The main objective of this study is to evaluate whether vignetting curves determined for a specific lens mounted on a particular camera can be used by other researchers using identical photographic material (that is, the same brand and model).
Some secondary objectives of this study are to check the radial symmetry of the lens vignetting, the noninfluence of the reflectance of the targets on the determined vignetting effect, and, finally, to verify the mapping function of the fisheye lens.
To achieve these aims, the vignetting characteristics of four similar devices (lens + camera) are determined in a field of 180 degrees, on the basis of gray and white targets, using HDR imaging techniques.
As a result of some pre-tests, this interval was reduced, at the center and the periphery of the arc, to 2.5 degrees, in order to improve the precision of the obtained vignetting curve.
As the vignetting effect is a function of the lens aperture width [Inanici 2006; Jacobs and Wilson 2007], all the possible apertures of CAM#1FE#1 and CAM#2FE#2 were studied.
In their study, Goldman and Chen showed that the intensity of the vignetting effect depends on some lens settings: the focal length, the aperture, and the lens focus [Goldman and Chen 2005].
In order to analyze the vignetting effect, HDR pictures were firstly created, for each aperture and each device, on the basis of the series of low dynamic range (LDR) pictures taken in the mirror box.
In addition to the determination of these vignetting functions, this experiment and its setup were an opportunity to check the projection formula given by the manufacturer, as the targets were arranged at known intervals.
The vignetting effect was determined, for each square, as the ratio between the luminance extracted from the calibrated HDR picture and the physical luminance measured with the luminance meter:
where [??] is the vignetting effect at [theta] = i[degrees], is the luminance measured at [theta] = i[degrees] with the luminance meter and weighted according to horizontal illuminance, and [??] is the luminance captured with the camera at [theta] = i[degrees] and calibrated.