A simple method to calibrate hemispherical photographs

Objectives Hemispherical photography is used to characterize the structure of canopies and measure the gap fraction directional variation to retrieve variables such as the leaf area index (LAI), the fAPAR {Jonckheere, 2004 #3541};{Weiss, 2004 #2872}. Optical systems are not perfect and at least two main characteristics are required: • The coordinates of the optical centre • The projection function Because in some situations the focal length may be manipulated by acting on the zoom system, the projection function must be also known for each focal length used. This short paper presents a simple method to characterize these features. Definition of the system An image can be defined by (Figure 1) • The number of pixels in the horizontal direction (Xsize) • The number of pixels in the vertical direction (Ysize) • The coordinates of the optical centre [XO, YO] • The projection function, P, i.e. the function θ=P(R) that relates the view angle θ (relative to optical axis) to the distance to the optical centre R.