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AD-A081 324 INSTITUTE FOR DEFENSE ANALYSES ARLINGTON VA SCIENCE A— ETC F/G 17/5
FIELD MANUAL TO DETERMINE DETECTION OR RECOGNITION RANGE OF A F— ETC(U)
SEP 79 L N SEEKAMP MDA-903-79-C-0202
UNCLASSIFIED IDA-P-1419 S0IE-AD-E5OO 112 NL
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ffiA PAPER P-1419
FIELD MANUAL TO DETERMINE DETECTION
OR RECOGNITION RANGE OF A FLIR SENSOR
Lynne N. Seekamp
September 1979
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If. KCT VOPOI (Conn otto on roooroo siOo it notomoory and iBmnttty by blotb nxmtbot)
forward-looking infrared systems, atmospheres, transmittance, aerosols,
attenuation, signal-to-noise ratio, detection, recognition,
range (distance)
^<1 ^e^muMR an rt»NM «id> ft moeobbotr onp lOmnnly by biotb numbor)
Forward-looking infrared (FLIR) sensor performance range estimates
over a horizontal path can be made by using a rapid estimation procedure.
These estimates can be calculated while in the field by using a hand
calculator for several different FLIR systems, atmospheric transmission
conditions, and levels of difficulty of the visual task.
\
00 U73 EDITION Of ' NOW *4 I* OMOLtT*
UNCLASSIFIED
SCCUNITV CLAJJIAiCAT'ON or >ll »*<ll r'.im Fnl*:*!
y-titU'
IDA PAPER P-1419
FIELD MANUAL TO DETERMINE DETECTION
OR RECOGNITION RANGE OF A FLIR SENSOR
Lynne N. Seekamp
September 1979
INSTITUTE FOR DEFENSE ANALYSES
SCIENCE AND TECHNOLOGY DIVISION
400 Army-Navy Drive, Arlington, Virginia 22202
Contract MDA 903 79 C 0202
Task T-136
ACKNOWLEDGMENTS
The methodology for the rapid calculation procedure .to
predict FLIR performance discussed in this paper was developed
by Dr. Robert E. Roberts of the Institute for Defense Analyses.
The author thanks R.E. Roberts, L.M. Biberman and M.L. Sullivan
of the Institute for Defense Analyses for their useful discus¬
sions and contributions to this paper.
RE: Classified references, distribut¬
ion unlimited-
Oelete classified references per Mr.
Walter Hanley, IDA/Security
ii
ACCESSION for I.
NTI$
ooc
Buff Section Ol
UNANNOUNCED
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iUSTIFICATION
nr
| WSTWBUTIOH/ArjBUWUn OODCS 1
I Dlst. AVAIL and/M
CONTENTS
Acknowledgments
ii
I. INTRODUCTION
II . METHODOLOGY
III. INPUT DATA
A. FLIR System Specifications
B. Task Level Factors
C. Target Specifications
D. Atmospheric Factors
11
12
13
15
16
IV. AN EXAMPLE OF THE CALCULATION PROCEDURE
References
25
iii
I. INTRODUCTION
This publication is designed to be a concise manual for
assessing forward-looking infrared (FLIR) sensor performance
ranges under a variety of conditions and thus is directed
toward the operator in the field. The purpose of this publi¬
cation is to present a summary of the methodology used to de¬
rive the FLIR performance rapid estimation procedure, present
tables of input values for several different FLIR systems,
atmospheric transmission conditions and levels of difficulty
of the visual task, and show an example of the calculation pro¬
cedure. In this paper we will use what we believe are the best
data bases and models currently available. However, uncertain¬
ties still exist regarding some of these data, particularly
with respect to the prediction of aerosol extinction. These
uncertainties will be discussed in the appropriate sections.
A previous publication described a computer code developed
to model the performance of a FLIR sensor (Ref. 1). The com¬
puter code (Program FLIR) was used to calculate the probabili¬
ties of detection and recognition of a target by an observer
using a FLIR sensor. Since that time a rapid approximation for
calculating the range at various probabilities of detection or
recognition for a given FLIR system has been developed. We
felt that it would be useful to publish a concise manual that
could be used in the field as a guide for making quick estimates
of FLIR performance. It should be noted that the procedure out¬
lined here is applicable only to estimating FLIR performance
over horizontal paths. The equation used to estimate FLIR per¬
formance was derived by R.E. Roberts of the Institute for De¬
fense Analyses (Refs. 2, 3).
1
The calculation method presented here is designed to be
used with a hand calculator when a fast determination of range
at various probabilities of detection or recognition is required.
II. METHODOLOGY
An equation has been derived which directly shows the range
at 50 percent probability (as well as at other probabilities) as
a function of target, system, environment, and task parameters.
An explanation of the derivation of this equation and the vali¬
dation are given in IDA Paper P-1284, A Simplified Approach to
Analyses of Infrared Sensor Performance Versus Weather: Theory
and Application to the Hannover Data Base (U) (Ref. 2). A brief
discussion of the methodology will be reviewed below.
The most common parameter used to characterize FLIR per¬
formance is the minimum resolvable temperature (MRT). Usually
this represents a plot of the values of minimum resolvable tem¬
perature difference between a pattern of four identical bars and
the three spaces between them for each of a number of spatial
frequencies. The bars represent a blackbody source of tempera¬
ture T + AT, where T is the background temperature (in degrees
Kelvin) and AT is the difference between the background tempera¬
ture and the target temperature. The spaces represent the back¬
ground temperature T. MRT then is the minimum AT that a stand¬
ard observer can resolve through a given FLIR. The four bars
and three equal-sized spaces form a square, and thus the aspect
(length: width) ratio of each bar and space is 7:1 (Fig. 1).
J. Johnson has shown that many objects may be represented
by pairs of black and white bars inside a square (Ref. 4). He
related the number of line pairs of a bar chart, where the pairs
fit inside the minor dimension of an object, with the ability
of an observer to detect (resolve one pair of bars) or recog¬
nize (resolve four pairs of bars) the object. The task level
TEMPERATURE = T
TEMPERATURE = T + A T
FIGURE 1. Standard four-bar MRT test pattern.
factor y is the number of line pairs; for example, for detec¬
tion y = 1 and for recognition y * Johnson's conclusion
was based on the assumption that the object or target and the
equivalent bar pattern were of the same size and contrast and
at the same distance.
F.A. Rosell introduced the concept of aspect corrections
for targets whose shapes are significantly different from the
square used in the standard equivalent bar patterns (Ref. 5).
As a result, the laboratory-measured value of MRT using the
standard four-bar square test pattern with an aspect ratio of
7:1 is divided by /e/7 in order to obtain an aspect-corrected
value of MRT. The letter e is the length-to-width ratio of a
single resolution bar in the pattern which represents the actual
target rectangular outline. Figure 2 shows an automobile with
major dimension (length) approximately twice the minor dimen¬
sion (height) and the corresponding bar patterns for detection
and recognition. In this figure the aspect ratio of a single
bar for detection is 4:1 and that for recognition is 16:1.
4
DETECTION
FIGURE 2. Object image and corresponding bar patterns
for detection and recognition.
The temperature difference between a target and its back¬
ground is represented by AT (in degrees Kelvin). However, at a
distance the apparent temperature differential between the tar¬
get and the background will be less because of atmospheric
attenuation of the target radiation. The atmospherically de¬
graded thermal contrast is obtained by multiplying AT by the
atmospheric transmission fatm-
The ratio of the atmospherically degraded thermal contrast
to the aspect-corrected value of MRT is a normalized signal-to-
noise ratio (SNR). Thus, the normalized SNR is given by the
expression :
AT t
snrn =
atm
MRT//e77
(1)
Equation 1 is the fundamental expression used in PLIR perform¬
ance modeling.
It has been shown that the probability of carrying out a
given task of detection or recognition is related to the nor¬
malized SNR as indicated In Fig. 3- These data were generated
5
0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00
SNRN =
mrt/v^T?
FIGURE 3. Probability of detection or recognition versus
normalized s i g na 1 - to- no i se ratio.
theoretically and from a series of experiments using many ob¬
servers (Ref. 6). The SNR is normalized in such a way that
when SNR,, = 1.0 the probability of achieving the task (detec¬
tion or recognition) is 50 percent. Other values of SNRTJ will
yield different probabilities of achieving the task (Fig. 3).
The solution to Sc. 1 for performance range is greatly
simplified by making the following assumptions.
First, atmospheric transmission often may be approximated
by Beer's law for narrow spectral intervals or spectral regions
where there is a relatively weak range dependence such as for
the water vapor continuum or aerosol extinction. If we assume
a 3eer's law dependence, we obtain
-6 , R
t = e atm
atm
6
where i\ltm la the extinction coefficient: of the atmosphere and
It la range (usually in kilometers). The coefficient g , Is
° at in
the sum of the extinction* coefficients due to molecular absorp¬
tion, water vapor continuum, and aerosols:
g ® g , + g , , . , + g
atm mol H-.0 cent aer
Look-up tables of ^ + 3n-,o coiit aro pf'-'acnt. ed later. It. is
evident from these tables of extinct ion coefficients for differ¬
ent path lengths that g^ ^ has a weak dependence on range. The
example provided will show how to deal with this problem in a
practical way. The dominant causes of atmospheric attenuation,
namely aerosols and the water vapor continuum, are relatively
Independent of range.
We next assume that the system MKT also can be adequately
approximated by an exponential function:
v
MKT = MKT e -•v . (j)
o
Figure shows MKT , g , and v on a plot of the logarithm of
O io y o
minimum resolvable temperature (MKT) versus spatial frequency
In eye les/tni 1 1 I rad Ian, where MKT ( Is the y-Intercept of the re¬
gression line, g. , Is the system ext lnct Ion coefficient , and
i>y o
v is the spatial I’requency In eye les/ml 1 1 1 rad I an . If the s 1 s.e
(:’-) of the target (the minor dimension In meters 1 and the task
1 ovel factor t>) defined according, to the Johnson equlvalent-
bar-p.at tern criteria are known, then we* have
v -
a sea Ling.
Th 1 s. equal Ion pr 'V Ides.
fad or for l tie abs.c I ssa I n
MRT
V = FREQUENCY (cycles/mrad)
FIGURE 4. Sample MRT.
8
Substituting ^ R for v in
MRT = MRT
o
Eq .
I
S
3 yields
6
sys
(4)
The performance range in kilometers at the 50 percent confidence
level is then obtained by substituting Eqs. 2 and 4 into Eq. 1
for eafcm and MRT, respectively, and by setting SNR^ = 1, which
by definition gives a probability of 50 percent of achieving
the task (Fig. 3 ) :
1 =
AT e
_SatmR
MRT e
o
X 8 R
S sys //£77
Equation 5 is then solved for R:
AT /S7T
In
MRT.
R =
B ^ + £ B
atm S sys
(5)
(6)
Table 1 shows values of MRT and B_,,„ For two FLIR systems
o sys
representing 1974 and 1978-79 technology devices. The coeffi-
cient of determination r“ is based on a regression on Eq. 3 and
is an indication that the two parameters MRT and B„,re are valid
o syb
descriptors of MRT.
TABLE 1. REPRESENTATIVE MRT AND B.v<; VALUES
8-12 um FLIR
1974 1978-79
_ T echnol ogy _ Technology
MRTq (°K) 0.0254 0.0112
B (mrad/cycle) 0.996 0.633
sys
r2 0.99 0.99
3-5 um FLIR
1974
T echnol ogy
0.0171
1 .006
0.99
Q
Equation 6 is the range performance at 50 percent confidence
level (SNR., =1). To determine range performance at the 10 per-
cent confidence level and the 90 percent confidence level refer
to Fig. 3. The value on the normalized curve for a probability
of 10 percent is SNR^ = 0.5, and for a probability of 90 percent
it is SNR^ = 1.5* Therefore, rewriting Eq. 6, we get
R
P
AT /uj\
mrtq )
sys
(7)
where Rp is the expected range for probability p of detection
or recognition and kp is the normalized SNR for probability p.
When, for example,
p = 0.90, kp = 1.5;
p = 0. 50, kp = 1. 0;
p = 0.10, kp = 0.5.
Validation of Eq. 7 has been shown in Ref. 2.
The next section presents some data that can be used as
input to Eq. 7.
1C
III. INPUT DATA
This section contains sample values for the parameters in
Eq. 7- These data are inputs that we have used at IDA and rep¬
resent our best understanding of the problem. These data are
only intended to be examples of the inputs necessary to calcu¬
late the range for certain probabilities of detection and recog¬
nition using the method discussed in this paper.
The sample input values are arranged by type of parameter:
FLIR system specifications , task difficulty factors, target
specifications, and atmospheric or environmental factors. A
discussion is presented wherever it is necessary to comment on
the source of the data and on reservations we may have about
the accuracy or validity of the models used.
11
A. FLIR SYSTEM SPECIFICATIONS
Parameter Description
MRT y-intercept of the regression line
' fitted to the values of the MRT in the
specifications of the particular FLIR
sensor of Interest (Fig. 4). This
relates to the overall FLIR sensitiv¬
ity.
S Slope of the regression line fitted to
y the values of the MRT in the specifica¬
tions of the particular FLIR sensor of
interest (Fig. 4). This relates to
the FLIR resolution.
Sample Values
8-12 ym FLIR
1974 _ 1978-79
MRTq (°K) 0.0254 0.0112
6syg (mrad/ cycle ) 0.996 0.633
3-5 um FLIR
1974
0.0171
1.006
B. TASK LEVEL FACTORS
Parameter
e
Y
k
P
Description
Bar aspect ratio (length-to-width ratio of
a single bar) of line pairs placed across
a rectangular cross section of the target
where width of the rectangle is equal to
the minor dimension of the target and
length is the major dimension (Fig. 5).
Task level factor, the number of bar
chart line pairs per minor dimension
of the object.
Scaling factor for determining range for
probability of detection or recognition
equal to p.
LENGTH
MINOR
DIMENSION
OF
TAR6ET
4M-7H
DETECTION
RECOGNITION
FIGURE 5. Bar test pattern for the front aspect of a tank.
Pi s cuss 1 on
Figure 5 shows the bar test pattern used for the front
aspect of a tank. For the front aspect of a tank the rectangle
is assumed to be approximately square so that the length and
13
width are both equal to the minor dimension of the tank (the
height). However, for the side aspect of a tank the length
would be increased, while the width of the rectangle would re¬
main equal to the height of the tank. For our sample values
we assume a tank that has length equal to approximately three
times its height.
Sample Values
The number of bars placed across the rectangle has been
determined to be 2 for detection and 8 for recognition (Ref. 4),
as shown in Fig. 5- Examples of aspect ratios are the following
Front Aspect Tank
Width=3m Heiqht=3m
Side Aspect Tank
Lenqth=9m Heiqht=3m
Rectangle Aspect
Ratio
1
: 1
3:
1
Detecti on
Re coqni ti on
Detecti on
Recoqni ti on
y (Number of
Line Pairs)
1
4
1
4
Number of Bars
2
8
2
8
Bar Aspect
Ratio
2:1
8: 1
6:1
24:1
e
2
8
6
24
Normalized SNR
for Probability
p ( k0) from
Fig. 3:
k . 90
1.5
1.5
1.5
1.5
k.50
1.0
1.0
1.0
1.0
k. 10
0.5
0.5
0.5
0.5
14
C. TARGET SPECIFICATIONS
DETERMINE TARGET MINOR
DIMENSION AND ATQ
4-3-791
Parameter Description
S Target size is the minor dimension of
the target expressed in meters.
AT Effective temperature difference (thermal
contrast) between the target and the back¬
ground in degrees Kelvin.
Sample Values for a Tank Target
S The minor dimension of a tank is its
height. Generally we have been using
3 meters as the height of U.S. tanks;
therefore S = 3 meters.
Front Aspect Tank Side Aspect Tank
AT £2°K j»6°K
15
D. ATMOSPHERIC FACTORS
Parameter Description
8 . Extinction coefficient of the atmosphere
(km-1), which is the sum of the extinctions
due to molecular absorption, water vapor
continuum, and aerosols:
8 , = 8 , + 8n . , + 8
atm mol H2O cont aer
Discussion
This atmospheric parameter is complex and requires a brief
review in this section. A detailed discussion of the knowledge
to date on this subject can be found in Ref. 7, Chapter III,
"Atmospheric Effects on Infrared Systems," by J.B. Goodell and
R.E. Roberts.
As indicated above, Batm comprises three components:
ex¬
tinction due to molecular absorption, water vapor continuum,
and aerosols. For this discussion of extinction Beer's law is
assumed (t ,
atm
atmosphere (t
= .-BR
= e
), and therefore transmission through the
atm
) will be calculated. Once
t , is determined
atm
and range R is selected, 8 can be obtained.
The two components molecular absorption and water vapor
continuum are computed in computer code LOWTRAN 3b, developed
by the Air Force Geophysics Laboratory to calculate atmospheric
transmittances (Ref. 8). This computer code is widely accepted
as the best model for computing molecular band absorption.
LOWTRAN 3b also calculates the aerosol component, but this will
be discussed separately.
The following tables enable the user to obtain a value for
the molecular extinction coefficient 8, given the atmospheric
temperature T& (°C), the dew point T^ (°C), and the range R
(km). The values of 8 are derived from the molecular and water
vapor continuum components of atmospheric transmission as com¬
puted using the LOWTRAN 3b code for a horizontal sea-level path,
and a weighting function corresponding to a blackbody source at
10°C.
16
p
Table 2 presents extinctions for the 3-5 ym band. Note
that atmospheric temperature Ta is not needed in order to find
&3_q; only the dew point Tdp and range R are necessary. For a
given Tdo> a change in T& does not produce any appreciable dif¬
ference in 63 3 . Therefore, all ranges appear together in one
table.
For the 8-12 um band, both T and T, are needed to find
a dp
the appropriate Sg_12> so a separate table is provided for each
range. Tables 3 through 6 correspond to ranges of 2, 4, 8, and
16 km, respectively.
The relationship between t tm and R assuming Beer's law
(Eq. 2) for the 8-12 ym band is not as strong as for the 3-5 ym
band. Therefore, the range R to be used in looking up the
appropriate 8mol + Bh20 cont in Tables 3 through 6 should be
estimated. Using the estimated value of R, the value for ex¬
tinction is selected, and Eq . 7 is solved for R. If R is some¬
what different from the R used to look up the extinction value,
Eq. 7 should be solved again using the more appropriate value
for extinction. This process is shown in the example presented
at the end of the paper.
For values of Ta, Tdp, or R other than those given, a
linear interpolation scheme between the nearest given values
will yield a fairly accurate result.
Again, these values of 6 account for only the molecular
and water vapor continuum components of extinction. To obtain
a realistic estimate of detector performance, the aerosol com¬
ponent of extinction must be taken into account as well.
There are many uncertainties regarding aerosol effects
on FLIR systems. LOWTRAN 3b contains aerosol models whose
validity is in doubt. However, the data given in LOWTRAN 3b
are used for our purposes. We have derived approximations based
on the LOWTRAN 3b aerosol data. The derivation of these aerosol
17
TABLE 2. 3-5 ym MOLECULAR PLUS H2O CONTINUUM EXTINCTION
COEFFICIENT FOR TARGET TEMPERATURE OF 10°C
'dP
7*rr
mm
-20
nu
BQ
-5
<5
5
msm
■H
20
m
30
35
4(3
0.5
.602
.643
.691
. 745
.810
.880
.956
1.038
1.128
1.225
1 . 331
1.439
1.557
1.0
.381
.41 1
.446
.486
.529
.576
.629
. 685
. 747
.810
.875
.947
1.024
.246
.268
.292
. 318
. 349
.381
.415
.452
.490
.532
.576
.622
.672
.161
.176
.192
.211
.231
.252
.275
.299
. 325
. 351
.379
.410
.443
8.0
.107
.117
.129
.141
.154
.168
.183
.199
.215
.233
.252
.275
. 300
16.0
.072
.079
.087
.095
.104
.113
.123
.133
.145
.158
.173
.190
.210
32.0
.049
.054
.059
.065
.070
.084
.091
.100
.111
.122
.136
.151
TABLE 3. 8-12 ym MOLECULAR PLUS H2O CONTINUUM EXTINCTION
COEFFICIENT FOR TARGET TEMPERATURE OF 10°C AND
PATH LENGTH R = 2.0 km
. . . _ LtJ
7T°cl
Ta (°C)
-20
wsm
-10
-5
0
5
10
15
20
mm
30
35
40
-20
.039
ap:-
.039
.047
.038
.047
.058
.038
.046
.057
.075
.038
.045
.056
.073
.099
5
.037
.044
.055
.071
.096
. 1 37
.037
.044
.054
.069
.093
.131
.195
15
.037
.043
.053
.067
.090
.126
.185
.283
20
.036
.043
.052
.066
.087
.121
.176
.267
. 41 7
25
.036
.042
.052
.064
.085
.117
.168
.254
. 393
.616
30
.036
.042
.051
.063
.082
.113
.161
.241
. 371
. 579
.907
35
.035
.042
.050
.062
.081
.230
. 352
.547
. 852
1 . 323
40
.035
.041
.050
.062
.079
.107
.150
. 334
.516
.805
1 . 244
1 . 908
TABLE 4. 8-12 pm MOLECULAR PLUS H2O CONTINUUM EXTINCTION
COEFFICIENT FOR TARGET TEMPERATURE OF 10°C AND
PATH LENGTH R=4.0 km
TABLE 5. 8-12 pm MOLECULAR PLUS H2O CONTINUUM EXTINCTION
COEFFICIENT FOR TARGET TEMPERATURE OF 10°C AND
PATH LENGTH R=8.0 km
A
1?
TABLE 6. 8-12 um MOLECULAR PLUS HoO CONTINUUM EXTINCTION
COEFFICIENT FOR TARGET TEMPERATURE OF 10°C AND
PATH LENGTH R=16.0 km
model approximations is discussed at length in Ref. 7. In addi¬
tion to the LOWTRAN 3b aerosol models (maritime, urban and rural)
an aerosol model for dry climates has been developed here. Vis¬
ibility (VIS) in kilometers is the only input value needed to
determine S by using the approximations (Table 7).
cLGiv
The uncertainties regarding the aerosol models must be
emphasized. There are three basic caveats to keep in mind:
1. The visibility required as input to the aerosol
models is not a reliable measure. It is very
common for two people to get different values
when measuring visibility. For a more detailed
discussion see Ref. 7.
2. It is unrealistic to expect any simple scaling
model will pertain to all atmospheric conditions.
For example, the continental model may not be
appropriate for all continental atmospheric con¬
ditions; for some limited-visibility conditions
2C
over the continent, the maritime model la a better
approximation of those conditions.
3. The models in Table 7 are for ground-level paths.
For air-to-ground cases significant differences
occur due to vertical structure which cannot he
predicted by these models.
TABLE 7.
EQUATIONS TO APPROXIMATE
^aer
Aerosol Model
8-12 um
3-5 um
Mari time
0.85
2.24
VTT~
FIT"
Rura 1
0.43
0.42
FTT-
wr
Urban
0.41
0.60
FIT"
FIT-
Dry
0.95
1 . 76
FIT"
FIT"
Thus, |3 tm may be determined by using the appropriate valu
obtained from Tables 2-b (B[uo^ + fn^O cont ^ at'd adding it. to
, calculated by using the approximations for different
el t? I
atmospheric conditions given in Table
IV. AN EXAMPLE OF THE CALCULATION PROCEDURE
I. Assume the following problem specifications:
A. FLIR System Specifications for a 1974 Generation 8-12 ym
FLIR:
MRTQ = 0.025^ °K
8 = O.996 mrad/cycle
sy s
B. Task Level Factors for a Front Aspect Tank 3 Meters in
Height for Probability of Detection of 50 Percent:
Y = 1
e = 2
kp = k. 50 = 1,0
C. Target Specifications:
S = 3 meters
AT = 2°K
D.
Atmospheric Factors when Visibility = 2 km under Mari¬
time Environment with T& = 10°C and T^ = 0 °C
0.85 _ 0.85 _
2.0 km
= 0.425 km
2. Estimate range (R ) to use in looking up appropri-
ate Smol + V cont in Tables 2-6:
22
Rest
AT /F7T\
MRTq J
S + X B
aer S sys
0.425 + j (0.996)
_ 3.740
0.757
= 4 . 9
Thus we will use Table 4 to look up 6 n ^
moj. H2O cont
since it is for range = 4 km, which is the closest range to
4.9 km in the tables presented in this report. For T. = 10°C
cL
and Tdp = 0 C and R = 4 km, we get Bmol + BHoQ cont = km
Thus, Batm * 0.425 + 0.078 = 0.503 km-1.
(Note: A linear interpolation could be done between values
found in Table 4, where range = 4 km, and Table 5, where range
= 8 km, to get Bmol + B^ CQnfc = 0.076 km"1.)
II. Solve Eq. 7 for all the input values given:
R
.50
In
0.503
/l 2 JT7 t\
\1 0.025V
+ j (0.996)
„ 3-740
0.335
= 4.48
23
Thus, the range at 50 percent probability of detection
for the given PLIR and under the given atmospheric conditions
is 4.5 km.
REFERENCES
1. Institute for Defense Analyses, Effect of Weather at
Hannover , Federal Republic of Germany , on Performance of
Electrooptical Imaging Systems: The Calculation Method¬
ology for a FLIR Using a FORTRAN Program , IDA Note N-842,
L.N. Seekamp, August 1977.
3.
4. J. Johnson, paper presented at Image Intensifier Symposium,
Ft. Belvoir, Virginia, 6-9 October 19-58.
5. F.A. Rosell and R.H. Willson, "Recent Psychophysical Experi¬
ments and the Display Signal-to-Noise Ratio Concept," Chap¬
ter 5 in L.M. Biberman, ed.. Perception of Displayed Infor¬
mation, Plenum Press, New York, 1973, pp. 167-232.
6. R.L. Legault, "Visual Detection Process for Electrooptical
Images: Man — The Final Stage of an Electrooptical Imaging
System," Chapter 4 in L.M. Biberman and S. Nudelman, eds.,
Photoelectronic Imaging Devices, Vol. 1, Physical Processes
and Methods of Analysis , Plenum Press, New York, 1971,
pp. 69-86.
7. U.S. Navy Electrooptical Technology Program Office/ Naval
Research Laboratory, The Fundamentals of Thermal Imaging
Systems, EOTPO Report 46/NRL Report 8311, F.A. Rosell and
G. Harvey, eds.. May 10, 1979-
3. Air Force Geophysics Laboratory, Atmospheric Transmittance
from 0.25 to 28.5 \xm : Supplement LOWTRAN 3b (1976), J.E.A.
Selby, E.P. Shettle, and R.A. McClatchey, November 1976.
25