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NBSIR 77-856

PROPOSED STANDARDS

FOR LADAR SIGNATURES

B. L. Danielson

Electromagnetics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

April 1977

Prepared for

Ballistic Missile Defense Advanced

Technology Center

P.O. Box 1500

Huntsville, Alabama 35807

NBSIR 77-856

PROPOSED STANDARDS

FOR LADAR SIGNATURES

B. L. Danielson

Electromagnetics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

April 1977

Prepared for

Ballistic Missile Defense Advanced

Tecfinology Center

P. 0. Box 1500

Huntsville, Alabama 35807

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Dr, Betsy Ancker-Johnson , Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director

CONTENTS

Page

1 . INTRODUCTION 1

2. UNITS AND RADIOMETRIC NOTATION 2 3. PROPOSED DEFINITIONS 4 3.1 Reflectance Nomenclature 4 a. Bidirectional Reflectance 4 b. Monostatic Bidirectional Reflectance 6 c. Bidirectional Reflectance Distribution Function 6 d. Directional Reflectance 6 e. Directional Hemispherical Reflectance 7 f. Reflectance 7 g. Other Terms in Ref lectometry 7 3.2 Radar Cross Sections 8 3.3 Laser Radar Cross Sections 9 a. Discussion 9 b. Units of LRCS 10

c. Polarization of Ladar Transmitter and Receiver 10

d. Assumptions and Conditions Applying to LRCS Definitions 10

e. Laser Radar Cross Section Definitions 11

(1) LRCS 11

(2) Copolarized LRCS 13

(3) Cross-polarized LRCS 13

(4) Total LRCS 13

f. Resolved LRCS ' s 15

(1) Range-resolved LRCS 15

(2) Doppler-resolved LRCS 15

(3) Distributed LRCS 15

3.4 Differential Scattering Cross Section 16

4. THEORETICAL LRCS OF IDEALIZED TARGETS 16

4.1 Specular Sphere 17

4.2 Lambertian Diffusers 17

5. LABORATORY CALIBRATION STANDARDS 20

5.1 Discussion 20

5.2 Specular Targets 20

5.3 Diffuse Targets 22

5.4 Retroref lectors 23

5.5 Preferred Standard: Summary Recommendation 23

6. CONCLUSIONS 23

7. REFERENCES 25

a. APPENDIX. RADIOMETRIC SYSTEMS 3 0 iii
LIST OF TABLES

Page

Table I. Symbols and Units 3 Table II. Monostatic LRCS of Some Idealized Standard Targets 19

Table A-1. Former American Standard Nomenclature for Radiometry

and Photometry 31

Table A-II. American National Standard Nomenclature Illuminating

Engineering — 32

Table A-III. Proposed Terms and Symbols for Radiometry 33

LIST OF FIGURES

'

• . Page

Figure 1. BDR and LRCS georuetrical parameters 5 Figure 2. Geometry for sphere LRCS 18

Figure 3. Mirror target dimensions 21

ACRONYMS

ASTM American Society for Testing and Materials

BDR bidirectional reflectance

6RDF bidirectional reflectance distribution function

BMDATC Ballistic Missile Defense Advanced Technology Center

DRCS Doppler resolved cross section

ERIM Environmental Research Institute of Michigan

GRC General Research Corporation

Ladar laser radar . LOS line of sight

LR laser radar (ladar)

LRCS laser radar cross section

MDAC McDonnell Douglas Astronautics Company

M.COM U.S. Army Missile Command

NBS National Bureau of Standards

RV reentry vehicle

RRCS range resolved cross section

VH vertical-horizontal polarization

VLOS vector line of sight

VV vertical-vertical polarization

iv
PROPOSED STANDARDS FOR LADAR SIGNATURES

B.L. Danielson

ABSTRACT

Tnis report attempts to assist in providing a common basis

for the reporting and intercomparison of laser radar cross section

(i^RCS) data generated at different laboratories for the Ballistic

Missile Defense Advanced Technology Center (BMDATC) laser radar

signatures program. We are concerned here with recommending

preferred aefinitions of some of the most commonly used LRCS

terms ana recommending -a calibration target standard.

Key words: jl^aser radar; laser radar signatures; target standards.

1. INTRODUCTION

The laser radar (LR) signatures program sponsored by the Ballistic

i-lissile Defense Advanced Technology Center is directed towards employing LR

target scattering for the identification and discrimination of threatening

OD^ects. The scattered target radiation is usually expressed in terms of

various types of laser radar cross sections (LRCS) . Unfortunately, in the

i-^ast tnere has not been universal agreement on the precise definitions of

tne LRCS ' s of interest, nor has there been a common traceable method for

calibrating the diverse systemiS used in measuring experimental values of

ijRCS ' s [1].* For example, cross section definitions based on radar use can uiffer Dy a factor of 4 from definitions based on the optical use of

aiffuse plates [2] . Polarization is another factor that is not consistently

taKen into account.

Tnis report represents an effort by the National Bureau of Standards

(.m'BS) to encourage the adoption of a common basis for LRCS measurements.

Tne major tnrust of this initial effort assumes two forms. We propose

stanaaru definitions of various terms employed in connection with LR signatures (section 3) , and we propose that all laboratory LRCS measurements be

ultimately referenced to a preferred type of calibration standard (section

0.3 j . Tne more important recommendations in the body of the text follow the

neaaing "Summary Recommendation."

It was our intention in the present work to base our recommendations

as mucn as possible on current usage, so that adoption of these proposals

woulu cause a minimum disruption m format reporting. To provide the

necessary Dackground, we conducted a survey of the appropriate literature, some of which is included in the references. Discussions were

nela witn representatives of the major BMDATC contractors. Finally, a written questionnaire was sent to these contractors to determine their

*Figures in brackets indicate the literature references at the end of this

paper

.
preferences on definitions and standards. Some substantive differences of

opinion became evident during the course of this study. Nevertheless, we

feel that our present conclusions represent a reasonable consensus on present

usage, along with some subjective opinions of our own. One of these subjective considerations was that current LR terminology should, wherever possible, be compatible with corresponding quantities used in the radar field.

Another conclusion was our recommendation that the specular sphere (or mirror)

should be the preferred standard calibration target for cross section measurements and that the cross section of diffuse secondary standard targets

should be determined by measurements relative to this specular sphere (or

mirror)

.

2. UNITS AND RADIOMETRIC NOTATION

The Systeme International d' Unites (International System of Units) with

the abbreviation SI is the modernized metric system which represents the

offically recognized basis of measurement adopted by NBS , The American

Society of Testing Materials (ASTM) , and many international standards

laboratories. It is the policy of NBS to encourage its universal acceptance.

We also feel that it is desirable to have all reported measurement data

ultimately traceable to the base SI units. These units, symbols, and con- version factors are detailed in many accessible publications [3-7]

.

While there are no serious alternatives to the use of SI units, there

is still no universally accepted system of symbols and definitions for

radiometry. In this report we will use the American National Standard

Nomenclature, although this should be considered only our own preference.

It has also been adopted for mandatory use by the Department of Defense

[63] . This system is discussed in a review article by Mayer-Arendt [8] , a tutorial review by Nicodemus [9] , and in table A-II in the present Appendix.

A summary of the terms, symbols, and units used in this report is given in

table 1. The nomenclature of radiometry and ref lectometry is still in a state of flux, and the interested reader will find many further articles in

the literature on these subjects [10-17,78,79]. The three main radiometric

systems are compared in the Appendix.

We will note in passing that there are several common sources of con- fusion in the area of radiometry. The first concerns the use of the term

"intensity." Many standard texts, for example Born and Wolf [18], identify

2 "intensity" with power per unit area (W/m ) . In radiometric notation

"intensity" refers to power per unit solid angle (W/sr), and is usually

restricted to a point source. ^ Here we will always refer to this latter

^Nicodemus has suggested the use of "pointance" in place of "intensity" to

avoid this confusion [78,79].

2
lable i. Is and Units

.

S-.-bol "Jnic

Abbreof 1

Radianc energy

Radianc flux density

Qw

j oule

watt '-eter

~

J

B-adianc po-.^er (radiant flux) watt W

I watt/ steradian W'sr

Radiance L W'att/ (-ecer~ • 5 ceradian) W • m

Phocon intensity

Irradiance of a surface

IP

E

quanta/ (sec • steradian)

watt/meter"

q • sec

-2

V". • ^ Photon flux density

Spectral irradiance

W

P

E,

A

quanta/ (seem")

watt/ (xeter^ • nanometer)

q • sec

— /

Solia angle steradian sr Projected solid angle -- steradian sr bidirectional reflectance r- ' steradian

— 1 sr directional reflectance dinensionless

Px.ef lectance P dimensionless

Pvange (distance from target

to receiver)

R neter m

H.adius at curvature of sphere meter m

Segment of sphere (cross

section dianeter)

uRCS

D meter

2

meter

m

2

m

Intercepted area (or

effective projected area)

E

2

meter 2

m

Copolarized LRCS

2

meter

2

m

Cross-polarized LRCS

Total LRCS G

i

oA meter

2 meter

2

m

2

m

Cross section per unit

projected area

0 a dimensionless

Aspect angle b radian rad

Bistatic angle B radian rad

Detector aperture 2

meter 2

m

-1

-1

niH

3
quantity as "radiant intensity" denoted with the symbol I. Another source

of confusion concerns the use of "projected solid angle" denoted here by n (as suggested by Nicodemus [14]) , and "solid angle" denoted by oj. Both have

units of steradians, but differ in the cosine of an aspect angle. Reference

[9], for example, elaborates on their distinction which is of importance in

the definition and application of radiance and bidirectional reflectance

(BDR) . A third common source of confusion originates in the similarity of

the symbol p (for reflectivity) and p' (for BDR), These, as defined in the

next section, are quite different quantities with different dimensions.

3. PROPOSED DEFINITIONS

3.1 Reflectance Nomenclature

This section discusses the terms and quantities employed in the LR

signatures program which we feel need some kind of standard definition. Not

all of these are controversial, but they are listed here for completeness.

Reflectance and radiometric quantities are important in the experimental

determination and theoretical prediction of cross section values, and these

will be reviewed first. ^ .

a. Bidirectional Reflectance

The BDR of a surface, denoted by p', completely specifies its reflectance characteristics. In general it is a function of wavelength, and

polarization and orientation of both incident and reflected radiations. The

appropriate geometrical configuration for its description relative to LR

scattering is shown in figure 1. This figure, as well as our general approach

to tne description of BDR, has been adapted from reference [20] . We define

r 2 BDR as the ratio of the radiance L (8^,(|)^) (W/m -sr) reflected by the sample

in the direction of the receiver ^.^I'P^ with polarization state y, to the

irradiance ^x^^i'^^^i^ (W/m^) incident on the target from the direction 9^,(1)^^ with polarization state x. To be consistent with our LRCS definitions later

on, we have taken E""" ( 0 .,((). ) to be the irradiance of the target surface and

d_ 1 12 W (6., 4).) to be the radiant flux density (W/m ) in the well-collimated

X 1 1 incident laser beam, so that E (9.,*.) = W (9.,*.) cos 0.. The BDR for a given wavelength can then be expressed as

,^ ^' ^ , ^y^^r'^r^ reflected W/(m"-sr)

Px v^^i'^J^i'^r'^r^ " i

2 (D ^'^ 1 1 r r

E^(0^,(J)^) incident W/m

and has the dimensions sr The reflected polarization state vector y and

incident polarization state vector x need to be specified relative to target

geometry in order for p' to have a unique value. In special cases the

4
Laser

D

Incident

i_aser Beam ^\

e

\7

1 /

Target

dA

0,

^Reflected Radiance

to Receiver

Radiance (W/m^-sr) with polarization state y reflected from target

Irradiance (W/m^) of target with polarization state x

Radiant flux density (Vj/ih"^) with polarization state x of laser beam

W'^ Radiant flux density (W/m^) with polarization state y at detector

entrance pupil

R Range (m)

3 Bistatic angle

D Detector

p Polarizer

Detector entrance pupil (m^)

k Surface normal

Figure 1. BDR and LRCS geometrical parameters. The azimuth reference

(i axis) is arbitrary. The polar angles are denoted by 5 and the

azimuth angles by (j). 5
polarization subscripts x and y can be written as perpendicular (x) or parallel (II) depending on the direction of the electric field vector relative to the plane of incidence or reflection. If the detector is insensitive

to polarization, i.e. senses the sum of the two polarizations, then the

appropriate reflection polarization subscript y is denoted by "total" (T)

.

For example, the symbol p' refers to conditions of parallel incident

irradiance and a detector that has no polarization preference. By definition

the following relationships exsit between BDR polarization states:

Since for diffuse targets p' and LRC3 are proportional, the notation used

here can be carried over directly to cross section definitions. Usually BDR

refers to a diffusing surface, although the reflected radiance of a specular

surface can be calculated using special forms of p' [14,15].

Summary Recommendation : Preferred definitions and notation for BDR are given by the Willow Run (now ERIM) reports [e.g. 20].

b . Monostatic Bidirectional Reflectance

This is the term used in the case where both incident and reflected

directions are the same (G^ = ^^r'Pj^ = 'P^. ^rid 6 s 0), i.e. bacJcscatter case.

c . Bidirectional Reflectance Distribution Function

This is the term employed by Nicodemus [14] , denoted by f^, and defined

by the relation

dL^(0 ,()) ) •• f„(e.,(^.) = —. (sr

dE^(e^,(J).)

where dE""" (0^ ,({)^) = L"^ ( 0^ , (|)^) cos 0^^ dco^ and L""" (0^ , (})^) is the radiance impinging

on an element of surface. Our eq . (1) is an adaptation of this concept.

d. Directional Reflectance

This term is denoted by p^{Q ^, ^) for a given wavelength. Its accepted

definition is the BDR averaged over the reflectance angles {Q^,<t>^). It is

usually employed in the case where the incident radiation is unpolarized

[20] . Analytically it is defined as the ratio of the power reflected into

6
the entire hemisphere to the unpolarized power incident on the sample, or

p^(e.,(b.) = / p' ^(e.,(f).;e ,<t) )cos e dto (3)

'^D 1 ^1 i, u.T I'^i r^r r r

27T where uj is the reflected solid angle. Since we integrate over this solid

angle, is a dimensionless quantity. For a lossless diffuse surface (see

section 4.2) the value of p^^ is 1.

There is another use of the term "directional reflectance" which is

used occasionally [68]. This quantity is denoted by p" and is defined as

p" = p' cos 0^.

The use of p" and "directional reflectance" in this context is discouraged,

e . Directional Hemispherical Reflectance

This is the term denoted by p (Q ^, (p ^; 2t\) which has been suggested by

lemus [1^

is identical,

Nicodemus [14] to replace "directional reflectance" or pj^. The definition

f . Reflectance

The reflectance is the ratio of the reflected radiant flux * to the ^r

incident radiant flux <p

*r

P = (4)

and is dimensionless. The reflectance should not be confused with BDR which

is a different quantity with difierent dimensions. Reflectance is sometimes

expressed as the sum of the regular (specular) reflectance p^ and the diffuse

reflectance p-,. d

P ^ Pr + Pd

It should be noted that "specular" is only meaningful in terms of geometry,

specifically when 0^ = 0^ and cf)^ = 0^ ± tt or when the surface normal bisect:

the bistatic angle g. The value of p is one for a non-absorbing surface.

g. Other Terms in Ref lectometry

For more details on the above definitions and others in the field of

reflectance and radiometry, the reader is referred to the comprehensive

report of Nicodemus [19]

.

7
3,2 Radar Cross Sections

Much of the work done with determination of LRCS's is based on earlier,

and similar, work in the field of radar. The radar cross section definition,

we feel, should also be directly applicable to LRCS measurements. However,

we recognize that there is more than a wavelength difference between laser

and radar systems (there are no radar gaussian beams, optical receivers are not normally polarization sensitive, etc.). The particular requirements of

ladar applications may require some distinctions in definitions. As defined

below, however, the LRCS and RCS will usually be equivalent.

Because of its importance, the RCS will be reviewed here. The original

RCS [21] was defined so that the only radiation considered at the receiver

was the component polarized parallel to the plane wave field incident on the

scatterer. This convention is still widely used [22] . Some other standard

references, however, do not make this distinction as to polarization [23,27],

implying that the total scattered signal (both linear polarizations) is

considered in defining the cross section. Since specular targets depolarize

the incident radiation only slightly, if at all, there often is no practical

difficulty associated with this polarization question. With diffuse surfaces, whose roughness is large compared to a wavelength, the distinction is

very important. The RCS is defined as the area intercepting that amount of

power which, when scattered isotropically , produces a scattered radiance

equal to that observed from the target. The bistatic RCS given by Blacksmith

[22] is, for a given wavelength, given by

, W^(0 ,(}) ) 0 (6 . ,4). ;e ,4, ) = lim 4ttR^ —. ^—^

m^ (5)

R-^cx> W^(e^,(})^)

r i using- the symbols of table I and figure 1. We assume that W and W are both plane polarized relative to an appropriate coordinate system [22] . Our

2 symbol W, as usual, refers to radiant flux density (W/m ). The reflected

radiant flux density, referred to the receiver entrance pupil, is denoted by

W (6^,cj)^). This quantity often is expressed in terms of the reflected

intensity (W/sr); I^{Q^,<i>^) = R^W^ ( 8^ , c})^) . The monostatic RCS is defined for the backscatter case: 0. = 6 and 1 j- (}).=(}).

1 ^r

The scattering cross section , as given by Blacksmith [22] , is identical

to the RCS of eq. (6) with the exception that W (6^,(fi^) now represents the

total reflected (scattered) radiant flux density regardless of polarization,

i.e. it is the RCS determined using an unpolarized receiver. In the

terminology of the next section, the scattering cross section is equivalent

to "total RCS."

8
3.3 Laser Radar Cross Sections

a. Discussion

The generally accepted approach to quantitatively describing the signature or characteristic ladar return from a particular target is in terms of

various laser radar cross sections. It would be desirable for the purposes

of analysis if the LRCS of a target could have a single numerical value

which is a function of the static and dynamic properties of the target

(size, shape, composition, spin rate, etc.) in addition to clearly identifiable properties of the beam (wavelength, polarization). This is rarely

the case for complex targets under operational conditions. The quantity

identified as the LRCS can be affected by range (near-field or far-field)

,

size of the ladar beam relative to the target, beam profile and curvature,

coherence, and other effects which enormously complicate the interpretation

of the return signal. In particular, the simple quantities we have identified as LRCS data may not be adequate to characterize the target completely.

Although other conditions are very important in practical cases, we will

emphasize here only the experimental definitions of LRCS made under specific

and very specialized environmental conditions. These will be discussed in

section 3.3.d.

As discussed by Wyman [2] , the LRCS is sometimes referenced to the

geometrical projected area of a diffusing plate, or diffuse standard. Under

this convention a LRCS is equal to the area of a lossless Lambertian surface

which produces the same amount of scattered power at the receiver as does

the target. This approach gives different LRCS values than our recommended

definitions (section 3.3.e) which are more conveniently referenced to a specular sphere, as is the RCS definition mentioned above. However, as long as the cross section is defined in terms of scattered radiant flux

density at the detector, rather than an equivalent projected surface area of

any standard target, it really is immaterial which standard target is used,

and this is the approach we will take in the following LRCS definitions.

Strictly speaking it is not correct to associate the LRCS of a specular

2 spnere (o = ira ) with the "effective" or "interception area a„ which removes

Hi an amount of power E a from the incident beam and scatters it isotropically

.

2 This "interception area" for a sphere is = 27Ta . This "extra" factor of

two IS necessary to account for the forward scattering, and is of some Historical interest. It is discussed in standard texts on scattering theory

[^4,25,26] . This is really of no significance as long as the LRCS is defined

analytically in terms of scattered radiant flux density, as it is below. We

point this out only as an illustration of another difficulty which can arise

when cross sections are referenced to "interception areas" of standard

targets

.

9
b. Units of LRCS

Laser radar cross sections have the dimensions of area, with a few

exceptions to be mentioned later. The accepted unit is the square meter

2 (m )

, or decibels above one square meter (dbsm) . Theoretical data are sometimes expressed relative to a square wavelength, but this practice is

discouraged.

c . Polarization of Ladar Transmitter and Receiver

The LRCS depends on the polarization of the radiation impinging on the

target, and the polarization selector associated with the detector (figure 2).

This implies that cross sections are really tensor quantities, or, alternatively, must be expressed in terms of a scattering matrix [27] . We will

not consider this approach here, but will only point out that if LRCS ' s are

to be meaningful, the polarization details of both transmitted and detected

radiation fields must be completely specified. We will emphasize this

consideration in the definitions to follow. Polarization is often stated in

terms of the transmitter-receiver-target coordinate system [28], e.g. linear

polarization parallel or perpendicular to the plane containing the transmitter, target, and receiver. For LR signature purposes, it is usually

better if the polarizations are specified in terms of the symmetry coordinates

of the target [29] . This implies that two coordinate systems are required;

one to describe the scattering properties of the target and another to

define the orientation of the target relative to the laser transmitterreceiver reference frame.

In early radar systems the receiver used the same antenna that served

for the transmitter. Under these conditions the receiver only responds to

the backscatter which is parallel to the transmitted radiation. It was natural then that the "RCS" should be interpreted as "copolarized RCS." On

the other hand, optical detectors are not intrinsically polarization sensitive. (This does not apply, of course, to heterodyne systems or cases where

a polarizer is introduced in front of the detector.) For targets that

depolarize the impinging radiation, this brings up the question as to whether

the LRCS definition should be based on the copolarized return radiation, or on the total (copolarized and cross-polarized) return. This is discussed in

sections 3.3.d and 3.3.e.

a . Assumptions and Conditions Applying to LRCS Definitions

In order to simplify our treatment of the LRCS definitions, we will

impose a number of conditions which will considerably restrict the scope of

their applicability, but hopefully this will help clarify the issues involved.

10
Tne somewhat idealized situation to be considered is illustrated in figure 1 We will assume that the following experimental conditions are met (with

certain exceptions to be considered later)

:

(1) Plane waves impinge on the target, and these plane waves have a constant phase and amplitude over the dimensions of the target.

2L

(2) The detector is in the far-field of the target, i.e. R > where L is the maximum dimension of the target; also the

2A^

detector area A, is such that R > —. This assures that the d A effective area of the detector is small compared with the cor- responding Airy disc of the target, and also implies that the

target is smaller than the detector field of view.

(3) For diffuse targets, an average is taken over many speckles.

(4) The geometrical optics limit applies; A << L.

(5) The laser is quasi-cw (long pulse approximation).

(6) The laser beam size is much greater than L at the target

(flood illumination)

.

(7) The laser transmitter is plane polarized.

In many practical cases of interest these conditions can be relaxed and

meaningful measurements still obtained. There are situations, however,

wnere LRCS values may be drastically altered if these conditions are not

met. A later report in the present series will attempt to expand on this

subject. With the above enumerated assumptions, we can now make our recommended LRCS definitions.

e . Laser Radar Cross Section Definitions

(1) LRCS — We feel that the basis of the LRCS definition should be

consistent with and have the same origin as the RCS described above. From

tne phenomenological point of view, the LRCS may be similarly defined as the area intercepting sufficient power out of the transmitted ladar beam to

produce the given echo by isotropic reradiation. However, the definition

must be specific about the polarization state of the echo that is being

considered. As in the case of the RCS definition, there is some disagreement on the form of this convention. We propose the following: that unless

otherwise specified LRCS with the symbol a should refer to the echo as received by a polarized detector. In the backscatter case this can be

identified with the "copolarized LRCS" where the received polarization is

parallel to that transmitted. If both mutually orthogonal polarization

states are measured by the detector, then the term "total LRCS" with the

symbol a should be used. For other polarization states, or to avoid

11
confusion in any case, the polarization should be made explicit with appropriate indices. With this understanding, and referring to figure 1, we define the bistatic LRCS as

^xv^^i'^^'i'^r'^r^ = (6)

or equivalently

:

^ w^(e ,d) ) „ 2 V r r 2 0 (e.,(±).;e ,(b ) = 4ttR -4 m . ^ ^ ^ ^

wNe.,^.) X 1^1

This is the same notation used with our definition of BDR and in table I. It is repeated here for convenience

:

1^(9 )

. Radiant intensity (W/sr) reflected from target in the direcy r tion 9j./<t^j- with polarization state y. r 2 W (6 , (j) ) Radiant flux density (W/m ) at detector entrance pupil rey r fleeted from target in the direction ^j.i'i'j. with polarization

state y.

W""" ( 6 .,({). ) Radiant flux density (W/m^) in laser beam at target from

direction Q^,(p^ with polarization state x. R Range (m) from target to receiver.

The bistatic LRCS can also be expressed in terms of quantities already

defined (see figure 1)

.

i^{e^,(p^) = J L^(e^,(i)^)cos dA (7) ^ surface

where from eq. (1)

L'^O ) = p' (6. ,(})•; 6 )W'^ (9 . ,4) • ) cos 9.. (8)

y r^r '^xy i^i r^r x i^i i

From eq. (6), the contribution to the LRCS da^^ ( 9^ , cf)^ ; 9^ , c))^) for a uniformly

diffusing surface element dA becomes

do^y (9^,(})^;9^,(J)^) = 4ii p^^ ( 6 ^ , tj)^ ; 9^ , (})^ ) cos 9^ cos 9^ dA (9)

This result will be used later to derive the LRCS ' s of various diffuse

targets

.

The subscripts x and y, for laser transmitter and scattered polarizations respectively,^ can be specified in a number of ways; for example, x ^This is the usual convention, and consistent with our BDR notation. However, note that Ruck [27] and some others use the left-most index to indicate

received polarization and the right-most subscript to indicate transmitter

polarization.

12
and y can refer to the polarization azimuth angle a between the electric

field polarization plane and the normal vector to the reference plane [20]

.

TT Thus a = 0 would correspond to perpendicular polarization x = -L , and a = -2 would correspond to parallel polarization x = II , etc. Another common notation

uses the indices V and H for vertical and horizontal.

To simplify our further discussion we will henceforth consider only the

monostatic LRCS ~ ^2-' = 0^. or 6 = 0) , and azimuthal target symmetry

such that the target orientation can be specified by a single aspect angle 9.

(2) Copolarized LRCS -- In the monostatic case this is the LRCS for

the component whose polarization is parallel to the transmitted polarization. In terms of eq. (6)

1^(0)

2 a^^(6) = 4tt m . (10)

wj(9)

This is usually abbrievated by a (6).

Summary Recommendation : The LRCS a as commonly used without further

polarization specification should be identified with the copolarized LRCS,

i.e. c E o„.

(3) Cross-polarized LRCS -- In the monostatic case, this is the LRCS

for the component whose polarization is perpendicular to the transmitted

polarization. In terms of eq. (6)

1^(9)

2 o (9) - 4^ -X xJ. y m (11)

W^(9)

x This cross section is usually abbreviated by Oi, a^^„, or a„,,. It should be

noted that, in general, o^^ ^ ^yx'

'^^^ cross-polarized LRCS is sometimes

referred to as the "depolarized" cross section [77], but this use is discouraged since "depolarized" often refers to scatter containing equal com- ponents in the parallel and perpendicular directions [74]. In the latter

case the "depolarized LRCS" is equal to 2oj_.

(4) Total LRCS -- The total laser radar cross section represents eq.

(6) in the case where I , or W , includes all the radiant power scattered

y y

^ from the target which is received by the detector. This total consists of

the sum of all constituent components. In the literature this division into

components has been done in many different ways: in terms of the sum of the

two linear polarization states [74] , the sum of the polarized and depolarized

components [71,75], and the sum of the coherent and incoherent parts [76].

13
It should be clear in the context of the work just what kind of total

or sumination is referred to. We consider the following form to be the

preferred definition:

Total LRCS denoting the sum of both linear reflected polarizations:

This notation is consistent with our BDR definition. Equation (12) is a direct result of eqs. (2) and (6). An obvious abbreviation for a X , T

is just o^. We feel that this is the most important interpretation of

the term "total LRCS." It is also the LRCS, eq. (6), using an un- polarized receiver. For the case where there is coherence between

scattered polarization components see references [70] and [71]

.

The term "total LRCS" is often used in various numerical calculation

techniques for LRCS computer codes [71] . These uses do not constitute a definition of a particular LRCS, but the terms are encountered often enough

in ladar signature work to justify explanation of their use here. They are:

Total LRCS denoting the sum over the i sub-elements of the target:

_ = I Aa. (13)

i

where Ao^ is given in eq. (9). The methods for adding the components Ao^

with the proper phase and scaling factors (for models) constitute one

of the most basic and difficult problems in calculating ladar cross

sections. We will not comment on these methods here other than to state

that the concepts can be quite meaningless for coherent radiation if

the phases of the sub-elements are not accounted for correctly.

Total LRCS denoting the sum of the cross section components resolved

or divided into n "bins" (see section 3.3.f), and summed over all the

"bins."

o„ = I a . (14)

T n

n The above remarks apply also in this case: It bears repeating that

egs. (13) and (14) are calculation techniques, not fundamental

definitions

.

Summary Conclusion : The appropriate LRCS to denote the case where an unpolarized receiver is used should be referred to as "total LRCS," o .

14
f . Resolved LRCS '

s

Resolved cross sections are interpreted as the usual LRCS definition

applied individually to the ladar return which has been subdivided into

various elements of range (range-resolved) , frequency (Doppler-resolved)

,

or area elements perpendicular to the range vector (spatially distributed)

.

It should be emphasized that, as discussed here, these terms merely refer

to quantities which are convenient for numerical calculation and display

and are not distinct in any fundamental sense from the concepts already

defined. A formulation for resolved cross sections which has proved to be

useful in ladar signature computer simulation is given in the GRC reports

[69,71] and will be discussed briefly below.

(1) Range-resolved LRCS — The range resolved cross section (RRCS)

represents the LRCS distributed along the vector line of sight (VLOS) . Each

one of the n range bins ("resolution elements" or "gate spacing") is of

length ct/2 where c is the speed of light and x is called the range gate

width. This corresponds to the cross-section contribution due to a slice of

the target of thickness ct/2 which is not masked out by other portions of

the target and which is perpendicular to the VLOS. This representation

integrates the return signal over finite ranges of delay time so that the

2 cross section is expressed in units of m /m.

(2) Doppler-resolved LRCS -- The Doppler-resolved cross section (DRCS)

applies to spinning or tumbling targets; the fixed frequency shift due to

translation is of no interest in target identification and discrimination.

This quantity is defined in a similar way to the RRCS except that the n range bins are replaced with n frequency bins. The width of the frequency

bins is referred to as the "filter bandwidth" or "filter spacing." The

cross section represented by each of the Doppler bins then corresponds to

the output of a series of ideal filters each centered at a different frequency. For a target spinning about the symmetry axis of rotation the DRCS

is independent of time, while for a tumbling target the DRCS is a function

2 of time. The units are square meters per Hz or m -sec.

(3) Distributed LRCS -- The distributed LRCS is sometimes referred to

as "angle-resolved" LRCS or LRCS per unit area. The usual symbol for this

type of cross section is a°. It represents the LRCS distributed in both

cross range directions perpendicular to the VLOS. The distributed cross section is well defined only for diffuse targets. Distributed cross sections

2 2 are usually expressed in terms of a cross section per unit area (m per m )

.

If this cross section is determined by scanning the target with a laser beam

small compared with target dimensions, the measured LRCS values may become a function of the beam parameters [55] .

15
Further details, and some of the problems involved in the determination

of resolved LRCS's, are given in reference [71].

3.4 Differential Scattering Cross Section

The differential scattering cross section , or simply differential cross section , is used extensively in physics to describe particle scattering

[30,31]. Only occasionally do these terms appear in a radar or ladar

application, e.g. reference [72], where they have a different meaning. The

do

duj'

differential cross section (per unit solid angle) -r—, as applied to photons

considered as particles, is given by

^ ,e , = liVV l! (15)

dco ' r ' ^r r,i , „ , - W 0 . , * . ; sr

p 1 ^ 1 2-1 r and has the dimensions of m * sr . The symbols I (6^,(j)^) for reflected

photon intensity, and W ( U • , (f)

. ) for incident photon flux density are defined

p 1 1 in table 1. We use the superscript r for "reflected" to be consistent with

earlier notation, but "scattered" would be a more appropriate designation

here. Note that ^ as defined here differs not only by a factor of 4tt from

tne LRCS definitions, but is actually a different concept, being defined in

terms of per unit solid angle.

The total cross section in this context [30] denotes an integration

over 4tt steradians about the scattering center. This is also distinctly

different from the "total cross section" as defined in section 3.3.e(4).

Summary Recommendation : We discourage both the LR use of "differential

cross section" and the use of "total cross section" in the sense of the

differential cross section, eq . (15), integrated over the solid angle

variable.

4. THEORETICAL LRCS OF IDEALIZED TARGETS

In this section we will summarize the LRCS values of some selected

standard targets as they have been defined in section 3.3. These targets

are the specular sphere with no absorption, and the perfect Lambertian

diffuser. Laboratory standards of a more practical nature are considered in

section 5

.

16
4 . 1 Specular Sphere

The LRCS of a specular sphere in the far field is the geometric pro2 jected area a = ira independent of polarization or bistatic angle 3.

Referring to figure 2, the exact near field case with 3 = 0 is given by

[36,56]

4tt

aR-j^R2

a(R-|^+R2) + 2R-|^R2 (16)

where we have assumed that the radius of curvature of the waves impinging

on the target sphere is R2 • For the case where ~ -^2 ~ ^' ^^^^

2 aR

a + R

2 which tends to the far field value ira as R ^ «=, as one would expect,

The effect of plane waves on the target can be seen by taking R2 °°. Then

(17)

a = 4tt aR^ - ^

a + 2R-^ (18)

which is different from the corresponding case, eq . (17), for incident waves

with a radius of curvature R^ • The usual practice is to employ incident

plane waves even when detectors are in the near field.

By our definition, a = = o,( for a perfectly reflecting sphere.

4 . 2 Lambertian Diffusers

As used here, a perfect Lambertian diffuser has the following

properties:

1. The absorption is zero. This implies that p' ^ = p' = — sr"*"

1 _-i HjJ- X/J-TT

and p

' = p, , = ^ sr [20] . 11,11 ± ,1. 2tj

2. The irradiance E (6) of the surface varies as cos 0 and the cor- responding radiance L is independent of 6. This is true no matter how the surface is illuminated.

3 . The emitted radiant power is equally divided between mutually

orthogonal polarizations also independent of the manner in

which the surface is illuminated.

4. The scattered radiation is uncorrelated so that the total pov7er

scattered by the target is a simple sum of the power scattered

by the constituent subregions.

Several authors have calculated the radiant intensity scattered

from simply shaped diffusing targets [58,59,60]. These results, along

with tne definitions and assumptions of section 3.3.e, give the LRCS values

summarized in table II.

17
Laser

Transmitter

Receiver

Target

Sphere

Figure 2. Geometry for sphere LRCS

18
03Ocu

(U

14-1

OS

(U00

CD

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'O

r-; nj

C/3

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OS

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cfl woGo

eg oi

Pi cs+ <

CM<

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00

03

00

iJ-l 00

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(U

-i-> o• '—1 oa

S-I OJ 01 i) 0)

S-i >-l CU T3 00

(U QJ (U >-i C!

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a ^ CU T3 03 x: r-l 00 t/) -T3 CO rH a

)-l 0) CO

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<-< U3 < CO CD CO 3 3 S-I d 3 3 3 03 a i-i O 03 y-i 03 4-1 •H 4-1 a

(U 03 14-1 (U <4-l -d <4-l S-I CL <4-< o, c •H u •H 03 •H o

CO ^ CO

w

Q 03Q S-IQ c

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CM &< IN ^ <3 o

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S-I o O S-I c

.-I 03 •U -H

CJ -u

OJ S-i M-l CU S-I

S-I XI o

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B U-l

a 03 J 4-1 03 X

CO (V T3 CO -U

0) (U e -H 0) 3 CO cu

CO CO C/D CO o

03 iH

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03 x: c!

03 0) S CO

4-) • 00

/-s S-I <I> 03

COo

XI6

>>

CO • CO M CI o o

U-i -H

4-1

M 033

0) cr rH 0) XI

03 00 ^ c

•Hc

•H

4-1 cu C X!

<U -M •H S-I O

(U <4-l XJ

II c

OJ Q.

03 4J 0)o

CO 03 •H y-iS^ ^ 3

a> CD 0 ooc

CO -H U 4-1 OS o

.H

01 4-1 ^ (U

0)0)

4-1

(U

CO 't3 w d

4) 03 00

CO 4-1 4-1 -H

0> -H

CO XI 3 03

<+-( CJ

U-i -H

•H rH

T3 Cu

ex

0) 03 x:

•U 4-4o

5-4 o

4-1 COao a 4-t

19
5. LABORATORY CALIBRATION STANDARDS

5.1 Discussion

The usual approach used for the experimental determination of laser

radar cross sections involves the use of calibrated standard targets [32].

The backscattered power from an unknown target cf). is compared with that

"car from a calibration target cf) , . If the geometry is unchanged whil-e the

C3.1. calibration target is substituted, the unknown target LRCS a. is related

to the calibration LRCS a -, by the simple relation

ca X ^tar _ tar (-Lgj

^cal cal

The value of a can be calculated (section 4) using measured values of

c a J. reflectivity or BDR. Alternatively a -, can be determined using the definic a X tions (section 3.2.e) and calibrated power meters.

Radiometric approaches for the calibration of CRCS systems have also

been considered [73] , but they are difficult to implement.

We will review here some properties of the more commonly used target

standards

.

5 . 2 Specular Targets

The sphere, or a spherical mirror, has long been used as the standard

target in RCS measurements and in many LRCS systems also. Some of the well

known properties of the sphere are:

1. In the far field, the scattering is isotropic.

2. For perfect specular reflectivity, there is no depolarization of

the incident plane polarized beam.

3. The theoretical cross section is not a function of wavelength in

the geometrical optics limit. This is largely true in practice

also since coatings such as gold have a fairly constant reflectivi

over large wavelength intervals in the infrared.

For backscatter measurements it is not necessary to use an entire

sphere, since only a small surface area of the sphere participates in the

scattering process in the backscatter direction. Referring to figure 3, the

necessary segment D is given by [35]

D >> /2Xa (20)

and

2 a = pTia

20
Loser

IReceiver

Mirror target dimensions

21
independent of D in the limit of 3 = 0 . The required segment size is determined from the condition that at least the first Fresnel zone is included on

tne surface. Also, care must be taken to avoid backscatter contributions

from the edges. Equation (17) implies that only a very small area of the

sphere is responsible for the scattering. As an example, for a mirror with

a radius of curvature of r = .1 m and a wavelength of A = 10.6 ym, this area

2 is about 1 mm . The standard target thus "samples" a rather small part of

the incident laser beam. If the impinging irradiance is not uniform, as can happen in the near field, variations in measured cross section values will

result. Also, imperfections on the mirror, or dust on the surface, can have

a similar effect. Statistical averaging of many measurements in different

configurations can minimize these problems.

The errors and uncertainties involved in the use of specular spheres or targets have been discussed in the literature. Corrections due to nearfield geometry or a radius of curvature on the impinging beam have been

mentioned before [36]. Also, errors due to surface roughness have been

discussed [37,38,39]. For example, for a sphere whose roughness depth is

-2

the order of 10 A, the change in RCS is less than .1 dB. Expected standard deviation of the backscatter as a function of roughness has been treated

by Senior [37] . The magnitude of this depolarized component has been re- ported [34]. In general, experimental LRCS ' s of a specular sphere or mirror

can be very close to the theoretically predicted values.

In conclusion it appears that the important properties of the specular

spherical target are sufficiently understood that we may consider it to be a well characterized device suitable for use as a standard target.

5 . 3 Diffuse Targets

Diffuse targets are not as well characterized as the specular sphere.

There are many reasons, however, for considering them as standard targets.

The main reason being that for many years diffuse surfaces have been used as reflectance standards in the visible [41,42] and ir [43,44], and this has

given rise to the convention of referencing LRCS values to them [2] . In

addition, diffuse standards are essential for Doppler LRCS comparisons, and

are convenient for making measurements with diffuse model targets, determining extinction ratios of polarizers, and making cross-polarized LRCS

system performance checks.

One characteristic of the backscatter from diffuse targets using

conerent radiation is the phenomenon of speckle [46,45]. This topic will

not be pursued here other than to note that speckle effects must be con- sidered in the interpretation of the backscatter information. We have

assumed here that a suitable average has been made over the speckle patterns

in all LRCS measurements.

22
In the visible region pressed BaSO^ , MgO, and a commercially available

wnite reflectance paint are commonly used as diffuse target scatterers

.

Tneir properties are well documented [47] . The reflectivity of these surfaces can be quite high, and their scattering properties approach those of

an ideal Lambertian diffuser. In the infrared region, particularly around

10.6 ym, there are no comparably good diffusing surfaces. Sandblasted metal

surfaces or gold-plated sandpaper are sometimes used [48] . Scattering from

tnis type of diffuser often contains a specular component, or is peaked in

tne specular direction. Also, depolarization is usually not complete,

tnougn gold-plated sandpaper is fairly good in this respect [49].

5 . 4 Re trore f lectors

Tnis type of target is not normally used as a standard, though it may

De useful in some applications requiring large backscatter returns. It

4ttA^ yields very large values of LRCS the order of -

^

2

largely independent

of aspect angle. A is the geometrical intercepted area. Its properties are well known [50-54, 57].

5 . 5 Preferred Standard: Summary Recommendation

Tne specular sphere, or spherical mirror, as discussed above appears to

offer tne most promise as a preferred standard calibration target, and as a basis for LRCS definitions. It is recommended that this be used as the

reference standard for LRCS calibrations. The LRCS of diffuse secondary

standards should be experimentally determined according to their backscatter

properties relative to the sphere or mirror.

Tne recommended tolerances, composition (coating), and other specifics

of specular standards as well as preferred types of diffuse standards will

oe discussed in a future report.

6. CONCLUSIONS

Tne main conclusions regarding our preliminary proposals for LR signature

standards can be summarized as follows:

1. The fundamental LRCS definitions should be based on, and consistent

with, RCS usage.

2. The polarization state of the laser radiation incident on and

scattered from the target should be explicitly reported. The

LRCS o without further polarization specification should refer to

tne copolarized LRCS, i.e. a h Ojj .

23
3. The specular sphere or mirror should be the fundamental calibration standard for laboratory LRCS measurements. The properties

of diffuse targets used as secondary standards should be traceable

to the specular sphere.

24
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.

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.

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27
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[63] "American National Standard Letter Symbols for Units Used in

Science and Technology," ANSI YlO. 19-1969 (Revision of USAS

YIO. 19-1967) (IEEE No. 260), approved by American National Standards

Institute and Adopted for Mandatory Use by the Department of Defense

on December 10, 1969, Sponsored and Published by the American

Society of Mechanical Engineers, United Engineering Center,

345 East 47th Street, New York, N.Y. 10017.

[64] "International Lighting Vocabulary," 3rd Edition, Common to the

CIE and lEC (International Electrotechnical Commission) , International Commission on Illumination (CIE) , Bureau Central de la CIE,

^ e

4 Av . du Recteur Poincare , 75-Paris 16 , France, Publication CIE

No. 17 (E-1. 1) (1970) . [65] Clark, Jones R. , "Terminology in Photometry and Radiometry,"

J. Opt. Soc. Amer. 53_, No. 11, 1314-1315 (Nov. 1963).

[66] Spiro, I.J., Jones, R. Clark, and Wark , D.Q., "Atmospheric Transmission

Concepts, Symbols, Units, and Nomenclature," Infrared Physics 5_, No. 1, 11-36 (March 1965).

28
[67] Gilbert, John, "Review of Optical Predictive Reflectance Models,"

General Research Corporation Report WGRC 75-3916 (March 1975)

.

[68] Mauck , J.D., Naar , J., Nephew, VI. A., and Peppers, N.A., "Implications of Evolving Laser Technology, " "Phase II. Observables

and Discriminants," (U) Samso Technical Report, No. 71-220,

Secret (July 1971)

.

[69] Gilbert, J.L., Kramer, P.J., Radley, R.J., and Wilson, J., "Laser

Signature Handbook," (U) , Vol. 1, "Total and Resolved Cross Sections,

(U) , General Research Corporation Report, WGRC 75-4014, Secret

(Sept. 1975)

.

[70] Leader, J.C., "Investigation of Laser Radar Cross Section Analysis,"

Report MDC A2990, McDonnell Douglas Corporation (Aug. 1974).

[71] "BMD Laser Signature Modeling Program," (U) , Final Technical

Report 566W-08-CR, General Research Corporation, Secret (Jan. 1976).

[72] Reference [27], p. 893.

[73] Spinak, Sidney, MDAC, private communication.

[74] Cheo, P.K, and Renau , J., "Wavelength Dependence of Total and

Depolarized Back-Scattered Laser Light from Rough Metallic

Surfaces," J. Opt. Soc . Amer. 59_, No. 7 , 823 (July 1969).

[75] Renau, J., Cheo, P.K., and Cooper, H.G., "Depolarization of Linearly

Polarized EM Waves Backscattered from Rough Metals and Inhomogeneous

Dielectrics," J. Opt. Soc. Amer. 57_, No. 4, 461 (April 1967).

[76] Boyd, M.L. and Deavenport, R.L., "Forward and Specular Scattering

from a Rough Surface: Theory and Experiment," J. Acous. Soc. Amer.

53_, No. 3 , 794 (1973) . [77] Leader, J.C. and W.A.J. Dalton, "Bidirectional Scattering of

Electromagnetic Waves from the Volume of Dielectric Materials,"

J. Appl. Phys. 43_, No. 7, 3086 (July 1972).

[78] Spiro, Irving J., "Radiometry and Photometry," Opt. Engineering 13 , No. 5, G183 (Sept. /Oct. 1974).

[79] Spiro, Irving J., "Radiometry and Photometry," Opt. Engineering 15 , No. 1, SR-7 (Jan. /Feb. 1976).

29
8. APPENDIX. RADIOMETRIC SYSTEMS

The three principal nomenclature systems for radiometry and photometry

are compared in the following three tables. This information has been taken

from the report by Nicodemus [19] on proposed military standard infrared

terms and definitions. The present report follows the nomenclature given in

table A-II. , .

30
Table A-1. Former American Standard Nomenclature for Radiometry and

Photometry

.

[taken from ASA Z58 . 1. 1-1953 ] [60]

Terms Symbols Units

1 Flux [$] flux

1(a) Radiant flux r [WJ watts

Kb) Luminous flux F [Im] lumens

1(c) (Photon flux) [q*s quanta per

2 ( Intensi tv ) [ <p sr J

2 (a.) RAdiflnl" "Lnten'?itv J [W sr""*"]

2 Cb") T.iiTTii nniis int'pn^lt'v I n -li

1 im sr ] 2(c) (Photon intensity) [q*s 'sr J

J [radiant or luminous J w , n, L, or h [ $ • cm J

3 1 ( Fttii f 1" an ^ 1 $ • cm 3.1(a) Radiant emittance W [W'cm J 3.1(b) Luminous emittance TL l_lm*cm J 3.1(c) (Photon emittance) [q'S 'cm J

3 . 2 [ <v • cm J 3.Z (a; Irradiance un [ w • cm J 3.2(b) Illuminance or Illumination E

_2

[ Im • cm ] 3.2 (c) [q • s • cm J

4 [$*cm 'sr J

4 (a) Radiance N rn -2 -1,

[ W • cm • s r J 4(b) Luminance B n ~2 -It [lm*cm 'sr J [photometric brightness]

4(c) [q*s "cm 'sr J

NOTE 1. Terms and symbols in parentheses are not given in the cited sou

but are simple logical extensions of that material Dashes represent

missing terms or symbols for which no such simple logical extension is

available.

NOTE 2. Although superseded, these terms and symbols are still used by

many in the U.S.A. and will be found in most standard texts and in a large majority of the reports in the files of NTIS (National Technical

Information Service)

.

31
Table A-II. American National Standard Nomenclature Illuminating

Engineering

.

[taken from ANSI Z7. 1-1967 (RP-16)] [62]

1

1(a)

Kb)

lie)

2

2(a)

2(b)

2(c)

3

3.1

3.1(a)

3.1(b)

3.1(c)

3.2

3.2(a)

3.2(b)

3.2(c)

4

4(a)

4(b)

4(c)

Te rms

Flux

Radiant flux

Luminous flux

(Photon flux)

Intensity

Radiant intensity

Luminous intensity

(Photon intensity)

Flux density at a surface

Exitance

Radiant exitance

Luminous exitance

(Photon exitance)

Symbols Units

Irradiance

Illumination [Illuminance]

Radiance

Luminance

e

$V

($ ) P

I

IV

M

M

eM

V

E

E

(Ep)

$] flux

W] watts

Im] lumens

q'S ^] quanta per second

$ 'sr ]

W'sr""""]

Im • s r ''"J -1 -1,

q'S 'sr J $ "cm ] $'cm J W • cm ^

] Im • cm ^

]

-1 -2,

q*s 'cm ] $*cm j W*cm ^]

lm*cm ^]

-1 -2,

q*s "cm J $*cm 'sr J

T7 -2 -In W*cm 'sr J

1 -2 -li Im'cm 'sr ] -1 -2 -1,

q'S 'cm 'sr ]

NOTE 1 . Terms and symbols in parentheses are not given in the cited source,

but are simple logical extensions of that material. Dashes represent

missing terms or symbols for which no such simple logical extension is

available

.

NOTE 2 . These terms and symbols are essentially the same as those adopted

internationally [CIE [64]] and have been adopted by Applied Optics, the

Journal of the Optical Society of America, and the Proceedings of IRIS

and by the National Bureau of Standards, as well as the Illuminating

Engineering Society and its Journal.

32
Table A-III. Proposed Terms and Symbols for Radiometry (Including

Photometry)

.

[based on the PHLUOMETRY scheme of R. Clark Jones] [65,66]

Terms

1 Flux

1(a) Radiant flux

1(b) Luminous flux

1(c) Photon flux

2 Intensity

2(a) Radiant intensity

2(b) Luminous intensity

2(c) Photon intensity

3 Flux density at a surface

3.1 Exitance

3.1(a) Radiant exitance

3.1(b) Luminous exitance

3.1(c) Photon exitance

3.2 Incidance

3.2(a) Radiant incidance (irradiance)

3.2(b) Luminous incidance (illuminance)

3.2(c) Photon incidance

4 Sterance

4(a) Radiant sterance (radiance)

4(b) Luminous sterance (luminance)

4(c) Photon sterance

Symbols Units

M

M

€ M

\

M

L

L

$] flux

W] watts

Im] lumens

q'S ] quanta per second

$*sr '']

W'sr"^]

Im'sr ''] -1 -1,

q-s 'Sr J -2

ii> • cm ] o • cm J -2

W • cm ] Im'cm J -1 -2,

q • s -cm J

5> • cm J -2

W • cm ] Im • cm ^

]

-1 -2.

q'S 'cm J ®'cm *sr J

TT -2 -li W • cm • s r J

T -2 -It Im • CTTi • s r J -1 -2 -1,

q

• s 'cm • s r J

NOTE: Also see references [/8,79] for further additions

33
NBS-lUA (REV. 7-73)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUl^LK ATION OR RI-:PORT NO.

NBSIR 77-856

2. Oov't Accession

No.

3. Recipient's Accession No.

4. TITLH AND SUBTITL1-:

Proposed Standards for Ladar Signatures

5. Publication Date April 1977

Performing Organization Code

276.08

7. AUTHOR(S) 8. Performing Organ. Report No. B. L,. Danielson

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

' WASHINGTON, D.C. 20234

10

11. Contract /Grant No

Project/Task/Work Unit No. 2761171

12. Sponsoring Organization Name and Cornplete Address (Street, City, State, ZIP)

Ballistic Missile Defense Advanced Technology Center

P. O. Box 1500

13. Type of Report & Period Covered

Final

Huntsville, Alabama

35807

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ARSTRAC'T (A 200-word or less factual summary of most si^ificant information. If document includes a significant

bibliography or literature survey, mention it here.)

This report attempts to assist in providing a common basis for

the reporting and intercomparison of laser radar cross section (LRCS)

data generated at different laboratories for the Ballistic Missile

Defense Advanced Technology Center (BMDATC) laser radar signatures

program. We are concerned here with recommending preferred

definitions of some of the most commonly used LRCS terms and

recommending a calibration target standard.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons

)

Laser radar; laser radar signatures; target standards

18. AVAILABILITY [^ Unlimited

I For Official Distribution. Do Not Release to NTIS

[3^ Order From Sup. of Doc, U.S. Government Printing Office Washington, D.C. 20402, SD Cat. No. C13

fX^ Order From National Technical Information Service (NTIS)

Springfield, Virginia 22151

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