NlSr

National Institute of

Standards and Technology

U.S. Department of Commerce

NIST Technical Note 1551

PB2009-101694

1/1111111111'111111111111/11111111

NIST Technical Note 1551

Recommended Terminology for

Microwave Radiometry

James Randa

Electromagnetics Division

Electronics and Electrical Engineering

Laboratory

National Institute of Standards and

Technology

Boulder, CO 80305-3328

Janne Lahtinen

Harp Technologies Ltd.

02150 Espoo, Finland

Adriano Camps

Department of Signal Theory and

Communications

Universitat Politecnica de Catalunya

Campus Nord

08034 Barcelona, Spain

A. J. Gasiewski

NOAA-CU Center for Environmental

Technology (CET)

Univ. of Colorado at Boulder

Boulder, CO 80309

August 2008

U.S. Department of Commerce

Carlos M. Gutierrez, Secretary

National Institute of Standards and Technology

James M. Turner, Deputy Director

Martti Hallikainen

Laboratory of Space Technology

Helsinki Univ. of Technology

02150 Espoo, Finland

David M. Le Vine

James Shiue

Jeff Piepmeier

NASA, Goddard Space Flight Center

Greenbelt, MD 20771

Manuel Martin-Neira

European Space Agency

2200 AG Noordwijk

The Netherlands

Philip W. Rosenkranz

Massachusetts Institute of Technology

Cambridge, MA 02139

Christopher S. Ruf

Space Physics Research Laboratory

Univ. of Michigan

Ann Arbor, MI48109

Niels Skou

Technical University of Denmark

B348, DK2800 Lyngby, Denmark
Certain commercial entities, equipment, or materials may be identified in this

document in order to describe an experimental procedure or concept adequately. Such

identification is not intended to imply recommendation or endorsement by the

National Institute of Standards and Teclmology, nor is it intended to imply that the

entities, materials, or equipment are necessarily the best available for the purpose.

National Institute of Standards and Technology Technical Note 1551

Natl. Inst. Stand. Technol. Tech. Note 1551,32 pages (August 2008)

CODEN: NTNOEF

u.s. Government Printing Office

Washington: 2008

For sale by the Superintendent of Documents, U.S. Government Printing Office

Internet bookstore: gpo.gov Phone: 202-512-1800 Fax: 202-512-2250

Mail: Stop SSOP, Washington, DC 20402-0001
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CONTENTS

BACKGROUND .

CHAPTER I. GENERAL TERMINOLOGy .

CHAPTER ll. REAL-APERTURE RADIOMETERS .

CHAPTER III. POLARIMETRIC RADIOMETRy .

REFERENCES .

ALPHABETICAL INDEX .

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RECOMMENDED TERMINOLOGY FOR MICROWAVE

RADIOMETRY

James Randa!, Janne Lahtinen2

, Adriano Camps', A. J. Gasiewski\

Martti Hallikainen5

, David M. Le Vine6

, Manuel Martin-Neira7

, JelTPiepmeier6

,

Philip W. Rosenkranz8

, Christopher S. Rut, James Shiue6

, and Niels Skou'o

'Electromagnetics Division, NIST, Boulder, CO 80305

2 Harp Technologies Ltd, 02150 Espoo, Finland

, Department of Signal Theory and Communications, Universitat Politecnica de

Catalunya, Campus Nord, 08034 Barcelona, Spain

4 NOAA-CU Center for Environmental Technology (CET), Univ. ofColorado at

Boulder, Boulder, CO 80309

5 Laboratory of Space Technology, Helsinki Univ. ofTechnology, 02150 Espoo,

Finland

6 NASA, Goddard Space Flight Center, Greenbelt, MD 20771

7 European Space Agency, 2200 AG Noordwijk, The Netherlands

8 Massachusetts Institute ofTechnology, Cambridge, MA 02139

9 Space Physics Research Laboratory, Univ. ofMichigan, Ann Arbor, MI 48109

10 Technical University ofDenmark, B348, DK2800 Lyngby, Denmark

Abstract: We present recommended definitions for common tenns in microwave remotesensing radiometry. Terms are grouped into three chapters: General Tenninology, RealAperture Radiometers, and Polarimetric Radiometry. An alphabetical index lists the

terms that are defined and the chapters in which the definitions are located.

Keywords: definitions, microwave radiometry, remote sensing, standard terminology

I
BACKGROUND

Several years ago, a project was begun under the auspices of the Committee on

Earth Observation Satellites (CEOS), Calibration and Validation Working Group, to

compile standard definitions for terms used in microwave remote-sensing radiometry. A

parallel effort was begun at about the same time in the NIST Electromagnetics Division,

and the two efforts soon merged. A compilation of standard terminology and practices

had been published for radiometry at optical frequencies [I], and had been found to be

very useful. Since much of the terminology for microwave radiometry differs from that

used at optical frequencies, a proj ect was begun to develop a corresponding set of

standard definitions for microwave radiometry. The effort was divided into four

chapters, covering General Terminology (Chapter I, or I), Real-Aperture Radiometers

(II), Polarimetric Radiometry (III), and Interferometric Radiometry (IV).

Recommendations and suggestions were solicited from the microwave radiometry

community, and a website [2] and e-mail circulation list were established forI andIl,to

accept suggestions and to post the current definitions. After an initial burst of activity,

the definitions for I and II stabilized, and they were presented to CEOS in 2003.

A "Radiometry Dictionary" page has now been added to the website of the IEEE

Geoscience and Remote Sensing Society (GRSS) [3], under "Technical Resources." The

purpose of the page is to increase the availability of the completed chapters, facilitate

completion of the unfinished chapter, and raise awareness of the standard definitions.

We expect that the list ofstandard definitions will evolve over time, with the completion

ofIV, as well as additions and modifications to I through III. The present paper contains

the initial versions ofI - III on the GRSS website. It thus constitutes a snapshot ofI - III,

documenting their state as of early 2008.

Many of the definitions have been drawn from other sources, in which case the

source is referenced. Two of the most common sources, particularly for the terms in I,

are the International Vocabulary of Basic and General Terms in Metrology (IVM) [4] and

the Guide to the Expression of Uncertainty in Measurement (GUM) [5]. For terms

contained in the IVM or GUM, we have tried to use those definitions. An alphabetical

index follows the three chapters of definitions; it lists the terms defined and indicates in

which chapter they are defined.

CHAPTER I. GENERAL TERMINOLOGY

Accuracy: closeness of the agreement between the result of a measurement and a true

value of the measurand. Because the true value cannot be determined exactly, the

measured or calculated value of highest available accuracy is typically taken to be the

true value. If a value of higher accuracy than the value in question is not available, then

the accuracy cannot be assigned a meaningful quantitative value.

Allan standard deviation (ASD): the square root of Allan variance. Both the ASD and

the Allan variance can be used to describe different noise types and drift of the response

2
of a radiometer receiver. Compared to Allan vanance, however, the ASD has the

advantage that the units are in kelvins.

Allan variance: a two-sample variance, where the variance is taken on the variable y.

Each value ofy in a set has been averaged over an interval T and the y's are taken in an

adjacent series, i.e., no delay between the measurements of each:

O"~(T)=+((!1Y)'),

where the brackets < > denote the expectation value, and Lly is the difference between

sequential values of y. The Allan variance can be used .to describe different noise types

and drift of a radiometer receiver. See also: Allan Standard Deviation (ASD).

Bias (of a measuring instrument): systematic error of the indication of a measuring

instrument. [4]

Note: The bias of a measuring instrument is normally estimated by averaging the error of

indication over an appropriate number ofrepeated measurements.

Brightness: the radiance, the radiated power per unit solid angle per unit area normal to

the direction defined by the solid angle Q.

Note: Brightness (of a surface) is often used for Spectral brightness density [6, 7]. The meaning

is usually clear from the context.

Calibration: set of operations that establish, under specified conditions, the relationship

between sets of values of quantities indicated by a measuring instrument or measuring

system and the corresponding values realized by standards. The result of a calibration

permits either the assignment of values of measurands to the indications or the

determination of corrections with respect to the indications. [4]

Calibration equation (of a microwave radiometer): equation relating the primary

measurand of the radiometer, e.g., the brightness temperature, to subsidiary measurands,

such as powers, and to calibration quantities, such as standard values. (similar to [1])

Check standard: a standard that is used routinely to check measurements.

Drift: slow change of a metrological characteristic of a measuring instrument. [4]

Emissivity (of a surface): the spectral radiance of the surface relative to the spectral

Lf(T,e,tjI) radiance of a peifect blackbody radiator at the same temperature, e(e, tjI) = .

L f,BB(T)

Effective blackbody brightness temperature: the physical temperature of a peifect

blackbody that would produce the same spectral brightness density or spectral radiance

density as that under consideration.

3
Error: result of a measurement minus a true value ofthe measurand. [4,5]

Notes: Since a true value cannot be detennined, in practice a conventional true value is used.

When it is necessary to distinguish "error" from "relative error," the former is sometimes called

the "absolute error."

Experimental standard deviation: for a series of n measurements of the same

measurand, the quantity s characterizing the dispersion of the results and given by the

formula

n

L(x, _X)2

S = \/-"=0=1 _

n-l

x, being the result of the ith measurement and x being the arithmetic mean ofthe n results

considered. [4,5]

Notes: Considering the series of n values as a sample of a distribution, X is an unbiased estimate

of the mean fl, and :l is an unbiased estimate of the variance ,; of that distribution. The

expression s / In is an estimate of the standard deviation of the distribution of X and is called

the experimental standard deviation ofthe mean.

Noise temperature (at a reference plane in a microwave circuit/network, Tn): the

available noise power spectral density at the reference plane divided by Boltzmann's

constant (kE); thus dPn

"' =kBT'" by definition, where the subscript n denotes "noise." For

df

a resistor at physical temperature Tphy" the noise temperature is given by

kBTn = , so that for k i «1, Tn'" Tphy, .

kT B p~, eBphYS_I

Quantization level: in the quantization process, the discrete value assigned to a

particular subrange ofthe analog signal being quantized. (adapted from [8])

Radiance (L): the radiated power per unit solid angle per unit area normal to the

direction defined by the solid angle Q,

L= dP

dnJA' " where dA1- = cos 8'dA, and 8' is the angle between the direction defined by the solid

angle and the normal to the area element dA.

Random error: result of a measurement minus the mean that would result from an

infinite number of measurements of the same measurand carried out under repeatability

conditions. [4,5]

Notes: Random error is equal to error minus systematic error. Because only a finite number of

measurements can be made, it is possible to detennine only an estimate ofrandom error.

Reference temperature (To): temperature used in ratios to set a scale, conventionally

taken as To = 290 K.

4
Relative error: error of measurement divided by a (conventional) true value of the

measurand. [4,5]

Relative uncertainty: uncertainty ofthe measurand divided by the nominal value of that

measurand.

Repeatability (of results of measurements): closeness of the agreement between the

results of successive measurements of the same measurand carried out under the same

conditions of measurement. [4]

Notes: Repeatability conditions include: the same measurement procedure, the same observer, the

same measuring instrument used under the same conditions, the same location, and repetition

over a short period of time. Repeatability may be expressed quantitatively in tenns of the

dispersion characteristics ofthe results.

Reproducibility (of results of measurements): closeness of the agreement between the

results of measurements of the same measurand carried out under changed conditions of

measurement. [4]

Notes: A valid statement of reproducibility requires specification of the conditions changed.

Reproducibility may be expressed quantitatively in tenns of the dispersion characteristics of the

results.

Resolution: smallest difference between values of a measurand that can be meaningfully

distinguished. (modified [4])

Response time: time interval between the instant when a stimulus is subjected to a

specified abrupt change and the instant when the response reaches and remains within

specified limits around its final steady value. [4]

Sensitivity: change in the response of a measunng instrument divided by the

corresponding change in the stimulus. [4]

Spectral brightness density: the brightness per unit frequency, the spectral radiance

density.

Spectral radiance density (Lf ): the radiance per unit frequency interval, Lf = dL

df

Stability: ability of a measuring instrument to maintain constant its metrological

characteristics with time. [4]

Notes: Stability may be quantified in several ways, for example: in tenns ofthe time over which a

metrological characteristic changes by a stated amount, or in tenns of the change in a

characteristic over a stated time.

Systematic error: mean that would result from an infinite number of measurements of

the same measurand carried out under repeatability conditions minus a true value of the

measurand. [4,5]

5
Notes: Systematic error is equal to error minus random error. Like true value, systematic error

and its causes canuot be completely known. For a measuring instrument, see "bias."

Traceability: property ofthe result of a measurement or the value of a standard whereby

it can be related to stated references, usually national or international standards, through

an unbroken chain of comparisons, all having stated uncertainties. [4]

True value: value consistent with the definition of a given particular quantity. [4,5]

Notes: This is a value that would be obtained by a perfect measurement. True values are by

nature indeterminate.

Type-A uncertainty: an uncertainty or component of uncertainty that is evaluated by the

statistical analysis ofseries of observations. (adapted from [5])

Type-B uncertainty: an uncertainty or component of uncertainty that is evaluated by

means other than the statistical analysis ofseries of observations. (adapted from [5])

Uncertainty budget: a detailed tabulation of the sources of uncertainty and their

respective contributions to the standard uncertainty in the measurand of interest;

sometimes referred to as "error budget."

Uncertainty of measurement: parameter, associated with the result of a measurement,

that characterizes the dispersion of the values that could reasonably be attributed to the

measurand; also a measure of the possible error in the estimated value of the measurand

as provided by the result of a measurement. See [5] or [9] for details.

Validation: the process of assessing, by independent means, the quality of the data

products derived from the system inputs.

Note: In a remote-sensing application, validation is commonly performed by comparing the

value of a higher-order data product (e.g. sea surface temperature) inferred from the measured

value ofthe brightness temperature, with a direct measurement ofthat quantity.

Verification: the testing and analysis necessary to provide confirmation that all (e.g.,

instrument) requirements have been met.

CHAPTER II. REAL-APERTURE RADIOMETERS

Absolute accuracy: commonly used to denote the total uncertainty, excluding the

radiometric resolution. When the radiometric resolution is evaluated by statistical means

(type-A uncertainty) and all other uncertainties are estimated by other means, the absolute

accuracy corresponds to the total type-B uncertainty.

Angular resolution: angular width of antenna beam, usually defined as the half-power

beam width. See also antenna beam width.

6
Antenna aperture temperature (TA,ap): the temperature of an ideal black body that

would result in the same received power at the antenna aperture as in the actual case. In

the Rayleigh-Jeans approximation, it is equal to the average incident brightness

temperature weighted by the antenna directivity pattern,

1

TAap(Qo)=- ffD(Q-Qo)Tb(.Q)dQ. , 47Z' 4"

The antenna aperture temperature corresponds to the antenna temperature at the

aperture ofthe antenna.

Antenna beam width: the (full) angle at which the antenna's radiation pattern (in power

units) is at half its maximum value. It is also known as the "Half-power full width"

(HPFW), or simply the "Half-power beam width," (HPBW). In engineering convention,

it is also known as the "3 dB beam width."

The antenna radiation pattern depends on the specific plane of cut, and two principal

planes are generally given. For a linearly polarized antenna they are the E-plane (the

plane containing the radiation maximum and the E-field) and the H-plane (the plane

containing the radiation maximum and the H-field, which plane is perpendicular to the Eplane).

Antenna gain (G(fJ,tp): the ratio of the radiation intensity in a given direction, to the

radiation intensity that would be obtained if the antenna pattern were isotropic. (adapted

from [10])

Note: This is equivalent to the commonly used defmition that the auteuna gain is the product of

the directivity aud the antenna ohmic efficiency, or radiation efficiency. If the direction is not

specified, the direction ofmaximum radiation is implied.

Antenna ohmic efficiency ('In): the ratio ofthe total radiated power divided by the total

power accepted by the antenna. It is also equivalent to the ratio of the antenna radiation

resistance (Rrad) divided by the sum of the antenna radiation resistance and the antenna

ohmic resistance (Ra.):

It is also commonly called the radiation efficiency [11].

Antenna output temperature (TA,out): the physical temperature of a matched impedance

that delivers to the receiver the same noise power as the antenna. It includes two terms:

the noise coming from the environment attenuated by the antenna ohmic efficiency and

the thermal noise added by the antenna ohmic losses. In the Rayleigh-Jeans

approximation,

7
where Tp is the physical temperature ofthe antenna and 1'/0 is the ohmic efficiency ofthe

antenna. The antenna output temperature is related to the input noise temperature of the

receiver (Tnc,in) by

hf

Trec,in = h~ .

kTAoul I e '-

Antenna temperature (Ta): the temperature (K) equivalent of the power received with

an antenna. The distinction between the antenna temperature, Ta, and the brightness

temperature, Tb , is as follows. The antenna temperature is the equivalent of Tb after

being spatially averaged by the direction-dependent antenna directivity D(il), To

eliminate ambiguity, one should specify the point to which the calibrated antenna

temperature is referenced. If no point is specified, it is assumed to be at the antenna

aperture, in which case it corresponds to the antenna aperture temperature.

For example, in traditional radio astronomy this point is usually the output port of the

antenna, because that is the point in the system where the calibration loads are situated.

In this case, the antenna temperature corresponds to the antenna output temperature. In

other systems, particularly those with small antennas, the calibration targets are outside

the antenna. In such a case, the calibrated antenna temperature refers to a point outside

the antenna aperture, and the ohmic losses of the antenna are irrelevant. In still other

cases, the calibration targets may lie between a large main reflector and a smaller feed

antenna, Then the calibration of antenna temperature would remove feed antenna losses

but not those ofthe main reflector.

Blackbody: see perfect blackbody.

Blackbody load: a microwave load with characteristics very close to those of a perfect

blackbody within a certain frequency range,

Boresight: the beam-maximum direction ofa highly directive antenna. [6]

Brightuess Temperature (Tb): the temperature (K) equivalent, by the inverse Planck

function, to a spectral radiance (W'Hz'l'm'2'sr'l), emitted by a blackbody at temperature

Tb.

In general, Tb is a function offrequency and direction Q, where Q stands for angles eand

¢. Thus, for unpolarized radiation, Tb is the temperature of a blackbody that would emit

the same radiance at the specified frequency and direction. By extension, for polarized

radiation, the brightness temperature of each polarization is the temperature of a

blackbody that would emit the same radiance in the specified polarization at the specified

frequency and direction. In the Rayleigh-Jeans limit, the microwave power per unit

bandwidth received by a radiometer is P=k Tb, where k is Boltzmann's constant.

Close-coupling: the technique by which the receiving aperture of a radiometer is coupled

to a blackbody load so that the system is closed to stray radiation.

8
Directivity (of antenna in a given direction (D(O,<p): the ratio of the radiation intensity

in a given direction from the antenna to the radiation intensity averaged over all

directions. [6]

Notes: The average radiation intensity is eqnal to the total power radiated by the antenna divided

by 41t. Ifthe direction is not specified, the direction ofmaximum radiation is implied.

Dwell time: time interval required for the antenna beam to scan across one beam width,

at constant speed, along the scan direction.

Note: This and the definition of radiometric resolution per beamwidth assume one sample per

footprint; if the radiometer samples at twice this rate, the integration time is halved and the

radiometric resolution per beam width is increased by a factor ofJ2 .

Effective Field of View (EFOV): When the radiometer antenna is scanning across the

earth's surface while the radiometer integrates, then the static instantaneousfield ofview

(IFOV, in length unit and along the scanning direction), which is based purely on

geometrical projections of the antenna beam and the earth's surface, is no longer valid.

Instead, the Scanned EFOV or ESFOV along the scan direction is used in its place. The

ESFOV takes into account the scan-induced "smear" effect, and in general is slightly

larger than the static IFOY. The extent of the smear depends on the length of the

integration time, the shape ofthe original antenna beam, and the scan speed with time.

In order to be specific, the cross-track EFOV (EFOV-CT) is defined only for the case in

which: (i) the scan speed is constant, and (ii) the integration time is equal to the time

required to move the antenna beam one IFOY. Again CT implies the scanning direction,

which mayor may not be the cross-track direction.

As an example, the EFOY-CT of a Gaussian shaped beam is 25 % larger than its IFOY,

according to the above definition (i) and (ii).

The EFOY-CT is determined as follows:

First obtain the Exposure function E(x), which is the integral of the product of the

antenna pattern G(x-m) and the integration time At,

E(x) = fG(x-m)Llt,

where m=vt is the coordinate of the antenna beam center, which is moving at a scan

velocity of v. The integration is from t=O to t='l'.

Following the same half-power point principle, the ESFOY-CT is determined by

obtaining the points xl and x2 (x2>xl assumed) where the values of E(x) are half of its

maximum value, and the ESFOY-CT value is equal to x2-xl.

Effective input noise temperature (of receiver, T,ec): the input termination noise

temperature which, when the input termination is connected to a noise-free equivalent of

the receiver, would result in the same output noise power as that of the actual receiver

connected to a noise-free input termination. [12] It is related to the receiver noise figure

by

9
F = (Tree + TO) rec T, ,

where To = 290 K. It is a function of frequency,

°

and it depends on the impedance or

reflection coefficient ofthe input termination. It also depends on the location ofthe input

reference plane; unless otherwise stated, the receiver noise temperature is assumed to be

defined at the receiver input.

End-to-end calibration: calibration of the entire radiometer system as a unit, achieved

by observing the values of output quantities (voltage, power, etc.) for known values of

incident radiance at the antenna aperture.

External calibration: a calibration method that applies reference signals from targets

that lie outside the radiometer. If these targets illuminate the antenna of the radiometer,

an end-to-end calibration is obtained.

Half-power bandwidth (R3dB): the width at which the power response IS half the

maximum value; also called the 3-dB bandwidth.

Instantaneous field of view (IFOV): the antenna beam width projected onto the earth's

surface. See also static IFOV

Since the antenna radiation pattern depends on the specific plane (containing the beam

axis) of cut, so does the IFOV value. Conventionally, IFOVs at two principal planes are

given: the E-plane (containing the E-vector of the equivalent dipole) and the H-plane

(perpendicular to the E-plane). When a single IFOV value is used, it is the (arithmetic)

mean of the IFOVs ofthe two principal planes.

Internal calibration: calibration of a radiometer by connecting embedded reference

noise sources.to the receiver chain; a common example is injection calibration, in which a

noise diode is used as the embedded reference noise source.

Limiting radiometric resolution: the radiometric resolution evaluated for the case of

zero input radiance or brightness temperature. Referred to as the "temperature sensitivity"

in Radio Astronomy.

Noise-eqnivalent bandwidth (Rn): the width of 'an ideal rectangular filter (or other

circuit or component) having the same maximum (available) gain as the real filter, and

which produces the same output available power (integrated over frequency) as the real

one when the input is white noise. In terms of the filter (available) gain G, 00

fG(f)df

Rn =-,,0 _

Gmax

Noise figure (of receiver): at a specified input frequency, the ratio of 1) the total noise

spectral power density at a corresponding output frequency available at the output port

when the noise temperature of the input termination is To = 290 K, to 2) that portion of

10
the total output noise spectral power density that is engendered by the input termination.

[12] The noise figure depends on the impedance or reflection coefficient of the input

termination and on the location of the input reference plane. Unless otherwise stated, the

receiver noise figure is assumed to be defined at the receiver input.

(Normalized) Antenna pattern (t(8,<p»: the antenna gain (or directivity) in a specified

direction divided by the maximum value of the antenna gain (or directivity). See

antenna gain for the relationship between antenna gain and directivity.

Operating noise figure (of receiver): at a specified input frequency, the ratio of 1) the

total noise spectral power density at a corresponding output frequency available at the

output port when the noise temperature of the input termination is the actual input noise

temperature (or brightness temperature, for a system), to 2) that portion ofthe total output

noise spectral power density that is engendered by the input termination. (adapted from

[13]) In terms ofthe effective input noise temperature, the operating noise figure is given

by

F. = (Tree + Tin) Op T ' In

where Tin is the nominal value of the input noise temperature.

Lf = c2(ehf/kBT -1)'

wherejis the frequency, h is Planck's constant, kB is Boltzmann's constant, and T is the

physical temperature ofthe blackbody. (adapted from [7])

Perfect blackbody: a perfect absorber (and therefore the best possible emitter) of

thermal electromagnetic radiation, whose spectral radiance density (or spectral

brightness density) is given by the Planck formula,

2hj3

Pixel-to-pixel accuracy: the brightness temperature accuracy in measuring only one

resolution element; the values of other resolution elements are not used for correction.

(Equivalent) Predetection bandwidth (Bp,,): the effective bandwidth of the

predetection section of a radiometer, used in computing the ideal radiometer resolution.

In terms ofthe gain G ofthe predetection section, Bp" ={IG(f)dj}

2

fG 2(f)dj

o

Radiation efficiency: see antenna ohmic efficiency. [11]

Radiation intensity: the magnitude of the Poynting vector, i.e., the flux density of the

radiation. Its dimensions are power per unit area.

11
estimated by using the ideal equation for a total-power radiometer, LlTmin

Radiometer: a very sensitive receiver, typically with an antenna input, that is used to

measure radiated electromagnetic power.

Radiometric (or radiometer) resolution: the smallest change in input brightness

temperature or radiance that can be detected in the system output. The radiometric

resolution can be measured by computing the Type-A uncertainty, e.g., the standard

deviation of the mean of a number of measurements of the same quantity made over a

short enough time period that the system can be considered to be stable. It is also often

Tsys

~,or

VBpreT

the variant ofthis equation that is appropriate for the particular radiometer in question.

Radiometric resolution per beam width: (for a continuously scanning radiometer) the

radiometric sensitivity evaluated for an integration time equal to the dwell time.

Radiometric sensitivity: often used to mean radiometric resolution, but this use IS

discouraged in view ofthe definition ofsensitivity.

Spatial resolution: the length of the major and/or minor axes diameters of the 3 dB

contour of the antenna pattern projected onto the earth's surface. These two diameters

may differ. See also IFOV

Static IFOV: When the IFOV is expressed in length units, it is used to express the

diameter (arc length) of a circular area that is the intersection of the antenna beam

(assumed to be a right circular cone) and the earth's surface (assumed to be a spherical

shell). This is valid in the case of normal incidence.

When the radiometer antenna is viewing the earth at an oblique angle, then the

intersection area (between the right circular cone of the antenna beam and the spherical

earth surface) is a pear-shaped figure. In this case two arc lengths are used to represent

the IFOV, a Major diameter or IFOV-Maj, and a Minor diameter or IFOV-Min.

Static IFOV-AT, static IFOV-CT: For a cross-track scanning beam, the words Minor

and Major diameters can be replaced by Along-Track and Cross-Track, respectively.

Here A-T and C-T also signify the directions parallel to, and perpendicular to the subsatellite track direction, respectively.

For a conical scanning beam, the terms A-T and C-T still apply.

System gain: There are three different definitions of power gain:

P ··G_PL • ower gaIn. p --,

P,

• Transfer power gain: GT =JLP ,

~G

12
P • Available power gain: Ga =~,

p~G

where PL is the power that is delivered to the load, Pi is the power that is delivered by the

source to the input port, and P"" G and P"" L are the available powers from the generator

and to the load, respectively.

These three definitions of power gain are related by the following relationships:

and

where Ii, I;" Ta, and IL are respectively the receiver (amplifier) input (i) and output (0)

reflection coefficients, and the source (G) and load (L) reflection coefficients. Mg and ML

are the mismatch factors [14] at the input (g) and output (L) reference planes.

We usually refer to Ga, since in practice the amplifiers, filters and other subsystems are

never perfectly matched.

Tip-curve calibration (or tipping-curve calibration): N-point calibration (N22) using

the atmosphere at different zenith angles as calibration target.

Two-point calibration: fixing the relationship between the input signal and the output

response of a radiometer using two distinct input stimuli. Assuming a linear receiver, all

possible input signal levels can now be retrieved from the radiometer output responses. In

the case of an external end-to-end calibration, the input signal equals the antenna

aperture temperature ofthe radiometer.

CHAPTER III. POLARIMETRIC RADIOMETRY

Note: In this chapter, the signals are assumed to be constant over frequency unless

otherwise stated.

Adding analog correlator: a cross-correlator that measures additional Stokes

parameters / modified Stokes parameters by post-detection summing of distinct principal

13
polarizations as well as the squared sums of them. In a polarization frame defined by

vertical polarization and horizontal polarization, for example, the third and fourth Stokes

parameters / modified Stokes parameters are measured in the following way: The sum of

the orthogonal waves is square detected, respectively, in phase and in quadrature,

followed by the subtraction of orthogonal autocorrelations. Using Stokes parameters in

brightness temperature / modified Stokes parameters in brightness temperature:

where 1] is the wave impedance of the medium, Ev is the vertical component of the

electric field, and Eh and Eh (_!:..) are, respectively, the horizontal component of the

2

electric field in phase and in quadrature with respect to the vertical one. Wavelength, the

wave impedance of the medium, bandwidth, and Boltzmann's constant are denoted by A,

1], B, and kB, respectively. See also: coherent detection, direct correlating correlator.

Analog correlator: see analog cross-correlator.

Analog cross-correlator: a cross-correlator based on analog technology, i. e., the signals

are not quantized prior to correlation. See also: adding analog correlator, coherent

detection, digital cross-correlator, direct correlating correlator.

Calibration coefficients: elements of the gain matrix and the offset vector. See also:

response ofafully polarimetric radiometer.

Channel (of a radiometer): a receiver chain that (in the ideal case) is sensitive to a

certain Stokes parameter/ modified Stokes parameter. See also: Stokes parameter mixing.

Circular polarization: see polarization.

Coherence matrix (sometimes called the coherency matrix): matrix representing the

auto- and cross-correlation terms of two distinct polarizations. For example, based on

vertical polarization and horizontalpolarization, the coherence matrix is

where E, and Eh are vertical and horizontal electric field components, respectively, and * denotes complex conjugate.

14
More conveniently for radiometric applications, the coherence matrix can also be

expressed in terms of brightness temperature, i.e. multiplying the above defined

parameters by the factor ;'?·kB-1'1]-1.B-1

, where A is the wavelength of the wave, kB is

Boltzmann's constant, I] is the wave impedance ofthe medium, and B is the bandwidth:

Coherent detection: measurement of Stokes parameters I modified Stokes parameters by

the cross-correlation ofsignals collected at principal polarizations; the technique requires

the preservation of phase coherence between the signals that are correlated. Either adding

analog correlator or directcorrelating correlator (analog or digital) can be used. In a

polarization frame defined by two orthogonal linear polarizations, for example, the third

and fourth Stokes parameters I modified Stokes parameters are measured by complex

cross-correlation of waves at these polarizations. The first and second modified Stokes

parameters are obtained by the autocorrelation of orthogonal signals; the retrieval of the

first and second Stokes parameters requires additional post-detection summing. See also:

direct correlating polarimetric radiometer.

Completely polarized wave: an electromagnetic wave with completely correlated

orthogonal polarizations, i.e., the determinant of its coherence matrix is zero. Using

Stokes parameters it can be written

I' = Q' +U 2 + V' ,

where I, Q, U, and V are the first, second, third, and fourth Stokes parameters,

respectively. Using modified Stokes parameters, on the other hand,

(S, +S.)' =(S,-sS + S~ + S;,

where Sv, Sh, S3, and S4 are the first, second, third, and fourth modified Stokes parameters,

respectively.

See also: completely unpolarized wave, partially polarized wave.

Completely unpolarized wave: regardless ofthe polarization frame, the first and second

modified Stokes parameters are equal (and the difference is thus zero) and the third and

fourth Stokes parameters / modified Stokes parameters are zero. Using the terminology of

Stokes parameters: Q = U = V = O. The determinant of its coherency matrix is equal to

the wave's intensity. See also: completely polarizedwave, partially polarized wave.

15
Complex correlator: complex cross-correlator.

Complex cross-correlator: a device that estimates the time average ofthe product ofthe

in-phase and quadrature components of two time-varying signals, x(t) and yet). The inphase component of a signal, I, is its even, or Fourier cosine, component; and the

quadrature component, Q, is its odd, or Fourier sine, component. If we use xCt) to set the

phase, the real part of the complex cross-correlation estimates <IxI?, and the imaginary

part estimates <IxQ? There are both digital and analog methods of implementing the

complex correlation of band-limited signals, either while they are modulated by a carrier

or at baseband.

Complex degree of coherence: the off-diagonal terms of the coherency matrix

normalized by the geometric mean ofthe diagonal terms. Using vertical polarization and

horizontal polarization, for example,

where E, and Eh are vertical and horizontal electric field components, respectively.

Correlator: see: cross-correlator.

Cross-correlator: a device that calculates the time average ofthe product oftwo distinct

input signals.

Degradation factor: a quantity representing the degradation of the signal-to-noise ratio

ofpolarimetric channels due to channel non-idealities:

00

rHIV)H;VW

D =r===o=======

fJ· fIHIVf!H;Vfdf

°

where HIC!) and H2(f) are the complex voltage transfer functions of channels I and 2,

respectively, prior to correlation, and fJ is the width of the pass-band. Note that the

degradation factor includes the fringe-washing effects generated by transfer function

differences, but not those generated by propagation time differences.

16
Degree of polarization: the ratio of completely polarized power to total power:

where Sv, Sh, S3, S4 are the first, second, third, and fourth modified Stokes parameters,

respectively, and I, Q, U, and V are the first, second, third, and fourth Stokes parameters,

respectively. See also: partially polarizedwave.

Delay line: a microwave component used to generate time delay. In a correlating

radiometer it is used to equalize the propagation times of distinct signals prior to crosscorrelation and reduce fringe-washing effects, or to introduce a specific delay in order to

compute the cross-correlation at different time lags.

Digital correlator: see: digital cross-correlator.

Digital cross-correlator: a cross-correlator based on digital technology, i.e., the

correlation of quantized signals is performed. Depending on the correlator configuration,

two or more quantization levels are applied. See also: analog cross-corre/ator, coherent

detection, direct correlating correIator.

Direct correlating correlator: an analog or digital device that directly estimates

additional Stokes parameters / modified Stokes parameters by cross-correlation ofthe

principalpolarizations without any post-detection addition. Conventionally, the third and

fourth Stokes parameters / modified Stokes parameters are estimated by correlating

vertical polarization and horizontalpolarization with each other. See also: adding analog

correlator, digital cross-correlator, analog cross-correlatar.

Direct correlating polal'imetric radiometer: a polarimetric radiometer based on

coherent detection and a direct correlating correlator. See also: polarization combining

radiometer.

Fringe-washing effect: degradation in the cross-correlation of two non-zero bandwidth

signals that can be caused by: 1) different transit times from the signal source to the

antennas; and/or 2) different group delay responses (time delay at each frequency) ofthe

receivers/correlators. The group delay response may include instrumental delays added in

the receiving chain, and it is uniquely related to the frequency response through the

following equation:

d<1>(m)

dm

where ()} is radian frequency and <1>(m) is the phase ofthe receiver's frequency response.

17
Fnlly polarimetric calibration: the determination ofthe offset and gain matrix elements

of afidly polarimetric radiometer. See also: response ofajUlly polarimetric radiometer,

tri-polarimetric calibration.

Fnlly polarimetric calibration standard: a device for performing external calibration of

polarimetric radiometers. It can generate at least four linearly independent polarized

reference signals. Along with an unpolarized calibration reference, a fully polarimetric

calibration standard enables the jUlly polarimetric calibration of jUlly polarimetric

radiometers. See also: tri-polarimetric calibration standard.

Fnlly polarimetric radiometer: a radiometer capable of directly or indirectly measuring

all four Stokes parameters I modified Stokes parameters.

Gain matrix: matrix that contains the amplification terms relating the observed Stokes

parameters in brightness temperature I modified Stokes parameters in brightness

temperature and the outputs ofthe radiometer channels. Diagonal elements ofthe matrix

represent autocorrelation channel gains; off-diagonal elements represent crosspolarization terms generated by interchannel cross-talk and antenna cross-polarization.

See also: offiet vector, response ofajUlly polarimetric radiometer.

Horizontal brightness temperatnre: brightness temperature derived from field

components in the direction of horizontal polarization. See also: vertical brightness

temperature.

Horizontal polarization: see polarization.

Incoherent detection: measurement of Stokes parameters I modified Stokes parameters

by post-detection summing of flux densities at distinct principal polarizations. Phase

coherence among channels is not required. In a polarization frame defined by vertical

polarization and horizontal polarization, for example, the third Stokes parameter I

modified Stokes parameter can be obtained as a difference between flux densities at +45°

and --45° skewed linear polarizations and the fourth Stokes parameter I modified Stokes

parameter as a difference between flux densities at left-handed and right-handed circular

polarizations. The first and second Stokes parameters are, respectively the sum and

difference of the detected vertical and horizontal flux densities; the first and second

modified Stokes parameters are, respectively, the detected vertical and horizontal flux

densities. See also: coherent detection, polarization combining radiometer.

Inter-channel cross-talk: non-ideality of a radiometer receiver leading to signal leakage

between channels. See also: Stokes parameter mixing.

Linear polarization: see: polanzation.

Linearly polarized calibration standard: tri-polarimetric calibration standard, which

is capable of generating reference signals at orthogonal linear polarizations and a linearly

polarized reference signal. See also:jUlly polarimetric calibration standard.

18
Modified Stokes parameters: the polarization of an electromagnetic wave is completely

described by the four Stokes parameters. However, in remote sensing the so-called

modified Stokes parameters are frequently used, where the first and second parameters

represent, respectively, the flux density at vertical polarization and horizontal

polarization. Using Stokes parameters, modified Stokes parameters are defined as:

S =I+Q

, 2

I-Q Sh=--

2

S3 =Su

S4 =Sv,

where I, Q, U, and V are, respectively, the first, second, third, and fourth Stokes

parameters. Note that in polarimetric remote-sensing radiometry, the modified Stokes

parameters are conventionally expressed in terms of brightness temperature, i.e., modified

Stokes parameters in brightness temperature.

Modified Stokes parameters in brightness temperature: modified Stokes parameters

expressed in terms of brightness temperature (in kelvins):

where A is the wavelength of the wave, kB is Boltzmann's constant, and B is the noiseequivalent bandwidth. The first, second, third and fourth modified Stokes parameters are

denoted by Sv, Sh, S3, and S4, respectively. See also: modified Stokes parameters, modified

Stokes vector in brightness temperature, Stokes parameters in brightness temperature.

Modified Stokes vector in brightuess temperatnre: vector containing all four modified

Stokes parameters in brightness temperature of a certain brightness temperature scene:

19
T"

Th

TB,mod ::::;

T3

T4

where T" Th, T3, and T4 denote the first, second, third and fourth modified Stokes

parameters, respectively. See also: Stokes vector in brightness temperature.

Offset vector: vector that contains the responses of the radiometer channels associated

with the zero input signal of each Stokes parameter. See also: gain matrix, response ofa

jUlly polarimetric radiometer.

Partially polarized wave: an electromagnetic wave consisting of completely polarized

wavers} and completely unpolarized wavers}, i.e., the degree ofpolarization is between 0

and I.

Phase modulation: an incoherent detection technique that enables the measurement of

all Stokes parameters / modified Stokes parameters by a single-channel radiometer

receiver. The phase modulating component can be installed prior to or after an antenna.

In the former case a quasi-optical device based, e.g., on a phase retardation plate or a

polarizing grid can be applied as a phase shifter.

Phase retardation plate: a quasi-optical microwave device that generates a phase shift

between orthogonal linear polarizations passing through the plate. Special cases are a

quarter-wave plate and a half-wave plate, which generate 7d2 and " phase shifts,

respectively. Retardation plates can be applied injUlly polarimetric calibration standards

to generate a circularly polarized signal from a linearly polarized signal, or in

polarimetric microwave receivers to generate phase modulation.

Platform motion compensation: a procedure for compensating the changes of the

observed Stokes parameters / modified Stokes parameters that are generated by the

motion of the radiometer platj'orm. These changes can be caused, e.g., by the rotation of

the polarization frame of the antenna(s), which may lead to Stokes parameter mixing

between the first three Stokes parameters / modified Stokes parameters, and variations in

incidence angle.

Poincare sphere: the polarization of any completely polarized electromagnetic wave can

be expressed by two angles, which define the position on the surface of the so-called

Poincare sphere (see figure below). In this representation, left and right hand circular

polarizations are on the North and South poles, respectively; and the four linear principal

polarizations are located symmetrically on the equator.

20
The Polarization State ora Sample Electromagnetic Wave

Polarimetric brightness temperatures: common name for the third and fourth Stokes

parameters in brightness temperature / modified Stokes parameters in brightness

temperature.

Polarimetric calibration: common name for tri-polarimetric calibration and jUlly

polarimetric calibration.

Polarimetric calibration standard: common name for jUlly polarimetric calibration

standards and tri-polarimetric calibration standards.

Polarimetric channels: common name for the radiometer channels that estimate the

third and/or fourth Stokes parameters / modified Stokes parameters.

Polarimetric radiometer: a radiometer that measures additional Stokes parameters

beyond the first and second Stokes parameters / modified Stokes parameters. Common

name for tri-polarimetric radiometers andjUlly polarimetric radiometers.

Polarization: the direction of the electric (E) or magnetic (H) field in a propagating

electromagnetic wave. A general, elliptically polarized electromagnetic plane wave

propagating in the I' direction can have its electric field expressed in phasor form as

where p and q are unit vectors oriented perpendicular to I' and satisfying

px Ii = r= I' /11'1 ' Ep and Eq are the complex amplitudes ofthe electric field in the p and

Ii directions, respectively, k is the wavenumber of the propagating wave, and r =11'1.

The physical time-varying electric field is given by E(r, t) = Re{EeJ&}, where I1J is the

21
frequency in rad/s. There are a number of special cases of polarization that are

commonly measured in radiometry:

Horizontal linear polarization satisfies: 1) jJ is oriented tangential to the earth's

surface; 2) q has a positive projection onto the normal ofthe surface; 3) E

p

*0; and

4) Eq =0.

Vertical linear polarization satisfies: 1) jJ is oriented tangential to the earth's surface;

2) q has a positive projection onto the normal of the surface; 3) Ep =0; and 4)

Eq *0.

+45° slant linear polarization satisfies: 1) jJ is oriented tangential to the earth's

surface; 2) q has a positive projection onto the normal of the surface; and 3)

lip =Ji~ *0.

-45° slant linear polarization satisfies: 1) jJ is oriented tangential to the earth's

surface; 2) q has a positive projection onto the normal of the surface; and 3)

Ep =-Eq *0.

Right hand circular polarization satisfies: 1) Ep*0; and 2) Eq=Epe-/,/2

Left hand circular polarization satisfies: I) E p*°;and 2) Eq = Epe/'/2 .

Polarization combining network: a microwave circuit that computes the sum or

difference oftwo principalpolarizations in-phase and/or quadrature to produce other

principal polarizations. See also: incoherent detection, polarization combining

radiometer.

Polarization combining radiometer: a polarimetric radiometer based on incoherent

detection; post-detection summing of principal polarizations is applied to measure

additional Stokes parameters / modified Stokes parameters. See also: direct correlating

polarimetric radiometer.

Polarization frame: any orthogonal coordinate basis relating polarizations to each other.

Polarized brightness temperatnre scene: a scene that emits electromagnetic waves that

are not completely randomly polarized. See also: degree of polarization, unpolarized

brightness temperature scene.

Polarizing grid: a quasi-optical device that consists of parallel conductors. In the ideal

case, in which the conductors have no ohmic losses and the grid is dense compared to the

wavelength, a wave with electric field perpendicular to the conductors passes through the

22
grid without attenuation, whereas a wave with electric field parallel to the conductors is

completely reflected. In other orientations part of the wave is passed, part is reflected,

and a cross-correlated (linearly polarized) wave component is generated. These

characteristics can be applied to fabricate a linearly polarized calibration standard or a

polarimetric radiometer based on phase modulation.

Principal polarizations: six polarizations by which an electromagnetic wave can be

completely characterized at a certain frequency: four linear polarizations skewed in 45°

intervals (0°, 45°, 90° 135° rotated with respect to the reference polarization frame) and

left- and right-handed circular polarizations. In remote sensing applications it is often

convenient to select an orthogonal linear polarization frame with 0° and 90° aligned with

horizontal polarization and vertical polarization, respectively. Then, 45° and 135°

skewed linear polarizations can be referred to as +45° and -45° skewed linear

polarizations, respectively.

Response of a fully polarimetric radiometer: the response of a radiometer is dependent

on the brightness temperature scene and the characteristics ofthe radiometer. In terms of

the modified Stokes vector in brightness temperature, this relationship for a fully

polarimetric radiometer is

r, g", g,h g'3 g" 1', 0,

rh ghv ghh gh3 gh' Th

+

°h

rmod = = +nmod = gmodTB.mod +Omod +nmod,

r3 g" g'h g" g'4 T, a,

r, g4, g'h g" g44 T, a,

where rmod is the low frequency output response vector, g mod is the gain matrix,

T B, mod is the modified Stokes vector in brightness temperature, Omod is the offiet

vector, and nmod is the zero-mean Gaussian instrument noise at the channel outputs. The

off-diagonal terms of the gain-matrix represent interchannel cross-talk. In terms of the

Stokes vector in brightness temperature, this relationship can be written as

rl gil glQ g/U g/V r; 0 1

rQ gQI gQQ gQu gQv TQ oQ - r= = + +n=gTB +o+n.

ru gU/ gUQ goo guv Tu °u

rv gVl gVQ gvu gvv Tv °v

Sense of polarization: for an elliptical or circularly polarized field vector, the sense of

rotation ofthe extremity ofthe field vector when its origin is fixed [6].

Stokes parameter mixing: contamination of a measured Stokes parameter I modified

Stokes parameter value by other parameters, with the result that a certain radiometer

channel is sensitive to more than one Stokes parameter I modified Stokes parameter.

23
Stokes parameter mixing can be generated by, e.g., inter-channel cross-talk, antenna

cross-polarization, and/or platform motion. See also: plaiform motion compensation,

response ofa fitlly polarimetric radiometer.

Stokes parameters: four parameters that completely characterize an electromagnetic

wave at a certain frequency. The first Stokes parameter (1) denotes the total Poynting

vector or flux density of the wave. Expressing the other parameters in terms of linearly

polarized components, the second Stokes parameter (Q) is the difference between the flux

densities polarized in two orthogonal directions in a given polarization frame, e.g.,

vertical polarization and horizontal polarization. The third (U) and fourth (V) Stokes

parameters respectively represent twice the real and imaginary parts of the cross

correlation between these orthogonal polarizations. The third Stokes parameter can also

be defined as a difference between +450 and -45° skewed linearly polarized flux

densities, and the fourth parameter as a difference between left-handed and right-handed

circularly polarized flux densities:

where S is the flux density ofthe wave (in W·m-2

). The subscripts v, h, +45, -45, Ic, and

rc represent respectively the vertically, horizontally, +45° skewed linearly, -45° skewed

linearly, left-handed circularly, and right-handed circularly polarized waves, 17 is the

wave impedance of the medium, and Ev and Eh are the electric field components with

vertical and horizontal polarizations, respectively. Note that in polarimetric remote

sensing radiometry the Stokes parameters are conventionally expressed in terms of

brightness temperature, i.e., Stokes parameters in brightness temperature. See also:

modified Stokes parameters, Stokes vector in brightness temperature.

Stokes parameters in brightness temperatnre: Stokes parameters expressed in terms of

brightness temperature (in kelvins):

)? T =--·1

I k.B

B

;I? T--·Q

Q - k·B ' B

24
A? T. =-_·u

U k.B

B

A' T. =-_·V

v k.B ' 8

where wavelength, Boltzmann's constant, and noise-equivalent bandwidth are denoted by

A., kB, and B, respectively. The first, second, third and fourth Stokes parameters are

denoted by I, Q, U, and V. Note that in the published literature on polarimetric remotesensing radiometry, I, Q, U, and V have also been used for the Stokes parameters in

brightness temperature (units kelvins). This practice may generate confusion and is

therefore discouraged. See also: modified Stokes parameters in brightness temperature,

Stokes vector in brightness temperature.

Stokes vector in brightness temperature: vector containing all four Stokes parameters

in brightness temperature of a certain brightness temperature scene:

where TJ, TQ, Tu, and Tv denote the first, second, third and fourth Stokes parameters in

brightness temperature, respectively. See also: modified Stokes vector in brightness

temperature.

Tri-polarimetric calibration: the determination of the offset and gain terms (see:

response ofa jUlly polarimetric radiometer) of a tri-polarimetric radiometer. See also:

jUlly polarimetric calibration.

Tri-polarimetric calibration standard: a device for external calibration of radiometers

that can generate three linearly independent polarized brightness temperature scenes.

Along with an unpolarized calibration standard, a tri-polarimetric calibration standard

enables tn-polarimetric calibration. See also: jUlly polarimetric calibration standard.

Tri-polarimetric radiometer: a radiometer that measures three of the four Stokes

parameters / modified Stokes parameters.

Unpolarized brightness temperature scene: a brightness temperature scene that emits

completely unpolarizedwaves, i.e., the waves are completely randomly polarized.

Unpolarized calibration: a calibration procedure applying only unpolarized reference

signals. Enables the determination of offset and diagonal gain terms (see: response ofa

jUlly polarimetric radiometer) of those radiometer channels, which are sensitive to

unpolarized signals. See also: unpolarized reference standard.

25
Unpolarized calibration standard: a calibration reference that generates unpolarized

signals. See also: polarimetric calibration standard, unpolarized calibration.

Vertical brightness temperature: a brightness temperature derived from field

components in the direction of vertical polarization. See also: horizontal brightness

temperature.

Vertical polarization: see polarization.

We are grateful to Dr. Andreas Colliander of the European Space Agency and

Professor Steven Reising of Colorado State University for very thorough and detailed

reviews. This document is significantly better than it would otherwise have been due to

their efforts. We also thank Dr. Paul Racette of NASA for early interest in and

contributions to this effort.

REFERENCES

[1] C. Wyatt, V. Provalsky, and R Datla, "Recommended practice; symbols, terms,

units and uncertainty analysis for radiometric sensor calibration," Nat!. Inst.

Stand. Techno!. Handbook 152 (1998 September).

[2] http://boulder.nist.gov/div818/stdterms/index.htm

[3] http://www.grss-ieee.org/

[4] International Vocabulary of Basic and General Terms, Second edition,

International Organization for Standardization (ISO), Switzerland (1993).

[5] Guide to the Expression of Uncertainty in Measurement, International

Organization for Standardization (ISO), Switzerland (1993).

[6] IEEE Standard Dictionary of Electrical and Electronics Terms, 4th ed.,

ANSIlIEEE Std 100-1988.

[7] J.D. Krauss, Radio Astronomy, chapter 3, McGraw-Hill, New York (1966).

[8] Adapted from U.S. Federal Standard 1037C.

[9] B.N. Taylor and c.E. Kuyatt, "Guidelines for evaluating and expressing the

uncertainty ofNIST measurement results," Nat!. Inst. Stand. Techno!. Tech. Note

1297 (1994 September).

26
[10] IEEE Standard 145-1993 (Standard Definitions of Terms for Antennas).

[II] D.M. Pozar, Microwave Engineering, chapter 12, John Wiley & Sons, New York

(1998).

[12] H.A. Haus et al., "IRE standards on methods of measuring nOIse In linear

twoports, 1959," Proc. IRE, vol. 48, pp. 60 - 68 (1960).

[13] H.A. Haus et al., "Description of the noise performance of amplifiers and

receiving systems," Proc. IEEE, vol. 51, pp. 436 - 442 (1963).

[14] G.F. Engen, Microwave Circuit Theory and Foundations of Microwave

Metrology, Ch. 3, Peter Perigrinus Ltd., London (1992).

ALPHABETICAL INDEX

Note: I, II, and III refer to chapters of the text. IVM and GUM indicate that the definition

is given in the IVM [4] and/or GUM [5] and is not repeated in this document.

Absolute accuracy, II

Accuracy, I; see also Absolute accuracy, Pixel-to-pixel accuracy

Accuracy of a measuring instrument, I

Adding analog correlator, III

Allan standard deviation, I

Allan variance, I

Analog correlator, III

Analog cross correlator, III

Angular resolution, II

Antenna beam width, II

Antenna gain, II

Antenna ohmic efficiency, II

Antenna pattern, see (Normalized) antenna pattern

Antenna temperature, II

Antenna aperture temperature, II

Antenna output temperature, II

Bandwidth

Half-power bandwidth, II

Noise-equivalent bandwidth, II

(Equivalent) predetection bandwidth, II

Bias, I

Blackbody, II

Blackbody load, II

Boresight, II

Brightness, I

Brightness temperature, I; see also Effective black-body brightness temperature.

27
Calibration, I

End-to-end calibration, II

External calibration, II

Internal calibration, II

Tip-curve calibration, II

Two-point calibration, II

Calibration coefficients, ill

Calibration equation, I

Channel (of a radiometer), ill

Circular polarization, III

Close-couple, II

Coherency matrix, ill

Coherent detection, ill

Completely polarized wave, ill

Completely unpolarized wave, ill

Complex correlator, ill

Complex cros-correlator, ill

Complex degree of coherence, III

Corrected result, IVM, GUM

Correlator, III

Cross-correlator, III

Degradation factor, III

Degree of polarization, ill

Delay line, III

Digital correlator, ill

Digital cross-correlator, III

Direct correlating correlator, III

Direct correlating polarimetric radiometer, III

Directivity, II

Drift, I

Dwell time, II

Effective black-body brightness temperature, I

Effective noise bandwidth, II

Emissivity ofsurface, I

Error, I

Experimental standard deviation, I

Field ofview

Effective field of view, II

Instantaneous field of view (IFOY), II

Static IFOY, II

Static IFOY-Cross Track, II

Static IFOY-Down Track, II

Fringe-washing effect, ill

Fully polarimetric calibration, III

Fully polarimetric calibration standard, III

28
Fully polarimetric radiometer, III

Gain, see Antenna gain, Receiver gain, System gain

Gain matrix, III

Horizontal brightness temperature, III

Horizontal polarization, III

Incoherent detection, III

Inter-channel cross-talk, III

Limiting radiometric resolution, II

Linear polarization, III

Linearly polarized calibration standard, III

Measurand, IVM, GUM

Modified Stokes parameters, III

Modified Stokes parameters in brightness temperature, III

Modified Stokes vector in brightness temperature, III

Noise-equivalent Bandwidth, II

Noise figure, II

Noise temperature, I; see also Receiver noise temperature, Reference temperature,

System noise temperature

(Normalized) antenna pattern, II

Offset vector, III

Operating noise figure, II

Partially polarized wave, III

Perfect blackbody, II

Phase modulation, III

Phase retardation plane, III

Pixel-to-pixel accuracy, II

Platform motion compensation, III

Poincare sphere, III

Polarimetric brightness temperautres, III

Polarimetric calibration, III

Polarimetric calibration standard, III

Polarimetric channels, III

Polarimetric radiometer, III

Polarization, III

Polarization combining network, III

Polarization combining radiometer, III

Polarization frame, III

Polarized brightness temperature scene, III

Polarizing grid, III

Principal polarizations, III

Quantization level, I

Radiance, I

Radiation intensity, II

Radiometer, II

Radiometric resolution, II

Radiometric sensitivity, II

29
Random error, I

Receiver gain, II

Receiver noise figure, II

Receiver noise temperature, II

Reference temperature, I

Relative error, I

Relative uncertainty, I

Repeatability, I

Reproducibility, I

Resolution, I

Limiting radiometric resolution, II

Radiometric resolution, II

Radiometric resolution per beam width, II

Spatial resolution, II

Response of a fully polarimetric radiometer, ill

Response time, I

Result of a measurement, IVM, GUM

Sense of polarization, ill

Sensitivity, I

Spectral brightness density, I

Spectral radiance density, I

Stability, I

Standard

Check standard, I

Measurement standard, IVM

Primary standard, IVM

Secondary standard, IVM

Reference standard, IVM

Working standard, IVM

Transfer standard, IVM

Stokes parameter mixing, III

Stokes parameters, III

Stokes parameters in brightness temperature, III

Stokes vector in brightness temperature, ill

Systematic error, I

System gain, II

System noise figure, II

System noise temperature, II

Traceability, I

Tri-polarimetric calibration, ill

Tri-polarimetric calibration standard, III

Tri-polarimetric radiometer, ill

True value, I

Type-A uncertainty, I

Type-B uncertainty, I

Uncertainty budget, I

30
Uncertainty ofmeasurement, I

Unpolarized brightness temperature scene, III

Unpolarized calibration, III

Unpolarized calibration standard, III

Validation, I

Verification, I

Vertical brightness temperature, III

Vertical polarization, III

31
i

I1
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