Abstract

Extended depth of field (EDoF) imaging remains desirable in the consumer market due to its reduced cost through omission of refocusing hardware. This paper describes the study of a heated plastic plate and its effect on EDoF imaging. It is shown that the depth of field of an imaging device can be extended by heating either the periphery or core of a homogeneous element—solving the heat equation for a parallel plate generates a radial gradient index structure, which can be modeled in Zemax ray-tracing software. For an $F/2$ system with the dimensions of a typical mobile-device camera, the heating arrangement shifts the peak value of the modulation transfer function (MTF) at Nyquist/2 from object distance 1350 to 750 mm. This study suggests the possibility of a fixed-focus camera with distinct modes: a “high-quality” mode operational over the standard depth of field when the plate is not heated; a “macro” mode triggered by heating the plate periphery; and a “wide-focus” mode triggered by heating the lens core. Importantly, the reduction in MTF generally associated with EDoF solutions is not present when the plate is unheated. The plate, having no optical power when unheated, can be added to existing off-the-shelf lens designs. Such a heating arrangement could provide a very-low-cost refocusing alternative where moving parts are not desirable.

© 2018 Optical Society of America