Simple calibration of fisheye lenses for hemispherical photography of the forest canopy

Canopy hemispherical photography (HP) is a technology for vegetation surveying that usually employs consumer-oriented devices. Variations on those devices are caused by technological advances and design. These variations, despite providing the potential for more reliable surveying, make the measurements challenging. The knowledge about how to standardize devices output is available, what is missing is a simple and inexpensive methodology to accomplish it. This is needed since the use of consumer-oriented devices creates an expectation of simplicity and affordability. To fill this methodology gap, we developed an easy-to-assemble calibration board of near-zero material cost (simple board) and outlined how to use it to develop device-specific functions: the projection function (fp) and the vignetting function (fv). The former relates view zenith angle (theta) with distance from image center, while fv models the radial decreasing of brightness known as vignetting effect. Explanations are accompanied by tailored R code. Altogether, we call it "the simple method". Three devices were used to test it: a Nikon Coolpix 5700 with a FC-E9 converter (D1), a Nikon D610 with a Nikkor 8 mm fisheye lens (D2), and an iPhone 6 Plus with an Olloclip fisheye converter (D3). The reference data was taken with D1, corrected for vignetting effect with a photometric sphere and reprojected to the standard equidistant projection with a fv developed by Delta-T Devices (www.delta-t.co.uk). The root mean square error (RMSE) of the simple method were 0.55 degrees theta and 0.021 relative radiance (RR) for D1; 1.8 degrees theta and 0.1 RR for D2; and 2.1 degrees theta and 0.066 RR for D3. This level of standardization will help to simplify the classification of canopy gaps, a key processing step in HP. And, if it is broadly adopted, will facilitate comparisons between independent studies and large time series.