U N I T
9
PHOTOGRAMMETRY
Richard Burns, PLS Caltrans Geometronics
Introduction The Manual of Photogrammetry defines photogrammetry as, “the art, science, and technology of obtaining reliable information about physical objects and the environment through processes of recording, measuring, and interpreting photographic images and patterns of electromagnetic radiant energy and other phenomena.” Land surveyors are primarily concerned with the photogrammetric applications involving aerial photography used for topographic mapping, including the ground location of physical objects, lines and points, and the determination of earthwork quantities. The Land Surveyors Act includes within the definition of surveying practice the determination of the “configuration or contour of the earth’s surface or the position of fixed objects thereon” by photogrammetric methods. Land surveyors must be able to use the basic principles of photogrammetry necessary for flight and ground control planning to ensure that photogrammetric projects will meet National Map Accuracy Standards or other project-specific standards.
Caltrans LS/LSIT Video Exam Preparation Course
Performance Expected on the Exams Change scales given as a ratio to scales given in ft per in. Explain the
difference between large- and small-scale mapping.
Calculate the flying height necessary for a given photo scale.
Explain the concept of C-factor.
State National Map Accuracy Standards.
Given required mapping scale, contour interval, and project limits, determine
the most efficient flight plan and ground control net for a photogrammetric
project.
Key Terms Focal length
Neat model
Fiducial marks
Overlap
Negative format
Sidelap
Photo scale
Ground control
Map scale
Premark
Contour interval
Flight line
Large scale
Crab
Small scale
Stereovision
Ratio scale
Block
Flight height
Halation
C-factor
Spot elevations
Terrain height
Plannimetrics
Datum height
Areotriangulation
Base sheets
Photo identification
National Map Accuracy Standards
9-2
Photogrammetry
Video Presentation Outline Photography • Cameras • Focal length
f = 6'
Terrain
f = 12'
Datum Scale: 1' = 250' 9' x 9' Photograph
Scale: 1' = 125' 9' x 9' Photograph
Figure 9-1. Relation of focal length to area coverage.
• Aerial photographs
9-3
Caltrans LS/LSIT Video Exam Preparation Course
Scale • Expression of scale 1 in = 250 ft or 1:3000 • Large scale/small scale
1 in = 100 ft (Smaller Scale) 1:1200
1 in = 50 ft (Larger Scale) 1:600 Figure 9-2. Large scale/small scale.
f d H -h H
D
Terrain h Datum
Figure 9-3. Determining photo scale.
9-4
Photogrammetry
• Basic formulas S =
f H-h
Where: S = scale given as in/ft or as a ratio f = focal length of camera as in or as ft if scale is given as ratio H = flying height above datum as ft h = average terrain elevation as ft S = d D Where: S = scale given as in/ft d = distance on photograph as in D = corresponding distance on ground as ft For ft per in S =
f = d H-h D
= 1 x
Where: x = ft/in on photograph • C-factor C-factor =
H-h C.I.
Where: H = flying height above datum h = average terrain elevation C.I. = contour interval • Flying tolerances
9-5
Caltrans LS/LSIT Video Exam Preparation Course
Models • Overlap
3.6' Flight Line
5.4' 1-4
1-3 Figure 9-4. Overlap of two successive photos.
•
Sidelap
Flight 2.7'
Line
1-2
Flight Line
6.3' 1-8
Figure 9-5. Sidelap of two flight lines.
9-6
Photogrammetry
• Neat model 1-9-92
1:3000 06-FRE-168 8-1
1:3000 06-FRE-168 8-2
7'
1-9-92
3.6'
Flight Line
Figure 9-6. Relationship of neat model to successive photos.
• Flight line and models Flight Line 1-6
1-5
1-4
1-3
1-2
1-1
Figure 9-7. Flight line and neat models.
• Blocks
9-7
Caltrans LS/LSIT Video Exam Preparation Course
Photo Control • Neat model (fully controlled)
Horizontal and Vertical Control Point Vertical Control Point
Figure 9-8. Control for neat model.
9-8
Photogrammetry
• Aerotriangulation
Premark with Horizontal and Vertical Control
Premark with Vertical Control
Pug with Horizontal and Vertical Control
Figure 9-9. Neat models with control.
Figure 9-10. Two flight lines with control.
9-9
Caltrans LS/LSIT Video Exam Preparation Course
• Premarks
Quick Reference Table for Planning of Photogrammetric Mapping
Plotting Scale/C.I.
1 in = 50 ft 2 ft
Photo Scale
1 in = 250 ft
1 in = 500 ft
1 in = 1000 ft
1 in = 2000 ft
Nominal. Will vary with relief.
Flying Height
1500 ft
3000 ft
6000 ft
12000 ft
Above average ground elevation.
Max. Range of Relief/Flight Line
300 ft
700 ft
1400 ft
2800 ft
For mapping area – exceptions can be made if more relief outside mapping area but within photocoverage, special instructions to photographer necessary.
Nominal Mapping Width/Flight Line
1400 ft
3000 ft
6000 ft
12000 ft
Nominal - may be reduced 15% - 20% with maximum relief range. May be extended after aerial photography is received.
Length of One Model
900 ft
1800 ft
3600 ft
7200 ft
Nominal with 60% forelap, will vary with relief.
No. Models/Mile
6
3
1.5
.75
Approximate, for estimating purposes.
Horizontal Control Premark Size
cloth or painted replica
cloth or painted replica with extensions
cross premark 12 ft x 1 ft
cross premark 24 ft x 2 ft
Horizontal Control Premark Interval
see control diagram
see control diagram
planned for specific projects
planned for specific projects
For aerotriangulation.
Vertical Control Premark Interval
see control diagram
see control diagram
planned for specific projects
planned for specific projects
For aerotriangulation.
Supplemental Horizontal Control Accuracy
3rd order
3rd order
3rd order
3rd order
Project Horizontal Control Accuracy
2nd order
2nd order
2nd order
2nd order
Supplemental Vertical Control Accuracy
0.1 ft
0.2 ft
0.5 ft
1.0 ft
Project Vertical Control Accuracy
2nd order
2nd order
3rd order
3rd order
9-10
1 in = 100 ft 5 ft
1 in = 200 ft 10 ft
1 in = 400 ft 20 ft
Comments
Bl ac k
A
Photogrammetry
D
C
E B NOTE: This is Not Part of Cloth Target
A
B
White
Cloth Premark or Painted Replica Photo Scale
Cross
Premark
1 in = 250 ft
1 in = 500 ft
1 in = 1000 ft
1 in = 2000 ft
A
45 in
45 in
12 ft
24 ft
B
4 in
4 in
1 ft
2 ft
C
7 in
7 in
D
Not Required
24 in
E
Not Required
6 in
Figure 9-11. Sizing premarks.
9-11
Caltrans LS/LSIT Video Exam Preparation Course
National Map Accuracy Standards* • “Photogrammetry for Highways Committee, 1968” Contours: 90% of elevations determined from solid line
contours must be within 1/2 contour interval (C.I.) and all within 1 C.I.
Spot elevations: 90% of spot elevations must be within 1/4 C.I. and all
within 1/2 C.I.
Planimetric Features: 90% of well defined features must be within 1/40 in and all within 1/20 in. • “Office of Management and Budget” Horizontal accuracy: Maps with publication scales larger than 1:20,000 can have no more than 10% of well defined points with an error of more that 1/30 in as measured on the publication scale; for maps with a publication scale of 1:20,000 or smaller 1/50 in. Vertical accuracy: No more than 10% of elevations tested can be in error by more that 1/2 C.I.
Mapping • Instruments • Base sheets
Steps to Completion of a Photogrammetric Project 1. Determination of mapping limits 2. Select scale and contour interval 3. Plan flight 4. Plan the ground control 5. Place premarks 6. Survey premarks 7. Aerial photography 8. Survey calculations 9. Check aerial photography 10. Aerotriangulation *Manual of Photogrammetry, 4th Ed., American Society of Photogrammetry, 1980, page 372.
9-12
Photogrammetry
11. Base sheets 12. Map compilation 13. Map checking 14. Map corrections 15. Map acceptance
Example Problem Problem A-3 1991 LS Your client owns Sections 9 and 16, and the westerly 4000 ft of Sections 10 and 15, T4S, R23W, S.B.M. You have been asked to provide horizontal and vertical control for the topographic mapping that is to be used for planning purposes. Vertical photography, taken with a 6-in focal length camera on a 9-in x 9-in focal plane, is to be used. Analytical bridging is not to be considered. The following factors control the project. Make no assumptions. 1. A 5-ft contour interval is required. 2. Model size is 3.6 x 7.0 in for a single flight line and 3.6 x 6.3 in for two or more adjacent flight lines. 3. The C-factor to be used for this project is 1,800 ft. 4. The map is to be compiled at a 5 to 1 ratio. 5. The average terrain elevation is 2,500 ft above sea level. 6. The minimum target size to be used for premarking the ground is not to be less than 0.001 x 0.01 in at the photo scale. 7. Per a recent Record of Survey, each section has been found to be standard dimensions. Required: 1. Based on the above specifications, determine the following. Show all work. A. The minimum number of flight lines required. B. The required flying height above sea level. C. The minimum number of models required. D. The minimum number of photographs required.
9-13
Caltrans LS/LSIT Video Exam Preparation Course
E. The minimum number of horizontal and vertical control stations required to provide for adequate checks. F. The negative scale. G. The nominal map scale. H. The minimum length and width of the target placed on the ground as a premark. 2. Give the accuracy requirements for each of the following based on requirements of the National Map Accuracy Standards: A. Contours B. Spot elevations C. Planimetric features Solution: 1. A. Minimum number of flight lines required = 1 Overall length = 10,560 ft Overall width = 9,280 in Model length = 5,400 ft Model width = 10,500 ft
9,280 ft
= 0.88 = 1 10,500 ft B. Flying height above sea level = 11,500 ft
C-factor x C.I. + elevation
1800 ft x 5 ft + 2,500 ft = 11,500 ft
C. Minimum number of models required = 2
Terrain width ÷ model length = 10,560 ft ÷ 5,400 - 1.96 = 2
D. Minimum number of photographs required = 3
Photos required = models + flight lines
2 models + 1 flight line = 3
E. Minimum number of horizontal control stations required = 4
Minimum number of vertical control stations required = 6
Control for scale/model = 2 + 1 for check
Control for elev./model = 3 + 1 for check
9-14
Photogrammetry
F. Negative scale = 1,500 ft C-factor x C.I. ÷ 6 (1800 ft x 5 ft) ÷ 6 = 1500 ft or 1:18,000 G. Nominal map scale = 1 in = 300 ft Mapping scale = (Photo scale) (Ratio) Photo scale = flying/focal length Photo scale = (9,000/6) (1/5) = 300 H. Minimum length (180 in is acceptable) = 15.0 ft = 1500 x 0.01 ft Minimum width (18 in is acceptable) = 1.5 ft = 1500 x 0.001 ft 2. A.
Accuracy = 90% Value = ±1/2 C.I. or Accuracy = not more than 10% exceed Value = ±2.50 ft
B.
Accuracy = 90% Value = ±1/4 C.I. or Accuracy = not more than 10% exceed Value = ±1.25 ft
C.
Accuracy = 90% of features Value = ±1/30 @ map scale or Accuracy = not more than 10% exceed Value = ±10 ft
9-15
Caltrans LS/LSIT Video Exam Preparation Course
Sample Test Questions The following questions are from Problem A-1 1988 LS You are asked by your client to prepare a topographic map for his proposed project. He tells you that he will use this map to design a subdivision (including grading plans and street plans). He also states that he wants this map at a scale of 1 in = 40 ft with a 1-ft C.I. and spot elevations to supplement contours when the contour lines are more than 2 in apart. Project site is 217 acres more or less, being a parcel 2700 ft north-south by 3500 ft east-west. Terrain: moderate relief. The photo control for this mapping project will be established by field surveys. Camera to be used for obtaining the mapping photography is equipped with a 6-in focal length lens and a 9-in x 9-in format (negative size). The map accuracy must comply with the U.S. Map Accuracy Standards. Required: Circle the correct answer.
1. U.S. Map Accuracy Standards are as follows: A. 90% of the contours shall be ±1/4 C.I. B. 90% of the spot elevations should be within 1/2 C.I. C. 80% of the spot elevations should be within 1/4 C.I. D. 90% of the spot elevations should be within 1/4 C.I. 2. The C-factor for a mapping system is determined by: A. Camera, aircraft, photo lab equipment, and stereo plotting equipment. B. Ground control, flying height, camera, and photo lab equipment. C. Flying height, weather, relief displacement, and camera. D. Stereo plotter operator, camera, ground control, and airplane altitude.
9-16
Photogrammetry
3. It was determined that a mapping system with a C-factor of 1500 will be used in the above project. This system is considered: A. B. C. D.
A first order system A second order system A third order system A fourth order system
4. What is the altitude from which the photography must be obtained? A. B. C. D.
4200 ft ASL (above sea level) 3000 ft AGL (above ground level) 1500 ft AGL 1500 ft ASL
5. The scale of the photography is: A. B. C. D.
1 in = 200 ft 1:3000 1 in = 100 ft 1:1500
6. The enlargement ratio from photography to final map is: A. B. C. D.
10 40 7.50 6.25
Assume for the following questions that the flight path is east-west. 7. How many photographs will be required to obtain complete stereoscopic coverage of the area? A. B. C. D.
10 8 11 7
8. How many models will be required to map the parcel? A. B. C. D.
10 8 11 7
9-17
Caltrans LS/LSIT Video Exam Preparation Course
9. How many control points will be required to fully control the mapping photography? A. B. C. D.
10 4 15 18
10. How many flight lines will be required? A. B. C. D.
1 2 3 4
The following questions are from Problem B-5 1989 LS Your client has requested that you provide a topographic map of the Jackson landfill by photogrammetric methods. In so doing, you are required to use the following criteria and equipment. • The map must fit on a single mylar sheet with borders as specified in the diagram below. • The common engineering map scale that allows the entire project to be compiled at the maximum size that will fit on the specified single sheet. • The camera focal length is 6 in; the film format is 9 x 9 in. • The plotter has 9-in x 9-in diapositive plate carriers and a C-factor of 2000, as shown in the diagram below. • A forward photo overlap of 60% and a sidelap of 30% or an accepted common practice are required. • The terrain varies from 1500 ft to 2100 ft above sea level. • The C.I. is 1 ft. 42'
1'
1'
9-18
30'
Compiled
Map
Area
3'
1'
Photogrammetry
N 7,000 E 11,000 N 6,500 E 9,000 N 6,000 E 8,000
N 6,100 E 10,700
Area to be Mapped
JACKSON LANDFILL N 5,500 E 8,000
N 5,700 E 9,500 N 5,000 E 10,500
N 5,500 E 11,500
9' 6'
Diapositive (Negative)
12' to 30' (Variable)
Compilation Surface
Determine the following: 11. Usable map sheet dimensions. 12. East-west, north-south limits (length and width) of area to be mapped. 13. Maximum flying height above average terrain. 14. Flying height above sea level. 15. Photo scale. 16. Compilation scale that will fit on one map sheet (see diagram) and be drawn in one of the following common engineering scales (10, 20, 30, 40, 50, 60, 100). 17. Definition of the “neat model.” 18. Dimensions of the “neat model.” 19. Number of models required to map the given area
9-19
Caltrans LS/LSIT Video Exam Preparation Course
The following questions are from Problem A-3, 1992, LS The following are intended to measure your knowledge of basic photogrammetry. Keep answers short, to the point, and in the correct sequence. Required: 20. What is the scale of vertical photography if taken with a 6-in focal-length camera at an altitude of 4,500 ft above mean terrain? 21. What is the absolute minimum number of exposures required for a single flight line? 22. What is the minimum number of horizontal stations required to control a single model? Explain. 23. What is the minimum number of vertical stations required to control a single model? Explain. 24. Define a “neat model.” 25. The mean elevation of the terrain being mapped is 1,600 ft above sea level (ASL). Vertical photography is taken with a 6-in focal-length camera at an ASL elevation of 4,000 ft. What is the nominal map scale utilizing an 8 to 1 plotting ratio?
Answer Key Problem A-1, 1988 LS 1. D 2. A is the best answer. Aircraft is a questionable term for a list that should include: camera, film, photo lab, plotting equipment, and operator. 3. A 4. C 5. B 6. D 7. A 8. B 9 D 10. B
9-20
Photogrammetry
Problem B-5, 1989, LS 11. Available dimension is the sheet size less the border dimensions. Therefore: North-south = 30 in - (2 x 1 in ) = 28 in East-west = 42 in - (1 in + 3 in) = 38 in 12. Area to be mapped is the east-west and north-south limits. North-south = 7000 - 5000 = 2000 East-west = 11500 - 8000 = 3500 13. Flying height above average terrain must be maximun height for maximum coverage that will not exceed the C-factor of the plotter. Maximum height = C-factor x contour interval = 2000 ft x 1 = 2000 ft 14. Flying height above sea level is the flying height plus the elevation of average terrain above sea level. highest elevation + lowest elevation 2 = 2100 ft + 1500 ft 2 = 1800 ft
Avg. terrain elevation =
Flying height above sea level = Flying height + elevation of average terrain = 2000 ft + 1800 ft = 3800 ft above sea level 15. Photo scale for maximum coverage camera focal length Photo scale = flying height = 6 in = 0.5 ft 2000 ft 2000 ft = 1:4000 or 1 in = 333.3 ft
9-21
Caltrans LS/LSIT Video Exam Preparation Course
16. Final mapping scale may vary depending on the projection distance set off in the plotter. The variation is related to photo scale divided by projection ratio; for plotters capable of ratios between 2 and 5. Mapping scale = 333 - 166 ft to 333 = 67 ft 2 5 The most appropriate listed common scale is required; therefore, final mapping scale is 1 in = 100 ft. 17. A “neat model” is the maximum compiling limits of a single stereo model. 18. Dimensions of the neat model are based on the forward and sidelaps relative to the flight line. (Note: Either A or B are acceptable solutions.) A. Common text reference Forward = (1 - overlap) x photo scale x photo width = (1 - .60) x 9 in x 333.3 ft = 1199 ft Sidelap = (1 - .3) x 9 in x 333.3 ft = 2089 ft Neat model = 1199 ft x 2089 ft 6.3 in x 3.6 in B. Common practice Forward = (1 - overlap) x photo scale x photo width = (1 - .60) 9 in x 333.3 ft = 1199 ft Sidelap = (1 - .222) 9 in x 333.3 ft = 2333 ft Neat model = 1199 ft x 2333 ft, 7 in x 3.6 ft 19. The required number of models is based on the neat model dimensions related to the dimension of the area to be mapped. If the flight line runs east-west, then:
9-22
Width
Length
Width is adequate for a single strip
Neat model 8a or 8b
1199 ft
Models required =
Area to map 2000 ft
3500 ft
3500 = 2.9 or 3 models 1199
Photogrammetry
Problem A-3, 1992 LS 20. S =
f H-h
1 in = 750 ft or 4,500 ft = 750 ft , 6 in 1 in
1
9,000
1 in = 750 ft,
6 in = 1
4,500 ft 9,000
21. The total number of models plus one. or A minimum of two exposures. 22. A. Two or three B. Two points are required to establish scale. or Two points are required to establish scale plus one additional point for check. 23. A. Three or four B. Any three points not in a straight line are required to establish a plane. or Any three points not in a straight line are required to establish a plane plus one additional point for check. 24. Examples of acceptable answers are: • The stereoscopic area between adjacent principal points and extending out sideways in both directions to the middle of the sidelap. (The mapping area of each stereopair.) • 3.6 x 7 in • 3.6 x 6.8 in 25.
4,000 - 1,600 = 2,400 2,400 = 400 6
400
= 50 8 Answer: 1 in = 50 ft or 1:600
9-23
Caltrans LS/LSIT Video Exam Preparation Course
References _________, Manual of Photogrammetry, Fourth Edition, American Society of Photogrammetry, Falls Church, VA, 1980. Moffitt, Francis H., and Mikhail, Photogrammetry, Third Edition,
International Textbook Co., Scranton, PA 1980.
Wolf, Paul R., Elements of Photogrammetry, McGraw Hill, New York, NY, 1983.
9-24