Thermal image for truncated object target in the presence of vibrations motions

Advances in Physics Theories and Applications www.iiste.org
ISSN 2224-719X (Paper) ISSN 2225-0638 (Online)
Vol.20, 2013
118
Thermal Image for Truncated Object Target in the Presence of
Vibrations Motions
Fadhil K. Fuliful Rajaa Hussein.A. Hind Kh.A. Azhr Abdulzahraa Raheem
University of Karbala, College of Science ,Department of Physics
Abstract
The effects of vibration (longitudinal &transverse) on thermal imaging for truncated object target are considered,
a conventional thermal camera and a Mathcad program to reconstruct the Bar Spread Function (BSF) degraded
because vibration of target .A aerial photography is used as application in imaging the target ,results indicates
that even low amplitude vibration greatly affects the predicted target detection.
Introduction
The typical vehicles used in aerial photography are airplane and helicopter. However, the production image with
these vehicles are expensive, aerial photography has wide applications in military, topographical mapping,
engineering, environmental studies and exploration for oil. Image distortion caused by vibration motion is one of
the most problems for a thermal imager. The reduction of image resolution due to image motion influences the
ability of optical eyes to detect the target. The effects of sinusoidal image motion, which often results from
mechanical vibrations, can be divided into longitudinal and transverse vibrations .A computational imaging
system [1] that contains an optical position sensing detector array, a conventional camera and a method to
predict the degraded of images by spatially variant platform motion blur. The vibration of the gyrocopter
platform [2] is one of the critical factors that should be considered during the data collection, which are wind-
induced oscillation, vibration induced by the motor, the propeller and the main rotor. To prevent negative effect
to the imaging process, vibration absorbers are used on the sensor platform. Describing a general method for
determining the distance of a point objects by measuring the degree of image blur, the method is more accurate
for closest objects than for distant objects [3].A computational model for Synthetic aperture radar (SAR) [4]
simulation of stable point targets was consider and mathematically define constant motion, acceleration and
vibration of point targets as well as extended rotating objects. Results illustrated some important effects of
moving targets. The presented model has flexibility. Image vibrations are a common parameter for imaging
systems which are unstabilized for using for target detection purposes [5], the reduction of the probability of
detection is affected by long distance targets and for large relative exposure interval. This result is illustrated by
increasing the observer time for getting the target, the best case repeats itself many times so that the target will
finally be acquired. It is clear that image motion and vibration can significantly affect target acquisition times
and ranges. Flight conditions usually cause disturbance of image quality [6]. The modulation transfer functions
(MTF) are convenient techniques for measuring the image quality of photographs. The MTF of the image
forming system is the result of the contributions of the camera, the film, image motion (in systems without
forward motion compensation, FMC), vibrations, and the atmosphere to produce images. The edge spread
function (ESF)in the diffraction images of an incoherent object [7] has been evaluated in the presence of
transverse and longitudinal sinusoidal vibrations, the obtained results illustrate graphically the degrading effects
of vibrations on the quality of the optical image. The effect of linear motion on the diffraction image of truncated
object was evaluated by calculating the degradation of intensity distribution for Bar image at different values of
linear motion factor [8].
The aim of this paper is to apply Bar Spread Function (BSF) technique to analyze for target detection in the
presence of vibration motion (longitudinal &transverse). The present Mathcad algorithms is used to calculate the
intensity distribution of the object in two cases with and without vibration movement, the amplitude of vibration
parameters dependent on the properties of thermal camera such as focal number as well as ranges and IR target
wave length.
Theory
The bar object is important in studies and scientific research because of its wide applications as aerial
photography many forms as possible to be bar object, such as highways, railways and wires of electric power.
The bar object consists of a set of linear objects, where they can find complex amplitude in the image of bar
using convolution theorem circumvents the complex amplitude in the object with the complex amplitude linear
incision and using bypass [3] convolution integral we get:

Vol.20, 2013
119
)1..(....................)().()(

dzzzHzTzT −= ∫
∞
∞−
Complex of image amplitude line object
Complex of image amplitude bar object
)3.......(..........)(.),()( )()(

dzezTdxdyeyxfzT yxZi
y x
yxZi −
∞
∞−
−
∫∫∫=
)4.........(..........).........,()( )(
yxtdzezT yxiz
=∫
∞
∞−
−−
Where t(x,y) : spectrum of bar object defined as pupils enter the optical system.
the complex amplitude of the bar with width (2d) as follows :
t (Z) =1 when d │≤ Z│
t (Z) =0 when d │> Z│
As:
),(
),( yxikw
eyxf =
By using mathematical method to simplify the equation get :
)5.(...........
)(
).sin(
)),()(sin(.
)(
).sin(
)),()(cos(2)(

dydx
yx
dyx
yxkwyxzidydx
yx
dyx
yxkwyxzzT
y x
−
−
+−+
−
−








+−= ∫ ∫
2
)()( zTzB =
)6........(
.
)(
).sin(
)),()(sin(.
)(
).sin(
.)),()(cos()(
2

2



















−
−
+−+








−
−








+−= ∫∫∫∫ dydx
yx
dyx
yxkwyxzdydx
yx
dyx
yxkwyxzNzB
xyy x
Where Eq.6 represent Bar Spread Function
Where (N): is the normalization factor
The effect of mechanical vibration on defection target using thermal imager can be divided into transverse and
longitudinal vibration movements, in the first case the Bar Spread Function become:
)7.........(....................)]........([
)(
)sin(
))(sin()]([.
)(
)sin(
))(cos(
1
)(
1
2

1
2

2

xxAJ
dxdy
yx
dyx
yxzxxAJdydx
yx
dyx
yxzzB
O
y x
O
y x
−


















−
−
−+−








−
−
−= ∫∫∫∫
π
π
π
Where
( − Is the transverse sinusoidal vibration is given by a zero-order Bessel function.
)2.....(......................).,()(
)

(

)(

dydxeeyxfzzH
y x
xzzi yzzi
∫∫
−
−−
=−
:)(

zT

Vol.20, 2013
120
Where [7]:
A: transverse vibration factor
f: focal length of the thermal camera (210 mm)
ѱ: transverse vibration movement (mm)
λ: wave length of incident ray (10µm)
F: focal number can be found from thermal camera characteristics as:
D
f
F = Where D is the diameter of thermal camera (90 mm)
Then value of F is (2.233).
Let's consider now the simulation procedure which is depending on the value of factor (A) according the table (1)
Ѱ mm A
0.03 0.54
0.04 0.72
0.05 0.9
0.06 1.08
0.09 1.62
0.1 1.8
Table (1) characteristics of the search process (transverse vibration)
In the second case the Bar Spread Function becomes:
Where [7] 2
F
L
H
λ
=
L: longitudinal vibration movement.
The simulation in this case depends on the value of factor (H) as show in table (2)
L mm H
0.1 2
0.2 4
0.3 6
0.4 8
0.5 10
0.6 12
0.7 14
0.8 16
Table (2) characteristics of the search process (longitudinal vibration)
Result and discussion
To find the effect of mechanical vibrations on the intensity distribution of thermal image of truncated object, a
certain cases for the target and the thermal camera are assumed. The assumption here is that the image vibration
is the factor most limiting image quality. The vibration induced by the motors in different industries. Image
motion reduces the overall (BSF) and therefore the reduction in the target acquisition probability for a given
range and wave length. The reduction with resolution in the image plane as result of image vibrations affects the
ability of imaging by aerial photography.
Figure (1) show that the intensity distribution of the Bar object image for different value of transverse vibration
amplitude (0.03,0.04,0.05,0.06,0.09 and 0.1 mm) which gives the transverse vibration factor
(A=0.54,0.72, ,0.90,1.08,1.62 and 1.80)respectively(see table 2) ,the image of Bar object or BSF with three
values of (A= 0.54,0.72, and 0.90) are similar to the Bar image with (A=0) only the half width
F
f
A
λ
ψ2
=
)8........(....................].........
2
)(
[
)(
)sin(
))(sin(]
2
)(
[.
)(
)sin(
))(cos(
1
)(
1
2

1
2

2

xx
HJ
dxdy
yx
dyx
yxz
xx
HJdydx
yx
dyx
yxzzB
O
y x
O
y x
−


















−
−
−+
−








−
−
−= ∫∫∫∫
π
π
π

Vol.20, 2013
121
increased and the resolution power decrease , therefore the object can be detected, but the Bar image with value
of (A = 1.08) is recognized only, also the images in cases ( A=1.62 &1.80 ) are different when it compared with
the image with (A=0),the peak value of (BSF) increased and shifted then the resolution power very decrease and
the images are very bluer therefore the object cannot be detected. For increased the( Bar Half Width d=5,7)i.e.
increased lightning as illustrated in the figures (2,3) when we use the same values of the factor (A),the image
with values (0.54,0.72, ,0.90 and 1.08) also show degradation in intensity distribution for image because of
decreasing in high intensity value and increasing in half width ,while the image is distortion and can’t determine
its properties in case of values (1.62 and 1.80) .
Figure (1) Thermal images of Bar object (d=3) with different value of (A)
Fig. (2)Thermal images of Bar object (d=5) with different value of (A)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
0 1 2 3 4 5 6 7 8 9 10 11
BSF
Z
A=0
A=0.54
A=0.72
A=0.9
A=1.08
A=1.62
A=1.8
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
0 1 2 3 4 5 6 7 8 9 10 11
BSF
Z
A=0
A=0.54
A=0.72
A=0.9
A=1.08
A=1.62
A=1.8

Vol.20, 2013
122
Fig. (3)Thermal images of Bar object (d=7) with different value of (A)
The effect of focus error (W20 =0.5) and transverse vibration factor (A) simultaneously on the images is shown in
figures (4,5,6) figure(4) illustrated increasing of high intensity value in all cases as shown in the table (3) :
Table (3) intensity distribution of (d=3)at different values of (A) and W20=o.5
The comparison (table 3) give low resolution power in all images, the images for (A) with values (1.62, 1.8) has
similar shapes of image with (A=0) although it’s high values of intensities. Figures (5,6) show the intensity
distribution of Bar image in case of increasing the lightning (d=5,7), the effects of transverse vibration factor
and defocusing (W20 =0.5) are less on peak intensity value except slight increase in peak intensity value at
(A=1.8 & d=5) (see table 4) ,therefore the BSF at values of transverse vibration factor (1.62,1.8) are very
characterless.BSF in Figure (6) where (d=7) suffer the same effect, the comparison in table (4)(different values
of d )show positive results at the intensity value (0.82501) in case (d=3).
Bar half
width (d)
A=0 A=1.08
W20=0.5
A=1.62
W20=0.5
A=1.8
W20=0.5
3 0.71958 0.82501 0.97427 1.01667
5 0.8979 0.84248 0.87343 0.90349
7 0.95476 0.92679 0.88761 0.88149
Table (4) comparison of intensity distribution at different values of (d) and (A)
A 0 0.54 0.72 0.90 1.08 1.62 1.80
High
intensity
value
0.71958 0.73827 0.75627 0.7832 0.82051 0.97427 1.01667
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
0 1 2 3 4 5 6 7 8 9 10 11
BSF
Z
A=0
A=0.54
A=0.72
A=0.9
A=1.08
A=1.62
A=1.8

Vol.20, 2013
123
Fig. (4)Thermal images of Bar object (d=3) with different value of (A) and defocusing
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
0 1 2 3 4 5 6 7 8 9 10 11
BSF
Z
A=0
A=0.54
A=0.72
A=0.9
A=1.08
A=1.62
A=1.8
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 1 2 3 4 5 6 7 8 9 10 11
BSF
Z
A=0
A=0.54
A=0.72
A=0.9
A=1.08
A=1.62
A=1.8

Vol.20, 2013
124
The effect of longitudinal vibration factor (H) on (BSF) has been presented in Fig’s (7,8,9) with values
(2,4,6,8,10,12,14,16) ,all images in figure(7) have low resolution and intensity distribution of images with (H)
values (2,4) has the same distribution in the case of (H=0) approximately while the other cases with (H) values
(6,8,10,12,14,16) has effect on the (BSF) and the images are foggy. Fig.(8) shows image of Bar object (BSF) in
case of (d=5) all curves has decreasing in peak intensity values also the degradation in intensity can be seen, only
the BSF with (H = 2) has same shape of image with (H=0) and the BSF at (H) of values (4,6,8,10,12,14,16)
give images cannot detect the object. Also the effect of longitudinal vibration factors on (BSF) in figure (9) as in
figure (8).
Fig. (7)Thermal images of Bar object (d=3) with different value of (H)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
0 1 2 3 4 5 6 7 8 9 10 11
BSF
Z
H=0
H=2
H=4
H=6
H=8
H=10
H=12
H=14
H=16
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
0 1 2 3 4 5 6 7 8 9 10 11
BSF
Z
A=0
A=0.54
A=0.72
A=0.9
A=1.08
A=1.62
A=1.8

Vol.20, 2013
125
The influence of longitudinal vibration factors and defocusing (W20) on (BSF) is shown in figures (10,11,12),
the behavior of BSF shown in table (5),the results (d=3) illustrated the detection of object for (H = 2) and other
values give low resolution then the object only recognized don’t detected (see fig.10).Fig’s (11,12) show low
resolution ,therefore the thermal images of object are characterless and distortion because of decreasing in
maximum intensity value.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
0 1 2 3 4 5 6 7 8 9 10 11
BSF
Z
H=0
H=2
H=4
H=6
H=8
H=10
H=12
H=14
H=16
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
0 1 2 3 4 5 6 7 8 9 10 11
BSF
Z
H=0
H=2
H=4
H=6
H=8
H=10
H=12
H=14
H=16

Vol.20, 2013
126
Table (5) Effect of (H) and W20 on intensity distribution of Bar image (BSF)
Fig. (10)Thermal images of Bar object (d=3) with different value of (H) and defocusing
Half
width(d)
H=0 H=2
W20=0.5
H=4
W20=0.5
H=6
W20=0.5
H=8
W20=0.5
H=10
W20=0.5
H=12
W20=0.5
H=14
W20=0.5
H=16
W20=0.5
3 0.71958 0.7247 0.74053 0.76704 0.79338 0.81136 0.82456 0.83453 0.84235
5 0.8979 0.88821 0.87261 0.86919 0.87853 0.88973 0.8982 0.9049 0.91015
7 0.95476 0.95165 0.94134 0.9293 0.92525 0.92914 0.93439 0.93876 0.94243
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 1 2 3 4 5 6 7 8 9 10 11
BSF
Z
H=0
H=2
H=4
H=6
H=8
H=10
H=12
H=14
H=16
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 1 2 3 4 5 6 7 8 9 10 11
BSF
Z
H=0
H=2
H=4
H=6
H=8
H=10
H=12
H=14
H=16

Vol.20, 2013
127
Conclusion
1-The half width (d=3) of Bar object is acceptable and give thermal image with high resolution.
2-The effect of transverse vibration factor (A) on thermal image of a target (Bar object) depends on its values
(A=0.54, 0.72, 0.90) the target can be detected but the value (A= 1.08) only recognized, while the values (A=1.62
&1.80) the target does not detect.
3- The effect of transverse vibration factor (A) and defocusing (W20=0.5) simultaneously gives positive case at
(A=1.08).
4-The effect of longitudinal vibration factor values (H) on the thermal images gives allowed values (H=2, 4) the
target can be detected and the other values larger than it are not allowed because the target is undetectable.
5-The effect of longitudinal vibration factor (H) and defocusing (W20=0.5) simultaneously gives added
distortion.
5- As the amount of factors (A&H) is increased the intensity in the tail of curves (BSF) is increased (i.e. High
distortion) this effect is clear in case of factor (H).
6- Transverse vibration factor are more damaging than longitudinal vibration factor.
References
1-Stephen J. Olivas, Michal ˇSorel, Nima Nikzad and Joseph E. Ford, Platform motion blur image restoration
system, Imaging and Applied Optics Technical Digest © Optical Society of America OSA ,2012 .
2-A. Miraliakbari , M. Hahn and J. Engels ,Vibration of A Gyrocopter –An Analysis Using Imus, International
Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume xxxix-B1,
2012xxii ISPRS Congress, Melbourne, Australia, , 25 August – 01 September 2012.
3-Muralidhara subbarao, Determining Distance from Defocused Image of Simple Objects, New York
Univ.NY11794-2350,USA,2006.
4-Maurice Ruegg , Erich Meier and Daniel Nuesch , Constant Motion, Acceleration, Vibration ,and Rotation of
Objects in SAR Data, Proc. of SPIE Vol. 5980, 598005, 2005 ·
5-O. Hadar, S. R. Rotman and N. S. Kopeika, Thermal Image Target Acquisition Probabilities in the Presence
of Vibration, Infrared Phys. Technol. Vol. 36, No. 3. pp. 691-702. 1995.
6-H.J. Tiziani, on the Measurement of Image Distribution in Aerial Photography SPIE Vol. 1971 8th Meeting on
Optical Engineering in Israel, 1992.
7- R.Rattan and K.Singh, A study of the effect of vibrations on the images of edge objects in Aerial Photography,
ACTA PHYSICA POLONICA, No.6, 1974 .
8-K. Sing, R. Rattan, and N.K. Jain , Diffraction Images of Truncated Sine and Square Wave Periodic Objects
in the Presence of Linear Image Motion ,Applied Optics ,Vol..12, No.8, p.1846. 1973.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
0 1 2 3 4 5 6 7 8 9 10 11
BSF
Z
H=0
H=2
H=4
H=6
H=8
H=10
H=12
H=14
H=16

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Thermal image for truncated object target in the presence of vibrations motions

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Thermal image for truncated object target in the presence of vibrations motions