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OPGALS PROPRIETARY
FLIR Concept
Prepared by Ernest Grimberg - Opgal chief scientist
OPGALS PROPRIETARY
Table of contain
•General background.
•Physical Constants.
•Basic radiometric concepts.
•Black body radiation.
•Optics - introduction.
•IR Detectors.
•Spatial resolution and thermal resolution.
•Signal processing block diagram.
OPGALS PROPRIETARY
General Background electromagnetic waves
OPGALS PROPRIETARY
General Background electromagnetic waves
Plane polarized EM wave
1
c
Speed of an EM wave

0
0
E  E  cos( K  x  w  t)
y
0
B  B  cos( K  x  w  t )
z
c 
0
w

K
E
B
0
0

E
B
Link to a more detailed paper
y
z
OPGALS PROPRIETARY
General Background electromagnetic waves
ENERGY TRANSPORTED BY AN EM WAVE
•The B and E fields of an electromagnetic wave contain energy.
e.g Heat from a light bulb
•The rate of energy flow per unit frontal area (Energy flux) ,
S 
EB

(watts/m2)
0
In general, the energy flux or POYNTING VECTOR .



S  (E
X
B) /  0
Notice how the vector product gives the travel direction of an EM
wave.
OPGALS PROPRIETARY
General Background electromagnetic waves
INTENSITY OF AN EM WAVE
Consider a point in space. Take x = 0 for convenience.
E  E  cos(w  t )
y
0
B B
z
E B
S
y

0
0
 cos( w  t )
2
z

E B cos
0
0

( wt )
2

0
2
E cos (wt )
c
0
0
2


Hence the average energy flux S  E ( cos2
c
0
0
2
E
Wave Intensity I = 2c
0
0
(wt ))
OPGALS PROPRIETARY
General Background electromagnetic waves
OPGALS PROPRIETARY
General Background electromagnetic waves propagation
OPGALS PROPRIETARY
Physical Constants
OPGALS PROPRIETARY
Angle definitions
Planar angle
=(arc length)/radius [radians]
Solid angle = (surface area)/radius [steradians]
  2    (1  cos( ))
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Angle approximations formulas
=²,
( in rad), for <0.4 rad (23°), Max. Error 1.5%
=sin ²() ( in rad), for <0.4 rad (23°), Max. Error 1.5%
OPGALS PROPRIETARY
Radiometric quantities and formulas
OPGALS PROPRIETARY
Blackbody Radiation
The spectral radiant emittance formula is:
2c 2 h
in W / m 2 m
M ( )  5 hc
 (e kT  1)

T is the absolute temperature in degrees Kelvin. Spectral radiance L() is
equal to M()/ because blackbodies are Lambertian sources:
L( )
2c 2 h

 (e
5
hc
kT
 1)
in
W /( m 2 ( sterad ) m)
OPGALS PROPRIETARY
Blackbody Radiation
OPGALS PROPRIETARY
Blackbody Radiation
OPGALS PROPRIETARY
Blackbody Radiation
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Optics, F/number
F/number (f#) or “speed” of a lens is a measure of the angular acceptance of
the lens.
f
F / number 
D
f represents the focal length
d represents the entrance pupil diameter of the lens
For small  angles the numerical aperture is approximately equal to 0.5F#.
OPGALS PROPRIETARY
Optics, F/number
When an optical lens is used to image a scene, of radiance equal Lsc, on a
detector faceplate or on film the faceplate radiance may be obtain from the
following formula:
Lfp 
Lsc  Tr
4  F # 2 (1  m) 2
Lfp represents detector faceplate radiance in W/(m*m*steradian)
Lsc represents scenery radiance in W/(m*m*steradian)
Tr represents the lens transmittance
m represents the magnification from scene to detector faceplate
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Optics, Diffraction limit
Diffraction, poses a fundamental limitation on any optical system.
Diffraction is always present, although its effects may be masked if the
system has significant aberrations. When an optical system is essentially
free from aberrations, its performance is limited solely by diffraction, and
it is referred to as diffraction limited.
In calculating diffraction, we simply need to know the focal length(s)
and aperture diameter(s); we do not consider other lens-related factors
such as shape or index of refraction.
Since diffraction increases with increasing f-number, and
aberrations decrease with increasing f-number, determining optimum
system performance often involves finding a point where the combination
of these factors has a minimum effect.
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Optics, Diffraction limit continue
Fraunhofer diffraction at a circular aperture dictates the fundamental limits of
performance for circular lenses. It is important to remember that the spot size,
caused by diffraction, of a circular lens is
where d is the diameter of the focused spot produced from plane-wave
illumination and  is the wavelength of light being focused. The diffraction
pattern resulting from a uniformly illuminated circular aperture is shown in the
image below. It consists of a central bright region, known as the Airy disc,
surrounded by a number of much fainter rings.
OPGALS PROPRIETARY
Optics, Diffraction limit continue
Each ring is separated by a circle of zero intensity. The irradiance distribution in this
pattern can be described by
where I0 = peak irradiance in the image.
J1(x) is a Bessel function of the first kind of order unity, and
where  is the wavelength, D is the aperture diameter, and  is the angular radius
from pattern maximum.
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Optics, Diffraction limit continue
Energy Distribution in the Diffraction Pattern of a Circular Aperture
Ring or Band Position (x)
Relative Intensity (Ix/I0)
Central Maximum
0.0
1.0
First Dark
1.22
0.0
First Bright
1.64
0.0175
Second Dark
2.23
0.0
Second Bright
2.68
0.0042
Third Dark
3.24
0.0
Third Bright
3.70
0.0016
Fourth Dark
4.24
0.0
Fourth Bright
4.71
0.0008
Fifth Dark
5.24
0.0
Energy in Ring (%)
83.8
7.2
2.8
1.5
1.0
OPGALS PROPRIETARY
Optics, Diffraction limit continue
The graph below shows the form of both circular and slit aperture diffraction patterns
when plotted on the same normalized scale. Aperture diameter is equal to slit width so
that patterns between x values and angular deviations in the far field are the same.
OPGALS PROPRIETARY
Optics, Diffraction limit continue
The graph below shows the diameter of the first circular bright disc versus optics f# for
two different wavelengths: 4 microns and 10 microns respectively.
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Optics Detector relations
Assuming that the detector is a two dimensional matrix of n_x by n_y
elements, and that each detector element size is d_x by d_y meters, and that
the optics focal length is f meters, the instantaneous field of view (IFOV), on X
and Y directions, are given by the following relations:
d_x
d_x
2
IFOV _ x _ directin  2  arctg (
)
f
f
d_y
d_y
IFOV _ y _ directin  2  arctg ( 2 ) 
f
f
[radians ]
[radians ]
OPGALS PROPRIETARY
Optics Detector relations continue
Assuming that the detector is a two dimensional matrix of n_x by n_y
elements, and that each detector element size is d_x by d_y meters, and that
the optics focal length is f meters, the field of view, on X and Y directions,
are given by the following relations:
d _ xn_ x
d _ xn_ x
2
FOV _ x _ directin  2  arctg (
)
f
f
d _ yn_ y
d _ yn_ y
2
FOV _ y _ directin  2  arctg (
)
f
f
[radians ]
[radians ]
OPGALS PROPRIETARY
Detection, Orientation, Recognition, and Identification
Task
Detection
Orientation
Recognition
Identification
Line Resolution per Target Minimum Dimension
1.0 ± 0.25 line pairs
1.4 ± 0.35 line pairs
4.0 ± 0.8 line pairs
6.4 ± 1.5 line pairs
OPGALS PROPRIETARY
IR Detectors Quantum noise limit
The quantum noise difference in temperature (QNETD) for cooled detectors is limited
by the signal quantum noise.
n 0.5
QNETD 

en d
dn
0.5
n

dt
sta rt
1
h  d
kt 2 (1  e
n represents the amount of photoelectrons collected from the scenery.

hc
kt
)
OPGALS PROPRIETARY
IR Detectors Quantum noise limit continue
The quantum noise difference in temperature (QNETD) for cooled detectors is limited
by the signal quantum noise.
Quantum noise limited performances 3 - 5
Minimum resolveble temperature
0.1 0.1
NEDT ( n)
0.01
3
1.73710
3
1 10
4
1 10
4
110
1 10
5
1 10
6
1 10
n
PFOTONS/FRAME
7
1 10
8
1 10
8
210
9
OPGALS PROPRIETARY
IR Detectors Quantum noise limit continue
The quantum noise difference in temperature (QNETD) for cooled detectors is limited
by the signal quantum noise.
Quantum noise limited performances 8-12
Minimum resolveble temperature
0.1 0.1
NEDT ( n)
0.01
3
3.91910
3
1 10
4
1 10
4
110
1 10
5
1 10
6
1 10
n
PFOTONS/FRAME
7
1 10
8
1 10
8
210
9
OPGALS PROPRIETARY
IR Detectors technology
There are two very distinctive detector technologies: the direct
detection (or photon counting ), and thermal detection.
Direct detection technology (photon counting) translates the
photons directly into electrons. The charge accumulated, the
current flow, or the change in conductivity is proportional to the
scenery view radiance. This category contains many detectors,
like: PbSe, HgCdTe, InSb, PtSi etc. Except for FLIRs working in
the SWIR range, all the FLIRs based on the direct detection
technology are cooling the detectors to low temperatures, close
to –200 degrees Celsius.
OPGALS PROPRIETARY
IR Detectors technology
Thermal detection technology.
These detectors are using secondary effects, like the relation
between conductivity, capacitance, expansion and detector
temperature. The following detectors are classified in this
category:
Bolometers,
Thermocouples,
Thermopiles,
Pyroelectrics etc. Usually these detectors do not require
cryogenic temperatures.
OPGALS PROPRIETARY
IR Detectors description
Any IR “detector” (except for the near IR spectra) is an assembly
that contains:
•A Focal Plane Array (FPA),
•A dewar or a vacuum package,
•A cooler or a temperature stabilization device,
•and in most of the cases a cold shield or a radiation shield.
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IR Detectors description continue
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IR Detectors, DEWARS Description
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IR Detectors, InSb spectral band description
320256 InSb FOCAL PLANE ARRAY DETECTOR
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Microbolometer detector basic concept
The original design disclosed by Honeywell.
OPGALS PROPRIETARY
Microbolometer detector basic concept
Illustration of Pixel
Row
Address
Line
VOx
Silicon Nitride
Film
Column
Address
Line
Readout
Electronics
The original design disclosed by Honeywell.
OPGALS PROPRIETARY
Microbolometer detector basic concept
Real picture. Sofradir’s detector.
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Spatial resolution and
thermal resolution.
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Spatial resolution and thermal resolution.
The spatial resolution and the thermal resolution will be analyzed
Assuming that the thermal cameras can be described by linear
models.
 
Input ( x, y ) 
  Input (s, p)  ( x  s, y  p)ds  dp
  
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Spatial resolution and thermal resolution continue
Thermal camera response to any input signal is given by :
Output ( x, y )  T ( Input ( x, y )) T represents camera’s transfer function.
 
Output ( x, y )  T (   Input ( s, p)  ( x  s, y  p)ds  dp)
  
Recoll: T depends on x,y only, therefore assuming linearity :
 
Output ( x, y ) 
  Input (s, p)  T (( x  s, y  p))ds  dp
  
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Spatial resolution and thermal resolution continue
Therefore the thermal camera response to any input signal is given
by :
 
Output ( x, y ) 
  Input (s, p)  h( x  s, y  p)ds  dp
  
h represents camera’s impulse response function.
The camera impulse response is given by convolving its subsystems.
h _ camera  h _ optics  h _ det ector  h _ electronics  h _ scanner  h _ stabilizat ion

represents the convolution operator.
OPGALS PROPRIETARY
Spatial resolution and thermal resolution continue
Example. Estimate the MTF of a FLIR camera based on a the uncooled
microbolometer detector manufactured by Sofradir.
The input data for performance estimation is:
1. Optics focal length = 0.1 m,
2. Optics f number = 1.17 ,
3. Optics transfer function at 1.1 cycles/milliradian = 0.75
4. Gimbals line of site stabilization standard deviation equals 100
microradian.
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Spatial resolution and thermal resolution continue
Assuming diffraction limit optics performances :
But according to the input data:
Optics transfer function at 1.1 cycles/milliradian = 0.75
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Spatial resolution and thermal resolution continue
Assuming geometrically limited optics :
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Spatial resolution and thermal resolution continue
Assuming that the detector impulse response is geometrically limited:
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Spatial resolution and thermal resolution continue
Stabilization impulse response for a standard deviation of 100 µrad :
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Spatial resolution and thermal resolution continue
The electronics is model as a low pass filter on horizontal direction therefore :
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Spatial resolution and thermal resolution continue
Entire system impulse response is estimated by the following process :
h _ camera  h _ optics  h _ det ector  h _ electronics  h _ scanner  h _ stabilizat ion
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Spatial resolution and thermal resolution continue
The horizontal and vertical modulation transfer function are defined by the
following relations:
Sys ( wx , wy )  Fourier _ transform(h _ camera( x, y ))
MTFx  ((Re al ( Sys( wx ,0)) 2  (Im( Sys( wx ,0)) 2 ) 0.5
MTFy  ((Re al (Sys(0, wy )) 2  (Im( Sys(0, wy )) 2 )0.5
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Spatial resolution and thermal resolution continue
The Fourier transform of system’s impulse response is presented in the following
Two dimensional graph.
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Spatial resolution and thermal resolution continue
The MTF on horizontal direction is presented in the following graph.
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Spatial resolution and thermal resolution continue
The MTF on vertical direction is presented in the following graph.
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Spatial resolution and thermal resolution continue
The thermal resolution is defined by the following two values:
NEDT – Noise equivalent temperature difference,
MRTD – Minimum resolvable temperature difference.
The NEDT is the minimum temperature difference, at the FLIR input, required in
order to overcame the noise. The NEDT is defined for the zero spatial frequency,
therefore NEDT is independent of spatial frequencies.
The MRTD is a two dimensional function of spatial frequency, defined as the
minimum input temperature required for any spatial frequency in order to be visible
at the FLIR output.
MRTD ( wx , wy ) 
NETD
MTF ( wx , wy )
OPGALS PROPRIETARY
Spatial resolution and thermal resolution continue
The dominant noise sources that affect cooled FLIR performances are:
• The Shot noise caused by the discreteness of electronic charge. The current Id
flowing through the responsive element is the result of current pulses produced by
the individual electrons and or holes.
I _ shot _ noise  2  q  Id  f
• The Readout noise caused by the electronic circuits that manipulates the signal
in order to reduce the number of video output lines between 1 to 8 although the
number of detector elements is much higher.
• The 1/f noise characterized by a noise power spectrum 1 / f n
0.8  n  2
• The fixed pattern noise caused by the insufficient correction of detector signal
non uniformity.
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Spatial resolution and thermal resolution continue
The dominant noise sources that affect uncooled FLIR performances are:
• The Johnson noise caused by the random motion of charge carriers in thermal
equilibrium.
1 4  K  Td  f
Tnoise, johnson(Td ) 
[deg rees ]
I d
R
• The Readout noise caused by the electronic circuits that manipulates the signal
in order to reduce to one (1) the number of video output lines although the
number of detector elements is much higher.
• The 1/f noise characterized by a noise power spectrum. 1 / f n
0.8  n  2
• The fixed pattern noise caused by the insufficient correction of detector signal
non uniformity.
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Spatial resolution and thermal resolution continue
The MRTD on horizontal direction for the example presented before is described
by the following graph:
EVS signal processing block diagram
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