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 24-Jul-2014
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## 5.5 Geometry Glossary

##### Table 5.5
Along Track See Azimuth below.
Aspect Angle

Description of the geometric orientation in the horizontal plane of an object in the scene with respect to the illuminating wavefront.

Azimuth

The term azimuth is used to indicate linear distance or image scale in the direction parallel to the radar flight path. In an image, azimuth is also known as along-track direction, since it is the relative along-track position of an object within the antenna'"s field of view following the radar's line of flight. Azimuth is predominately used in radar terminology. The azimuth direction is perpendicular to the range direction. The resolution of an image in the azimuth directions for a SAR image is constant and is independent of the range. For two objects to be resolved, they must be separated in the azimuth direction by a distance greater than the beamwidth on the ground.

##### Azimuth
Azimuth Direction Direction parallel to the line of flight, also referred to as the along-track direction. (See Azimuth )

Azimuth Line

A line of constant range. Each azimuth line is parallel to the flight path. Note that this usage is not universal; some researchers use 'azimuth line' to refer to what is here called 'range line' (and vice versa).

##### Azimuth Line
Beamwidth

Beamwidth is a measure of the width of the radiation pattern of an antenna. For SAR applications, both the vertical beamwidth, affecting the width of the illuminated swath, and the horizontal or azimuth pattern, which determines, indirectly, the azimuth resolution, are frequently used. Beamwidth may be measured in the one-way or two-way form, and in either voltage or power.

##### Beamwidth

Depression Angle

Depression angle usually refers to the line of sight from the radar to an illuminated object as measured from the horizontal plane at the radar. For image interpretation, use of the term is not recommended because it does not account for the effects of Earth curvature, and it does not conveniently include effects of local slope in the scene. It is more appropriate for an engineering description of the vertical antenna pattern at the radar itself.

##### Depression Angle
Digital Elevation Model ( DEM ) A quantitative model of a landform in digital form, normally given as metres above sea level (including the height of the vegetation), and referenced to a geographic co-ordinate system.
Elevation Angle The elevation angle is that which is located between the slant range and the nadir. It closely approximates the incidence angle, but there are differences as a result of the curvature of the Earth. ( See also Depression Angle and Imaging Geometry)
Elevation Displacement

Elevation displacement, also referred to as geometric distortion, is the image displacement in a remote sensing image toward the nadir point in radar imagery due to sensor/target imaging geometries. In a radar image the displacement is toward the sensor and can become quite large when the sensor is nearly overhead. The displacement increases with decreasing incidence angle. The four characteristics resulting from the geometric relationship between the sensor and the terrain that are unique to radar imagery are foreshortening, pseudo-shadowing, layover, and shadowing. Topographic features like mountains, as well as artificial targets like tall buildings, will be displaced from their desired orthographic position in an image. The effect may be used to create stereo images. It may be removed from an image through independent knowledge of the terrain profile. In many applications, an approximate correction may be derived through shape-from-shading techniques. Elevation displacement will be greater in slant range than ground range due to the fact that the image is more compressed in a slant range presentation. Elevation displacement is also most pronounced at near range.

##### Elevation displacement
Ellipsoid A model used to describe the shape of the planet Earth, which is not a true sphere but an oblate spheroid compressed along the polar axis and bulging slightly around the equator.
Ellipticity Angle Defined as the magnitude of the arctangent of the ratio of the polarisation ellipse'"s minor and major axes. If negative, the ellipse rotation is right-handed; if positive, is the ellipse rotation is left-handed.
Far Range Portion of the radar image farthest from the flight path. ( See also "Imaging Geometry" )
Foreshortening

Foreshortening is the spatial distortion whereby terrain slopes facing a side-looking radar's (SLAR) illumination are mapped as having a compressed scale relative to its appearance, as if the same terrain were level. Foreshortening is a special case of elevation displacement. The effect is more pronounced for steeper slopes and for radars that use steeper incidence angles. ( See also Shadow in Products glossary.

##### Foreshortening
Ground Range Ground Range is the perpendicular distance from the ground track to a given object on the Earth'"s surface. Also defined as the range direction of a side-looking radar image as projected onto the nominally horizontal reference plane, similar to the spatial display of conventional maps. Ground range projection requires a geometric transformation from slant range to ground range; for spacecraft data, a geoid model of the Earth is used, whereas for airborne radar data, a planar approximation is sufficient. This can lead to relief or elevation displacement, foreshortening, and layover on radar images. However, if terrain elevation information is used, the effect on viewing geometry can be minimised. ( See also "Imaging Geometry" , "Depression Angle" and "ASAR Level 1B Algorithm Physical Justification" - Radar Geometry 2.6.1.1.2. , as well as )
Imaging Geometry

The imaging geometry of a radar system is different from the framing and scanning systems commonly employed for optical remote sensing. Similar to optical systems, the platform travels forward in the flight direction (A) with the nadir (B) directly beneath the platform. The microwave beam is transmitted obliquely at right angles to the direction of flight illuminating a swath (C) which is offset from nadir. Range (D) refers to the across-track dimension perpendicular to the flight direction, while azimuth (E) refers to the along-track dimension parallel to the flight direction. This side-looking viewing geometry is typical of imaging radar systems (airborne or spaceborne).

##### Imaging Geometry

The portion of the image swath closest to the nadir track of the radar platform is called the near range (A) while the portion of the swath farthest from the nadir is called the far range (B). The incidence angle is the angle between the radar beam and ground surface (A) which increases, moving across the swath from near to far range. The look angle (B) is the angle at which the radar looks at the surface. In the near range, the viewing geometry may be referred to as being steep, relative to the far range, where the viewing geometry is shallow. At all ranges the radar antenna measures the radial line of sight distance between the radar and each target on the surface. This is the slant range distance (C). The ground range distance (D) is the true horizontal distance along the ground corresponding to each point measured in slant range.

Incidence Angle

The incidence angle is the angle defined by the incident radar beam and the vertical (normal) to the intercepting surface. In general, reflectivity from distributed scatterers decreases with increasing incidence angle. The incidence angle is commonly used to describe the angular relationship between the radar beam and the ground, surface layer or a target. A change of the radar illumination angle often affects the radar backscattering behaviour of a surface or target. The incidence angle changes across the radar image swath; it increases from near range to far range. In the case of satellite radar imagery, the change of incidence angle for flat terrain across the imaging swath tends to be rather small, usually on the order of several degrees. In the case of an inclined surface (slope), the local incidence angle (L) is defined as the angle between the incident radar beam and a line that is normal to that surface. The local incidence angle determining, in part, the brightness, or image tone, for each picture element (pixel) and slope facet, is a key element in the prominent rendition of terrain features in radar imagery.

##### Incidence Angle

Microwave interactions with the surface are complex and different scattering mechanisms may occur in different angular regions. Returns due to surface scattering are normally strong at low incidence angles and decrease with increasing incidence angle, with a slower rate of decrease for rougher surfaces. Returns due to volume scattering from an heterogeneous medium with low dielectric constant tend to be more uniform for all incidence angles. Thus, radar backscatter has an angular dependence, and there is potential for choosing optimum configurations for different applications.

Lambert Conformal Conic (LCC) map projection

The Lambert Conformal Conic (LCC) map projection is a State Plane Co-ordinate System that consists of 120 zones designed to optimally represent sections of the individual states. Points on the earth are projected onto a cone that intersects the earth's surface at two parallels of latitude. Along these two circles the scale will be exact. If the parallels are close in a north-south direction, the map scale will be reasonably accurate no matter how far the map is extended in an east-west direction. The Lambert projection is useful for mapping states that are relatively wide in an east-west direction. This projection is said to be conformal because the scales in all directions are equivalent.

##### Lambert Conformal Conic (LCC) map projection
Latitude

Latitude is the number of degrees north or south of the equator, an imaginary circle on the Earth's surface everywhere equidistant between the two poles.

##### Geocentric and Geodetic Latitudes
Layover

Layover is an extreme form of elevation displacement or foreshortening in which the top of a reflecting object, such as mountain, is closer to the radar (in slant range) than are the lower parts of the object. The image of such a feature appears to have fallen over towards the radar. Also defined as the displacement of the top of an elevated feature with respect to its base on the radar image. The peaks look like dip-slopes. The effect is more pronounced for radars having smaller incidence angle. ( See also Shadow in Products glossary.

##### Layover
Location Co-ordinates (geodetic latitude, longitude) of a point on the geoid, expressed in the Earth-fixed co-ordinate system.
Longitude The angular distance on the Earth, or on a globe or map, east or west of the prime meridian at Greenwich, England to the point on the Earth's surface for which the longitude is being ascertained, expressed in degrees, or in hours, minutes and seconds.
Map Projections

ASAR processing supports 6 different map projections: Mercator (MERC), Transverse Mercator (TM), Universal Transverse Mercator ( UTM), Polar Stereographic Mercator (PS), Universal Polar Stereographic (UPS) , and the Lambert Conformal Conic (LCC).

Cylindical projections are based upon the various methods of projecting the Earth upon a cylinder that is either tangent to the equator (normal or equatorial form), a meridian (transverse) or obliquely aligned. Any of these classes are available in both conformal and equal area form. These projections are best used in mapping applications involving a zone near the line of tangency.[e.g. Mercator, Transverse Mercator (TM), Universal Transverse Mercator (UTM)]. Applications should be limited to equatorial regions, but it is frequently used for navigational charts with latitude of true scale specified within or near the chart's boundaries.

Conic projections involve the transformations to a cone either secant or tangent to the Earth's surface.[e.g. Lambert Conformal Conic (LCC)]

Stereograhic projections are those in which perspective is a point at the opposite end of the globe. In other words, the light is a point source shown from a point on the globe through to the other end of the globe (e.g., a South Pole point of projection would shine light through to the North Pole). An example of a stereographic projection is the North Polar Stereographic Projection shown below:

##### ( image courtesy of Peter H. Dana California State University )

[e.g. Universal Polar Stereographic (UPS) Projection, Polar Stereographic Mercator (PS)]

Mercator (MERC) Map Projection

The Mercator (MERC) map projection, sometimes referred to as the Plain Mercator, is made from the centre of the Earth onto a cylinder surrounding and touching it at the Equator. Therefore, the meridians are equally spaced, parallel and vertical lines, and the parallels of latitude are parallel, horizontal staight lines, spaced farther and farther apart as their distance from the Equator increases.

##### Mercator map projection
Nadir Nadir is a single point, or locus of points on the surface of the Earth directly below a sensor as it progresses along its line of flight. Nadir can be both a point and a line. In other words, when a straight line is drawn between the sensor and the centre of the Earth, the nadir is the point where that line intersects the surface of the Earth. When the contiguous nadir points are joined along the ground, they form the nadir line. For radar, the nadir line corresponds to the beginning of the range. ( See also "Imaging Geometry" )
National Systems Projection (NSP) A National Systems map Projection (NSP) is any of 4 map projections used in ASAR processing, other that the UTM or UPS projections. These are the LCC, TM, MERC and PS projections.
Near Range Refers to the portion of a radar image closest to the satellite flight path. ( See also "Imaging Geometry" )
One-Way Numbers relating to only one direction of propagation are denoted as one-way, and the corresponding numbers that include the round trip are called two-way. The radar illuminates the scene through the transmit pattern of the antenna. It receives the backscattered energy through the receive pattern of the antenna. Thus the received pulse must travel two ways, out to each object at range , and back again the same distance. The difference between one-way and two-way is important in measuring effective antenna pattern widths, in signal phase, and in the relationship between two-way delay time and range distance.
Orbit The path of a satellite as it revolves around the Earth is its orbit. (For the ASAR Orbit State Vectors see the section entitled "Auxiliary Data Sets for Level 1B Processing" in chapter 2 ).
Pixel Geometry A set of angles (sun zenith angle, viewing zenith angle and azimuth difference angle) specifying how the pixel is seen from the instrument and from the sun.
Polarisation Signature A three-dimensional plot of the received backscattered power as a function of the ellipticity and orientation angles of a polarimetric antenna.
Polar Stereographic Mercator (PS) Map projection ( See Map Projections and Mercator Map Projection )

Radar polarisation is the orientation of the electric (E) vector in an electromagnetic wave, frequently horizontal or vertical , in conventional imaging radar systems. Polarisation refers to the orientation of the plane of the electric field (E), as opposed to the magnetic field (M)

Remote sensing radars are usually designed to transmit either vertically polarised or horizontally polarised radiation. This means that the electric field of the wave is in a vertical plane or a horizontal plane. Likewise, the radar can receive either vertically or horizontally polarised radiation, and sometimes both. The planes of transmitted and received polarisation are designated by the letters H for Horizontal and V for Vertical. Thus the polarisation of a radar image can be HH, for horizontal transmit, horizontal receive, VV for vertical transmit, vertical receive, HV for horizontal transmit vertical receive, and vice versa (VH).

When the polarisation of received radiation is the same as the transmitted radiation, the image is said to be like-polarised When the polarisation of received radiation is the opposite of the transmitted radiation, the image is said to be cross-polarised cross polarisation requires multiple-scattering by the target and therefore results in weaker backscatter than like-polarisation Satellite radars generally use like-polarisation because the cross-polarised signals are too weak to produce a good image.

Polarisation is established by the antenna, which may be adjusted to be different on transmit and on receive. Reflectivity of microwaves from an object depends on the relationship between the polarisation state and the geometric structure of the object. Possible states of polarisation, in addition to vertical and horizontal, include all angular orientations of the E vector, and time varying orientations leading to elliptical and circular polarisations.

( See also the section entitled "Dual Polarisation" 1.1.5.1. in chapter 1 ).

Range Range is the line of sight distance between the radar and each illuminated scatterer (target). In SAR usage, the term is applied to the dimension of an image perpendicular to the line of flight of the radar. Slant range is the distance from the radar, toward each target and measured perpendicular to the line of flight. Ground range is the same distance, projected using a geometrical transformation onto a reference surface such as a map. Radar data are collected in the slant range domain, but usually are projected onto the ground range plane when these data are processed into an image. The resolution of the image in the range direction is dependent on the length of the emitted pulse; shorter pulses result in finer resolution. ( see also "ASAR Level 1B Algorithm Physical Justification" - Radar Geometry 2.6.1.1.2. )
Range Curvature Describes the changing distance between the radar and an object during the time that the object is illuminated by the antenna. Range curvature is more important for long range systems such as satellite SARs, and must be compensated in the processor as a part of image focusing.
Range Gate Bias
Range Migration The changing range delay to a point target as the target passes through the antenna beam. See the discussion "Range Cell Migration Correction (RCMC)" 2.6.1.2.3.1.4. in the section entitled "Range Doppler" in chapter 2.
Side-Looking Where the radar antenna beam is pointed sideways, typically nearly perpendicular to the flight direction of the spacecraft. (See also SLAR in the "Radar and SAR glossary" and "ASAR Level 1B Algorithm Physical Justification" - Radar Geometry 2.6.1.1.2. )
Slant Range Represents the distance measured along a line between the radar antenna and the target. Image direction as measured along the sequence of line-of-sight rays from the radar to each and every reflecting point in the illuminated scene. Since a SAR looks down and to the side, the slant range to ground range transformation has an inherent geometric scale which changes across the image swath. ( See also "Imaging Geometry" and "ASAR Level 1B Algorithm Physical Justification" - Radar Geometry 2.6.1.1.2. , as well as )
State Plane Co-ordinate System (SPCS) The State Plane Co-ordinate System (SPCS), was established in 1935 in the United States. Each of the States have defined, by State legislative action, one or more spcs zones in terms of datum, geographical extent and cartographic projection parameters relating geographic coordinates to the cartesian coordinates used in land surveying.
Swath Angle An angle sub-tending the arc between swath centre and a point
Transverse Mercator (TM) map projection

The Transverse Mercator (TM) map projection is a State Plane Co-ordinate system that consists of 120 zones designed to optimally represent sections of the individual states. It uses a cylindrical surface that intersects the earth along two lines parallel to a meridian of longitude, called the central meridian. The scale will be exact along the two north-south lines of intersection. This projection is reasonably accurate within a narrow east-west zone, and may be extended indefinably in a north-south direction. It is therefore useful for states that are narrow in the east-west direction.

##### Tranverse Mercator (TM) map projection
Trihedral Reflector Corner reflector formed from three mutually orthogonal surfaces.
Universal Polar Stereographic (UPS) Map Projection

The Universal Polar Stereographic (UPS) map projection is a special case polar aspect of the azimuthal stereographic projection, which is based upon projections to a plane tangent to the Earth's surface.

##### Universal Polar Stereographic (UPS) Map Projection
Universal Transverse Mercator (UTM)

The Universal Transverse Mercator (UTM) projection is a special ellipsoidal form of the general Transverse Mercator (TM) projection . It is a planar map projection, that provides a specific geographic coordinate system to which data can be referenced. It is based on a series of 60 zones worldwide, each covering 6 degrees of longitude in a north-south strip.

##### Universal Transverse Mercator (UTM) Zone
Width - Radar 3dB. Width of a distribution equal to the distance between the outer two points on the distribution having power level half of that at the peak.
Width, Equivalent Rectangle A standard definition to measure the effective width of a distribution. The width is that of a rectangular distribution with the same amplitude as the maximum of the distribution, and having the same area in the rectangle as is in the measured distribution.
Zero Doppler Direction The angle from the satellite to the target, relative to the broadside
Zero Doppler Range The closest approach range from the satellite to the target.