Sandau R. Digital Airborne Camera: Introduction and Technology
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4.2 Optics and Mechanics 173
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
400 450 500 550 600 650 700 750 800 850 900
Wavelength [nm]
0 Grad.
20Grad.
35 Grad.
Transmission
Fig. 4.2-20 Measured transmission values on a 14-element lens system with 22 glass-air transi-
tions (ADS40) in the range between 400 and 900 nm for different field angles 0
◦
,20
◦
and 35
◦
.The
high transmission figures, consistent particularly over the field angle, can only be obtained with
extremely complex lens coating processes [Swissoptic AG, 2005]
bandwidth. This means that finer object details can only be transmitted with reduced
contrast. There is a spatial frequency at which the contrast transmitted is so small
that it is lost in the noise on the film or in the electronics. If a test image with known
initial contrast is chosen as the object, this cut-off frequency is also given as a spatial
“resolution” for this initial contrast.
Well corrected optical systems can be described as “linear” light intensity transfer
systems and can therefore be characterised by a transfer function similar to electron-
ics: this is called the OTF (Optical Transfer Function). The spatial intensity spectrum
of our object, e.g. a city landscape, is then multiplied by the OTF for the optical sys-
tem, resulting in the spectrum present at the sensor’s position. As the OTF has a
cut-off frequency, the aerial image spectrum at the sensor, prior to its recording by
the film or the CCDs, is already reduced in resolution and contrast. In principle,
therefore, we lose information during imaging. The Fourier transform of the OTF is
also called the “incoherent” point spread function that defines how blurred an object
point appears on the sensor.
In the case of diffraction-limited imaging it is found that
OTF
dl
(k
x
,k
y
) =
⎧
⎪
⎨
⎪
⎩
2
π
#
arccos
λ
f
D
k
−λ
f
D
k
1 −
λ
f
D
k
2
$
··· for λ
f
D
k ≤ 1
0 ··· otherwise
.
(4.2-24)
The diffraction at the edge of a circular aperture of a lens results in a diffrac-
tion pattern with an intensity described by the radially symmetrical Airy function
176 4 Structure of a Digital Airborne Camera
OTF Measurement
50 100 150 200 250 300 350 400 450 500
0
0.2
0.4
0.6
0.8
1
position (pixel)
0 50 100 150 200 250 300
–0.5
0
0.5
1
frequency (lp/mm)
MTF>0.6:
ν<
22.8 lp/mm
MTF>0.3:
ν<
60.9 lp/mm
MTF>0.1:
ν<
150.7 lp/mm
Fig. 4.2-23 Polychromatic OTF for a test lens: the graph at the top show the test pattern, a bar
code image and the related detected image. The loss of contrast as a function of the width of the
code bar can be seen. In the lower graph, this situation is plotted as a as a function of the spatial
frequency, for both the MTF and the PTF
indicative of possible internal decentring of lens groups, which clearly is not the
case here.
The OTF for a real lens cannot exceed the ideal OTF of purely diffraction-limited
imaging. If the OTF is less than this ideal, the reduction is, e.g., due to residual
aberrations in the design, as well as manufacturing tolerances. Diffraction-limited
imaging is unaffordable for lenses as complex as those for aerial cameras, but it is
also not necessary.
To design the optics MTF optimally, it is necessary to consider the entire infor-
mation transfer chain. At this point we will limit ourselves to the case where the
pixel layout on the detector is the limiting factor. If x is the pixel spacing and, for
simplicity, also the pixel width, then k
pix
= 1/(2x) is the related cut-off frequency
(Nyquist frequency), so for x = 3.25 μmwehavek
pix
= 153 lp/mm. It is therefore
unnecessary to develop a lens with higher resolution if the sensor is the limiting
factor. The lens must therefore transmit information at spatial frequencies below the
Nyquist frequency with the maximum possible contrast, but after this the contrast
ideally should be reduced to zero.
There are two reasons for this. The high contrast in the low to medium frequency
range is necessary since, during airborne use, the atmosphere also acts as a “low
pass filter” owing to turbulence and other refractive effects and therefore prevents
the optics “seeing” high resolution details on the ground. Nor should the contrast on
coarser details be reduced by the optical system. Good lenses perform well in terms
of contrast transfer at half the Nyquist frequency.
4.2 Optics and Mechanics 177
The second requirement, to keep the OTF as low as possible for frequen-
cies above the Nyquist frequency, is justified by the so-called “aliasing effect”. If
details on the ground with frequencies above the Nyquist frequency are transmitted
with good contrast, sensor undersampling will cause Moiré-like artefacts that will
seriously degrade the image and can only be eliminated with extensive effort.
All the above results in an awkward situation for the optical system: the OTF
cannot be engineered such that it is equal to one up to the Nyquist frequency and
zero after it. It is therefore necessary also to optimise the OTF beyond the Nyquist
frequency, but the contrast at frequencies above the Nyquist frequency must then be
reduced using measures such as a slight defocus, double-refracting filters or other
manipulations.
4.2.15 Field Dependency of the Optical Transfer Function
An important quality criterion for the imaging optics is the consistency of the poly-
chromatic MTF over the field of view, that is, measured over the entire area of the
sensor. It is now generally accepted that special averages must be computed for this
figure; though the definition of the averages varies depending on whether the optical
system is assessed for a two-dimensional array or a linear array.
4.2.15.1 Area Weighting
In the case of two-dimensional sensors such as film or a sensor array, the sensor
area is divided into annular zones and the weighting is calculated from the ratio
of the annular zone area to the total area. For example, a lens has a focal length of
f =62.5 mm and is used for field angles up to +/−35
◦
, corresponding to a maximum
radius in the image of f tan(35
◦
) = 43.7 mm. The sensor is a square film with a half-
diagonal of 50 mm. If the field of view is divided into 5
◦
steps, eight field angles
and, accordingly, eight image radii are obtained. Contiguous annular zones are now
placed around these radius values and the area ratio calculated relative to the square
film format. This situation is shown in Fig. 4.2-24 below: it can be seen that the
centre of the image and the edge of the image have relatively low area weighting,
while the image zones at 25
◦
and 30
◦
make major contributions. This weighting
makes sense only if the measured image quality of the optical system is rotationally
symmetrical.
In practice area-weighted averages are used for various quality criteria, such
as the resolution, called AWAR (Area Weighted Average Resolution). For a high-
performance lens an AWAR value of 120 lp/mm is appropriate. These figures
are determined by imaging so-called “test codes”, that is, standardised bar code
patterns of variable frequency, in the annular zones and determining the local res-
olution. The code figures are arranged in the radial and azimuthal directions, as
an optical system with astigmatism would produce different resolutions in the two
directions.
178 4 Structure of a Digital Airborne Camera
0 0.0047
5.0 0.0383
10.0 0.0789
15.0 0.1247
20.0 0.1791
25.0 0.2469
30.0 0.2398
35.0 0.0875
Fig. 4.2-24 Area weightings for a lens with a maximum field angle of 35
◦
for eight annular zones
within a square sensor area of 50 mm half-diagonal
Similarly defined quality variables are AWAF and AWAM figures, where F and M
denote frequency and modulation respectively. For AWAF the frequencies at which
the MTF has a specific value, for example 0.4, are determined; this figure is then
stated as AWAF (0.4) = 70 lp/mm. For AWAM an average of the MTF values at a
specific frequency is formed, for example, AWAM (65 lp/mm) = 0.42.
4.2.15.2 Equal Weighting
Referring to the radial symmetry, however, makes no sense for line sensors in
push broom mode, such as the ADC40. In this case several rows of CCDs are
arranged in the focal plane of the lens, perpendicular to the aircraft’s headin. The
polychromatic MTF figures or the resolution figures are determined in the direc-
tion of the aircraft’s heading and perpendicular to the aircraft’s heading instead
of radially and in azimuth. Area weighting is then not required, as each sensor
pixel is evaluated with unit weighting in both directions. Instead of AWAR, AWAM
and AWAF, EWAR, EWAM and EWAF are used where the letter E stands for
“equally”. It is clear that the E weightings are much sharper than the A weight-
ings, as they include the centre of the image and the edge of the image in their
entirety.
Realistic measurements on an ADS40 test lens with focal length f = 62.7 mm
are given in Table 4.2-2. The first column contains the field angle between 0
◦
and
35
◦
, and the seven columns to the right, the defocus, i.e. the distance between
the sensor and a mechanical support, varying between 2.100 and 1.980 mm.
For each field angle the “test codes” were exposed on film and visually eval-
uated after the film was developed. The frequency of the just resolvable test
image is given for both orthogonal directions. R denotes radial, i.e. the code bars
point in the radial direction, while T for tangential means that the code lines
point in the azimuthal direction. Finally, M stands for the geometric mean of R
and T.
4.2 Optics and Mechanics 179
Table 4.2-2 Measured resolution values for different field angles and defocus settings as
well as averaged values AWAR and EWAR (data form an ADS40 with f = 62.7 mm)
EWAR
w_deg EE
∗
2.100
∗
2.080
∗
2.060
∗
2.040
∗
2.020
∗
2.000
∗
1.980
∗
0.0 R
∗
128.0
∗
144.0
∗
144.0
∗
144.0
∗
128.0
∗
128.0
∗
102.0∗
0.0 T
∗
128.0
∗
144.0
∗
144.0
∗
144.0
∗
144.0
∗
128.0
∗
114.0∗
5.0 R
∗
128.0
∗
143.0
∗
128.0
∗
128.0
∗
143.0
∗
128.0
∗
114.0∗
5.0 T
∗
127.0
∗
127.0
∗
127.0
∗
143.0
∗
143.0
∗
127.0
∗
113.0∗
10.0 R
∗
126.0
∗
141.0
∗
159.0
∗
126.0
∗
126.0
∗
112.0
∗
112.0∗
10.0 T
∗
111.0
∗
139.0
∗
139.0
∗
139.0
∗
124.0
∗
111.0
∗
124.0∗
15.0 R
∗
124.0
∗
139.0
∗
139.0
∗
139.0
∗
124.0
∗
124.0
∗
98.0∗
15.0 T
∗
119.0
∗
134.0
∗
134.0
∗
119.0
∗
119.0
∗
119.0
∗
106.0∗
20.0 R
∗
107.0
∗
120.0
∗
135.0
∗
135.0
∗
135.0
∗
135.0
∗
107.0∗
20.0 T
∗
101.0
∗
101.0
∗
113.0
∗
113.0
∗
113.0
∗
113.0
∗
90.0∗
25.0 R
∗
92.0
∗
116.0
∗
146.0
∗
146.0
∗
139.0
∗
116.0
∗
103.0∗
25.0 T
∗
105.0
∗
105.0
∗
118.0
∗
118.0
∗
118.0
∗
118.0
∗
94.0∗
30.0 R
∗
78.0
∗
111.0
∗
140.0
∗
140.0
∗
140.0
∗
124.0
∗
111.0∗
30.0 T
∗
108.0
∗
108.0
∗
108.0
∗
121.0
∗
121.0
∗
108.0
∗
108.0∗
35.0 R
∗
53.0
∗
66.0
∗
93.0
∗
132.0
∗
148.0
∗
148.0
∗
118.0∗
35.0 T
∗
86.0
∗
96.0
∗
108.0
∗
136.0
∗
128.0
∗
136.0
∗
121.0
AWAR
R
∗
96.1
∗
117.1
∗
137.4
∗
138.2
∗
136.5
∗
125.3
∗
107.5
T
∗
106.5
∗
111.5
∗
118.0
∗
122.3
∗
120.4
∗
116.2
∗
103.7
M
∗
101.2
∗
114.3
∗
127.3
∗
130.0
∗
128.2
∗
120.7
∗
105.6
DoF(>100 lp/mm)
∗
0.120
EWAR
R
∗
104.5
∗
122.5
∗
135.5
∗
136.3
∗
135.4
∗
126.9
∗
108.1
T
∗
110.6
∗
119.3
∗
123.9
∗
129.1
∗
126.3
∗
120.0
∗
108.8
M
∗
107.5
∗
120.9
∗
129.6
∗
132.6
∗
130.7
∗
123.4
∗
108.4
DoF(>100 lp/mm)
∗
0.120
4.2.15.3 Conclusions
It can be seen from the measurements above that over the entire image field of ±35
◦
the resolution is very high and above all very homogenous. The AWAR and EWAR
figures are almost the same, so the lens can be used equally well for two-dimensional
arrays and line sensors. Final inspection in the optics factory will “stake” the lens at
a system dimension of 2.040 mm, that is, mechanically position the sensors at the
distance where the AWAR figures are highest.
If AWAR figures >100 lp/mm are taken as minimum values for acceptable
image quality, a “useable” depth of focus DoF of z
IMA
= 0.120 mm results. This
focus range is much larger than the value for an equivalent diffraction-limited lens
z
DIFF
=±2λ (F#)
2
=±0.016 mm (z
DIFF
=0.032 mm), when using λ =0.5 μm
for the wavelength and F# = 4.
The design included such a large depth of field for two reasons. Firstly, it cor-
responds to z
OBJ
= f
2
/z
IMA
= 33 m in object space, meaning that the lens
can be operated without refocusing for object distances from 33 m to infinity.
Secondly, and more importantly, we took into account the robustness of the lens
180 4 Structure of a Digital Airborne Camera
under changing environmental conditions. In the case of temperature changes, for
example between a warm lens and a variable cold environment, thermal gradients
of the glass parameters appear in the radial direction, especially for the large lens
elements. Consequently, the refractive index of the lens changes radially with time
and temperature, leading to a variable defocus between image centre (still warm)
and image edge (already cold). Thus we obtain an image curvature aberration that
varies through time. But since the useable DoF is designed to be large enough,
no serious degradation of the image quality occurs. The lens can be operated even
under severe conditions without degradation of image quality and, more importantly,
image magnification.
In conclusion we found that a lens can be effectively assessed by studying the
relationship between its EWAR and DoF values.
4.3 Filter
Filters are required to adapt the airborne camera to the task and conditions, taking
into account properties specific to the camera (lens, CCD line). They can be dis-
tinguished by their action (graded light filers, edge filters) and operating principles
(absorption filters, interference filters). At this point, we do not discuss polarisation
filters, which operate on a different principle.
As a rule, graded light filters are spectrally neutral grey filters of the absorption
type, which are used as anti-vignetting filters in aerial film cameras. The angle-
dependent edge intensity drop is compensated by transmittance that increases from
the centre to the edge. To save costs, this component can be dispensed with in digital
airborne cameras, because correction can be made to the data electronically without
signal loss and without exerting a negative influence on the signal-to-noise ratio.
We concentrate here on the properties of colour filters (band pass filters), which
are required for true-colour reconstruction of recorded image strips as well as for
measurement of reflected intensities as required in remote sensing for the thematic
interpretation of data from recorded areas. Band-pass filters are required for the
applications mentioned before; they can be in the form of absorption filters or inter-
ference filters. Figure 4.3-1 and the table below it provide definitions of some terms
used in describing filters
4.3.1 Absorption Filters
Absorption filters can be produced with coloured glass or with organic substances
deposited directly on to the CCD. The organic substances that are directly deposited
by CCD are clearly suitable for true-colour reconstruction. Long-term stability of
the filter properties under the challenging storage and service conditions with regard
to temperature and humidity should be checked on an individual basis. As a rule,
coloured glass filters are used. Band-pass filters can be composed of a number of
182 4 Structure of a Digital Airborne Camera
Fig. 4.3-2 Transmission curves for coloured glass with band-pass charactristics (Oriel, 2004)
Fig. 4.3-3 Transmission curves for coloured glass, showing blocking edge gradations (Oriel,
2004)
edges are difficult to achieve. The gradation of the rising flanks is also very coarse
for remote sensing applications. Glass filter combinations, however, produce very
good results in true-colour reconstruction. It should also be noted that spectral
transmission consists of two components
T(λ) = P(λ) ·T
g
(λ), (4.3-1)
where T
g
(λ)is the spectral transmission of the glass itself and P(λ)isanalmost
constant factor which describes the losses at the two air-glass transitions and which,
by means of appropriate surface coating, can be set approximately equal to 1.
Tilting does not affect spectral properties, but it extends the optical paths and
hence reduces transmission. Temperature has little influence. An increase in tem-
perature shifts the edges towards longer wavelengths. The shift is reversible and,