PILOT-81 VVA EXPERIMENT-Analysis of the Multi-Path 

Transmissometer-Radiometer Measurements 

R.A. Sutherland and J.E. Butterfield 

ARL-TR-2953 April 2003

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Army Research Laboratory 

White Sands Missile Range, NM 88002-5513 

ARL-TR-2953 April 2003

PILOT-81 VVA EXPERIMENT-Analysis of the Multi-Path 

Transmissometer-Radiometer Measurements 

R.A. Sutherland and J.E. Butterfield 

Survivability/Lethality Analysis Directorate, ARL 

Approved for public release; distribution unlimited. 

Contents

Preface vi

Acknowledgements vii

Executive Summary 1

1. Introduction 3

2. Overview of the Experiment 5

2.1 General Layout................................................................................................................6 

2.2 Description of Trials .......................................................................................................6

2.3 Meteorological Measurements........................................................................................8 

3. MPTR Field Data Reduction 10

3.1 Transmissometer Mode Figure 4a.................................................................................11 

3.2 Radiometer Mode..........................................................................................................12

4. Examples of Field-Processed Data 13

4.1 Transmittance Data .......................................................................................................14

4.2 Radiance data: ...............................................................................................................14 

5. Analytical Methods 15

5.1 Multiple Scattering Emissivity And Reflectivity Functions.........................................15 

5.2 Beer’s Law and Linear Models.....................................................................................17 

5.3 Semi-empirical Methods. ..............................................................................................18 

5.4 Transmissometer Analysis, Log-T Method...................................................................18 

5.5 Radiometer Analysis, Log-R Method ...........................................................................20 

6. Example From Multi-trial Analysis (Near IR Band) 21 

iii
7. Results from IR Imagery (Mid- and Far Infrared) 24

7.1 Estimation of Optical Thickness...................................................................................24 

7.2 Determination of Path Radiance ...................................................................................25 

8. Summary and Discussion 26

8.1 Performance of Semi-empirical Methods .....................................................................26 

8.2 Performance of Log-R/T Correlation Methods of Analysis .........................................27 

8.3 Relationship to the Sky-to-Ground Ratio .................................................................28 

8.4 Limitations of Linear Models-Path Radiance ...............................................................29 

8.5 Limitations of Linear Models-Transmittance ...............................................................30 

8.6 Caveats and Comments.................................................................................................31 

8.7 Future Requirements.....................................................................................................32 

9. References 33

Appendix A. MPTR Theory 35

Appendix B. Clear Air Constants 39

Appendix C. Multi-Trial Summary 41

Appendix D. Multi-Pixel Data From Ir Imagery 45

Acronyms 48 

Report Documentation Page 49 

iv
List of Figures 

Figure 1. Sketch of field set-up at the SLAD 100 ft tower site .......................................................5 

Figure 2. Photographs of test site and smoke generation ................................................................7 

Figure 3. On site meteorological measurements..............................................................................9 

Figure 4. Examples of MPTR signals for (a) transmissometer modeand (b) radiometer mode ....10 

Figure 5. Example of multi-band MPTR field data (trial 21608, graphite)...................................13 

Figure 6. Theoretical calculations of emissivity and reflectivity (1).............................................17 

Figure 7. Demonstration of the Log T correlation method applied to the MPTR 

transmissometer data .....................................................................................................19 

Figure 8. Demonstration of Log-R correlation method applied to MPTR radiometer data ..........20 

Figure 9. Example of multi-trial analysis for graphite, near IR.....................................................21 

Figure 10. Example of multi-trial analysis for brass, near IR .......................................................22 

Figure 11. Plots showing results from analysis of imagery...........................................................25 

Figure 12. Example comparing linear models with theory............................................................29 

Figure C1. Multi-trial summary, graphite-visible..........................................................................41 

Figure C2. Multi-trial summary, graphite mid-ir...........................................................................42 

Figure C3. Multi-trial summary, brass-visible ..............................................................................43 

Figure C4. Multi-trial summary, brass mid-ir ...............................................................................44 

Figure D1. Photograph of single data frame from IR imager........................................................45 

Figure D2. Dual band multi-pixel time scans of total radiance for graphite .................................46 

Figure D3. Dual band multi-pixel time scans of total radiance for brass......................................47 

Tables

Table 1. Identification of MPTR Bandpasses..................................................................................6 

Table 2. Trial data for 16 February 1999........................................................................................6 

Table 3. Summary of semi-empirical parameters derived from measurements............................27 

Table B1. MPTR Clear Air Normalization Constants..................................................................39 

v
Preface 

In modeling the effects of infrared (IR) screening smokes on battlefield operations, one must 

account for the fact that the obscurant itself can be a strong source of IR radiation, often 

generating signals comparable to, or even much greater than, those from potential targets. The 

degree to which this happens is dependent upon the aerosol optical thickness, emissivity, and 

temperature as they affect absorption, scattering, and natural blackbody (thermal) emissions, 

which for the conditions normally encountered in terrestrial applications, are strongest at the IR 

wavelengths. The problem has been recognized for some time by the user community and 

requirements for incorporating emissive effects into the classical wargame models such as 

CASTFOREM have been put forth by both the U.S. Army Training and Doctrine Command 

(TRADOC ) and the National Ground Intelligence Center (NGIC). The problem was addressed 

by the U.S. Army Research Laboratory (ARL)/Survivability Lethality Analyses Directorate 

(SLAD) staff in the mid-1990s as part of a pilot program from which arose the creation of a 

formal technical program called SCIMITAR1

 which eventually led to the development of the 

PILOT812 model for simulating emissive sources and later to the execution of the field 

experiment of the same name described herein. All work was performed in-house through 

various SLAD tools, techniques, and met (TTM)] programs supported with 6.2 (development) 

funding and in cooperation with SLAD system leaders supported with 6.6 (analysis) funding. 

The major purpose of the experiment was to provide an accurate and reliable database for the 

development and verification of the PILOT81 model (and any others of similar capability). The 

main source of data was acquired with the ARL/SLAD Multiple-Path Transmissometer 

Radiometer System, or MPTR, which provided the measurements necessary to determine both 

the obscurant direct transmittance and the more illusive path emission and radiance required for 

modeling emissive smokes. These initial experiments were limited in scope to eight field trials 

and two obscurant types released into the atmosphere at temperatures slightly above ambient and 

thus include effects of both thermal emission and multiple in-scattering over four spectral bands 

from the visible through far IR. 

 1

 Anderson, L., Chenault, T., Churchman, J., Homack, R. and T. Smelker, 1999, “SCIMITAR-Scene and Countermeasure 

Integration for Munition Interaction with Targets”, U.S. Army Research Laboratory Technical report, ARL-TR-1633, September 

1999. 

vi

2 Sutherland, R.A, 2002, “Determination and use of IR band Emissivities in a Multiple Scattering and Thermally Emitting Aerosol 

Medium”, U.S. Army Research Laboratory Technical Report, ARL-TR-2688, July 2002. 
Acknowledgements 

The following U. S. Army Research Laboratory, Survivability/Lethality Analyses Directorate 

personnel participated in the field experiment: Joe Churchman, Test Conductor; Lon Anderson, 

infrared imagery; Steve Lacy, meteorological data; Eric Boschert and Ron Hagy, Aerosol 

Generator. Charlie Garret wrote the environmental impact statement and did the search of 

existing obscurants databases; and Felicia Chamberlain supervised the safety requirements. 

Charles Lopez, New Mexico Sate University student, performed the data reduction on the dual 

band imagery and helped with the data. Mr. Pete Schugart, Training and Doctrine Command 

Analysis Center /White Sands Missile Range and Mr. Frank Poleski, National Ground 

Intelligence Center, were the original catalysts driving the requirements for emissive smokes 

modeling. 

vii

Executive Summary 

The PILOT81 Emissive Sources Verification Experiment produced one of the few databases 

available for quantifying the radiative emissions of infrared (IR) screening smokes and the 

potential effects on multi-band sensor systems. The major source of data was the U.S. Army

Research Laboratory (ARL), Survivability/Lethality Analyses Directorate (SLAD) Multi-Path 

Transmissometer Radiometer (MPTR) system which provided near simultaneous and collinear 

measurements of both direct transmission and total radiance over three sampling paths (two 

transmission and one total radiance) and four spectral bands from the visible through far IR. 

Other on-site instrumentation included a 

• dual band IR imager 

• meteorological van 

• high volume aerosol generator 

The experiments, per se, consisted of eight trials utilizing both brass and graphite flakes as the 

(airborne) emissive obscurant. Obscurants were released into the atmosphere at four distinct 

mass flow rates producing semi-continuous aerosol clouds corresponding to a range of optical 

depths from τ=0 to a maximum of about τ=8. The formal objective of the experiment was to 

provide a database for developing and evaluating obscuration models used in IR scene 

simulations such as SCIMITAR1. The study also utilized the newly invented “Log-R” 

correlation method to enable a direct experimental determination of the “sky-to-ground” 

parameter which is a key input for contemporary sensor performance models and a requirement 

for modeling such systems in tactical wargames such as (CASTFOREM)2

. The experiments also 

filled a significant void in the Army’s program of “Smoke Weeks” which offers a wealth of

information on aerosol transmissivity but leaves a significant dearth of information on aerosol 

emissivity (and reflectivity) which are key to modeling emissive aerosol effects. The primary 

models chosen as representative of the current state-of-the-art in Army modeling applications are 

COMBIC3 for determining cloud transmittance and PILOT814 for determining path 

emission/radiance. Overall the MPTR measurements produced convincing evidence for the 

validity of the newly developed Log R method for analyzing path radiance as well as the more 

usual Log T method for analyzing transmission measurements. In general, the obscurant mass 

extinction coefficients determined from the MPTR transmissometer measurements agreed with 

COMBIC for all four spectral bands that were considered. Also the results from the MPTR 

 1

 Anderson, L., Chenault, T. Churchman, J., Homack, R. and T. Smelker, 1999, “SCIMITAR-Scene and Countermeasure 

Integration for Munition Interaction with Targets”, U.S. Army Research Laboratory Technical report, ARL-TR-1633, September 

1999. 

2

 Mackey, D.C., Dixon, D.S., Jensen, K.G., Loncarich, and J.T. Swaim, 1992, “CASTFOREM (Combined Arms and Support Task

Force Evaluation Model). Update: Methodologies”, Department of the Army Technical Documentation, TRAC-WSMR-TD-92-011. 

3 Wetmore, A. and S.D. Ayres, “COMBIC-Combined Obscuration Model for Battlefield Induced Contaminants”, US Army

Research Laboratory Technical Report, ARL-TR-1831, August 2000. 

1

4

 Sutherland R.A., 2002, “Determination and use of IR band Emissivities in a Multiple Scattering and Thermally Emitting Aerosol 

Medium”, U.S. Army Research Laboratory Technical Report, ARL-TR-2688, July 2002. 
radiometer measurements were in good qualitative agreement with PILOT81 over all optical 

depths considered; however, the quantitative performance was improved by “tweaking” the 

results using semi-empirical emissivity and reflectivity functions in place of the more 

theoretically rigorous multiple scattering solutions developed (strictly) for isothermal clouds of 

radial symmetry. The experiments were limited in scope to two emissive smoke types and 

obscurant temperatures of a few degrees above ambient. 

2
1. Introduction 

Possibly the two most important radiative parameters needed to characterize the effects of 

airborne obscurants on the performance of modern IR systems is the direct beam transmittance 

and the integrated path radiance. Together, these two parameters can be used to model the total 

radiant signal available at the entrance aperture of the receiver a given optical system as: 

I ( ) I T ( ) I S( , ) rec tgt i bkg i τ = τ + ω τ (1)

where τ is the obscurant optical thickness, Ti(τ) is the direct transmittance, ωi is the obscurant 

single scattering albedo and the index ‘i’ refers to the particular receiver spectral bandpass of 

interest (tab. 2). Defined as such, the first term in eq 1 represents that fraction of the received 

signal having originated from some “hard” target of surface radiance, Itgt, that reaches the 

receiver essentially unimpeded by the intervening medium (i.e., direct transmission) and the 

second represents all other “stray” contributions from the aerosol cloud and/or the ambient 

surroundings at all points along the propagation path (i.e., path radiance). In eq 1, the 

(normalized) path radiance function, S(ωi;τ), is generally comprised of two parts accounting for 

both the reflective and emissive properties of the aerosol cloud as: 

(2) S( ; ) a R( ; ) b E( ; ) i i i i i ω τ = ω τ + ω τ

path radiance function :

where the first term accounts for all contributions due to in-scatter originating from the ambient 

surroundings, and the second accounts for all contributions originating from thermal emissions 

internal to the aerosol cloud. In writing the above expressions as such, ambient inputs were 

assumed to be isotropic and the obscurant temperature can be treated as uniform. These 

approximations are made for convenience in establishing manageable guidelines for the analysis 

of the field data to follow and do not necessarily reflect any limitations on the scope of the study. 

A more complete description of the underlying theory and the physical processes involved is 

given in the PILOT81 documentation (1). With this being the case, the parameters, ai and bi 

become the sole ambient drivers representing, respectively, the atmospheric sources for inscatter and the aerosol (obscurant) sources for thermal emission. For IR scenarios it is 

furthermore customary to express these parameters in terms of their equivalent blackbody 

temperatures as: 

) T . I

F (T )

; b T

I

F (T )

a cld

bkg .

cld

*

i

i

amb

bkg

amb

*

i

i 3

atmospheric drivers:

4 4

π

σ

π

σ = = (3) 

where Text and Tcld represent the equivalent blackbody temperature (absolute) of the ambient 

atmosphere and the aerosol cloud, respectively, and the functions Fi

*

 (T) represents the 

calculated fractional blackbody irradiance within the particular spectral band of concern. It may 

be noticed in eq 3 that the “background” radiance, Ibkg, as used here turns out to be a simple 

3
normalizing factor that actually “cancels out” when used in eq 1. Later this parameter will be 

associated with “clear air” radiometer measurements in the analysis. 

In all of the above expressions and those to follow, the obscurant optical thickness, or optical 

depth, τ , is the independent variable representing the obscurant and is defined formally in terms 

of the path integrated aerosol concentration and is related to the Beer’s Law for direct 

transmittance as: 

 optical (4)

∫ =

= −

L

o

i C r dr

T

( ') '

 thickness;

( ) exp( )

transmittance :

τ α

τ τ

where C(r ́) represents the aerosol mass concentration at any point, r ́, along the target-receiver 

path of propagation, and L is the total path length. The (band dependent) obscurant mass 

extinction coefficient, αi, accounts for both absorption and out-scattering along the path [i.e., 

α=αabs + αsct] and is related to the single scattering albedo as [ω=αsct/(αabs+αsct)]. In applications, 

the path integral in eq 4 is sometimes referred to as the “concentration path length”, or simply 

the “CL Product” and is a property of the aerosol mass properties, independent of the receiver 

bandpass. Reasonable estimates of the optical properties of a wide range of military obscurants 

can be found in the COMBIC documentation (2). 

The main purpose of the analysis described herein was to develop and test methods for 

determining the relationships between the obscurant optical thickness, the direct transmittance, 

and the normalized path radiance using measurements obtained from the SLAD or MPTR, 

system (3). As it happens, methods for determining the obscurant direct transmittance have been 

developed and refined over the years in the course of the various Smoke Weeks conducted by 

the U.S. Army and summarized in detail elsewhere (4). However, methods for determining the 

path radiance are not as well understood and there is little quantitative data available, especially 

for wavelengths in the IR where the effects of both multiple scattering and thermal emission can 

be important. Despite this dearth of information, it is nevertheless important to realize that for 

emissive sources it is actually the (interfering) path radiance that can limit system performance 

and not necessarily the directly transmitted signal alone, a fact that has often been overlooked in 

the past but one that has again been addressed in recent experimental studies (5). It is this latter 

deficiency that is most fully addressed in this report. 

The ultimate application for the analysis here is to improve the representation of emissive 

obscurant effects in scene simulations models such as SCIMITAR (6), systems performance 

models such as TARGAC (7), and wargame simulations such as CASTFOREM (8). 

In the remainder of the report, sections 2, 3, and 4 are used to describe the experimental set-up, 

develop the MPTR theory, and present examples of actual field measurements. Section 5 

includes a brief description of the use of the aerosol emissivity and reflectivity functions, both 

theoretical and semi-empirical, and the rationale behind the Log R/T correlation methods for 

extracting the aerosol transmittance and path radiance from the MPTR data. Sections 7 and 8 

4
present an overview of the entirety of the multi-trial experiments using both the MPTR and the 

supporting IR imagery. In the final section we demonstrate utility of the results in modeling 

emissive obscurant effects using semi-empirical methods, explain the relationship of the MPTR 

measurements to the sky-to-ground parameters used in the older models, and discuss the 

limitations of the of other modeling approaches based on linear approximations. There are four 

appendices; the first three providing details of the MPTR measurements and the fourth giving 

more detail on the use of conventional IR imagery. 

2. Overview of the Experiment 

A unique and defining feature of the experiment was the simultaneous measurement of direct 

transmission and total radiance over multiple paths and multiple spectral bands through 

artificially generated aerosol clouds of varied optical thicknesses. Radiative measurements were 

performed with both the MPTR system and a research grade dual band IR imager. The 

experiments were conducted near the SLAD 100 ft tower site at the White Sands Missile Range, 

NM. The general experimental layout is shown in figure 1. 

WIND 

Plume 

Generator 

GS-1 Background 

GS-2 

Receiver 

North 

Figure 1. Sketch of field set-up at the SLAD 100 ft tower site. 

Key elements of the experiment were; (a) three horizontal sampling lines, two for transmission, 

one for radiance, (b) a variable rate aerosol generator for either brass or graphite, (c) supporting 

meteorological measurements, (d) visible band video documentation, and (e) supporting IR dual 

band imagery.

5
2.1 General Layout 

In the figure. 1, the central line of sight (bold arrow) was directed outward along a heading of 

roughly 44°and was the main path over which the MPTR total radiance was measured against 

the distant natural background. Simultaneous measurements of direct transmission were 

performed along the two outer (dashed) paths terminating at the locations labeled GS-1 and GS-2 

where the MPTR guide sources were located. The total distance from the MPTR receiver to the 

guide sources was about 525 m and the angle separating the two transmissometer paths was 

approximately 4°. In all cases the lines of sight were parallel to the (earth) surface and fixed at a 

height of 2 m. All transmission and radiance measurements were synchronized to within about 

1/10 s and were carried out simultaneously over the four spectral bands identified in table 1. 

Table 1. Identification of MPTR Bandpasses. 

 Band 1: ∆λ1=0.40-0.70 um, visible 

 Band 2: ∆λ2=1.06 um, near infrared 

 Band 3: ∆λ3=3-5 um, mid infrared 

 Band 4: ∆λ4=8-12 um, far infrared 

 

The experiments (eight trials total) were carried out in a single day over the course of about 90 

min under generally fair weather conditions (see meteorological data later). The aerosol 

generator was located at a point about half the distance between the MPTR receiver and the 

transmissometer guide sources and from 25 to 50 m upwind of and generally perpendicular to the 

main path- the exact distance and location depending upon the wind speed and direction. 

2.2 Description of Trials 

There were eight full trials of roughly 6 min duration each and all conducted successively in 

alternating pairs of either graphite or brass powder using the general scheme of table 2. 

Table 2. Trial data for 16 February 1999. 

Trial No Start End Type R(#/m)

21601 12:45:59 12:55:56 Dust N/A

21602 12:56:59 13:08:28 Graphite 10.0

21603 13:09:45 13:23:12 Brass 10.0

21604 13:24:14 13:34:17 Graphite 8.0

21605 13:34:59 13:45:27 Brass 8.0

21606 13:46:29 13:58:22 Graphite 4.0

21607 13:59:15 14:09:27 Brass 4.0

21608 14:09:59 14:20:27 Graphite 2.0

21609 14:20:59 14:31:28 Brass 2.0

6
The first column in table 2 identifies the trial number by date (216) and set (01through 09), the 

next two columns identify the precise time of day (Mountain Standard Time (MST)) for the start 

and end of each trial, the fourth column identifies the obscurant type, and the fifth column gives 

the generator mass emission rate setting. As noted, the generator mass emission rate for the first 

pair of trials was set at 10 lb per minute (the maximum used) and then adjusted incrementally 

downward to a minimum of 2 lb per minute for the final set. The first trial was a “shakedown” 

run using locally generated dust and is not included in the formal analysis. The main trials were 

conducted in rapid succession in an attempt to complete all of the experiments during nearly 

constant meteorological conditions (see meteorological data later). The general appearance of the 

obscurant clouds is demonstrated in the photographs of figure 2 which were taken with a 

commercial visible band digital camera. 

Figure 2. Photographs of test site and smoke generation. 

The two upper photographs in figure 2 were taken from near the top of the 100 ft tower looking 

generally eastward and downward along the main sampling path and the lower two were taken 

from ground level near the base of the tower. In both cases the left photograph refers to brass and 

the right refers to graphite. In the uppermost photographs, the aerosol generator and supply 

vehicle can be seen to the immediate right of the aerosol plume. Other objects are the bare dirt 

7
road, power poles, and a variety of other natural and manmade features in the background. In the 

lower photographs, the large object in the foreground is the blackbody source used for 

calibration and the two bright lights most apparent at the left and right extremities in the brass 

example are the MPTR guide sources at the locations labeled GS-1 and GS-2 in figure 1. 

The brass powder produced a visibly bright, brownish, cloud similar in color to the appearance 

in bulk samples. Likewise, the graphite powder produced a visibly dark, nearly black, cloud with 

occasional patches of a light gray most often seen near the cloud edges. In all cases the method 

of aerosol generation produced reasonably well-defined, semi-continuous plumes of about the 

size and concentration expected and with the characteristic internal chaotic structure 

characteristic of such clouds when generated in the real (turbulent) atmosphere. Overall the 

plumes were well behaved in that they were constrained to near the ground and maintained a 

reasonably coherent large scale structure over the testing distance. However, some cases of local 

vertical lofting could be seen in the visible band imagery which most often occurred for the 

graphite trials at points nearest the generator and was later evidenced in the transmissometer 

data. 

2.3 Meteorological Measurements 

The weather during the earlier part of the week of the experiments was characterized by strong 

frontal activity that caused excessively high winds the day prior to the experiments; however, by 

the time the trials were conducted the conditions had changed to generally fair and cloud free 

with light to moderate winds. Figure 3 shows the on-site measurements for the full diurnal period 

that were obtained from a mobile van located approximately 100 m southwest of the main area. 

8
Figure 3. On site meteorological measurements. 

With reference to the measurements shown in figure 3, the winds during the morning were light 

and variable in both speed and direction making it more or less unsuitable for testing because of 

the problems encountered in correctly placing the aerosol generator such as to intersect the 

instrumented line. By the afternoon, however, the winds had stabilized noticeably and eventually 

settled in to a direction consistently from the south (180o) in general agreement with the forecast 

from the nearby range “C” station. The time period during which the experiments were 

conducted are indicated by the vertical hash marks in figure 3. As noted, the experiments were 

started near 1130 hrs (MST) shortly after the winds had stabilized to a mean speed of about 3 

m/s; however, they did increase during the course of the experiment to a value of about 5 m/s by 

the end. This timeframe was slightly past local noon, thus the sun was near apex at about 30o

south roughly along the same heading as the plume centerline and perpendicular to the main 

sampling line. According to the radiometer data, the solar (direct + diffuse) irradiance that day 

was at a midday maximum of about 650 W/m2

 during the beginning of the experiment and 

decreased to about 600 W/m2

 by the time the trials were completed. Air temperature was 

nominally about 45 C at the beginning and dropped to about 40 C by the end. 

9
3. MPTR Field Data Reduction 

The SLAD MPTR system as employed for this test provides a measure of the total radiance 

against a natural background over a central line of sight plus a measure of the direct radiance 

from the guide sources over two adjoining lines of sight as noted previously in figure 1. Prior to 

the analysis, the raw signals are subjected to a certain amount of calibration, normalization, and 

manipulation to compensate for clear air atmospheric effects so that the reduced data is 

representative solely of the aerosol cloud. In the final analysis, the data are used to yield 

estimates of the relative transmittance and normalized path radiance as defined in the 

introduction of section 1. The methods for doing this are described in detail in appendix A. In 

this section the process is discussed in somewhat abbreviated detail using the examples of raw 

data plotted in figure 4 as a reference. 

Figure 4. Examples of MPTR signals for (a) transmissometer mode and (b) radiometer mode. 

In figure 4, the upper sketch refers to the transmissometer mode (trial 21608, graphite) and the 

lower sketch refers to the radiometer mode (trial 21609, brass). As indicated, a typical trial takes 

about 5–7 min (i.e., 600+ s), which includes time for both data collection during the (smoke) 

event and time before and after to allow for calibration. The onset and duration of these various 

time periods, annotated on the figure, are usually clear from inspection of the raw signals and are 

evidenced by a sudden changes in signal level; these time periods will not be overly elaborated 

on in this section. Both sets of data were taken in the visible band and are discussed more fully in 

the following paragraphs. 

10
3.1 Transmissometer Mode (Figure 4a) 

In normal MPTR operation all raw transmissometer signals are calibrated and scaled in the field 

to give real time measures of what is called the relative (aerosol) transmittance. The calibration 

process involves taking measurements for some short time period before (and sometimes after) 

each trial. These data are then used to “normalize” the signal to the clear air readings. More 

details are given in appendix A but the procedure ultimately produces a time dependent relative 

transmittance, Ti(t), extracted from the raw data as follows: 

max min

i min

i X X

X (t ) X T (t ) −

− = (5)

where Xi(t) represents the raw (voltage) signal received in one of the four optical channels 

identified previously in table 2 (i.e., i=1,4) and t is elapsed time. 

The scaling parameters, Xmax and Xmin , are obtained from readings taken in the time period just 

prior to the release of the obscurant. In the example of figure 4a, the first 20 s or so labeled 

“start” represent the initial clear air reading to determine Xmax, which is followed immediately by 

a nominal 60–80 s time period labeled “shutter closed” to determine a “zero” reading, Xmin. The 

net effect of eq 5 is thus to produce a signal “normalized” to the clear air value such that the new 

clear air reference is set to 100 percent. Note that this normalization procedure also eliminates 

the need to know the actual value of the radiance from the guide sources. After another short 

period of clear air readings labeled “shutter open,” the obscurant is released and reaches the 

sampling line a short time later as evidenced by an immediate decrease in the signal at the point 

labeled “obscurant on.”∗

 (After some specified elapsed time (five min for these trials), the 

generator is turned off, and the signal slowly rises as the smoke clears as is evident near the end 

of the trace in the region marked “off”. Although the effects of generator fluctuations cannot be 

entirely ruled out, the intense and very rapid fluctuations in the signal during the time that the 

obscurant is on is due, for the most part, to mechanical wind turbulence as it affects aerosol 

concentration and is often observed in experiments of this type when conducted during daytime 

conditions. 

Calibrated and scaled as such the reduced signal now represents the aerosol transmittance from

which can be immediately calculated the optical depth and path integrated concentration as a 

function of time using the inverted form of Beer’s Law, that is: 

CL(t ) (t ) i

i

i

τ

α

τ

1

path concentration :

(t) -Ln[T (t)]

optical thickness :

i

=

=

(6)

 

11

∗

The initial and less pronounced signal reduction just prior to the obscurant release is an artifact due to dust and other debris 

created by the generator startup and is to be ignored in the analysis. 
where it is to be noted that the CL product, being a measure of the obscurant mass, is 

independent of the particular bandpass selected and thus should yield the same result for all four 

optical channels. Note also that the CL product cannot be determined from the transmittance 

measurements alone unless there is an independent measurement of αi, the band-dependent mass 

extinction coefficient (assumed to be a constant for a given spectral region and independent of 

time). In calculating the CL product for later use, an average was computed based on all four 

spectral bands assuming a known value for the mean as determined from laboratory data. This 

data, for the record, were taken to be <α>= 1.0 (m2

/gm) for brass and <α>=1.45 (m2/gm) for 

graphite. These and other assumptions concerning the obscurant optical behavior are discussed 

in later sections. 

3.2 Radiometer Mode (Figure 4b) 

The initial steps in the radiometer mode are very similar to those of the transmissometer mode. 

However, in this case there are no artificial guide sources in the path so that the pre-event 

readings in this case correspond the clear air readings taken against the natural background. Thus 

the corresponding equation for the radiometer mode is identical in form to that of eq 5, that is: 

max min

i min

i Y Y

Y (t ) Y R (t ) −

− = (7)

where, in this case Yi(t) represents the time-dependent radiometer signal. The scaling parameters 

Ymin and Ymax are obtained in the same manner as before using the pre-event opened and closed 

shutter readings. In figure4b, it is interesting to note that in this case the signal actually increases 

when the obscurant (brass) is introduced. This indicates that the loss in signal due to extinction 

(i.e., lower transmittance) is more that compensated by the gain in signal due to the path 

radiance. However, in most other cases, the IR in particular, the obscured signal is more likely to 

decrease as will be seen in later examples. 

With the raw data so calibrated the resultant signal now represents a measurement of the total 

received radiance (actually normalized to the clear air) discussed in section 1. The next task is to 

separate out the transmittance and path radiance contributions using the basic relationship of eq 

1. There is a problem because measurements are not all collinear; however, any errors are 

minimized provided that the obscurant concentration distributions over the three sampling lines 

are not inordinately different. Thus, it is valid to calculate the path radiance from the measured 

data by performing a point by point differencing at each time interval using the simultaneous 

measurements from all three paths, ignoring for the moment the slight delay due to obscurant 

transport. That is, using and rearranging the time-dependent normalized version of eq 1, for each 

time sample, t, the result is: 

(8) S (t ) R (t ) T (t ) i = i − i

path radiance :

where the total radiance, Ri(t), is obtained from the radiometer sampling path and the 

transmittance, Ti(t) is obtained by averaging over the two transmissometer paths. At this point it 

is also necessary to assume that the time lag for obscurant transport between the sampling lines 

is small compared to the averaging time which is the same as assuming that the measurements 

are essentially time synchronized. The fact that these conditions are approximately maintained 

12
was qualitatively verified from the imagery data and more quantitatively from the correlation 

analysis discussed in later sections. 

4. Examples of Field-Processed Data 

Before proceeding to the actual analysis it is worthwhile to examine some general trends that 

become more or less immediately apparent from casual inspection of the field-processed raw 

data. The example for graphite (trial 21608) shown in figure 5 will serve as a reference for 

discussion. 

NOTES: 

(a) LOS-1relative transmittance measurements performed over LOS-1 

(b) LOS-0 total radiance measurements performed over LOS-0 

(c) LOS-2 relative transmittance measurements performed over LOS-2 

Figure 5. Example of multi-band MPTR field data (trial 21608, graphite). 

13
In all cases (fig. 5), the introduction of the obscurant marking the beginning of the event near the 

60 s mark and the ending some 300 s later is immediately evident from the traces and need not 

be elaborated upon further. The four rows in each matrix correspond to the four spectral bands 

identified table 1. Note that the center column, (b) LOS-0, shows both the original, nearly 

featureless, total signal plus a mathematically “enhanced” version that shows more detail in the 

fluctuations. 

4.1 Transmittance Data 

Perhaps the most distinctive feature seen in the measured data is the fact that the transmittance 

traces for all four bands are nearly identical for each of the two transmissometer lines of sight. 

This statement applies not only to the overall magnitude of the signal but also to the details of 

the fluctuations. This observation was later found to be true for all trials, both brass and graphite, 

and is not necessarily unexpected since it is known from other sources that the mass extinction 

coefficients for both obscurant types are nearly independent of wavelength (2). It is somewhat 

more interesting to note that there is also a high degree of correlation between the traces for the 

two (separated) transmissometer paths. This, too, is not entirely unexpected since, in both cases, 

the measurements are based on the same cloud sampled over slightly different paths, but it does 

attest indirectly to the consistency of the data in the sense that there appear to be no artifacts 

brought about by faulty sampling techniques. It is also noteworthy that the transmittance along 

the path nearest the generator source (i.e., upwind, LOS-2 is slightly higher than that along the 

farther downwind path (i.e., LOS-1). This difference was more evident for graphite than for 

brass and was probably due to aerodynamic and thermal lofting of the cloud as a whole which 

was also observed in the video data. Another observation of some interest is the fact that the path 

nearest the source has some very high frequency components that appear to be damped farther 

downwind which may be indicative of the increased mixing generally predicted by diffusion 

theory. Overall the same general behavior describe here was also observed for brass (not shown) 

although it was consistently found that, for a given trial pair, the mean transmittance for graphite 

was lower than that for brass which is consistent with other findings on the relative magnitude of 

the mass extinction coefficient for the two obscurant types discussed earlier. 

4.2 Radiance Data 

Looking first at the two shorter wavelength bands, perhaps the most immediate and distinctive 

feature of the (unenhanced) radiance plots of figure 5 is the fact that the measured total radiance 

is almost unaffected by the introduction of the obscurant. This behavior was noted previously 

and is an indication of the near zero balance between the competing processes of signal 

attenuation and path emission which actually resulted in a net increase in total radiance for the 

case of brass that was noted earlier (fig. 4b). For the graphite sample, however, the signal is 

reduced in both cases indicating that attenuation is the more dominant mechanism although the 

difference is small. The enhanced plots show that the net effect is about the same for the visible 

and the near IR bands, even in the details of the fluctuations. 

At the longer wavelengths it appears that attenuation becomes relatively more significant as 

evidenced by the fact that both traces decrease when the obscurant is introduced, much more so 

for the far IR band than for the mid-IR band. However, at this point it becomes clear that the far 

14
IR signal has approached the lower threshold of the MPTR sensitivity as evidenced by the 

consistent “capping out” at low signal levels. This effect was even more evident from the other 

trails and for this reason the far IR data from the MPTR was not used in the analysis. However, 

the qualitative aspects of the data were later verified with the thermal imagery where it was 

observed that total radiance in the far IR band was consistently lower that in the mid IR band as 

discussed in more detail in section 8. 

Another interesting feature seen from the radiance plots is the near perfect correlation in the 

fluctuations between the visible and near IR bands which is most clearly shown in the enhanced 

plots. The same may be said of the correlations between the mid- and far IR bands although the 

evidence is less convincing due to the problem with the threshold. It is reasonably clear, 

however, that the correlations between the longer and shorter bands are not nearly as strong. For 

brass (not shown), the cross-band correlations in total radiance were not nearly as strong as for 

the graphite example for any of the bands studied. The reasons for the specific behavior are not 

totally clear but may be due to the fact that the dominant mechanisms at the shorter wavelengths 

derive mainly from ambient in-scatter while those at the longer wavelengths derive mainly from

internal thermal emission. In a later section the correlations are analyzed analytically using all 

trials. 

5. Analytical Methods 

In this section the theoretical framework is reviewed and analytical procedures brought to bear in 

the analysis of the experimental data. The underlying assumptions are; (1) that the processed 

field measurements do indeed provide an accurate measure of multi-band transmittance and the 

corresponding (near) simultaneous multi-band path radiance for each of the spectral bands 

considered, (2) that the transmittance data can be tested in terms of the Beer’s Law relationship, 

and (3) that the path radiance results can be explained using semi-empirical methods based on 

theoretical calculations of emissivity and reflectivity. There is, of course, the possibility that the 

data may contain new findings beyond the scope of existing theory. It is thus left for the analysis 

to provide the means necessary to test the various relationships predicted by existing theory and 

to determine tests for validating new findings. 

For the direct transmittance measurements, the applicable method is the well known “Log-T” 

correlation technique which essentially tests the data against the Beer’s Law relationship. For the 

path radiance measurements, the methods are not so well-known and necessitated the invention 

of an analogous new technique, which we called the Log-R method that essentially exposes 

departures from “ideal” linear behavior. Semi-empirical methods were then developed based on 

exact calculations supplied by PILOT81 model which was compared with the measurements. 

5.1 Multiple Scattering Emissivity and Reflectivity Functions 

The difficulty in applying the expressions of section 1 to the task at hand lies in the fact that the 

emissivity and reflectivity functions are generally not known from measurements and are 

difficult to calculate in real world applications. However, it is possible to generate exact 

15
solutions that are rigorous for certain idealized situations that might be similar to those of the 

real world that can be used as guidelines for the analysis and this is the philosophy behind the 

semi-analytical approach taken here. 

For a homogeneous and isotropic cloud of radial symmetry, the emissivity and reflectivity 

functions can be computed exactly over any path through the cloud from integral expressions of 

the following form (1): 

(9)

ω τ ω τ τ τ

τ

= ′ ′ ′ − ′

∫ E( , ) J ( ; )e d

o

emissivity :

where J ́(ω;τ) is the so-named emissive source function, generally obtained from models such as 

PILOT81 (1), and τ is the optical thickness as calculated over the total length of the targetreceiver path. A similar calculation can be performed for the reflectivity function; however, for 

an isothermal cloud, it is simpler to use the following conservation relationship: 

(10) E(ω;τ ) + R(ω;τ ) = 1−T(τ )

isothermal clouds:

where the expression on the right side is identical to the classical definition of absorptivity, (i.e., 

A(τ)=1-T(τ)), although this terminology is something of a misnomer since the transmittance 

accounts for both absorption and out-scattering. Equation 10 is valid for all spectral bands and 

all cloud geometries but, as noted, is strictly applicable only for the case of isothermal clouds 

and the condition of isotropic scattering. 

Some plots of the emissivity and reflectivity functions for optical depths up to τ=4 based upon 

source functions obtained with PILOT81 are shown in figure 6. 

16
Figure 6. Theoretical calculations of emissivity and reflectivity (1). 

As is evident from inspection, the functions are well-behaved and predictable in the sense that all 

curves increase monotonically with increasing optical depth, being somewhat linear in the 

beginning and then leveling off as the optical depth increases to the point becoming more or less 

insensitive to changes at the higher values. Note the similarities but also the reversal of the 

ordering of the curves for albedo in the two cases. The logarithmic plots are shown here for later 

reference and are useful in that they demonstrate a linear tendency, especially for the emissivity 

case and smaller values of optical depth and the extremes of albedo. 

5.2 Beer’s Law and Linear Models 

Perhaps the simplest approximation that can be applied for the analysis is to assume the source 

function , J ́(ω;τ), to be constant over the path of interest. In this case the integration in eq 9 can 

be performed immediately to yield the following simple Beer’s Law form for the normalized 

path radiance. 

 (11) 

 1 

1

Beer's Law (path radiance):

0

[ exp( CL )]

S ( ) [ T ( )]

i

i i

α

τ τ

= − −

= −

17
where the superscript ‘o’ is used to denote “zeroth’ order and the transmissivity is expanded in 

terms of the obscurant mass extinction coefficient and CL Product. The Beer’s Law is referred to 

as a “linear” model, in part, because it is linear with respect to transmittance, but, of more 

importance, is the fact that it is also linear with respect to the logarithm [Ln(1-S)] , the 

significance of which will be made more clear later in this section. Despite the simplistic 

appearance and limited range of validity, the above expression plays a central role in modeling 

and analysis. 

5.3 Semi-empirical Methods 

For thin optical depths and for some other special cases, the Beer’s Law, or “linear” form given 

by eq 11 is sufficient for estimating path radiance; however, for the more general case involving 

both thermal emission and multiple in-scatter the need for a more comprehensive approach is 

anticipated and, thus, define a higher order semi-empirical “intuitive” approximation based on 

the general form of the plots of figure 6 as follows: 

1 absorptivity

reflectivity

1 emissivity

semi - empirical :

1

2

A( ) exp( )............

R( ) A( ) E( )...........

E( ) [ exp( )].........

τ

τ

τ

τ τ τ

τ

τ

τ β

= − −

= −

= − −

(12)

where the various constants [β,τ1,τ2] are empirically based, band dependent, scaling parameters 

to be derived from the analysis. In practice, it was found that these functions did an accurate job 

in maintaining the overall qualitative features of the rigorous solutions while at the same time 

offering a more flexible basis for analysis. 

5.4 Transmissometer Analysis, Log-T Method 

The Log-T correlation technique is an often-used method for analyzing transmittance 

measurements and is based solely on the Beer’s Law of extinction. Briefly, the approach is to 

first define a test metric, Zi(t) as follows: 

(13) Z (t ) Ln[T (t )] i = − i

Ln T Correlation Method :

where Ti(t) represents the (time dependent) measured transmittance as determined in the manner 

described in section 3 . It is clear from inspection that a point by point plot of Zi(t) versus CL(t) 

should, if all assumptions are correct, yield a straight line intersecting the origin with a slope 

equal to the value, αi , the obscurant mass extinction coefficient for the spectral band of interest. 

This is the essence of the Log-T correlation method and an example of how it works using real 

measured data is demonstrated in figure 7. 

18
Figure 7. Demonstration of the Log T correlation method applied to the MPTR transmissometer data. 

In figure 7, the upper plot labeled (a) is taken as the starting point and shows the raw time 

dependent transmittance measurements taken, for this particular example from Trail 21604 

(graphite). The next step, illustrated in the plot labeled (b), is to compute the test variable, Zi(t), 

using the logarithmic expression of eq 13 at each time step. Next the test variable, Zi(t) is plotted 

versus CL(t) in the plot labeled (c), which is the essence of the Log-T correlation method for 

which the result here does indeed indicate a clear linear relationship as expected. In this case, the 

analysis yields a slope slightly greater than unity, indicating that the mass extinction coefficient 

for this particular spectral band is somewhat smaller than the mean. The last plot labeled (d) is 

formed by inverting eq 13 to recover the point-by-point transmittance plus the corresponding 

Beer’s Law analytical fit. The particular results here are more or less representative of all trials 

which, when taken together, give convincing evidence of the validity of the theory and the 

various underlying assumptions, more of which will be discussed in later sections. 

19
5.5 Radiometer Analysis, Log-R Method 

The Log-R correlation approach is similar to the Log-T approach except that the underlying 

framework is based on the Beer’s Law expression for attenuation [i.e., A(τ)=1-T(τ)] rather than 

extinction. The analogous test metric in this case becomes: 

Z (t ) Ln[ S (t )] i = − 1− i

Ln R Correlation Method :

(14)

where Si(t) is the normalized path radiance. The rationale behind this particular choice of test 

metric lies in the form of the zeroth order solution of eq 11. That is, upon taking the appropriate 

logarithm as suggested by eq 14 and following through with the Beer’s Law expression, a pointby-point plot of the new metric, Zi(t), versus CL(t) should, if the assumptions are correct, yield a 

straight line intercepting the origin and, as before, with slope equal to the value of the mass 

extinction coefficient. Of course deviations from a straight line then indicate departures from the 

underlying assumptions, the most likely involving issues of thermal emission, multiple 

scattering, and combinations thereof not treated in the linear approximation. An example of how 

the method works using real measured data from trial 21606 (graphite) is shown in figure 8. 

Figure 8. Demonstration of Log-R correlation method applied to MPTR radiometer data. 

20
In this case, the starting point, labeled (a) in figure 8, is represented by a plot of the total 

radiance plus the corresponding transmittance (taken as the average over the two 

transmissometer paths). The next step is to subtract the direct transmittance from the total 

radiance to obtain the normalized path radiance in accordance with the discussion leading up to 

eq 8 in section 4. The result from this step is shown in the plot labeled (b) where the interesting 

fact is noted the that the path radiance in this cases accounts for approximately 70–80 percent of 

the total radiance. The next step is to take the appropriate logarithm and form the correlation 

with optical depth which is shown in the plot labeled (c), and in inverted form in the plot labeled 

(d). This is the essence of the Log-R correlation method which does, indeed, show evidence of 

an initial linear relationship (dashed line) with significant departures at higher optical depths as 

expected. The smooth curves in the final two plots represent analytical representations based on 

the semi-empirical relationships described in section 5. 

6. Example From Multi-trial Analysis (Near IR Band) 

In this section, the analysis methodologies are applied to the entirety of the eight trials making 

up the experiment (tab. 2) using the near IR band as an example. Results for the other bands are 

presented in appendix C. The purpose in performing multiple trials was to get a good database 

covering a wide range of optical depths, or “mass loadings,” for both obscurant types. The 

entirety of the experiment was done in as short a time as possible so that the meteorological and 

atmospheric conditions did not change appreciably. The results for the near IR band are 

summarized in the plots of figure 9 for all graphite trials and figure 10 for all brass trials. 

Figure 9. Example of multi-trial analysis for graphite, near IR. 

21
Figure 10. Example of multi-trial analysis for brass, near IR. 

In each of the figures, the results are grouped into a 4x4 matrix of plots with the rows and 

columns defined as follows. The first column in each set represents the measured transmittance 

plotted as a function of time along with the corresponding optical depth (x10) as determined 

from the Beer’s Law relationship at each time step. In both cases the plots represent the average 

over the two transmissometer paths. The second column represents the measured total radiance 

along with the calculated path radiance as determined from eq 8. Both the transmittance and 

radiance data refer to relative values as determined by normalizing to the clear air readings as 

discussed in section 4. The remaining two columns represent the results of the Log-T analysis 

applied to the transmissometer data (third column) and the corresponding results of the Log R 

analysis applied to the radiometer data (fourth column). In all cases the horizontal rows refer to 

each of the four generator settings (mass emission rate) as indicated on the margin to the right. 

Some insight can be gained immediately from even a casual inspection of the general trends in 

the various plots. For example, it is clear from examination of the transmittance plots that the 

optical thickness increases (and consequently the transmittance decreases) with increasing mass 

loading and the fact that, for the same mass loading, the graphite optical thickness is generally 

higher than the corresponding value for brass (actually most noticeable at the lower mass 

loadings). There was some early concern that, at the higher mass loadings, the transmittance may 

be so low as to exceed the lower threshold of the MPTR system. Evidently this is true for the 

extreme cases where the transmittance appears to “bottom out” and the optical thickness appears 

to exceed the upper limit near τ=12. Later it was established that this limit occurred for 

measurements performed at optical depths exceeding τ=8 which were subsequently ignored in 

the analysis. 

22
Referring now to the radiance data (second column), it is apparent that the measured total 

radiance is much less sensitive to mass loading than either the optical thickness or the 

transmittance. In fact, there is almost no change in the measured value of either the path radiance 

(lower trace) or the total radiance (upper trace) in the lower three scans for either sample. 

Another important qualitative observation is the fact that the total radiance is relatively 

insensitive to the optical depth fluctuations, much unlike either the path radiance or 

transmittance. The reason for this behavior is, of course, due to the nature of the competition 

between the direct and diffuse contributions alluded to in previous sections. It is also 

immediately apparent from the second column that the path radiance is initially higher for 

graphite (75 percent) than for brass (50 percent) and that both increase with increasing mass 

loading, quickly reaching a “saturation level” most evident in the extreme rates where the path 

radiance makes up the near entirety of the total radiance, a fact most apparent in the extreme for 

graphite. 

Turning now to the Log-T analysis results (third column) it is clear that, despite the variations 

and fluctuations in the raw transmittance measurements, the results of the analysis show a much 

more ordered view as manifested by the near straight line relationships. The apparent “noise” in 

the data which generally appears to increase with increasing optical thickness could be due to 

real world (turbulent-driven) fluctuations but is more likely due to experimental errors often 

observed in these type experiments when the transmission is very low. For both samples, the 

results strongly support the Beer’s Law formulation as evidenced by the near straight lines in 

most cases although there is some indication of a “mass loading” effect manifested by a slight 

increase in slope with increased obscurant rate for optical depths approaching the MPTR limit. 

Overall, however, the plots are “well-behaved” and tend to verify the initial assumptions 

concerning the expected obscurant behavior upon which the experiments were based. 

Turning next to the Log-R analysis (fourth column), a cursory inspection of the results confirms

our earlier findings supporting the linear dependence at the lower optical depths which is 

apparent in both cases. However, the breakdown of the linear region is also immediately 

apparent as evidenced by the flattening out of the plots in the “saturation region” at the higher 

optical depths which is most apparent in the graphite sample. Direct comparison between of the 

graphite and brass show a difference in the path radiance behavior, most evident in the maximum

value attained (~3 for graphite, ~ 4 for brass) and due presumably to the difference in the 

obscurant optical properties, most likely the single scattering albedo. 

To summarize to this point, the results thus far tend to support the underlying theory and, this not 

necessarily unexpected, for the transmittance measurements which have been the subject of past 

experiments. The major new surprise lies in the success of the Log-R method in presenting the 

results in the form of “well- behaved” correlation plots which show major promise as a new tool 

for quantifying path radiance. Although the conclusions, to this point, are based only on the 

MPTR near IR measurements, similar results apply for the other bands and are presented either 

in appendix C or in the section to follow. 

23
7. Results from IR Imagery (Mid- and Far Infrared) 

The full set of measurements from the dual band IR imager was not available at the time of this 

report, but some preliminary data were extracted from the first two trails to more or less 

corroborate the MPTR results. In this section, an analysis similar to that of section 6 is described 

using a selected portion from each (time-dependent) frame of the IR imagery. The IR data were 

collected at a rate of 30 frames per second with each frame consisting of a 320x240 pixel matrix 

for each of the two spectral bands (i.e., mid-and far IR) and are described in more detail in 

appendix D. The analysis here applies to the average radiance from a 10x10 pixel area located 

approximately half way between the transmissometer guide sources which is roughly the same

area sampled by the MPRT (cf. fig. 1, appendix D). 

A major technical advantage offered by the MPTR is the use of the transmissometer guide 

sources to determine the cloud transmittance and the subsequent optical depth neither of which 

are directly attainable from conventional imagery taken alone. Thus the first major task is to 

determine an accurate method for calculating the (time-dependent) optical thickness for the path 

corresponding to the selected pixel area. Once this is done, then the path radiance can be 

calculated from the IR imagery using eq 8, and the analysis can proceed in the same manner as 

described in section 6. 

7.1 Estimation Of Optical Thickness 

For the particular situation here, a fortuitous circumstance exists wherein the extinction 

coefficient, and, hence, the transmittance is (nearly) the same for both the mid- and far IR bands 

suggesting that a band differencing approach may be accurate and feasible for calculating the 

optical depth using the empirical relationships of section 5. Stated briefly, the method is to 

iteratively adjust the optical thickness at every time step so as to simultaneously balance the 

fundamental relationship of eq 1 for the two spectral bands treated. That is: 

(15) Y ( ,t ) R (t ) Y ( ,t ) R (t ) 4 4 3 3

imagery analysis:

τ − = τ −

where, R3 (t) and R4 (t), refer respectively to the measured mid- and far IR total radiance 

obtained directly from the imagery and Y3(τ,t) and Y4(τ,t) refer to modeled values based on the 

empirical parameters derived from the MPTR analysis. Equation 15 is solved using iterative 

methods to find the optimal optical depth at each time step which is then assumed the same for 

both spectral regions. In practice, the method worked better than expected with the biggest 

uncertainties being in the inherently ill-conditioned “saturation” region occurring at the higher 

optical depths. 

24
7.2 Determination of Path Radiance 

The results of the frame-by-frame extraction of the IR signal and the corresponding calculated 

optical depth are shown in figure 11. The plots produced the equivalent of a time scan of total 

radiance comparable, in principle, to that obtained with MPTR radiometer. In figure 11, the plots 

on the left refer to graphite, and those on the right refer to brass. 

Figure 11. Plots showing results from analysis of imagery. 

In figure 11, the upper two plots show time traces of the normalized total radiance for the two 

bands as obtained in the manner described in section 6 plus the calculated optical depth (shown 

x10) as determined from eq 15. The lower two plots represent the results of the corresponding 

Log-R analysis and the subsequent comparison with the semi-empirical expressions. 

Looking first at the upper traces in the radiance plots, in all cases, the effect of the obscurant is 

not necessarily large, resulting at most in a reduction of the total radiance by only 20 percent 

which occurs for the far IR brass case. It is also evident from the mid-IR results that, upon the 

introduction of the obscurant, the total radiance decreases slightly for the graphite sample but 

increases slightly for the brass sample. Both of these observations are in qualitative agreement 

with the MPTR data although it does appear that the earlier results showed a more marked effect 

25
than those from the imagery. An examination of other pixel areas in the mid-IR imagery 

confirmed the fact that the total radiance in most cases is less affected by the graphite and, in 

some cases showing an actual increase when the obscurant is introduced (appendix D). Perhaps 

the most significant new finding from the imagery to this point is the fact that, for both obscurant 

types, the total radiance for the far IR band is measurably lower than that for the mid-IR band 

with the effect being more pronounced for the brass sample than for the graphite sample. This 

may be due, in part, to the slightly smaller mass extinction coefficient in the far IR band 

although this alone cannot explain the magnitude of the difference. Another plausible 

explanation may be based on differences in the obscurant albedos, although any conclusions at 

this point are risky due to the interacting environmental and obscurant factors identified in the 

fundamental relationship of section 1 which are all present in the IR bands. 

Turning now to the lower plots of figure 11, the Log R method for the far IR again resulted in 

well-behaved correlation plots with the same characteristic features observed from the MPTR 

analysis. The linear theory in both cases appears to be valid only for optical depths less than 

about 0.50 for graphite and only about 0.25 for brass which is a much lower threshold than was 

observed for the mid IR. There also appears to be more scatter in the graphite correlation plots 

when compared with brass and this again may be due to differences in the balance between 

emissive and reflective processes for the different obscurant types as predicted by theory. 

However, some caution is needed in interpreting the results as some artifacts were found in the 

imagery due presumable to time lags, and one adjustment on the order of a few seconds was 

required for the graphite data. 

8. Summary and Discussion 

From the evidence presented, clearly the MPTR measurements, coupled with the Log-R/T 

correlation methods, provide a reliable source of data for the experimental determination of both 

the aerosol transmittance and path emission/radiance. The same statement may be applied to the 

IR imagery although the results at this point are not conclusive. In this sense, the major object of 

the experiment was accomplished; however, a number of new findings surfaced in the course of 

the analysis which are briefly summarized in this section. In the final two paragraphs some of the 

more significant technical caveats are reviewed and some future requirements are discussed. 

8.1 Performance of Semi-empirical Methods 

From a modeling point of view, perhaps the most significant finding thus far is that the measured 

data can be represented by fairly simple semi-empirical expressions that are consistent with the 

existing theory underlying the ARL COMBIC and PILOT81 methods. It is equally important 

that the analysis allows for the separation of the purely obscurant effects from the purely ambient 

effects such that the results can be applied to arbitrary ambient conditions other than those of the 

experiment, per se. This latter point is conveniently summarized in quantitative form in table 3 

which gives our best estimates of the semi-empirically derived parameters discussed in section 6. 

The corresponding semi-empirical mathematical expressions are formed by recasting the 

equations of section 1 into a slightly more practical form as follows: 

26
(16)

I (t ) I (t ) { I R (t ) I E (t )

I (t ) I T (t )

T (t ) exp[ CL(t )]

total dir amb i cld i

dir src i

i i

= + +

=

= −

total radiance :

direct radiance :

transmittance :

α

where CL(t) is the time-dependent path integrated concentration, or CL Product, which we 

assume to be known or derived from the analysis. In this expression, the quantities Iamb and Icld

take the place of the relative parameters ai and bi in eq 2 and are assumed known or calculated 

from the ambient temperatures using eq 4 or some equivalent measurement. Likewise, the 

quantity, Isrc is assumed to be a known input representing either the “target” or “background” 

depending upon the specific application. The remaining unknowns in eq 16 are the obscurant 

cloud reflectivity and emissivity functions which, in general, can be estimated from first 

principles using models such as PILOT81, provided that the mass extinction coefficient and 

albedo are known, or, more accurately, from the semi-empirical relationships of eq 12 and the 

parameters of table 2 if the obscurant under consideration is one of those tested. 

Table 3. Summary of semi-empirical parameters derived from measurements. 

a. graphite α τ1 τ2 β ai bi

mid ir 1.37 1.00 1.152 0.742 0.750 1.021

far ir 1.31 1.00 0.750 0.387 0.120 0.950

b. brass α τ1 τ2 β ai bi

mid ir 0.97 1.00 0.575 0.856 0.750 1.021

far ir 0.95 1.00 0.650 0.542 0.120 0.950

For completeness the first two columns of table 3 lists the best estimates of the obscurant mass 

extinction coefficient and single scattering albedo which are based either upon the Log R/T 

analysis or from other sources in the literature. The next three columns are the best estimates of

the parameters needed to calculate the emissivity and reflectivity functions using the semiempirical relationships of eq 12. The final two columns give the best estimates of the 

environmental parameters (ai and bi) that best describe the environmental inputs appropriate for 

the particular atmospheric conditions experienced during the experiments and are related to the 

appropriate clear air readings as discussed in appendix B. 

8.2 Performance of Log-R/T Correlation Methods of Analysis 

In general, the Log-T correlation method worked well in analyzing the MPTR transmissometer 

measurements. For the most part, all plots consistently produced reasonable linear relationships 

for all mass loadings and good estimates for the corresponding empirically derived optical 

constants (tab. 3) which are in general good agreement with theory (i.e., COMBIC) and with 

experimental findings from other studies. Likewise, the analogous Log-R correlation method 

27
worked well in analyzing the MPTR radiometer measurements. In particular, the path radiance 

results at the smaller optical depths exhibiting the expected linear behavior, and the results at the 

larger optical depths exhibited large deviations due to higher order effects that are generally 

consistent with theory (i.e., PILOT81). The exercise using the dual band “Delta R” method for 

estimating optical depth (eq 15) from the IR imagery offers a significant technical improvement 

over the linear method and was surprisingly successful, but preliminary. 

8.3 Relationship to the Sky-to-Ground Ratio 

One of the most important parameters used to model the effects of target-background contrast 

and the consequent effects on military systems is the so-named sky-to-ground parameter, which 

is a key input in tactical wargame simulations such as CASTFOREM and discussed in detail in 

the older literature (9). Although there have been numerous concept papers written on the 

importance of obscurant-induced contrast effects, there is little direct data on quantitative field 

measurements comparable to the study here. As it turns out, the normalized path radiance as 

defined here can be used to determine other obscurant parameters such as the target-background 

contrast and contrast transmission and is thus entirely equivalent to a sky-to-ground parameter 

measurement. This is shown by starting with the usual definition of target background: 

 contrast

I( )

I( ) I( ) ( )

bkg

tgt bkg

τ

C

τ τ

τ − = (17)

which can be evaluated immediately by applying eq 1 of the main text twice, once for the targetreceiver path and once for the background-receiver path accounting for the total radiance in each 

case. That is: 

I ( o )[T( ) S( )]

I ( o )[T( ) S( )] I ( o )[T( ) S( )] C( )

bkg bkg bkg

tgt tgt tgt bkg bkg bkg

τ τ

τ τ τ τ

τ

+

+ − + = (18) 

where, as in all cases throughout, T(τ) is the aerosol transmittance and S(τ) is the normalized 

total path radiance. 

It is usual in applications to assume that the two paths (target and background) are nearly 

coincident so that the following approximations apply: 

S( ) S( ) S( )

T( ) T( ) T( )

tgt bkg

tgt bkg

τ τ τ

τ τ τ

≈ =

≈ = (19)

which, upon following through in eq 18, leads to a cancellation of the path radiance terms in the 

numerator and a subsequently less involved expression. That is, after some rearranging: 

] T( ) S( )

T( ) ][ I ( o )

I ( o ) I ( o ) C( ) [

bkg

tgt bkg

τ τ

τ

τ

+

− = (20)

where the first term in square brackets is called the intrinsic (or unobscured) target-background 

contrast, and the function in the second set of brackets is called the contrast transmission which 

28
is formally defined as the ratio of the (obscured) contrast to the (unobscured) contrast. That is, 

defining C(o) as the intrinsic contrast and substituting the exponential form for transmittance, 

results in: 

} S( )/ T( )C( ) C( o ){

τ τ

τ − = 1

1 (21)

which is identical to the usual expression if S(τ) is identified with the sky-to-ground parameter. 

It should be remarked that the origin of the sky-to-ground ratio terminology traces to the 

treatment of clear air scenarios and a semi-infinite plane layer atmosphere applied along a 

horizontal path in which case the Beer’s Law expressions are adequate. The extension here, 

however, represents the more general case making the associations with the sky and the 

unqualified usage of the Beer’s Law somewhat misleading to the uninitiated reader. 

8.4 Limitations of Linear Models-Path Radiance 

The results of the Log-R correlation analysis discussed in the various figures of section 5 clearly 

demonstrate the limitations of the linear approximations in accurately modeling path radiance, 

especially at the higher optical depths. The usage of such models to determine optical thickness 

from radiance measurements is also inaccurate and misleading, especially in the saturation 

region identified in figure 11. However, a quick dismissal of such models as a valid 

approximation is somewhat premature for reasons that will be made apparent later in this 

section. To illustrate the results are re-examined using the example of figure 12 as a reference. 

Figure 12. Example comparing linear models with theory. 

The plot on the left was produced using the Log-R method as described in section 7 as applied to 

a typical graphite trial using the near IR measurements. As usual the path radiance data plots are 

characterized by an initial linear region followed by a transition to the “saturation” region where 

the plots tend to a constant value as the cloud becomes optically thick, much in the manner 

predicted by PILOT81 (fig. 6). The Cirrus model represented by the upper straight line in Fig. 12 

is reported to be derived from single scattering and is included here at the request of the 

29
SCIMITAR group (10). The lower straight line represents a limit that is referred to as the 

“modified linear” region. 

The example here demonstrates the limitations of models based on the linear approach although 

it is clear that the performance can be improved significantly by adopting the modified empirical 

method suggested in figure 12. However, the real significance of this example is that the linear 

region extends up to an optical depth of about τ=3 which is surprisingly larger than might be 

expected. The case for brass in the visible band (fig. 3, appendix C) is even more surprising in 

that the linear region extends up to almost τ=8. On the other hand, for brass in the far IR (fig. 12) 

the linear region extends up to only about τ=0.50. In the following paragraphs these findings are 

examined in light of the more general theory underlying the PILOT81 model. 

The fact that the plots are initially linear is not necessarily unexpected, and this observation 

might be interpreted (although not necessarily so) as an indication of the predominance of single 

scattering. Although this latter statement is true, it can be misleading because there are a number 

of other situations where a linear form is theoretically predicted. To understand why this 

“unexpected” linear behavior might be happening consider that there are at least four other 

common situations wherein the theory predicts linear behavior even in the multiple scattering 

and emission regime. The first obvious case is the situation where the source function is 

essentially constant over the path of propagation which was already discussed in connection with 

eq 12. This is the situation commonly modeled in clear air scenarios for horizontal propagation 

through plane parallel layers that historically lead to the development of the sky-to-ground 

parameter. Another “obvious” situation is the case of temperature equilibrium which occurs 

when the ambient input radiance is equal to the cloud blackbody radiance (i.e., when ai=bi) in 

which case, according to eq 10, the path radiance expression reduces to the linear form. The third 

case occurs for the extreme of conservative scattering (i.e., ω=1) which is apparently the 

situation noted earlier for brass. The fourth situation occurs for the extreme of total absorption 

(i.e., ω=0) in which case all multiple and single scattering contributions are zero, and the linear 

form is strictly applicable. It is interesting that the results from the experiments suggest that 

some of these conditions are not far from those that actually were experienced during some of 

the field trials. 

8.5 Limitations of Linear Models-Transmittance 

The results thus far are encouraging in the sense that the linear model may often be a good 

approximation for modeling path radiance from the known optical thickness, even in cases where 

there is strong emission and multiple scattering. On the other hand one must proceed with more 

caution when dealing with the inverse application to determine the optical depth from radiance 

measurements as is sometimes attempted with field imagery. The reason for caution is clear from

casual inspection of the saturation region in the Log-R plots wherein the path radiance attains a 

constant value independent of any changes in the actual optical thickness. This “ill conditioning” 

of the process can be demonstrated by examining the error, ∆τ, introduced in using the linear 

approximation, that is: 

∆τ ≈ τ − Ln[1− S(ω;τ )] (22)

30
where, τ, represents the actual measured optical depth and the second term represents the 

expected error, which is immediately recognized as being identical to the argument, Z(t), used 

in the Log-R method of eq 14. Thus the magnitude of the error can be read directly from fig. 12 

as the difference between the linear model curve and the corresponding data points. This is 

demonstrated in fig. 12b which demonstrates the error introduced by using the linear 

approximation to calculate transmittance solely from radiance measurements. It is immediately 

clear that the linear method is adequate for small optical depths but the error grows rapidly 

beyond the linear threshold and ultimately exceeds two orders of magnitude at the extreme, thus 

seriously under-predicting sensor performance. Unfortunately, much of the data of record from

the Smoke Weeks apply to the saturation region where the largest uncertainties occur. This 

situation was, of course, not unanticipated here and was motivation for using the MPTR system

and for designing the experiment to cover a wide range of light to heavy mass loadings. 

8.6 Caveats and Comments 

The review of results and the various cross-checks suggest that the experiment was successful in 

obtaining an accurate and reliable database on the simultaneous measurements of path radiance 

and optical thickness for a wide range of obscurant mass loadings. On the other hand, there are a 

number of caveats that need to be addressed, the first is that the measurements were all obtained 

over a single set of horizontal paths and over (near) constant ambient conditions and, thus, some

caution needs to exercised in extending to more universal scenarios. However, the manner in 

which the analysis was conducted to separately extract weather dependent and obscurant 

dependent parameters allows for scaling of the results over a wide range of ambient conditions 

as implied in eq 16. This hypothesis is based on good theoretical grounds but has not necessarily 

been tested with real data. 

The second caveat is that, in performing the analysis the implicit assumption of isotropic 

scattering was also made but this assumption also was not tested directly. In practice, this means 

that somewhat different results might be expected if different viewing angles were used and this 

would be especially important at the shorter wavelengths and thinner optical depths where 

angular dependent solar in-scattering is most significant. Such details can be addressed with 

modeling but are difficult to verify in the field due to the inordinate difficulty in measuring all of

the necessary inputs. These details are quantitatively important but probably do not alter most of 

the broader qualitative information derived from the experiments. 

The third caveat involved scaling the results to higher (or lower) values for the environmental 

inputs (i.e., eq 16). All input radiative sources were implicitly assumed to be isotropic and for the 

obscurant cloud to be isothermal. Again, these assumptions do not necessarily reflect on the 

capability of the models but are more a matter of practical concern in the difficulty in actually 

measuring all possible inputs accurately. However, based on the a posteriori results, no direct 

evidence shows that a more accurate characterization of the ambient inputs would change any of 

the major conclusions. Finally, the assumption that the cloud is isothermal is probably not 

serious for the experimental situation here because the aerosol generation process does not heat 

the cloud much beyond the ambient, and, thus, details of the cloud temperature structure are of 

lessened significance. 

31
8.7 Future Requirements 

Besides the usual problem of trying to quantitatively extend the findings to arbitrary scenarios of

the real world which itself is “unquantifiable” in a practical sense, there are a number of more 

realizable goals for the immediate future. The first requirement is to validate the thermal imagery 

data using some of the same techniques and relationships as used here for the MPTR. Our 

experience (somewhat limited) with the IR imagery (appendix D) suggests a new method for 

extending the analysis to the spatial regime and techniques that may eliminate the bias in 

estimating the optical thickness from imagery. A more practical requirement is to exploit the fact 

that we have produced a method for obtaining a near direct measurement of the traditional skyto-ground parameter needed by the user community. 

Other more esoteric requirements involve the analysis of the statistical relationship between the 

directly transmitted signal and the interfering path radiance signal. These two quantities seem to 

correlate quite well in some applications and not so well in other applications and may explain 

some of the scatter in the correlation plots. From a theoretical standpoint this is a problem that 

needs to be addressed using a stochastic modeling approach which was more or less avoided in 

the analysis thus far. There are also practical applications for developing this type of analytical 

approach for synthetic scene development for future systems analysis where the requirements on 

accurate statistical renderings are of increased significance. From a practical viewpoint, two 

immediate follow-on experiments are evident. The first is to repeat the experiments during 

nighttime so as to eliminate the effect of solar loading and thus the measurements would lend 

more accurate information on the aerosol emissivity. The second is to include a set of 

experiments with the obscurant heated to a temperature that may be several (or even several 

hundred) degrees higher than the ambient temperature. Such strongly emissive conditions are 

expected to affect IR sensor performance, and the need for accurate modeling for this case has 

been pointed out by the user community. It was, in fact, this latter deficiency that lead to the 

development of the PILOT81 model and was a prime motivator in performing the analysis of the 

experimental data. 

32
9. References 

1 Sutherland, R.A., “Determination and use of IR band Emissivities in a Multiple 

Scattering and Thermally Emitting Aerosol Medium”, ARL Technical report, in review. 

2. Wetmore, A. and S.D. Ayres, “COMBIC-Combined Obscuration Model for Battlefield 

Induced Contaminants”, US Army Research Laboratory Technical Report, ARL-TR-1831, 

August 2000. 

3. de Jong, A.H.,1984, “Results of NL Transmission and Emission Measurements during 

Smoke Week VB and VI, Proceedings of Smoke Symposium VIII, April, 1984. 

4. Hoock, D.W. and R.A. Sutherland, 1993, (Obscurant Countermeasures), Chapter 7 in the 

EO/IR Handbook, published by SPIE, Bellingham, WA. 

5. Kuhlman, M.R., et. al., 1995, “Evaluation of Physical Properties of a Foreign Smoke” 

FMTR-1620-90030-001-94, prepared for National Ground Intelligence Center, August 1995. 

6. Anderson, L., Chenault, T., Churchman, J., Hornack, R. and T. Smelker, 1999, “Scene 

and Countermeasure Integration for Munition Interaction with Targets”, U.S. Army

Research Laboratory Technical report, ARL-TR-1633, September 1999. 

7. Gillespie, P.S.,1995, “TARGAC Technical Description and User’s Guide”, U.S. Army

Research Laboratory Technical Report, ARL-TR-273-3, April 1995. 

8. Mackey, D.C., Dixon, D.S., Jensen, K.G., Loncarich, and J.T. Swaim,1992, 

“CASTFOREM (Combined Arms and Support Task Force Evaluation Model) Update: 

Methodologies”, Department of the Army Technical Documentation, TRAC-WSMR-TD-92-

011. 

9. Seagraves, M.A. and J.M. Davis, 1989, “Target Acquisition Tactical Decision Aid 

Software Technical Documentation”, ASL-TR-0252, September 1989. 

10. Chenault, T., Equation of the form P=J(1-e-t ) , Cirrus computer program, unpublished. 

11. Lopez, C. and R.A. Sutherland, 2002, “Software Methods for Imagery Analysis”, U.S. 

Army Research Laboratory Technical Note, in preparation, December 2002. 

33

Appendix A. MPTR Theory 

In the basic transmissometer configuration, the raw signal is generally assumed to be comprised 

of the following contributions, including signal, noise, and interference components of various 

origin: 

 (A1) 

 noise, atmsophere& system

 path radiance, atmosphere

 path radiance, aerosol

 forward scatter

direct transmittance

N } N (s).........................

[I ( ) I ( )].............

[I ( ) I ( )]..............

[I f ( , ) I f ( , )]...........

S ( ) R (s){[( I I )e ]..........

atm sys

atm

*

atm sct

*

ems

aer

*

aer sct

*

ems

src dir bkg bkg

( )

dir i sys src bkg aer atm

+ +

+ +

+ +

+ +

∆ = + − +

τ τ

τ τ

δω τ δω τ

λ τ τ

In eq A1, the quantity labeled Rsys(s), is the system response function that converts the optical 

signal (s) to a voltage signal (Sdir) and is usually assumed to be a linear function for signal levels 

in the region of practical interest; although this assumption can break down at very high signal 

levels called the saturation region. In eq A1, the total path optical thickness includes 

contributions from both the smoke aerosol, taer , and the intervening atmosphere, τatm, which 

taken together make up the total path optical thickness (τ=τaer+τatm). Also, in eq A1, the first term

inside the curly braces represents the totality of any directly transmitted radiance and can include 

contributions from both the transmissometer source, Isrc, plus any “spill over” from the 

background, Ibkg, within the receiver field of view. The second term represents any contribution 

due to forward scattering within the field of view, δω, of the transmitter-receiver optical path. 

Most transmissometer systems are designed such that: 

I ( ) I ( ) bkg ∆λi << src ∆λi (A2)

where acknowledgment of the fact that both the background and source intensities are dependent 

upon the particular bandpass (∆i) under consideration. Thus, from eq A2 it is clear that the 

background terms can be neglected in comparison with the (very intense) artificial source terms, 

a condition that greatly simplifies the expression for practical applications. 

The third and fourth terms in eq A1 arise from either thermal emission, I*

ems(τ), or in-scatter 

from the surroundings, I*

sct(τ), either from the smoke aerosol, I*

(τaer), or the intervening 

atmosphere, I*

(τatm). In, the usual transmissometer configuration, the source beam, Isrc, is 

optically modulated with a mechanical chopper at the transmitter aperture to create an alternating 

current (ac) signal which is synchronized to the receiver electronics. The signal is then 

synchronously detected at the chopper frequency (usually around 1000 Hz) in such a way that 

any direct current (dc) component such as that due to a constant background is not sensed. This 

method of detection will eliminate most of the path radiance term, thus for all practical purposes 

the radiance terms are not measured. Therefore for the modulated signal that the transmissometer 

system actually “sees”, eq A1was replaced with the following more simplified form: 

35
 (A3) dir atm sys

( ) Smod ( ∆ i ) = Rsys(s){ Isrc [ e aer atm + f ( , )] + N } + N − + λ δω τ τ τ

where the condition of eq A2was accounted for by ignoring the terms involving Ibkg and by using 

the subscript “mod” to distinguish from the direct signal. For an ideal instrument, the forward 

scattering term can be minimized by using narrow beam receiver optics and collimated 

transmitter beams. For obscurants comprised of particles very much larger than the wavelength, 

the forward scattering lobe is very narrow and very concentrated and can even dominate the 

signal; however, for the types obscurants used here, the effect is generally negligible. The 

remaining noise terms in eq A1 represent both optical and electronic noise originating either 

from the intervening atmospheric path, Natm or purely from the system hardware, Nsys. In practice 

neither of these terms can be completely eliminated but can be accounted for, in the mean, such 

that: 

0

0

< >=

< >=

......................... N (t )

........................ N (t )

sys

atm (A4)

where the symbol <X(t)> is used to denote a (short term) average with respect to time. Thus the 

mean level of noise can be eliminated; however, fluctuations about the mean are almost always 

present in the field data. 

The basic radiometer configuration is similar to the transmissometer configuration except that 

the artificial optically chopped light source is eliminated thus leaving only the natural 

background for the clear air source. Also, the forward scatter component in this case forms an 

authentic contribution to the path radiance since Ibkg is from a natural ambient source and, along 

this same line of reasoning, the atmospheric-induced noise contribution is a bona fide component 

of the atmospheric source function. Thus in the radiance mode, eq A3is replaced with the 

following expression:

(A5)

N (r )

I ( ) I ( }

I ( ) I ( )

S ( ) R (r ){ I e

sys

atm

*

atm sct

*

ems

aer

*

aer sct

*

ems

( )

rad i sys bkg atm atm

+

+ +

+ +

∆ = − +

 

 

 

τ τ

τ τ

λ τ τ

where, in this case, Rsys(r) is the system response function for the radiometer receiver and Nsys(r) 

is the corresponding radiometric system noise. 

In the following paragraphs, the assumption is that either eq A3 or eq A5 represents the 

relationship between the received optical signal and the system output for the transmissometer 

and radiometer modes respectively. It will turn out that the situation can be simplified even 

further by “normalized” the signals to their clear air readings which has the effect of eliminating 

the system response function, Rsys, which “cancels” out. It is necessary, however, that the 

response function be linear in order for this to be valid. 

36

Thus, provided that all sources of error have been kept at a negligible level , then the net result of 

the data processing procedure should yield a measurement very nearly equal to the aerosol 

transmittance. That is, assuming Smin to be zero (on average) for the calibrated signal and 
realizing that Smax refers to the clear air transmittance (mean=100%), we have from eq A5, for 

the ideal case: 

≈ = for δω → 0

+

+

∆ =

−

−

− +

−

− +

e , e

e ...................

R (s)I [ e f ( , )

R (s)I [ e f ( , )]] T ( ,t )

aer

atm

aer atm

atm

aer atm

( r )

atm

( )

sys src

tot

( )

sys src

rel i

τ

τ

τ

τ

τ τ

δω τ

δω τ

λ

 (A6) 

which implies that the relative reading so normalized is a good estimate of the aerosol 

transmittance provided that the forward scattering contribution is negligible; an assumption that 

was later tested with the a posteriori data. 

With the data so calibrated and again assuming the noise terms to be eliminated and noting that 

Smax again refers to the clear air case, and proceeding in a manner similar to that leading to eq 

A6, the radiometric mode is: 

(A7) 

I e I ( )

I e [I ( ) I ( )] R

atm

*

bkg atm

atm

*

aer atm

*

aer

( )

bkg

rel atm

aer atm

τ

τ τ

τ

τ τ

+

+ + = −

− +

 

which, in this case represents the ratio of the total (direct + diffuse) radiance to the pre-event 

clear air total radiance. In most field tests, the atmospheric contribution is kept small by 

conducting the trials only under clear air conditions in which case, assuming a near horizontal 

path, we have: 

(A8) 0 for τ 0

1

≈ atm →

= − −

........... ;....

J( ) J ( e ) atm

atm o

τ τ

where Jo is a constant less than or equal to unity depending upon the obscurant albedo and is 

referred to as the atmospheric optical source function. Inserting this approximation for J(τatm) in 

the limit and assuming [exp(-τatm)~1], after some minor rearrangement and cancellation, the 

following expression analogous to the final form of eq A6: 

......... T( ) S ( )

I

I e I ( ) R

aer

*

are aer

bkg

aer

*

bkg aer

rel

aer

τ τ

τ τ

= +

+ =

−

 

 (A9) 

where the first term on the right is the direct transmittance which can be independently 

calculated from the transmissometer mode measurement, and the second is an additional 

contribution brought about by the inclusion of the path radiance and can be thought of as a 

normalized, or relative, path radiance. That is: 

37
bkg

aer

*

* aer

gr I

I ( ) S ( ) τ

τ = (A10)

which is also referred to as the sky-to-ground ratio discussed in the main text. Thus the MPTR 

system provides all of the information needed to account for the two major obscuration 

parameters used in sensor performance modeling. 

38
Appendix B. Clear Air Constants 

In executing the experiments, an effort was made to complete the entire set of trials as quickly as 

possible so as to avoid any problems associated with variations in the atmospheric conditions 

which could influence the clear air readings. In this section, the values of the clear air readings 

obtained along the three main sampling paths as measured near the beginning of each trial are 

documented. 

The data in table B1 refer to a the original 12-bit digital readings, or counts, which are assumed 

proportional to the incoming radiant signal. Inspection of the table values indicates that the most 

significant variations were in the visible band readings where differences were as high as 30 

percent. On the other hand, the near IR readings were the most consistent with differences no 

higher than 5 percent or so. The effect of the variations here are, of course, strongly mitigated by 

the fact that independent calibrations were performed prior to each event, thus avoiding any 

large error. 

Table B1. MPTR Clear Air Normalization Constants. 

(a) Transmissometer 

TrialÆ 21601 21602 21603 21604 21605 21606 21607 21608 21609

LOS-1 

Visible 2382 1975 2102 2942 2964 2695 2950 2118 2978

Near ir 3722 3730 3728 3769 3804 3864 3579 3575 3728

mid ir 3095 3066 3048 3036 3051 3049 3049 3046 3053

Far ir 2887 2861 2749 2649 2700 2756 2657 2636 2614

LOS-2 

Visible 2236 1531 1746 2532 2527 2077 2418 1770 2514

Near ir 3291 3334 3308 3339 3331 3334 3254 3304 3358

mid ir 2585 2606 2620 2615 2597 2574 2597 2600 2616

Far ir 2875 2633 2613 2565 2548 2609 2631 2576 2621

(b) Radiometer 

TrialÆ 21601 21602 21603 21604 21605 21606 21607 21608 21609

LOS-0

Visible 2678 2692 2708 2731 2742 2750 2770 2779 2790

near ir 2196 2200 2204 2209 2210 2210 2215 2216 2218

mid ir 1999 1937 2115 1979 2064 1988 2119 2059 2053

far ir 1970 0844 1896 1814 1942 1750 2151 1871 1808

39

Appendix C. Multi-Trial Summary 

Presented in this section, is the remainder of the results from the multi-trial analysis discussed 

briefly for the single set of near IR results for both graphite and brass presented in section 6. 

Figures C1–C4 present the remainder of the results for visible and mid-IR bands in the same

format as that used in figures 9 and 10. 

Figure C1. Multi-trial summary, graphite-visible. 

41
Figure C2. Multi-trial summary, graphite mid-ir. 

42
Figure C3. Multi-trial summary, brass-visible. 

43
Figure C4. Multi-trial summary, brass mid-ir. 

It is reasonably clear from examination of either of the transmissometer correlation plots that the 

experiments yielded consistent and well-behaved results. This is particularly clear from the third 

column representing the transmittance correlation plots which are, in all cases, produced highly 

convincing evidence of linear relationships as predicted by theory. There are, however, some

indications of an upward curvature trend in the plots being most noticeable at the higher mass 

loadings which may be due to effects beyond the scope of the present study. It is also apparent 

that the scatter in the plots tends to increase with increasing optical depth which is to be expected 

because of the smaller signals involved. 

The results from the path radiance correlation plots are also consistent and well-behaved in that 

all show a initial linear trend, consistent with the Beer’s Law of attenuation, in the thin layer 

region but with significant departures at higher optical depths and eventually approaching the 

classical limit in the extreme at the higher mass loadings. A most interesting exception is shown 

for the case of brass in the visible band which exhibits the linear trend throughout the full range 

of optical thickness. 

44
Appendix D. Multi-Pixel Data From Ir Imagery 

In the main text, the use of the dual band IR imagery data was limited to only a few pixels 

mainly for the purpose of verifying the MPTR results. However, we do have plans to extend the 

analysis into the spatial regime using the IR imagery. Some of our preliminary findings suggest 

that a pixel by pixel analysis of the time scans such as those discussed in section 7 may offer 

advantages beyond those obtained using conventional imaging analysis tools. The method of 

sampling the IR imagery is demonstrated in figure D1 (11). 

Figure D1. Photograph of single data frame from IR imager. 

The photograph of figure D1 represents a single frame taken from the mid-IR imagery file and 

represents a roughly 320x240 pixel area scanned at a rate of 30 frames per second. The task in 

this section was to sample the imagery at each of the nine discrete points labeled a through i for 

each time step and thus produce a time trace of total radiance similar to those of figures 9 and 10. 

45
The results for both the mid- and far IR bands are shown in figure D2 (graphite, trial 21608) and 

figure D3 (brass, trial 21609). 

Figure D2. Dual band multi-pixel time scans of total radiance for graphite. 

46
Figure D3. Dual band multi-pixel time scans of total radiance for brass. 

In each of the figures, the two distinct columns refer either to the 3–5 um band or the 8–12 um

band as noted. Note also that both the extreme upper and extreme lower scans in all cases 

correspond to paths terminated by the tranmissometer sources and are thus much more intense 

than the others which are terminated by the natural background, whatever it may be. 

Several things are immediately apparent from even a causal inspection of the plots. First, for the 

mid-IR band, the net effect of the obscurant is not large especially for the case of brass 

whereupon the total radiance, in most cases, actually increases when the obscurant is introduced 

as was observed earlier. On the other hand the effect of the obscurant on the far IR band is much 

more pronounced and more so for the brass example where the traces actually “bottom out” at 

the lower threshold. This too was noted in the earlier discussions of Section 9. Another 

interesting feature of the plots is the high degree of correlation between and among the various 

scans which is most evident in figures D2 and D3 from the plots along rows of a given column

where the traces appear to be almost identical except for a small time lag that is almost 

imperceptible at the scale shown here. This high degree of correlation is, of course, not entirely 

unexpected since the scans represent the same cloud distribution sampled simultaneously at 

different locations. A further study to quantify the cross-band correlations using a variety of 

statistical approaches is being pursued elsewhere. 

47
48

Acronyms 

TRADOC U.S. Army Training and Doctrine Command 

NGIC National Ground Intelligence Center 

ARL U. S. Army Research Laboratory 

SLAD Survivability Lethality Analyses Directorate 

TTM tools, techniques, and methods 

MPTR Multiple-Path Transmissometer Radiometer System 

COMBIC Combined Model for Battlefield Induced Contaminants 

IR infrared 

ac alternating current 

dc direct current 

TRAC TRADOC Analysis Center (TRADOC=Training and Doctrine Command) 

SCIMITAR Scene and Countermeasure Integration for Munition Interaction with 

Targets 

CASTFOREM Combined Arms and Support Task Force Evaluation Model 
49

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PILOT-81 VVA EXPERIMENT-Analysis of the Multi-Path TransmissometerRadiometer Measurements 

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R.A Sutherland and J.E. Butterfield 

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Survivability/Lethality Analysis Directorate ATTN: AMSRL-SL-EM 

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Key words: transmissometers, radiometers, obscurants, smokes, transmittance, contrast transmission, path radiance, aerosol 

emissivity, aerosol reflectivity, field measurements. 

14. ABSTRACT 

This report presents results and findings from the PILOT81 Emissive Sources Verification Experiments carried out at the 

Survivability/Lethality Analysis Directorate (SLAD), U.S. Army Research Laboratory Tower site at the White Sands Missile 

Range during February 1999. The experiments involved (near) simultaneous measurements of direct transmittance and 

normalized path emission/radiance sampled over three slightly diverging lines of sight through intervening obscurants 

comprised of either graphite flakes or brass powers of varying concentration levels. Specifically this report presents 

measurements of direct transmission and total radiance obtained over four spectral bands from the visible through far infrared 

using the SLAD Multiple Path Transmissometer-Radiometer (MPTR) system augmented with a conventional dual band infrared 

scanning imager. From the combined transmissometer and radiometer results we are able to determine both the multi-band 

transmittance and normalized path radiance, or “sky-to-ground” ratio, for cloud optical depths ranging from τ=0 to about τ= 8.

15. SUBJECT TERMS

Tranmissometers, radiometers, obscuranrts, emissivity, modeling, radiative transfer, field measurements 

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R.A. Sutherland 

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