1. Definition
Remember parallax? When using a telescoped instrument, parallax occurs when the sighted object and crosshairs don't come to exact foucs on the back of the observer's eye, Figure E1. Moving the head slightly will cause one image to move across the other.
(a) Initial sight 
(b) Eye slightly shifted sideways 
Figure E1 Parallax 
We don't want parallax when using a telescope because it causes sighting error BUT in stereophotography, parallax helps us determine point distances. Parallax is the amount a point moves between two photos.
Figure E2 shows two points at different elevations appearing on two successive photos.
Figure E2 Successive Photos 
The parallax for each point can be compared by overlaying the photos, Figure E3.
Figure E3 Parallax Distances 
From Figures E2 and E3 it is apparent that parallax is:
 a measurable quantity
 related to elevation: the higher the point, the larger its parallax.
Since parallax can be measured, elevations can be determined provided sufficient support information is available.
2. Measuring Parallax
There are two ways to measure parallax depending on object type and accuracy: monoscopic and stereoscopic.
a. Monoscopic
Parallax direction is parallel with the flight direction. Since the photo x axis is in the direction of flight, parallax can be computed from x coordinates, Figure E4 and Equation E1.
Figure E4 Parallax Direction 
The coordinate system should be based on the flight path since the images shift in that direction (see Chapter D Section 4 of this topic). However unless there is severe course change between photos, using the fiducial system on both photos should be sufficient for most surveying applications.
To visualize parallax distances, Figure E5 shows the left and right images of points a and b on a single diagram.
Figure E5 Parallax determination 
Equation E1 
In order to use the monoscopic method, the image point(s) must be distinct on both photographs. Is is extremely difficult, if not impossible, to determine parallax for points in open fields, on water, etc. For those and similar situations, the stereoscopic method must be used.
b. Stereoscopic
In the stereoscopic method parallax is measured in the 3D view using a floating mark. A floating mark is an artificial object added to both photos so it appears in the 3D view. As the two marks are moved closer together or further apart, it will appear to float higher or lower in the model.
Figure E6 shows two floating marks on a stereogram.

In the 3D view, they appear at different elevations because of their different parallaxes.
The floating marks are etched on glass plates attached to a measurement scale which allows their spacing to be changed. The device is called a parallax bar, Figure E7.
Figure E7 Parallax Bar 
The glass plates are placed on the images, Figure E8, and their spacing adjusted until the floating mark "sits" on the object in the 3D model. That places the individual marks at correct parallax distance for the elevation.
Figure E8 Using a Parallax Bar 
The parallax distance is determined using Equation E2.
Equation E2  
C: Parallax bar constant 
The constant is determined by using Equation E1 to determine the parallax of a point, then measuring it with the parallax bar, Equation E3.
Equation E3 
The advantage of a parallax bar it it can be used on indistinct as well as distinct points.
3. Parallax Equations
a. Ground Coordinates
The ground coordinate system is similar to that of a single vertical photo. The origin and axes directions are defined by the left photo, Figure E9, using the actual flight direction.
Figure E9 Ground Coordinate System 
Coordinates and elevation of ground points can be determined from parallax measurements using equations E4 through E6.
Equation E4  
Equation E5  
Equation E6 
b. Elevations by Parallax
Figure E10 shows the basic parallax and elevation geometry for two points.
Figure E10 Parallax and Elevation Difference 
If we can measure the parallax of both points, we can determine one point's elevation based on the other, Equation E7.
Equation E7 
4. Examples
Example 1
Two vertical control points appear on adjacent aerial photographs. Photography flying height is unknown although it is needed for later computations. The elevation and and x coordinate on each photo for the points are:
Point  Elev (ft)  x (mm)  x' (mm) 
T34  882.53  60.922  35.909 
M60  849.93  29.538  66.379 
Determine the flying height.
Solution
Compute parallax for both points
Rearrange Equation E8 to solve flying height
H = 4.30x10^{3} ft
Example 2
A telecommunication tower appears on overlapping photographs. Coordinates of its top and bottom are:
Left  Right  
Point  x, mm  y, mm  x, mm  y, mm 
Bottom  23.84  15.61  12.41  15.62 
Top  29.75  47.85  18.23  47.89 
The terrain is generally flat and elevation at the tower base 1125 ft. The flying height was 3550 ft and camera focal length 152.44 mm. What is the tower height?
Solution
Compute parallax for tower top and bottom
Use Equation E7 but don't add the tower's base elevation.
Elev = 590 ft