Photogrammetry, Remote Sensing and GPS
Scale of vertical photographs, relief displacement, overlap and number of photographs, parallax heights, remote sensing principles and resolutions, GIS basics, GPS and total station.
Modern surveying uses photographs, satellites and electronic instruments to map large areas quickly.
Aerial photogrammetry
For a vertical photograph taken by a camera of focal length f from flying height H above datum, for ground at elevation h:
- Scale = f/(H − h).
- Relief displacement of a point at height h, radial distance r from the principal point: d = r h/H (displaced away from the centre). It is used to find heights of tall objects.
- Overlap: about 60% forward (along the flight line) and 30% side overlap, so each point appears on at least two photos for stereoscopic viewing.
- Ground coverage of one photo (side L on the ground): L = photo size × (H − h)/f.
- Number of photos ≈ (area)/(net area covered by one photo), with the net area reduced by the overlaps.
- Parallax: heights from the difference in parallax between two photos: Δh = (H − h) Δp/(b + Δp) for photo base b.
Remote sensing
Sensors detect electromagnetic energy reflected or emitted by the Earth.
- Passive (uses sunlight: optical, thermal) and active (sends its own energy: radar, LiDAR).
- Atmospheric windows: wavelengths that pass through the air (visible, near infrared, thermal infrared, microwave).
- Resolutions: spatial (ground size of a pixel), spectral (number and width of bands), radiometric (grey levels, bits), temporal (revisit time).
- Healthy vegetation reflects strongly in the near infrared: NDVI = (NIR − Red)/(NIR + Red).
GIS
A geographic information system stores, analyses and displays spatial data: vector (points, lines, polygons) and raster (grid cells) formats; overlay and buffer analysis.
GPS and total station
- GNSS/GPS finds position from the ranges to at least 4 satellites (3 for position plus 1 for the receiver clock error). Differential GPS (DGPS) and RTK improve accuracy to centimetres.
- Total station: electronic theodolite + EDM (electronic distance measurement), recording data digitally.
Worked example
A camera with f = 150 mm flies 3000 m above datum over ground at 500 m.
- Scale = 0.15/(3000 − 500) = 1/16,667.
Practice
A photograph is taken with f = 152 mm from 2280 m above ground. What is the scale denominator (1 : x)?
Show answer and explanation
Answer: 15000Scale = f/H = 0.152/2280 = 1/15,000.
A tower top appears 60 mm from the principal point on a photo taken from 1500 m above its base; the relief displacement is 4 mm. What is the tower height in m?
Show answer and explanation
Answer: 100h = dH/r = 4 × 1500/60 = 100 m.
A pixel has NIR = 0.5 and Red = 0.1. What is its NDVI? (Give 3 decimal places.)
Show answer and explanation
Answer: 0.667NDVI = 0.4/0.6 = 0.667 (dense healthy vegetation).
What is the minimum number of GPS satellites needed for a 3D position fix with an unknown receiver clock error?
Show answer and explanation
Answer: 4Three unknown coordinates plus the receiver clock bias need four ranges.