A differential pair of convergent and divergent lenses with adjustable lens spacing (“differential lens”) was devised as a varifocal lens and was successfully integrated into an object-space telecentric lens to build a focus mechanism with constant magnification. This integration was done by placing the front principal point of the varifocal lens at the rear focal point of the telecentric lens within a practical tolerance of positioning. Although the constant-magnification focus mechanism is a parallel projection system, a system for perfect perspective projection imaging without shifting the projection center during focusing could be built simply by properly setting this focus mechanism between an image-taking lens with image-space telecentricity and an image sensor. The focus resolution experimentally obtained was 0.92 µm (σ) for the parallel projection system with a depth range of 1.0 mm and this was 0.25 mm (σ) for the perspective projection system with a range from 120 to 350 mm within a desktop space. A marginal image resolution of 100 lp/mm was obtained with optical distortion of less than 0.2% in the parallel projection system. The differential lens could work up to 55 Hz for a sinusoidal change in lens spacing with a peak-to-valley amplitude of 425 µm when a tiny divergent lens that was plano-concave was translated by a piezoelectric positioner. Therefore, images that were entirely in focus were generated at a frame rate of 30 Hz for an object moving at a speed of around 150 mm/s in depth within the desk top space. Thus, three-dimensional (3-D) imaging that provided 3-D resolution based on fast focusing was accomplished in both microscopic and macroscopic spaces.

In this paper, we describe a novel focusing mechanism that uses a varifocal mirror and its application to measuring the shape of solder bumps arrayed on an LSI package board based on the shape-from-focus technique. We used a copper-alloy mirror deformed by a piezoelectric actuator as a varifocal mirror to build a simple yet fast focusing mechanism. The varifocal mirror was situated at the focal point of the image-taking lens in image space so that the lateral magnification was constant during focusing and an orthographic projection was perfectly established. The focused plane could be shifted along the optical axis with a precision of 1.4 µm in a depth range of 1.3 mm by driving the varifocal mirror. A magnification of 1.97 was maintained during focusing. Evaluating the curvature of field and removing its effect from the depth data reduced errors. The shapes of 208 solder bumps, 260 µm high and arrayed at a pitch of 500 µm on the board, were measured. The entire 10 mm10 mm board was segmented into 34 partly overlapping sections. We captured 101 images in each section with a high-resolution camera at different focal points at 15 µm intervals. The shape of almost the entire upper hemisphere of a solder bump could be measured. The error in measuring the bump heights was less than 12 µm.