International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B7, 2012

XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia

2. ATMOSPHERIC EFFECTS

2.1 Viewing Geometry

The viewing geometry of line sensors simplifies radiometric

corrections considerably since for a single flight line the view

azimuth p is constant for every pixel, assuming the airplane

movements are compensated by a stabilized platform. The area

of a constant view zenith angle 6, is an image column (cf.

Figure 1).

Column average =

mean reflectance

for constant view

zenith angle 6, and

constant relative

azimuth angle ¢

Figure 1. Viewing geometry for a line scan sensor.

For frame sensors the area of constant view zenith angle is a

circle and still has a varying view azimuth (cf. Figure 2).

constant view /

zenith angle 0, and /

varying relative

azimuth angle @

Figure 2. Viewing geometry for a frame sensor.

2.2 Reflectance Calibration of Aerial Images

2.2.1 Radiative Transfer Equation: For the physical

description of the nadir looking passive Earth observation the

radiative transfer theory of Chandrasekhar is used (Fraser et al.,

1992).

p ST, doy Lo

L,=L, +2 (1)

(1-sp)

where Lm= measured at-sensor radiance

Lo = path radiance for zero ground reflectance

p = surface reflectance

p = average surface reflectance of surrounding area

S = mean solar spectral irradiance

Town = total downward transmittance from top of the

atmosphere (TOA) to the ground

T, = total upward transmittance from ground to sensor

s = spherical albedo of the atmosphere, i.e. the fraction

of the upward radiance which is backscattered by the

atmosphere

For the case of atmospheric correction the surface reflectance p

has to be calculated from the observed at sensor radiance L,,

Solving eqn (1) for p gives:

zl -L1,) =

zu rl.

ST.T (1- sg)

wn up

@)

Suppose p is known then the quantities Lo, Taowns Tup> $, and S

have to be calculated.

The extraterrestrial irradiance S is given by a standard formula

depending on the geographical latitude and the day of the year.

2.2.2 Model Inversion: Photogrammetric image processing

has to deal with huge amounts of data, so a very efficient

algorithm is needed to calculate Ly, Tyown, Typ, and s. Therefore

the modified Song-Lu-Wesely method described in (Beisl et al.,

2008) is used.

The basic idea is the following: Standard atmospheric models

calculate the at-sensor radiance, irradiance and transmittances

based on a given ground reflectance, atmosphere and aerosol

load. Since the ground reflectance is the unknown quantity, the

model has to be inverted for a given at-sensor radiance.

Unfortunately, none of the atmospheric parameters is known in

case of aerial images. So standard values are assumed for all

atmospheric and aerosol parameters except the horizontal

visibility (which is related to the aerosol concentration) and,

which has the biggest influence on the radiative transfer.

A series of forward model runs is performed with all

combinations of the input variables (ground elevation, flying

height, sun zenith angle, view zenith angle, relative azimuth

angle, and visibility), giving a multi-dimensional look-up table.

The total transmittances are calculated indirectly from runs at

three ground reflectances, because radiative transfer programs

will typically only output the direct transmittance between sun

and ground and between ground and sensor.

The aim is to replace the non-observable quantity visibility by

an observable quantity. The only available choice is the

atmospheric reflectance à, in nadir view which is determined

from the observed atmospheric reflectance à of a dark pixel

viewed from a certain view zenith and azimuth angle.

The atmospheric reflectance à is defined here as the difference

of the observed top-of-atmosphere (TOA) reflectance a and the

ground reflectance p of the dark pixel (eqn 3). The TOA

reflectance is calculated from the at-sensor radiance L,, and the

TOA irradiance S (eqn 4).

ózo-p | (3)

zl,

S

(4)

For the dark pixel we assume an average reflectance p of 2 %. If

the true reflectance spectrum of the dark pixel were known, a

more accurate modelling would be possible. But if a wrong

spectrum is taken then the whole image will be calibrated with

this spectral error. Therefore a spectrally constant dark pixel

reflectance is chosen.