Constant-Magnification Varifocal Mirror and Its Application to Measuring Three-Dimensional (3-D) Shape of Solder Bump

Akira ISHII
Jun MITSUDO

Publication
IEICE TRANSACTIONS on Electronics   Vol.E90-C    No.1    pp.6-11
Publication Date: 2007/01/01
Online ISSN: 1745-1353
DOI: 10.1093/ietele/e90-c.1.6
Print ISSN: 0916-8516
Type of Manuscript: Special Section INVITED PAPER (Special Section on Microoptomechatronics)
Category: 
Keyword: 
varifocal mirror,  constant magnification,  shape from focus,  3-D shape measurement,  solder bump,  

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Summary: 
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.