectral Power radiated from A2 to A1 = L() A11 mW/cm-1 {Note: A1 A2 / R2 = A11 = A22 } Radiance from surface = L() mW/m2 sr cm-1 Instrument Collection area Earth pixel

Approaches To Separate Radiation into Spectral B in addition to s radiometer – uses filters to separate spectrum by reflection in addition to transmission (wavelengths are selectively reflected in addition to transmitted) prism – separates spectrum by refraction (different wavelengths bend into different paths) grating spectrometer – spatially separates spectrum by diffraction (wavelets from different slits will be in phase in different locations depending on wavelength) interferometer – separates spectrum by interference patterns spread out temporally (wavelets from different paths will be in phase at different times depending on wavelength) Radiation is characterized by wavelength in addition to amplitude a Interference: positive (a) as long as two waves almost in phase in addition to negative (b) as long as two waves almost out of phase

Combining two waves of slightly different wavelength Spectral Separation with a Prism: longer wavelengths deflected less Spectral Separation with a Grating: path difference from slits produces positive in addition to negative wavelet interference on screen

Spectral Separation with an Interferometer – path difference (or delay) from two mirrors produces positive in addition to negative wavelet interference Separation of Spectra Interferometer measurements compared with atmospheric physics calculations CO2 Lines

Design Considerations (1) Diffraction Mirror diameter defines ability of radiometer to resolve two point sources on the earth surface. Rayleigh criterion indicates that angle of separation , , between two points just resolved (maxima of diffraction pattern of one point lies on minima of diffraction pattern of other point) sin = / d where d is diameter of mirror in addition to is wavelength. Geo satellite mirror diameter of 30 cm at infrared window wavelengths (10 microns) has resolution of about 1 km. This follows from 10-5 m / 3 x 10-1 m = 3.3 x 10-5 = r / 36,000 km or r = 1 km = resolution. Energy distribution from diffraction through a circular aperture Max number energy location of ring Central max E 0 1.22 / d Second max 0.084E 1.22 2.23 / d Third max 0.033E 2.23 3.24 / d Fourth max 0.018E 3.24 4.24 / d Fifth max 0.011E 4.24 5.24 / d Thus as long as a given aperture size more energy is collected within a given FOV size as long as shorter vs. longer wavelengths Central 2 3 4 5 Energy distribution of 4 micron radiation going through a geo 30 cm diameter circular aperture to the focal point Max number % Energy radius of source Central max 82% 0.58 km Second max 91% 1.06 km Third max 94% 1.54 km Fourth max 95% 2.02 km Tenth max 98% 4.88 km Twentieth max 99% 30.3 km Fortieth max 99.5% 50.6 km Central 2 3 4 5

Energy distribution of 10 micron radiation going through a geo 30 cm diameter circular aperture to the focal point Max number % Energy radius of source Central max 82% 1.45 km Second max 91% 2.65 km Third max 94% 3.84 km Fourth max 95% 5.04 km Tenth max 98% 12.2 km Twentieth max 99% 75.7 km Fortieth max 99.5% 126.4 km Central 2 3 4 5 Energy distribution of 10 micron radiation going through a geo 50 cm diameter circular aperture to the focal point Max number % Energy radius of source Central max 82% 0.84 km Second max 91% 1.59 km Third max 94% 2.30 km Fourth max 95% 3.02 km Tenth max 98% 7.32 km Twentieth max 99% 45.4 km Fortieth max 99.5% 75.8 km Central 2 3 4 5 Distribution of 10 um energy sources focused by 30 cm mirror onto 112 urad square detector (total detected signal emanating from circle of given size) % of signal emanating from circle with diameter of (FOV = 4km) 60% one FOV 73% 1.25 FOV 79% 1.5 FOV Effect of nearby 220 K clouds on 300K clear scene as long as clear sky brightness temperature (CSBT) to be within 1 K clear area must have at least 30 km diameter Rule of thumb is 1% 220 K cloud in addition to 99% 300 K clear sky results in CSBT off by 0.5 K at 10 microns

Calculated diffraction effects as long as Geo 30 cm mirror as long as infrared window radiation with a 2 km radius FOV in a clear scene of brightness temperature 300 K surrounded by clouds of 220, 260, or 280 K. Brightness temperature of a 10 radius clear hole is too cold by about 1.5 K. Design Considerations (2) Impulse or Step Response Function Detector collects incident photons over a sampling time in addition to accumulates voltage response, which is filtered electronically. This is characterized by impulse (or step) response function, detailing what response of sensor is to delta (or step) function input signal. Response function is determined from characteristics of prealiasing filter which collects voltage signal from detector at sampling times. Perfect response of detector continuously sampling scene with 100% contrast bar extending one FOV. Scene radiance Detector response Percentage of total signal appearing in samples preceding in addition to following correlated sample peak; as long as GOES-8 infrared window samples sample N-2 has 4.3% of total signal, N-1 has 26.5%, N peaks with 44.8%, N+1 has 23.4%, in addition to N+2 has 1.0%. This causes smearing of cloud edges in addition to other radiance gradients.

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Design Considerations (3) Detector Signal to Noise Noise equivalent radiance as long as infrared detector can be expressed as NEDR() = [Ad f] 1/2 / [Ao () D ] where is preamplifier degradation factor Ad is detector area in cm2 f is effective electronic b in addition to width of radiometer Ao is mirror aperture area in cm2 () is transmission factor of radiometer optics in spectral interval is solid angle of FOV in steradians D is specific spectral detectivity of detector in spectral b in addition to in cm Hz1/2 / watt, in addition to is spectral b in addition to width of radiometer at wavenumber in cm-1. NEDR as long as GOES-8 imager HgCdTe detectivity drops off drastically in CO2 b in addition to (~13um) Can stretch detectivity to longer wavelengths by reducing it at shorter wavelengths Radiation from >13um usually detecting smoother upper atmosphere so S/N can be regained with spatial averaging Can also filter radiances (principal component, )

Guaranteed NEdN in addition to NEdT Per as long as mance 15% Margin Included in NEdNs in addition to NEdTs Values Include All Expected Error Effects Design Goals ITT Guaranteed Per as long as mance ITT Guaranteed Per as long as mance System Per as long as mance NEdNs Are Much Better Than Government Design Goals HgCdTe detectivity drops off drastically in CO2 b in addition to (~13um) Can stretch detectivity to longer wavelengths by reducing it at shorter wavelengths Radiation from >13um usually detecting smoother upper atmosphere so S/N can be regained with spatial averaging Can also filter radiances (principal component, ) Design Considerations (4) Infrared Calibration Radiometer detectors are assumed to have linear response to infrared radiation, where target output voltage is given by Vt = Rt + Vo in addition to Rt is target input radiance, is radiometer responsivity, in addition to Vo is system offset voltage. Calibration consists of determining in addition to Vo. This is accomplished by exposing radiometer to two different external radiation targets of known radiance. A blackbody of known temperature in addition to space (assumed to emit no measurable radiance) are often used as the two references. If z refers to space, bb blackbody, calibration can be written as Vz = Rz + Vo Vbb = Rbb + Vo where = [Vbb – Vz]/[Rbb – Rz] Vo = [Rbb Vz – Rz Vbb]/[Rbb – Rz] Using Rz=0 this yields Rt = Rbb [Vt – Vz] / [Vbb – Vz].

MODIS TPW 22 May 2002 SSMI

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