# 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


The following examples exemplify the conversion of raw Blue band digital numbers into Radiance and Reflectance.

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}) )"


#### Automatising Conversions

The conversion process ca be scripted to avoid repeating the same steps for each band separately. In bash, such a script might be as the following example. Note, however, in this example script constants, band parameters and acquisition related metadata are hard-coded!

#!/bin/bash

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

# bands to process -- hardcoded!
Spectral_Bands="Pan Blue Green Red NIR"

# loop over all bands
for BAND in ${Spectral_Bands}; do echo "Processing the${BAND} spectral band"

# set region
g.region rast=${BAND}_DNs # echo something? # set band parameters as variables eval BAND_CalCoef="${BAND}_CalCoef"
eval BAND_Width="${BAND}_Width"; echo "Band Parameters set to CalCoef=${!BAND_CalCoef}, Bandwidth=${!BAND_Width}" # conversion to Radiance r.mapcalc "${BAND}_Radiance = ( ( 10^4 * ${BAND}_DNs ) / (${!BAND_CalCoef} * ${!BAND_Width} ) )" # add info r.support map=${BAND}_Radiance \
title="" \
units="W / m2 / μm / ster" \
description="At-sensor echo ${BAND} band spectral Radiance (W/m2/μm/sr)" \ source1='"IKONOS Planetary Reflectance and Mean Solar Exoatmospheric Irradiance", by Martin Taylor, Geoeye' # Pi constant PI=3.14159265358 # band parameters DOY=166; ESD=1.0157675 # get Sun Zenith Angle SEA=52.78880; SZA=$(echo "90 - ${SEA}" | bc ) eval BAND_Esun="${BAND}_Esun"; echo "Using Esun=${!BAND_Esun}" # calculate ToAR r.mapcalc "${BAND}_ToAR = \
( ${PI} *${BAND}_Radiance * ${ESD}^2 ) / (${!BAND_Esun} * cos(${SZA}) )" # add some metadata r.support map=${BAND}_ToAR \
title="echo ${BAND} band (Top of Atmosphere Reflectance)" \ units="Unitless planetary reflectance" \ description="Top of Atmosphere echo${BAND} band spectral Reflectance (unitless)" \
source1='"IKONOS Planetary Reflectance and Mean Solar Exoatmospheric Irradiance", by Martin Taylor, Geoeye' \
source2="e.g., the Image Provider!" \
history="PI=3.14159265358; ESD=1.0157675; BAND_Esun=1930.9; SZA=37.21120"

done


## Post-Processing

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

### Pan Sharpening

Pan-Sharpening / Fusion is the process of merging high-resolution panchromatic and lower resolution multi-spectral imagery. GRASS 7 holds a dedicated pan-sharpening module, i.pansharpen which features three techniques for sharpening, namely the Brovey transformation, the classical IHS method and one that is based on Principal Components Analysis (PCA).

One approach inside GRASS-GIS to get an acceptable color-balanced composite image after Pan-sharpening 11-bit IKONOS spectral bands comprises the following steps

1. rescale the 11-bit IKONOS spectral bands to 8-bit ranging in [0, 255] (r.rescale)
2. pan-sharpen with any of the featured methods (Brovey, IHS, PCA) (i.pansharpen)
3. color-balance by using the i.landsat.rgb module or manually adjusting the color tables of the bands of interest
4. create a composite image by using the r.compose module

#### Example Instructions

i.pansharpen works fine with 8-bit raster maps as an input. If the data to be processed are out of this range, that is out of ${\displaystyle [0,255]}$, they can be rescaled to fit into this range by using GRASS' r.rescale module.

Given an IKONOS set of 11-bit spectral bands (Blue, Green, Red, NIR and Pan) ranging between ${\displaystyle [0,2047]}$, and then querying for example the Blue band r.info Blue_DNs -r, would return

min=0
max=2047


Rescaling the Blue band to range between [0, 255]

r.rescale in=Blue_DNs out=Blue_DNs_255 from=0,2047 to=0,255


The same step applies to both the rest of the multi-spectral bands and the Panchromatic band of interest.

As usual when working with GRASS, it is required to set the region of interest, i.e. g.region rast=Blue_DNs_255 to match the extent of the band(s) or else. The resolution itself is taken care in this particular case by the module and the resulting pan-sharpened raster maps will of the same high(er) resolution as the Panchromatic band.

An example command for an IHS-based Pan-Sharpening action might look like

i.pansharpen pan=Pan_DNs_255 ms1=Blue_DNs_255 ms2=Green_DNs_255 ms3=Red_DNs_255 output=sharptest255 sharpen=ihs


After the process completion, the module outputs

...
The following pan-sharpened output maps have been generated:
sharptest255_red
sharptest255_green
sharptest255_blue

To visualize output, run: g.region -p rast=sharptest255.red
d.rgb r=sharptest255_red g=sharptest255_green b=sharptest255_blue

If desired, combine channels into a single RGB map with 'r.composite'.


Normally it should be enough to re-balance the colors after the pan-sharpening action by using for example the i.landsat.rgb module or manual adjustment of each of the three bands that would compose an RGB image.

i.landsat.rgb r=sharptest255_red g=sharptest255_green b=sharptest255_blue -p