Testing the Reciprocity Law in Digital Photography

An experimental and theoretical methodology based on spectroradiometric measures is proposed to test if the reciprocity law is verified in digital photography. Taking into account that the spectral exposure H(λ) is proportional to the spectral radiance Le(λ) of the object and the photosite integration time t of the electronic shutter time and inversely proportional to the f-number N of the zoom-lens, this radiometric law declares that identical values of spectral exposure yield identical responses even if the fnumber N and/or the exposure time t change. Historically, the photochemical materials present some deviations to this law, but it is not clear if this law holds for the image sensors of digital cameras. The test is based on the new concept of the opto-electronic spectral function (OECSF), that is, the empirical relationship between the normalized digital output level of the camera and the spectral exposure obtained by a monochromator set-up. The transition curve that fits the OECSFs in the color channels for our digital image capture device is the sigmoid function with four parameters. Varying exclusively the f-number N, the OECSFs in some irradiance scale exposure series (Le(λ) and N free, t fixed) overlap in any color channel. The same occurs with time scale exposure series (Le(λ) and t free, N fixed) or mixed scale exposure series (Le(λ), N and t free). These results indicate that this radiometric law, unlike in photochemical photography, is verified in digital photography with monochromatic light.