Additivity constraints and visual task considerations in mesopic photometry

It has been recently suggested that a mesopic photometry based on off-axis reaction times would be superior to one based on large-field brightness matching because the former exhibits Abney's law of additivity and the latter does not. We show that additivity is not a requirement for mesopic photometry and that no mesopic luminance function that transitions between scotopic and photopic sensitivity can satisfy the requirements for additivity. A comparison of the proposed reaction time and mesopic brightness matching functions shows that they can be surprisingly similar. This suggests that a broadly based mesopic photometry may be possible. We provide a closed-form expression for off-axis mesopic luminance efficacies that depends only on the photopic luminance and the scotopic/photopic ratio.