# Difference between revisions of "IKONOS"

IKONOS is a commercial earth observation satellite. Details about the sensor are provided at Digital Globe's IKONOS Data Sheet

## Pre-Processing Overview

Typically, multispectral satellite data are converted into physical quantities such as Radiance or Reflectance before they are subjected in multispectral analysis techniques (image interpretation, band arithmetic, vegetation indices, matrix transformations, etc.). The latter can be differentiated in Top of Atmosphere Reflectance (ToAR) which does not account for atmospheric effects (absorption or scattering) and in Top of Canopy Reflectance (ToCR) which introduces a "correction" for atmospheric effects.

In order to derive Reflectance values, likewise as with remotely sensed data acquired by other sensors, IKONOS raw image digital numbers (DNs) need to be converted to at-sensor spectral Radiance values. At-sensor spectral Radiance values are an important input for the equation to derive Reflectance values. Note, Spectal Radiance is the measure of the quantity of radiation that hits the sensor and typically expressed in ${\displaystyle {\frac {W}{m^{2}*sr*nm}}}$, that is watts per unit source area, per unit solid angle, and per unit wavelength.

Converting DNs to at-sensor Radiance can be done by using the following equation:

${\displaystyle L\lambda ={\frac {10^{4}*DN\lambda }{CalCoef\lambda *Bandwidth\lambda }}}$

Converting to Top of Atmosphere Reflectance, also referred to as Planetary Reflectance, can be done by using the following equation:

${\displaystyle \rho _{p}={\frac {\pi *L\lambda *d^{2}}{ESUN\lambda *cos(\Theta _{S})}}}$

where:

• ${\displaystyle \rho }$ - Unitless Planetary Reflectance
• ${\displaystyle \pi }$ - mathematical constant (3.14159265358)
• ${\displaystyle L\lambda }$ spectral Radiance at the sensor's aperture, from equation... ToADD
• ${\displaystyle d}$ - Earth-Sun distance in astronomical units, interpolated values
• ${\displaystyle Esun}$ - Mean solar exoatmospheric irradiance(s) (W/m2/μm), interpolated values
• ${\displaystyle cos(\Theta _{s})}$ - Solar zenith angle, from the image acquisition's metadata

## Pre-Processing

### Deriving Physical Quantities

Converting Digital Numbers to Radiance/Reflectance requires knowledge about the sensor's specific spectral band parameters. Those are, as extracted from the document IKONOS Planetary Reflectance and Mean Solar Exoatmospheric Irradiance, by Martin Taylor (see references):

 Pan_CalCoef=161	;	Pan_Width=403		;	Pan_Esun=1375.8
Blue_CalCoef=728	;	Blue_Width=71.3		;	Blue_Esun=1930.9
Green_CalCoef=720	;	Green_Width=88.6	;	Green_Esun=1854.8
Red_CalCoef=949	;	Red_Width=65.8		;	Red_Esun=1556.5
NIR_CalCoef=843	;	NIR_Width=95.4		;	NIR_Esun=1156.9


Converting a Blue Band (Digital Numbers) in to Spectral at-sensor Radiance in the correct units to be further used for the conversion in to unitless Reflectance:

r.mapcalc "Blue_Radiance = ( (10000 * IKONOS_Blue_Band_DN) / (728 * 71.3) )"


#### Planetary Reflectance

The equation to derive Reflectance values incorporates in addition:

• The mathematical constant Pi PI=3.14159265358.
• The Earth-Sun distance in astronomical units which depends on the acquisition's day of year (DOY -- also referred to as Julian day, Ordinal_date) and can be retrieved from the following spreadsheet <http://landsathandbook.gsfc.nasa.gov/excel_docs/d.xls>.
• The mean solar exoatmospheric irradiance in ${\displaystyle {\frac {W}{m^{2}*\mu m}}}$. See 3rd column of (interplated) values given above.
• The cosine of the Solar Zenith Angle (SZA) at the time of the acquisition. The SZA can be calculated from its complementary Solar Elevation Angle (SEA) given in the image acquisition's metadata.

In the following example we accept as the acquisition's DOY=166 and SEA=52.78880. Hence, we get the Earth-Sun distance ESD=1.0157675 and SZA = 37.21120 deg.

Converting the in-Blue spectral band at-sensor Radiance in to Planerary Reflectance:

PI=3.14159265358; ESD=1.0157675; BAND_Esun=1930.9; SZA=37.21120
r.mapcalc "Blue_Reflectance = ( ${PI} * Blue_Radiance *${ESD}^2 ) / ( ${BAND_Esun} * cos(${SZA}) )"


## Post-Processing

Having beforehand satellite image data expressed in physical quantities (radiance or reflectance) is preferred to follow-up with digital image analysis techniques.