GELE Photogrammetry & Cartography — Aerial Photography and Camera GeometrySummary

The focal length is the perpendicular distance from the camera lens's optical center to the focal plane (where the image is formed on the film or sensor). For metric aerial cameras used in professional surveying, focal length is precisely calibrated and certified. Typical values range from 88 mm to 610 mm, with 152 mm being common for general surveying and 210 mm for large-area coverage. The focal length is a fundamental constant determined during camera calibration and remains unchanged during a flight mission.

Flying height is the vertical distance from the aircraft to the ground surface being photographed. It is measured above the mean ground elevation of the survey area, not above sea level or mean sea level (this is a critical distinction often tested in PRC exams). For terrain with significant relief, use the average ground elevation. Flying height is typically expressed in meters and is selected based on the desired photo scale and ground coverage. If the aircraft altitude above sea level is known, subtract the mean ground elevation to obtain H for scale calculations.

Photo scale is the ratio of a linear distance on the photograph to the corresponding ground distance. It is expressed as a fraction (e.g., 1/10,000 means one unit on the photo represents 10,000 units on the ground). The fundamental formula is: Scale = f/H, where f is focal length and H is flying height above the terrain. This simple proportion arises from the similar-triangle relationship in the optical projection. For example, at f = 152 mm and H = 1,520 m (1,520,000 mm), Scale = 152/1,520,000 = 1/10,000. Photo scale is ALWAYS LESS THAN 1 (photo is smaller than reality). On terrain with variable elevation, the scale varies; average scale uses mean ground elevation.

Once photo scale is known, any linear measurement on the photo can be converted to ground distance using: Ground Distance = Photo Distance × Scale Denominator. For example, if two points are 45 mm apart on a 1/10,000 scale photo, the ground distance = 45 mm × 10,000 = 450,000 mm = 450 m. This conversion is straightforward multiplication by the scale denominator (the 'S' in 1/S notation). Careful unit consistency is essential: if measuring in mm on the photo, result will be in mm on the ground; conversion to meters requires dividing by 1,000.

The camera format is the physical size of the negative or image frame, typically square (e.g., 230 mm × 230 mm for standard metric aerial cameras). The ground coverage of a single photo is determined by: Ground Side = Photo Format × Scale Denominator, and Ground Area = (Photo Format × Scale Denominator)². For a 230 mm × 230 mm format at scale 1/10,000: Ground Side = 0.230 m × 10,000 = 2,300 m = 2.3 km, and Ground Area = (2.3 km)² = 5.29 km² = 529 hectares. Understanding ground coverage is essential for flight planning and determining how many photos are needed to cover a survey area.

The principal point (principal place/principal plane point) is the point where the optical axis of the camera intersects the photograph (image plane). For a perfectly vertical photograph, the principal point and nadir (the ground point directly below the camera) project to the same location on the photo. The principal point is typically marked on metric aerial photos and is determined during camera calibration. Its precise location (coordinates relative to the fiducial marks) is essential for accurate photogrammetric computations in stereophotogrammetry and orthophoto production.

A vertical photograph is taken with the camera axis perpendicular to the ground surface (or as nearly perpendicular as possible from an aircraft). This chapter focuses exclusively on vertical photography, which has a simple, straightforward geometric model (similar triangles). Oblique photography (camera tilted at an angle) has more complex geometry, variable scale across the image, and is less commonly used for metric surveying, though it appears in some reconnaissance or specialized applications. Vertical photography is the standard for professional surveying in the Philippines.

To achieve complete stereo coverage and ensure no gaps in the survey area, successive photographs along a flight line must overlap (forward overlap, typically 60%), and adjacent flight lines must overlap laterally (sidelap, typically 30%). Forward overlap is the longitudinal overlap along the flight direction; sidelap is the overlap between adjacent parallel flight lines. At 60% forward overlap, 40% of each photo is 'new' ground, so the air-base (ground distance between consecutive exposures) = 0.40 × Ground Side. For a 2,300 m ground side at 60% forward overlap: Air-Base = 0.40 × 2,300 = 920 m. These overlap percentages ensure continuous stereoscopic viewing and are specified in RA 4374 technical guidelines for professional surveying.

When terrain has significant elevation changes, the flying height H varies relative to different points on the ground. Points on hills are closer to the aircraft (smaller H, larger scale) than points in valleys (larger H, smaller scale). The effective focal length and height relationship becomes: Scale at a point = f/(H + elevation of that point relative to datum). For a survey area with topographic relief, use the average ground elevation for mean scale calculations. High-relief terrain requires careful attention to scale variation, particularly in mountainous regions of the Philippines (Cordillera, Sierra Madre, etc.). This variation is often overlooked but is critical for accurate geodetic work.

A metric aerial camera is a precision instrument designed for surveying and mapping. Key characteristics include: (1) precisely calibrated and certified focal length, (2) stable, flat focal plane, (3) fiducial marks (usually four or eight) to define the image frame and principal point, (4) a shutter that exposes the entire frame nearly simultaneously, (5) lens distortion characterized by known lens distortion parameters (calibration report), (6) temperature and pressure-stable construction to maintain focal length, and (7) precision film or digital sensor. The camera must be certified per PD 1529 and professional standards. Non-metric cameras (e.g., smartphones, consumer DSLRs) lack these characteristics and are unsuitable for professional surveying without additional calibration and control.

When planning an aerial survey for land registration (RA 4374, PD 1529), the geodetic engineer must determine required flying height and photo scale based on cadastral accuracy requirements (typically 1:5,000 to 1:10,000 scale for Philippine applications). Using the camera's focal length, the engineer calculates H = f × S (where S is the desired scale denominator), then determines ground coverage, air-base at 60% forward overlap, flight line spacing at 30% sidelap, and total number of photos required. For a 1,000 ha municipality needing 1/5,000 scale photos with 230 mm format: Ground side = 0.230 × 5,000 = 1,150 m, Area per photo = 1.32 km². Required photos ≈ 1,000 ha / 132 ha ≈ 8 photos (minimum). With 60% overlap, actual photos ≈ 13-15; with sidelap for 2-3 flight lines, total mission ≈ 30-40 photos. This calculation is typical of PRC board exam problems.

For urban mapping projects generating orthophotos for municipalities, accurate photo scale determines both the geometric accuracy of orthophoto products and their utility for planning. At scale 1/5,000, ground objects 1 m apart are approximately 0.2 mm apart on the photo; precise measurement requires careful scale determination. The orthophoto products are then georeferenced to PPCS/UTM coordinates using ground control points, and the photo scale is used to establish the pixel ground sample distance (GSD) in the digital product. A 0.5 m GSD orthophoto at 1:2,000 scale is common for detailed urban planning in Philippine municipalities.

In the Cordillera, Sierra Madre, and Mindanao mountain regions, terrain relief of 500-2,000 m across a survey area is common. A surveyor planning an aerial mission at fixed altitude will experience significant scale variation due to relief. For a 1,500 m altitude flying height above mean terrain elevation of 800 m MSL: points at 1,300 m MSL elevation see H = 1,000 m (scale 1/6,667); points at 200 m elevation see H = 2,100 m (scale 1/13,789). This 2× scale variation is critical for cadastral work. The solution is to use average scale for general coverage or to acquire multiple passes at different altitudes. This relief-scale interaction is a practical concern in many Philippine projects and a frequent examination topic.

After typhoons, earthquakes, or floods, rapid aerial photography is used to assess damage and plan relief operations. A quick calculation of ground coverage is essential: with f = 152 mm at H = 1,200 m (scale 1/7,895), ground coverage ≈ 1,817 m side, area ≈ 330 ha. For a barangay of 2,000 ha, approximately 6 photos are needed for initial reconnaissance. At 60% overlap with air-base = 727 m, a single flight line takes ≈ 1 hour. This rapid calculation supports emergency response coordination and is a practical skill for geodetic engineers in the Philippines.

For large land subdivisions requiring documentation per CA 141 (Public Land Act), aerial photographs provide evidence of development and boundary locations. A 1/5,000 scale photo showing 0.1 ha lot sizes (approximately 31 m × 31 m) with visibility of roads, utilities, and topographic features is standard. The surveyor converts photo measurements to ground coordinates using the scale, then surveys ground control points to register the photo to PPCS/UTM coordinates. Precise scale knowledge ensures lot boundary locations are accurate for registration.

The Department of Environment and Natural Resources (DENR) uses aerial photographs for forest inventory and land cover mapping. At 1/10,000 scale, forest stand boundaries visible on photos correspond to ground features ≥2-3 m resolution. Ground coverage of 529 ha per photo (230 mm format) allows efficient sampling of large forest blocks in Sierra Madre, Palawan, and Mindanao. Combining photo interpretation with ground-truth measurements provides cost-effective inventory data for sustainable resource management.

The Department of Agriculture uses aerial photos for agricultural land classification and productivity assessment. Scale 1/5,000 to 1/10,000 is typical, allowing identification of crop types, irrigation patterns, and soil conditions. Ground control points tied to PPCS reference system enable georeferenced crop maps. Scale determines the minimum mapping unit—at 1/5,000, features <250 m × 250 m (e.g., small rice paddies) become visible and measurable.

Highway departments, electrical utilities, and water resource agencies use aerial photos for route planning and asset mapping. Photo scale of 1/5,000 to 1/10,000 provides sufficient detail for alignment studies, while ground coverage of 529-2,116 ha enables efficient strip surveys along corridors. A 200 km highway corridor might require 400-800 photos; overlap specifications ensure continuous documentation. Georeferencing to PPCS/UTM allows integration with existing infrastructure databases.