flir concept

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FLIR Concept

Prepared by Ernest Grimberg - Opgal chief scientist

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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.

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General Background electromagnetic waves

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General Background electromagnetic waves Plane polarized EM wave

Speed of an EM wave

00

1c

)cos(0

twxKEE y

)cos(0

twxKBBz

BE

BE

z

y

K

wc

0

0

Link to a more detailed paper

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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) ,

(watts/m2)

In general, the energy flux or POYNTING VECTOR .

Notice how the vector product gives the travel direction of an EM wave.

0

BES

0/)( BES X

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INTENSITY OF AN EM WAVE

Consider a point in space. Take x = 0 for convenience.

Hence the average energy flux

Wave Intensity I =

)cos(0

twEE y

)cos(0

twBBz

cEBEBE wtwt

S zy

0

22

0

0

2

00

0

)()( coscos

))(2( cos0

2

0 wtc

ES

cE

20

2

0

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General Background electromagnetic waves propagation

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Physical Constants

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Angle definitions

Planar angle =(arc length)/radius [radians]

Solid angle = (surface area)/radius [steradians]

))cos(1(2

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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%

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Radiometric quantities and formulas

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Blackbody Radiation

The spectral radiant emittance formula is:

mmWinhc

eM

kT

hc2

5

2

/)1(

2)(

T is the absolute temperature in degrees Kelvin. Spectral radiance L() is equal to M()/ because blackbodies are Lambertian sources:

))(/()1(

2 2

5

2

)( msteradmWinhc

eL

kT

hc

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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.

D

fnumberF /

f represents the focal length d represents the entrance pupil diameter of the lensFor small angles the numerical aperture is approximately equal to 0.5F#.

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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 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

22 )1(#4 mF

TrLscLfp

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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.

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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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Energy Distribution in the Diffraction Pattern of a Circular Aperture

Ring or Band Position (x) Relative Intensity (Ix/I0) Energy in Ring (%)

Central Maximum 0.0 1.0 83.8

First Dark 1.22 0.0

First Bright 1.64 0.0175 7.2

Second Dark 2.23 0.0

Second Bright 2.68 0.0042 2.8

Third Dark 3.24 0.0

Third Bright 3.70 0.0016 1.5

Fourth Dark 4.24 0.0

Fourth Bright 4.71 0.0008 1.0

Fifth Dark 5.24 0.0

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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.

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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:

][_

)2

_

(2__ radiansf

xd

f

xd

arctgdirectinxIFOV

][_

)2

_

(2__ radiansf

yd

f

yd

arctgdirectinyIFOV

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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:

][__

)2

__

(2__ radiansf

xnxd

f

xnxd

arctgdirectinxFOV

][__

)2

__

(2__ radiansf

ynyd

f

ynyd

arctgdirectinyFOV

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Detection, Orientation, Recognition, and Identification

Task Line Resolution per Target Minimum Dimension

Detection 1.0 ± 0.25 line pairsOrientation 1.4 ± 0.35 line pairs Recognition 4.0 ± 0.8 line pairsIdentification 6.4 ± 1.5 line pairs

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IR Detectors Quantum noise limit

The quantum noise difference in temperature (QNETD) for cooled detectors is limited by the signal quantum noise.

end

start kt

hc

ekt

dhndt

dnn

QNETD

)1(

1

2

5.0

5.0

n represents the amount of photoelectrons collected from the scenery.

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IR Detectors Quantum noise limit continue


1 104

1 105

1 106

1 107

1 108

1 109

1 103

0.01

0.1Quantum noise limited performances 3 - 5

PFOTONS/FRAME

Min

imum

res

olve

ble

tem

pera

ture

0.1

1.737 103

NEDT n( )

2 1081 10

4 n

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IR Detectors Quantum noise limit continue


1 104

1 105

1 106

1 107

1 108

1 109

1 103

0.01

0.1Quantum noise limited performances 8-12

PFOTONS/FRAME

Min

imum

res

olve

ble

tem

pera

ture

0.1

3.919 103

NEDT n( )

2 1081 10

4 n

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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.

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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.

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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

320256 InSb FOCAL PLANE ARRAY DETECTOR

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Microbolometer detector basic concept

The original design disclosed by Honeywell.

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The original design disclosed by Honeywell.

Illustration of Pixel

Silicon NitrideFilm

VOx

RowAddress

Line

ReadoutElectronicsColumn

AddressLine

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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 analyzedAssuming that the thermal cameras can be described by linear models.

dpdspysxpsInputyxInput ),(),(),(

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Spatial resolution and thermal resolution continue

Thermal camera response to any input signal is given by :

)),((),( yxInputTyxOutput T represents camera’s transfer function.

)),(),((),( dpdspysxpsInputTyxOutput

Recoll: T depends on x,y only, therefore assuming linearity :

dpdspysxTpsInputyxOutput )),((),(),(

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Therefore the thermal camera response to any input signal is given by :

h represents camera’s impulse response function.The camera impulse response is given by convolving its subsystems.

dpdspysxhpsInputyxOutput ),(),(),(

ionstabilizathscannerhselectronichectorhopticshcamerah ___det___

represents the convolution operator.

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Example. Estimate the MTF of a FLIR camera based on a the

uncooledmicrobolometer 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 = 0.754. Gimbals line of site stabilization standard deviation equals 100

microradian.

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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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Assuming geometrically limited optics :

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Assuming that the detector impulse response is geometrically limited:

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Stabilization impulse response for a standard deviation of 100 µrad :

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The electronics is model as a low pass filter on horizontal direction therefore :

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Entire system impulse response is estimated by the following process :

ionstabilizathscannerhselectronichectorhopticshcamerah ___det___

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The horizontal and vertical modulation transfer function are defined by thefollowing relations:

)),(_(_),( yxcamerahtransformFourierwwSys yx 5.022 )))0,((Im())0,((((Re xxx wSyswSysalMTF

5.022 ))),0((Im()),0((((Re yyy wSyswSysalMTF

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The Fourier transform of system’s impulse response is presented in the followingTwo dimensional graph.

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The MTF on horizontal direction is presented in the following graph.

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The MTF on vertical direction is presented in the following graph.

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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 inorder 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 visibleat the FLIR output.

),(),(

yxyx wwMTF

NETDwwMRTD

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The dominant noise sources that affect cooled FLIR performances are:• The Shot noise caused by the discreteness of electronic charge. The current Idflowing through the responsive element is the result of current pulses produced bythe individual electrons and or holes.

• The Readout noise caused by the electronic circuits that manipulates the signalin order to reduce the number of video output lines between 1 to 8 although thenumber of detector elements is much higher.• The 1/f noise characterized by a noise power spectrum • The fixed pattern noise caused by the insufficient correction of detector signalnon uniformity.

fIdqnoiseshotI 2__

28.0/1 nf n

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The dominant noise sources that affect uncooled FLIR performances are:• The Johnson noise caused by the random motion of charge carriers in thermalequilibrium.

• The Readout noise caused by the electronic circuits that manipulates the signalin order to reduce to one (1) the number of video output lines although thenumber of detector elements is much higher.• The 1/f noise characterized by a noise power spectrum. • The fixed pattern noise caused by the insufficient correction of detector signalnon uniformity.

28.0/1 nf n

][deg41

)(, reesR

fTK

ITT d

ddjohnsonnoise

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The MRTD on horizontal direction for the example presented before is describedby the following graph:

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EVS signal processing block diagram

flir concept

Documents

diffraction limit diffraction

fraunhofer diffraction

wattsm2in general

optical lens

formulas blackbody radiation

detector faceplate radiance

spectral radiance

lens transmittance