Aberration analysis of the putative projector for Lorenzo Lotto's Husband and wife: Image analysis through computer ray-tracing

摘要

A recent theory claims that the late-Italian Renaissance painter Lorenzo Lotto secretly built a concave-mirror projector to project an image of a carpet onto his canvas and trace it during the execution of Husband and wife (c. 1543). Key evidence adduced to support this claim includes "perspective anomalies" and changes in "magnification" that the theory's proponents ascribe to Lotto refocusing his projector to overcome its limitations in depth of field. We find, though, that there are important geometrical constraints upon such a putative optical projector not incorporated into the proponents' analyses, and that when properly included, the argument for the use of optics loses its force. We used Zemax optical design software to create a simple model of Lotto's studio and putative projector, and incorporated the optical properties proponents inferred from geometrical properties of the depicted carpet. Our central contribution derives from including the 116-cm-wide canvas screen; we found that this screen forces the incident light to strike the concave mirror at large angles (≥ 15°) and that this, in turn, means that the projected image would reveal severe off-axis aberrations, particularly astigmatism. Such aberrations are roughly as severe as the defocus blur claimed to have led Lotto to refocus the projector. In short, we find that the projected images would not have gone in and out of focus in the way claimed by proponents, a result that undercuts their claim that Lotto used a projector for this painting. We speculate on the value of further uses of sophisticated ray-tracing analyses in the study of fine arts.