In this paper, we present a novel approach that addresses the blind reconstruction problem in scanning electron microscope (SEM) photometric stereo. Using only two observed images that suffer from shadowing effects, our method automatically calibrates the parameter and resolves shadowing errors for estimating an accurate three-dimensional (3D) shape and underlying shadowless images. We introduce a novel shadowing compensation model using image intensities for both cases of presence and absence of shadowing. With this model, the proposed de-shadowing algorithm iteratively compensates for image intensities and modifies the corresponding 3D surface. Besides de-shadowing, we introduce a practically useful self-calibration criterion by enforcing a good reconstruction. We show that incorrect parameters will engender significant distortions of 3D reconstructions in shadowed regions during the de-shadowing procedure. This motivated us to design the self-calibration criterion by utilizing shadowing to pursue the proper parameter that produces the best reconstruction with least distortions. As a result, we develop a bootstrapping approach for simultaneous de-shadowing and self-calibration in SEM photometric stereo. Extensive experiments on real image data demonstrate the effectiveness of our method.

Deshan CHEN†a) , Nonmember, Atsushi MIYAMOTO † †b) , and Shun'ichi KANEKO †c) , Members SUMMARY This paper describes a robust three-dimensional (3D) surface reconstruction method that can automatically eliminate shadowing errors. For modeling shadowing effect, a new shadowing compensation model based on the angle distribution of backscattered electrons is introduced. Further, it is modified with respect to some practical factors. Moreover, the proposed iterative shadowing compensation method, which performs commutatively between the compensation of image intensities and the modification of the corresponding 3D surface, can effectively provide both an accurate 3D surface and compensated shadowless images after convergence. key words: scanning electron microscope (SEM), surface reconstruction, shadowing compensation, backscattering electron IntroductionThe scanning electron microscope (SEM) is a very important tool for observing micro-structure and has been widely used in the areas of medical observation, semiconductors, material analysis, etc. The need for three-dimensional (3D) surface measurements is significantly increasing. For instance, 3D surface information can provide valuable clues for inspecting and analyzing defects in products of semiconductor manufacturing processes, such as recognition of device patterns and defect regions, classification of defects in terms of the processes responsible for their generation (surface/embedded defects [1]) and the impact on electric properties (volume or shorting/disconnection defect), and specification and control of the issue process, etc.Attempts have been made to transform SEM into a 3D measuring tool for almost 30 years, and scientific research on 3D surface reconstruction in SEM continues to be intensively studied. Different approaches, which can be broadly classified into two groups, have been utilized. One popular group is generally referred to as the "stereometric" method [2]- [4], in which a pair of stereo images of a specimen at different inclination angles are taken, and the height or depth is determined by measuring the deviations of corresponding points on the two images. However, this method can only be applied to the measurements of surface points Manuscript received November 20, 2012. Manuscript revised April 19, 2013. † The authors are with the Graduate School of Information Science and Technology, Hokkaido University, Sapporo-shi, 060-0814 Japan.† † The author is with the Yokohama Research Laboratory, Hitachi, Ltd., Yokohama-shi, 244-0817 Japan.a) E-mail: chen@ssc.ssi.ist.hokudai.ac.jp b) E-mail: atsushi.miyamoto.ts@hitachi.com c) E-mail: kaneko@ssi.ist.hokudai.ac. where recognizable fine structures exist. In general, it cannot be used on smooth surfaces or to reconstruct a continuous surface profile at high magnification. The second group of approaches is the so-called "shape from shading" or "photometric stereo" method [5]- [10], in which multiple secondary or backscattered electron detectors (generally two or four) are symmetrically positioned a...

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