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Premium member Presentation Transcript Slide1: Gamma Rays – emitted or absorbed by changes in the energy state of protons or neutrons in the nucleus Gamma Rays tell us about the nucleus X-rays – Inner shell of electrons X-rays tell us about atoms Slide2: Gamma Rays – emitted or absorbed by changes in the energy state of protons or neutrons in the nucleus Gamma Rays tell us about the nucleus X-rays – Inner shell of electrons X-rays tell us about atoms Slide3: UV, Visible, Reflected Infrared – Outer shells of transition metals iron, nickel, zinc, copper, manganese, chromium, titanium, vanadium, cobalt, scandium Partially occupied 3d or 4s electron energy levels Fe3+ shades of red, yellow, orange, purple, and rusty brown in rocks Fe2+ and Cu2+ shades of green and blue in rocks These bands tell us about atomsSlide4: UV, Visible, Reflected Infrared – Outer shells of transition metals iron, nickel, zinc, copper, manganese, chromium, titanium, vanadium, cobalt, scandium Partially occupied 3d or 4s electron energy levels Fe3+ shades of red, yellow, orange, purple, and rusty brown in rocks Fe2+ and Cu2+ shades of green and blue in rocks These bands tell us about atomsSlide5: Thermal Infrared – Twisting, rotational, vibrations, among ions in a compound Thermal Infrared tells us about molecules and temperature Microwave and Radar – Tells us very little about composition Can tell us much about temperature, roughness, particle size and shapeSlide6: Thermal Infrared – Twisting, rotational, vibrations, among ions in a compound Thermal Infrared tells us about molecules and temperature Microwave and Radar – Tells us very little about composition Can tell us much about temperature, roughness, particle size and shapeStuff you need to know/learn I: Stuff you need to know/learn I The speed of light in a vacuum The meaning and units of frequency and wavelength The relationship between frequency and wavelength in a vacuum The basic interactions of electromagnetic energy with surfaces and volumes The electromagnetic spectrum Common names given to bands of the spectrum Approximate wavelengths of common bands of the spectrum Association of spectral bands with atomic, molecular, and shape properties of surfaces Image Characteristics: Scale: Image Characteristics: Scale 1:500,000 means 1 cm = 5 km or 1 in. = 8 mi or 1 mm = 500,000 mm Small scale is scale greater than 1:500,000 Intermediate scale is 1:50,000 to 1:500,000 Large scale is scale less than 1:50,000 Scale is a property of an image, not of the systemImage Characteristics: Brightness and Tone: Image Characteristics: Brightness and Tone Brightness is the magnitude of response produced in the eye by light. It is subjective and poorly quantified. Luminance is a quantitative measure of intensity from a source, measured with a photometer. Each distinguishable difference in brightness in a gray scale is called a tone. Tone is usually used in a comparative rather than quantitative way.Image Characteristics: Contrast Ratio: Image Characteristics: Contrast Ratio Contrast Ratio (CR) is the ratio between the brightest and darkest parts of the image. Using a brightness scale of 0-10: High contrast CR=9/2=4.5 Medium contrast CR=5/2=2.5 Low contrast CR=3/2=1.5 Low contrast images are referred to as “washed-out” Low contrast can be caused by: Small differences in properties of the target Atmospheric scattering System may lack sensitivity or recording technique may be poor Low contrast generally repaired by digital enhancementImage Characteristics: Spatial Resolution & Resolving Power: Image Characteristics: Spatial Resolution & Resolving Power Spatial resolution is the ability to distinguish between two finely spaced objects in an image Resolving power is the ability, usually theoretical, of a remote sensing system to distinguish between two finely spaced objectsSlide17: Object distance Image distanceSlide18: Pupil mostly concentrates light on fovea for maximum acuity. Lens primarily supports accommodation (focusing). Rods (B&W; low light) and cones (color; daylight) distributed on retina. Rods and cones concentrated near fovea.Slide19: The diameter of receptor cells in the fovea is 3 um Correct this for refractive index of vitreous humor gives effective diameter of 4 um The image distance is 20 mm or 20000 um. Width of receptors is 1/5000 of image distance Image distance is proportional to object distance Therefore adjacent objects must be separated by 1/5000 of the object distance to be resolved How far apart is that at 10 m? How far apart is that from 500 km?Other Image Characteristics: Other Image Characteristics Detectability – generally smaller than the resolving power Recognizability – generally greater than the resolving power Signature – characteristics that allow object to be recognized, often spectral Texture – frequency of change and arrangement of tones in an image Interpretation Key – characteristic or combination of characteristics that enables a complex object to be recognizedSlide21: Framing SystemSlide22: Acquisition systems for mono- or pan-spectral imagesWhat controls the strength of the signal in a detector?: What controls the strength of the signal in a detector? Energy flux from the target – brighter is better Altitude – inverse square law Spectral bandwidth of detector – trade-off of spectral resolution and signal strength Instantaneous field of view – trade-off of spatial resolution and signal strength Dwell time – longer better; but slower or requires more detectorsSlide26: Spectral Reflectance Curves Field reflectance spectrometers Absorption features Reflectance peaks Spectral Libraries Color: Color http://www2.ncsu.edu/scivis/lessons/colormodels/color_models2.html http://hyperphysics.phy-astr.gsu.edu/hbase/vision/cie.html 24 bit color Indexed color Gray scale Slide29: Introduction to Geodetic Datums Geodetic datums define the size and shape of the earth and the origin and orientation of the coordinate systems used to map the earth. Hundreds of different datums have been used to frame position descriptions since the first estimates of the earth's size were made by Aristotle. Datums have evolved from those describing a spherical earth to ellipsoidal models derived from years of satellite measurements. Modern geodetic datums range from flat-earth models used for plane surveying to complex models used for international applications which completely describe the size, shape, orientation, gravity field, and angular velocity of the earth. While cartography, surveying, navigation, and astronomy all make use of geodetic datums, the science of geodesy is the central discipline for the topic. Referencing geodetic coordinates to the wrong datum can result in position errors of hundreds of meters. Different nations and agencies use different datums as the basis for coordinate systems used to identify positions in geographic information systems, precise positioning systems, and navigation systems. The diversity of datums in use today and the technological advancements that have made possible global positioning measurements with sub-meter accuracies requires careful datum selection and careful conversion between coordinates in different datums. Slide30: The Figure of the Earth Geodetic datums and the coordinate reference systems based on them were developed to describe geographic positions for surveying, mapping, and navigation. Through a long history, the "figure of the earth" was refined from flat-earth models to spherical models of sufficient accuracy to allow global exploration, navigation and mapping. True geodetic datums were employed only after the late 1700s when measurements showed that the earth was ellipsoidal in shape. Slide31: Geometric Earth Models Early ideas of the figure of the earth resulted in descriptions of the earth as an oyster (The Babylonians before 3000 B.C.), a rectangular box, a circular disk, a cylindrical column, a spherical ball, and a very round pear (Columbus in the last years of his life). Flat earth models are still used for plane surveying, over distances short enough so that earth curvature is insignificant (less than 10 kms). Spherical earth models represent the shape of the earth with a sphere of a specified radius. Spherical earth models are often used for short range navigation (VOR-DME) and for global distance approximations. Spherical models fail to model the actual shape of the earth. The slight flattening of the earth at the poles results in about a twenty kilometer difference at the poles between an average spherical radius and the measured polar radius of the earth. Ellipsoidal earth models are required for accurate range and bearing calculations over long distances. Loran-C, and GPS navigation receivers use ellipsoidal earth models to compute position and waypoint information. Ellipsoidal models define an ellipsoid with an equatorial radius and a polar radius. The best of these models can represent the shape of the earth over the smoothed, averaged sea-surface to within about one-hundred meters. Slide32: Reference Ellipsoids Reference ellipsoids are usually defined by semi-major (equatorial radius) and flattening (the relationship between equatorial and polar radii). Other reference ellipsoid parameters such as semi-minor axis (polar radius) and eccentricity can computed from these terms. Reference Ellipsoid Parameters Many reference ellipsoids are in use by different nations and agencies. Selected Reference Ellipsoids A More Complete List of Reference Ellipsoids Slide33: Earth Surfaces The earth has a highly irregular and constantly changing surface. Models of the surface of the earth are used in navigation, surveying, and mapping. Topographic and sea-level models attempt to model the physical variations of the surface, while gravity models and geoids are used to represent local variations in gravity that change the local definition of a level surface. Earth Surfaces The topographical surface of the earth is the actual surface of the land and sea at some moment in time. Aircraft navigators have a special interest in maintaining a positive height vector above this surface. Sea level is the average (methods and temporal spans vary) surface of the oceans. Tidal forces and gravity differences from location to location cause even this smoothed surface to vary over the globe by hundreds of meters. Gravity models attempt to describe in detail the variations in the gravity field. The importance of this effort is related to the idea of leveling. Plane and geodetic surveying uses the idea of a plane perpendicular to the gravity surface of the earth, the direction perpendicular to a plumb bob pointing toward the center of mass of the earth. Local variations in gravity, caused by variations in the earth's core and surface materials, cause this gravity surface to be irregular. Slide34: Geoid models attempt to represent the surface of the entire earth over both land and ocean as though the surface resulted from gravity alone. Bomford described this surface as the surface that would exist if the sea was admitted under the land portion of the earth by small frictionless channels. The WGS-84 Geoid defines geoid heights for the entire earth. The U. S. National Imagery and Mapping Agency (formerly the Defense Mapping Agency) publishes a ten by ten degree grid of geoid heights for the WGS-84 geoid. WGS-84 Geoid Heights Slide35: Global Coordinate Systems Coordinate systems to specify locations on the surface of the earth have been used for centuries. In western geodesy the equator, the tropics of Cancer and Capricorn, and then lines of latitude and longitude were used to locate positions on the earth. Eastern cartographers like Phei Hsiu used other rectangular grid systems as early as 270 A. D. Various units of length and angular distance have been used over history. The meter is related to both linear and angular distance, having been defined in the late 18th century as one ten-millionth of the distance from the pole to the equator. Slide36: Latitude, Longitude, and Height The most commonly used coordinate system today is the latitude, longitude, and height system. The Prime Meridian and the Equator are the reference planes used to define latitude and longitude. Equator and Prime Meridian The geodetic latitude (there are many other defined latitudes) of a point is the angle from the equatorial plane to the vertical direction of a line normal to the reference ellipsoid. The geodetic longitude of a point is the angle between a reference plane and a plane passing through the point, both planes being perpendicular to the equatorial plane. The geodetic height at a point is the distance from the reference ellipsoid to the point in a direction normal to the ellipsoid. Geodetic Latitude, Longitude, and Height Slide37: Earth Centered, Earth Fixed X, Y, and Z Earth Centered, Earth Fixed Cartesian coordinates are also used to define three dimensional positions. Earth centered, earth-fixed, X, Y, and Z, Cartesian coordinates (XYZ) define three dimensional positions with respect to the center of mass of the reference ellipsoid. The Z-axis points toward the North Pole. The X-axis is defined by the intersection of the plane defined by the prime meridian and the equatorial plane. The Y-axis completes a right handed orthogonal system by a plane 90° east of the X-axis and its intersection with the equator. ECEF X, Y, and Z Slide38: Geodetic Datums Datum Types Datum types include horizontal, vertical and complete datums. Datums in Use Hundreds of geodetic datums are in use around the world. The Global Positioning system is based on the World Geodetic System 1984 (WGS-84). Parameters for simple XYZ conversion between many datums and WGS-84 are published by the Defense mapping Agency. List of Geodetic Datums Datum Shifts Coordinate values resulting from interpreting latitude, longitude, and height values based on one datum as though they were based in another datum can cause position errors in three dimensions of up to one kilometer. Slide39: Coordinate Systems There are many different coordinate systems, based on a variety of geodetic datums, units, projections, and reference systems in use today. As an example, this overview often uses the position of one of the thousands of geodetic control points in the United States, the star in the hand of the Goddess of Liberty atop the Capitol building in Austin, Texas. The Texas Capitol Building The Star in the Hand of The Goddess of Liberty One Location Described by a Variety of Systems Slide40: Map projections are attempts to portray the surface of the earth or a portion of the earth on a flat surface. Some distortions of conformality, distance, direction, scale, and area always result from this process. Some projections minimize distortions in some of these properties at the expense of maximizing errors in others. Some projections are attempts to only moderately distort all of these properties. Different map projections result in different spatial relationships between regions. Three Different Map Projections of the United States Albers Equal Area and Lambert Conformal Conic Projections of North America Map ProjectionsSlide41: Conformality When the scale of a map at any point on the map is the same in any direction, the projection is conformal. Meridians (lines of longitude) and parallels (lines of latitude) intersect at right angles. Shape is preserved locally on conformal maps. Distance A map is equidistant when it portrays distances from the center of the projection to any other place on the map. Direction A map preserves direction when azimuths (angles from a point on a line to another point) are portrayed correctly in all directions. Scale Scale is the relationship between a distance portrayed on a map and the same distance on the Earth. Area When a map portrays areas over the entire map so that all mapped areas have the same proportional relationship to the areas on the Earth that they represent, the map is an equal-area map. Slide42: Map projections fall into four general classes. Cylindrical projections result from projecting a spherical surface onto a cylinder. When the cylinder is tangent to the sphere contact is along a great circle (the circle formed on the surface of the Earth by a plane passing through the center of the Earth).. Projection of a Sphere onto a Cylinder (Tangent Case) In the secant case, the cylinder touches the sphere along two lines, both small circles (a circle formed on the surface of the Earth by a plane not passing through the center of the Earth). Projection of a Sphere onto a Cylinder (Secant Case) When the cylinder upon which the sphere is projected is at right angles to the poles, the cylinder and resulting projection are transverse. Transverse Projection of a Sphere onto a Cylinder (Tangent Case) When the cylinder is at some other, non-orthogonal, angle with respect to the poles, the cylinder and resulting projection is oblique. Oblique Projection of a Sphere onto a Cylinder (Tangent Case) Slide43: Conic projections result from projecting a spherical surface onto a cone. When the cone is tangent to the sphere contact is along a small circle. Projection of a Sphere onto a Cone (Tangent Case) In the secant case, the cone touches the sphere along two lines, one a great circle, the other a small circle. Projection of a Sphere onto a Cone (Secant Case) Slide44: Azimuthal projections result from projecting a spherical surface onto a plane. When the plane is tangent to the sphere contact is at a single point on the surface of the Earth. Projection of a Sphere onto a Plane (Tangent Case) In the secant case, the plane touches the sphere along a small circle if the plane does not pass through the center of the earth, when it will touch along a great circle. Projection of a Sphere onto a Plane (Secant Case) Miscellaneous projections include unprojected ones such as rectangular latitude and longitude grids and other examples of that do not fall into the cylindrical, conic, or azimuthal categories You do not have the permission to view this presentation. In order to view it, please contact the author of the presentation.
esci450 spr 06 lec2 Altoro Download Post to : URL : Related Presentations : Share Add to Flag Embed Email Send to Blogs and Networks Add to Channel Uploaded from authorPOINTLite Insert YouTube videos in PowerPont slides with aS Desktop Copy embed code: (To copy code, click on the text box) Embed: URL: Thumbnail: WordPress Embed Customize Embed The presentation is successfully added In Your Favorites. Views: 66 Category: Entertainment License: All Rights Reserved Like it (0) Dislike it (0) Added: November 15, 2007 This Presentation is Public Favorites: 0 Presentation Description No description available. Comments Posting comment... Premium member Presentation Transcript Slide1: Gamma Rays – emitted or absorbed by changes in the energy state of protons or neutrons in the nucleus Gamma Rays tell us about the nucleus X-rays – Inner shell of electrons X-rays tell us about atoms Slide2: Gamma Rays – emitted or absorbed by changes in the energy state of protons or neutrons in the nucleus Gamma Rays tell us about the nucleus X-rays – Inner shell of electrons X-rays tell us about atoms Slide3: UV, Visible, Reflected Infrared – Outer shells of transition metals iron, nickel, zinc, copper, manganese, chromium, titanium, vanadium, cobalt, scandium Partially occupied 3d or 4s electron energy levels Fe3+ shades of red, yellow, orange, purple, and rusty brown in rocks Fe2+ and Cu2+ shades of green and blue in rocks These bands tell us about atomsSlide4: UV, Visible, Reflected Infrared – Outer shells of transition metals iron, nickel, zinc, copper, manganese, chromium, titanium, vanadium, cobalt, scandium Partially occupied 3d or 4s electron energy levels Fe3+ shades of red, yellow, orange, purple, and rusty brown in rocks Fe2+ and Cu2+ shades of green and blue in rocks These bands tell us about atomsSlide5: Thermal Infrared – Twisting, rotational, vibrations, among ions in a compound Thermal Infrared tells us about molecules and temperature Microwave and Radar – Tells us very little about composition Can tell us much about temperature, roughness, particle size and shapeSlide6: Thermal Infrared – Twisting, rotational, vibrations, among ions in a compound Thermal Infrared tells us about molecules and temperature Microwave and Radar – Tells us very little about composition Can tell us much about temperature, roughness, particle size and shapeStuff you need to know/learn I: Stuff you need to know/learn I The speed of light in a vacuum The meaning and units of frequency and wavelength The relationship between frequency and wavelength in a vacuum The basic interactions of electromagnetic energy with surfaces and volumes The electromagnetic spectrum Common names given to bands of the spectrum Approximate wavelengths of common bands of the spectrum Association of spectral bands with atomic, molecular, and shape properties of surfaces Image Characteristics: Scale: Image Characteristics: Scale 1:500,000 means 1 cm = 5 km or 1 in. = 8 mi or 1 mm = 500,000 mm Small scale is scale greater than 1:500,000 Intermediate scale is 1:50,000 to 1:500,000 Large scale is scale less than 1:50,000 Scale is a property of an image, not of the systemImage Characteristics: Brightness and Tone: Image Characteristics: Brightness and Tone Brightness is the magnitude of response produced in the eye by light. It is subjective and poorly quantified. Luminance is a quantitative measure of intensity from a source, measured with a photometer. Each distinguishable difference in brightness in a gray scale is called a tone. Tone is usually used in a comparative rather than quantitative way.Image Characteristics: Contrast Ratio: Image Characteristics: Contrast Ratio Contrast Ratio (CR) is the ratio between the brightest and darkest parts of the image. Using a brightness scale of 0-10: High contrast CR=9/2=4.5 Medium contrast CR=5/2=2.5 Low contrast CR=3/2=1.5 Low contrast images are referred to as “washed-out” Low contrast can be caused by: Small differences in properties of the target Atmospheric scattering System may lack sensitivity or recording technique may be poor Low contrast generally repaired by digital enhancementImage Characteristics: Spatial Resolution & Resolving Power: Image Characteristics: Spatial Resolution & Resolving Power Spatial resolution is the ability to distinguish between two finely spaced objects in an image Resolving power is the ability, usually theoretical, of a remote sensing system to distinguish between two finely spaced objectsSlide17: Object distance Image distanceSlide18: Pupil mostly concentrates light on fovea for maximum acuity. Lens primarily supports accommodation (focusing). Rods (B&W; low light) and cones (color; daylight) distributed on retina. Rods and cones concentrated near fovea.Slide19: The diameter of receptor cells in the fovea is 3 um Correct this for refractive index of vitreous humor gives effective diameter of 4 um The image distance is 20 mm or 20000 um. Width of receptors is 1/5000 of image distance Image distance is proportional to object distance Therefore adjacent objects must be separated by 1/5000 of the object distance to be resolved How far apart is that at 10 m? How far apart is that from 500 km?Other Image Characteristics: Other Image Characteristics Detectability – generally smaller than the resolving power Recognizability – generally greater than the resolving power Signature – characteristics that allow object to be recognized, often spectral Texture – frequency of change and arrangement of tones in an image Interpretation Key – characteristic or combination of characteristics that enables a complex object to be recognizedSlide21: Framing SystemSlide22: Acquisition systems for mono- or pan-spectral imagesWhat controls the strength of the signal in a detector?: What controls the strength of the signal in a detector? Energy flux from the target – brighter is better Altitude – inverse square law Spectral bandwidth of detector – trade-off of spectral resolution and signal strength Instantaneous field of view – trade-off of spatial resolution and signal strength Dwell time – longer better; but slower or requires more detectorsSlide26: Spectral Reflectance Curves Field reflectance spectrometers Absorption features Reflectance peaks Spectral Libraries Color: Color http://www2.ncsu.edu/scivis/lessons/colormodels/color_models2.html http://hyperphysics.phy-astr.gsu.edu/hbase/vision/cie.html 24 bit color Indexed color Gray scale Slide29: Introduction to Geodetic Datums Geodetic datums define the size and shape of the earth and the origin and orientation of the coordinate systems used to map the earth. Hundreds of different datums have been used to frame position descriptions since the first estimates of the earth's size were made by Aristotle. Datums have evolved from those describing a spherical earth to ellipsoidal models derived from years of satellite measurements. Modern geodetic datums range from flat-earth models used for plane surveying to complex models used for international applications which completely describe the size, shape, orientation, gravity field, and angular velocity of the earth. While cartography, surveying, navigation, and astronomy all make use of geodetic datums, the science of geodesy is the central discipline for the topic. Referencing geodetic coordinates to the wrong datum can result in position errors of hundreds of meters. Different nations and agencies use different datums as the basis for coordinate systems used to identify positions in geographic information systems, precise positioning systems, and navigation systems. The diversity of datums in use today and the technological advancements that have made possible global positioning measurements with sub-meter accuracies requires careful datum selection and careful conversion between coordinates in different datums. Slide30: The Figure of the Earth Geodetic datums and the coordinate reference systems based on them were developed to describe geographic positions for surveying, mapping, and navigation. Through a long history, the "figure of the earth" was refined from flat-earth models to spherical models of sufficient accuracy to allow global exploration, navigation and mapping. True geodetic datums were employed only after the late 1700s when measurements showed that the earth was ellipsoidal in shape. Slide31: Geometric Earth Models Early ideas of the figure of the earth resulted in descriptions of the earth as an oyster (The Babylonians before 3000 B.C.), a rectangular box, a circular disk, a cylindrical column, a spherical ball, and a very round pear (Columbus in the last years of his life). Flat earth models are still used for plane surveying, over distances short enough so that earth curvature is insignificant (less than 10 kms). Spherical earth models represent the shape of the earth with a sphere of a specified radius. Spherical earth models are often used for short range navigation (VOR-DME) and for global distance approximations. Spherical models fail to model the actual shape of the earth. The slight flattening of the earth at the poles results in about a twenty kilometer difference at the poles between an average spherical radius and the measured polar radius of the earth. Ellipsoidal earth models are required for accurate range and bearing calculations over long distances. Loran-C, and GPS navigation receivers use ellipsoidal earth models to compute position and waypoint information. Ellipsoidal models define an ellipsoid with an equatorial radius and a polar radius. The best of these models can represent the shape of the earth over the smoothed, averaged sea-surface to within about one-hundred meters. Slide32: Reference Ellipsoids Reference ellipsoids are usually defined by semi-major (equatorial radius) and flattening (the relationship between equatorial and polar radii). Other reference ellipsoid parameters such as semi-minor axis (polar radius) and eccentricity can computed from these terms. Reference Ellipsoid Parameters Many reference ellipsoids are in use by different nations and agencies. Selected Reference Ellipsoids A More Complete List of Reference Ellipsoids Slide33: Earth Surfaces The earth has a highly irregular and constantly changing surface. Models of the surface of the earth are used in navigation, surveying, and mapping. Topographic and sea-level models attempt to model the physical variations of the surface, while gravity models and geoids are used to represent local variations in gravity that change the local definition of a level surface. Earth Surfaces The topographical surface of the earth is the actual surface of the land and sea at some moment in time. Aircraft navigators have a special interest in maintaining a positive height vector above this surface. Sea level is the average (methods and temporal spans vary) surface of the oceans. Tidal forces and gravity differences from location to location cause even this smoothed surface to vary over the globe by hundreds of meters. Gravity models attempt to describe in detail the variations in the gravity field. The importance of this effort is related to the idea of leveling. Plane and geodetic surveying uses the idea of a plane perpendicular to the gravity surface of the earth, the direction perpendicular to a plumb bob pointing toward the center of mass of the earth. Local variations in gravity, caused by variations in the earth's core and surface materials, cause this gravity surface to be irregular. Slide34: Geoid models attempt to represent the surface of the entire earth over both land and ocean as though the surface resulted from gravity alone. Bomford described this surface as the surface that would exist if the sea was admitted under the land portion of the earth by small frictionless channels. The WGS-84 Geoid defines geoid heights for the entire earth. The U. S. National Imagery and Mapping Agency (formerly the Defense Mapping Agency) publishes a ten by ten degree grid of geoid heights for the WGS-84 geoid. WGS-84 Geoid Heights Slide35: Global Coordinate Systems Coordinate systems to specify locations on the surface of the earth have been used for centuries. In western geodesy the equator, the tropics of Cancer and Capricorn, and then lines of latitude and longitude were used to locate positions on the earth. Eastern cartographers like Phei Hsiu used other rectangular grid systems as early as 270 A. D. Various units of length and angular distance have been used over history. The meter is related to both linear and angular distance, having been defined in the late 18th century as one ten-millionth of the distance from the pole to the equator. Slide36: Latitude, Longitude, and Height The most commonly used coordinate system today is the latitude, longitude, and height system. The Prime Meridian and the Equator are the reference planes used to define latitude and longitude. Equator and Prime Meridian The geodetic latitude (there are many other defined latitudes) of a point is the angle from the equatorial plane to the vertical direction of a line normal to the reference ellipsoid. The geodetic longitude of a point is the angle between a reference plane and a plane passing through the point, both planes being perpendicular to the equatorial plane. The geodetic height at a point is the distance from the reference ellipsoid to the point in a direction normal to the ellipsoid. Geodetic Latitude, Longitude, and Height Slide37: Earth Centered, Earth Fixed X, Y, and Z Earth Centered, Earth Fixed Cartesian coordinates are also used to define three dimensional positions. Earth centered, earth-fixed, X, Y, and Z, Cartesian coordinates (XYZ) define three dimensional positions with respect to the center of mass of the reference ellipsoid. The Z-axis points toward the North Pole. The X-axis is defined by the intersection of the plane defined by the prime meridian and the equatorial plane. The Y-axis completes a right handed orthogonal system by a plane 90° east of the X-axis and its intersection with the equator. ECEF X, Y, and Z Slide38: Geodetic Datums Datum Types Datum types include horizontal, vertical and complete datums. Datums in Use Hundreds of geodetic datums are in use around the world. The Global Positioning system is based on the World Geodetic System 1984 (WGS-84). Parameters for simple XYZ conversion between many datums and WGS-84 are published by the Defense mapping Agency. List of Geodetic Datums Datum Shifts Coordinate values resulting from interpreting latitude, longitude, and height values based on one datum as though they were based in another datum can cause position errors in three dimensions of up to one kilometer. Slide39: Coordinate Systems There are many different coordinate systems, based on a variety of geodetic datums, units, projections, and reference systems in use today. As an example, this overview often uses the position of one of the thousands of geodetic control points in the United States, the star in the hand of the Goddess of Liberty atop the Capitol building in Austin, Texas. The Texas Capitol Building The Star in the Hand of The Goddess of Liberty One Location Described by a Variety of Systems Slide40: Map projections are attempts to portray the surface of the earth or a portion of the earth on a flat surface. Some distortions of conformality, distance, direction, scale, and area always result from this process. Some projections minimize distortions in some of these properties at the expense of maximizing errors in others. Some projections are attempts to only moderately distort all of these properties. Different map projections result in different spatial relationships between regions. Three Different Map Projections of the United States Albers Equal Area and Lambert Conformal Conic Projections of North America Map ProjectionsSlide41: Conformality When the scale of a map at any point on the map is the same in any direction, the projection is conformal. Meridians (lines of longitude) and parallels (lines of latitude) intersect at right angles. Shape is preserved locally on conformal maps. Distance A map is equidistant when it portrays distances from the center of the projection to any other place on the map. Direction A map preserves direction when azimuths (angles from a point on a line to another point) are portrayed correctly in all directions. Scale Scale is the relationship between a distance portrayed on a map and the same distance on the Earth. Area When a map portrays areas over the entire map so that all mapped areas have the same proportional relationship to the areas on the Earth that they represent, the map is an equal-area map. Slide42: Map projections fall into four general classes. Cylindrical projections result from projecting a spherical surface onto a cylinder. When the cylinder is tangent to the sphere contact is along a great circle (the circle formed on the surface of the Earth by a plane passing through the center of the Earth).. Projection of a Sphere onto a Cylinder (Tangent Case) In the secant case, the cylinder touches the sphere along two lines, both small circles (a circle formed on the surface of the Earth by a plane not passing through the center of the Earth). Projection of a Sphere onto a Cylinder (Secant Case) When the cylinder upon which the sphere is projected is at right angles to the poles, the cylinder and resulting projection are transverse. Transverse Projection of a Sphere onto a Cylinder (Tangent Case) When the cylinder is at some other, non-orthogonal, angle with respect to the poles, the cylinder and resulting projection is oblique. Oblique Projection of a Sphere onto a Cylinder (Tangent Case) Slide43: Conic projections result from projecting a spherical surface onto a cone. When the cone is tangent to the sphere contact is along a small circle. Projection of a Sphere onto a Cone (Tangent Case) In the secant case, the cone touches the sphere along two lines, one a great circle, the other a small circle. Projection of a Sphere onto a Cone (Secant Case) Slide44: Azimuthal projections result from projecting a spherical surface onto a plane. When the plane is tangent to the sphere contact is at a single point on the surface of the Earth. Projection of a Sphere onto a Plane (Tangent Case) In the secant case, the plane touches the sphere along a small circle if the plane does not pass through the center of the earth, when it will touch along a great circle. Projection of a Sphere onto a Plane (Secant Case) Miscellaneous projections include unprojected ones such as rectangular latitude and longitude grids and other examples of that do not fall into the cylindrical, conic, or azimuthal categories