Sandau R. Digital Airborne Camera: Introduction and Technology

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134 3 The Imaged Object and the Atmosphere

Figure 3.1-4 reveals that the ultraviolet and blue parts of the sunlight are removed

from the solar spectrum to a great extent owing to scattering by air molecules when

zenith distances are large. In contrast, the infrared parts of the sunlight are almost

completely unattenuated at the Earth’s surface even for θ ≈ 84

◦

(this means that

≈ 15). Thus the maximum solar energy at the Earth’s surface shifts from the

blue-green spectral range to the red domain.

The radiation scattered by air molecules and aerosols is partly backscattered into

the upper atmosphere (dotted arrows in Fig. 3.1-1) and escapes into space. Part of

this backscattered radiation hits the sensor in the aircraft or satellite (Fig. 3.2-1) and

is termed path radiance. The part scattered into the lower atmosphere is called dif-

fuse sky radiation and reaches the Earth’s surface or the target to be detected. Thus

the incoming radiation at the target on the Earth’s surface consists of the direct solar

radiation and the diffuse sky radiation. A rough rule of thumb is that under cloudless

conditions the diffuse sky radiation amounts to 18% of the total incoming radiation.

The direct solar radiation attenuated by penetrating the atmosphere and the diffuse

sky radiation strike the Earth’s surface (Fig. 3.1-1) and there are reﬂected according

to the optical properties of the particular surface. This reﬂected radiation – after a

second passage through the atmosphere to the sensor – generates the required image

of the target. Different surfaces reﬂect very differently in the various spectral ranges.

Some reference values for the spectral albedo are listed in Table 3.1-1. The spectral

albedo is the ratio of the reﬂected irradiance [W/m

] to the incoming irradiance

[W/m

] in the spectral domain under consideration.

Table 3.1-1 Reference values of the spectral albedo of different surfaces

Spectral domain Bare soil (dry clay) Vegetation (grass) Snow (dry) Bare soil (dry clay)

Blue 0.169 0.007 0.89 0.026

Green 0.268 0.051 0.906 0.049

Red 0.329 0.040 0.91 0.041

Near infrared 0.418 0.654 0.89 0.000

3.2 Radiation at the Sensor

The different radiation components striking the sensor are depicted in Fig. 3.2-1,

assuming a ﬂat area. On the target detected at timet comes the direct radiation (E

)

and diffuse radiation (E

). The direct radiation is the solar radiation incident on the

surface after one passage through the atmosphere. As mentioned above, the diffuse

sky radiation emerges from the scattering processes caused by the air molecules and

aerosols. It is sunlight deﬂected by scattering from the primary direction and comes

now to the surface target from all directions of the hemisphere. These components

+ E

) are reﬂected according to the reﬂectance ρ

λ

and reach the sensor after

a second passage through the atmosphere (ray 2 in Fig. 3.2-1). During their second

3.2 Radiation at the Sensor 135

Fig. 3.2-1 Schematic

diagram of the solar radiation

components arriving at the

sensor above a ﬂat terrain

[source: Rese (2004)]

pass through the atmosphere E

and E

are impaired according to the transmis-

sion function T

λ, H

(H indicates the altitude of the sensor above the Earth’s

surface). The components (E

+ E

) include the required information about the

surface target.

λ, at the sensor

(

)

λ

λ, H

λ0

In addition to these components carrying the information about the target, other

radiation components arrive at the sensor at the time t. These are the so-called path

radiance L

λ0

(ray 1 in Fig. 3.2-1) and the radiation L

reﬂected by the adjacent

pixels (ray 3 in Fig. 3.2-1, also known as adjacency effect or blurring effect). The

components 1(L

λ0

) and 3 (L

) blur the image. They emerge also from the scat-

tering process. Due to scattering L

λ0

is directed to the sensor without ever having

reached the surface. L

, as a part of the radiation reﬂected by the adjacent pixels, can

be incident at the sensor at the time t owing to scattering, too (ray 3 in Fig. 3.2-1).

The contributions of these unwanted components to the required signal are much

stronger in the blue spectral region than in the near infrared, because the scatter-

ing by the air molecules depends very strongly on the wavelength. In addition the

content and the size distribution of the aerosols play a role.

In Tables 3.2-1, 3.2-2, 3.2-3 and 3.2-4 the contributions of the path radiance

λ0

) and the total radiance in front of the sensor L

λ, in front of the sensor

are listed

Table 3.2-1 Radiances in front of the sensor and path radiance above different surfaces; values

are for the blue spectral channel (430−490 nm) and the conditions mentioned in the text

Flight altitude

[km]

Path radiance

λ0

[μW/(cm

sr)]

Water Lλ, in front

of the sensor

[μW/(cm

sr)]

Vegetation Lλ,in

front of the sensor

[μW/(cm

sr)]

Snow Lλ, in front

of the sensor

[μW/(cm

sr)]

1 55 124 73.6 2,967

3 140 209 154 2,929

5 190 255 208 2,921

136 3 The Imaged Object and the Atmosphere

Table 3.2-2 Path radiance as percentage of the total radiance in front of the sensor in the blue

spectral domain (430−490 nm)

Flight altitude [km] Water [%] Vegetation [%] Snow [%]

144751.9

367914.8

575926.5

Table 3.2-3 Radiances in front of the sensor and path radiance in the near infrared spectral channel

(820−870 nm) above different surfaces

Flight altitude

[km]

Path radiance

λ0

[μW/(cm

sr)]

Water Lλ, in front

of the sensor

[μW/(cm

sr)]

Vegetation Lλ,in

front of the sensor

[μW/(cm

sr)]

Snow Lλ, in front

of the sensor

[μW/(cm

sr)]

1 9.9 9.9 1,179.3 1,627

3 21 21 1,150 1,582

5 25.4 25.4 1,143 1,571

Table 3.2-4 Path radiance as percentage of the total radiance in front of the sensor in the near

infrared spectral domain (820−870 nm)

Flight altitude [km] Water [%] Vegetation [%] Snow [%]

1 100 0.84 0.61

3 100 1.83 1.3

5 100 2.2 1.6

for a mid-latitude summer atmosphere with low aerosol content. The values are

given for different ﬂight altitudes. For the calculation of L

λ, in front of the sensor

,the

albedo from Table 3.2-1 has been used.

The impact of the adjacency effect depends on the aerosol concentration and

very strongly on the heterogeneity of the scene and the spatial resolution. It

will not be discussed here in greater detail. If we use calibrated digital cameras

both disturbing effects can be partly corrected by the application of appropriate

software.

In addition to these effects the object itself is blurred owing to scattering of the

light in the atmosphere, so a point spread function (PSF) has to be attributed to

the atmosphere. Figure 3.2-2 demonstrates this schematically. A ray starting from

point A is imaged in the image plane at point a under the assumption of ideal

optics. If the ray is scattered at point S, however, and therefore detected in point

b, it will appear to be started in point B. The illumination of the object at point A

is moved to the location B outside the object A; thus the object is blurred in the

image plane. The PSF of the atmosphere can be approximated using a 2D Gaussian

distribution:

138 3 The Imaged Object and the Atmosphere



max

−r

min

max

min

, (3.3-1)

where E

is the path radiance, multiplied by π, and E

is the global irradiance. A

schematic diagram is given in Fig. 3.3-1.

min

max

min

T + E

Surface (S)

35 Grad.

750

max

T + E

Fig. 3.3-1 Schematic

diagram for deriving the

scene contrast C’ (taking into

account the atmosphere)

after:

http://www rss.chalmers.

se/gem/Education/RSES-

2002/Imaging_systems.pdf

Figure 3.3-2 gives an idea about the values determining the scene contrast C’

((3.3-1) and Fig. 3.3-1). The ordinate on the left hand side gives the values of

the path radiance arriving at the airborne sensor, whereas the transmission scale

is shown on the right hand side. On the x-axis is the ﬂight altitude. The calculations

were done with the radiation transfer code MODTRAN4 for a model atmosphere at

midday in summer for 48

◦

N and 15

◦

E. A rural aerosol is assumed as well as a hori-

zontal visibility of 23 km. These assumptions characterise a very clean atmosphere.

The results are given for the blue spectral range (430−490 nm) and the near infrared

spectral domain (820−870 nm).

Figure 3.3-2 demonstrates again the strong impact of scattering by the air

molecules, because a very slight aerosol concentration was selected in the model.

The global irradiance E

at the surface comprises the direct solar irradiance and

the diffuse sky irradiance. The value depends on the sun’s position and the atmo-

spheric conditions (aerosol, water vapour). Clouds are generally neglected in this

chapter.

For the model atmosphere mentioned above, Fig. 3.3-3 depicts the altitude-

dependent curve of the contrast, taking into consideration the effect of the

atmosphere. The contrast C’ is again shown for the blue and near infrared spec-

tral regions. The albedo used was taken from Table 3.1-1 for bare soil and

vegetation.

3.4 Bi-directional Reﬂectance Distribution Function BRDF

Up to this point in the calculations, the spectral albedo has been used, given by

the ratio of two irradiances. Irradiances always refer to the radiation incident from

the atmosphere (hemisphere) or reﬂected into the atmosphere (hemisphere). This

3.4 Bi-directional Reﬂectance Distribution Function BRDF 141

For the calculations, discrete BRDF values measured in the near infrared spec-

tral region have been approximated (ﬁtted to a function) by using a model (Roujean

model). With this model and the radiation transfer code MODTRAN4, the radiances

expected at the sensor (ADS40 in this case) have been calculated. In Fig. 3.4-2, the

relative azimuth is marked on the x-axis: the values from 0

◦

to 90

◦

symbolise the

backscattering region (the area which describes the scattering back to the sun) and

the values from 90

◦

to 180

◦

characterise the forward scattering. The graph on the

left-hand side of Fig. 3.4-2 depicts the results for an atmosphere free of aerosols.

Owing to the fact that the scattering caused by the air molecules does not have

a noticeable effect in the near infrared spectral domain, the graph describes the

reﬂected radiation above the surface, i.e. the typical distribution of the reﬂectance

directly above the vegetation selected for this study. In the middle image the calcu-

lations depicted are performed under the asumption that rural aerosols exist in the

atmosphere that result in a horizontal visibility of 23 km. It is seen that owing to the

scattering properties of the aerosols the backscattering decreases and the forward

scattering increases. This effect becomes more pronounced with increasing aerosol

content, as conﬁrmed by modelling an atmosphere with a horizontal visibility of

only 11.5 km (right-hand graph).