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Vertical photography
Reason Mlambo
Lecture outline
 Photographic coordinate System
 Faulty fiducial marks
 Reducing coordinates to the principal point
Photographic
Coordinate
System
 Rectangular coordinates are the most common
type of measurement.
 Measurements can be done directly on
negatives or positives printed on paper, glass,
film, etc.
 Axes are formed by joining opposite fiducial
marks.
 X axis is parallel to the direction of flight.
 Y axis is perpendicular to the x axis.
 Origin of system is the intersection of the
fiducial marks.
 Point is called centre of collimation is very close
to the principal point.
Photographic
Coordinate
System
Photographic
Coordinate
System
 Position of point a is given by its coordinates 𝑥𝑎
and 𝑦𝑎 and b is given by 𝑥𝑏and 𝑦𝑏
 For corner fiducial marks, one of the fiducial
marks is the origin of the 𝑥’, 𝑦’ system
 Coordinates are then reduced to the
conventional system with origin at the principal
point as follows:
𝑥𝑎 = 𝑥𝑎
′
− 𝑥𝑜
𝑦𝑎 = 𝑦𝑎
′ – 𝑦𝑜
 Where: 𝑥𝑜 =
𝑥𝐵
′
+ 𝑥𝐶
′
4
and 𝑦𝑜 =
𝑦𝐷
′
+ 𝑦𝐶
′
4
Faulty Fiducial
Marks
 The amount by which x axis misses the fiducial
marks are 𝑦𝑎 and 𝑦𝑐
 The amount by which y axis misses the fiducial
marks are 𝑥𝑏 and 𝑥𝑑
 Measured x and y fiducial distances are 𝑥𝑚 and
𝑦𝑚
 General expressions for calculating corrected
coordinates 𝑥𝑒
′ and 𝑦𝑒
′ of point e are as follows:
𝑥𝑒
′
= 𝑥𝑒 + 𝑥𝑑 + (𝑥𝑏 + 𝑥𝑑)
𝑦𝑚
2
− 𝑦𝑒
𝑦𝑚
𝑦𝑒
′ = 𝑦𝑒 + 𝑦𝑎 + (𝑦𝑐 − 𝑦𝑎)
𝑥𝑚
2
− 𝑥𝑒
𝑥𝑚
Correcting
Faulty Fiducial
Marks
Reduction of
coordinates to
an origin at the
principal point
 Principal point does not occur at the
intersection of the fiducial lines.
 𝑥𝑜 and𝑦𝑜 actual coordinates of principal point
w.r.t. fiducial axes
 Obtained through calibration
 Coordinates are reduced to the principal axis
system
 For point a, the coordinates are corrected as
follows:
𝑥𝑎
′
= 𝑥𝑎 − 𝑥𝑜
𝑦𝑎
′ = 𝑦𝑎 − 𝑦𝑜
Reduction of
coordinates to
an origin at the
principal point
Corrections
applied
1. Shrinkage and expansion of photographic
films and papers
2. Radial lens distortions
3. Atmospheric refraction
4. Earth curvature

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Lecture_4_Vertical Photography_in_to.pdf

  • 2. Lecture outline  Photographic coordinate System  Faulty fiducial marks  Reducing coordinates to the principal point
  • 3. Photographic Coordinate System  Rectangular coordinates are the most common type of measurement.  Measurements can be done directly on negatives or positives printed on paper, glass, film, etc.  Axes are formed by joining opposite fiducial marks.  X axis is parallel to the direction of flight.  Y axis is perpendicular to the x axis.  Origin of system is the intersection of the fiducial marks.  Point is called centre of collimation is very close to the principal point.
  • 5. Photographic Coordinate System  Position of point a is given by its coordinates 𝑥𝑎 and 𝑦𝑎 and b is given by 𝑥𝑏and 𝑦𝑏  For corner fiducial marks, one of the fiducial marks is the origin of the 𝑥’, 𝑦’ system  Coordinates are then reduced to the conventional system with origin at the principal point as follows: 𝑥𝑎 = 𝑥𝑎 ′ − 𝑥𝑜 𝑦𝑎 = 𝑦𝑎 ′ – 𝑦𝑜  Where: 𝑥𝑜 = 𝑥𝐵 ′ + 𝑥𝐶 ′ 4 and 𝑦𝑜 = 𝑦𝐷 ′ + 𝑦𝐶 ′ 4
  • 6. Faulty Fiducial Marks  The amount by which x axis misses the fiducial marks are 𝑦𝑎 and 𝑦𝑐  The amount by which y axis misses the fiducial marks are 𝑥𝑏 and 𝑥𝑑  Measured x and y fiducial distances are 𝑥𝑚 and 𝑦𝑚  General expressions for calculating corrected coordinates 𝑥𝑒 ′ and 𝑦𝑒 ′ of point e are as follows: 𝑥𝑒 ′ = 𝑥𝑒 + 𝑥𝑑 + (𝑥𝑏 + 𝑥𝑑) 𝑦𝑚 2 − 𝑦𝑒 𝑦𝑚 𝑦𝑒 ′ = 𝑦𝑒 + 𝑦𝑎 + (𝑦𝑐 − 𝑦𝑎) 𝑥𝑚 2 − 𝑥𝑒 𝑥𝑚
  • 8. Reduction of coordinates to an origin at the principal point  Principal point does not occur at the intersection of the fiducial lines.  𝑥𝑜 and𝑦𝑜 actual coordinates of principal point w.r.t. fiducial axes  Obtained through calibration  Coordinates are reduced to the principal axis system  For point a, the coordinates are corrected as follows: 𝑥𝑎 ′ = 𝑥𝑎 − 𝑥𝑜 𝑦𝑎 ′ = 𝑦𝑎 − 𝑦𝑜
  • 9. Reduction of coordinates to an origin at the principal point
  • 10. Corrections applied 1. Shrinkage and expansion of photographic films and papers 2. Radial lens distortions 3. Atmospheric refraction 4. Earth curvature