Accurate image distortion correction in high magnification imaging systems

For decades, experimentalists seeking improved understanding of basic solid and fluid systems have employed photographic imaging. Today, digital storage has replaced film, and contemporary processing and computer vision can rapidly convert images into accurate full-field measurements of shape, deformation, and/or velocity. Digital image correlation (DIC), one of the most common approaches, tracks images of a region that bear a characteristic random pattern. DIC has been used to measure surface strains with point-to-point accuracy of 1× 10⁻⁴ on structures ranging in size from millimeters to several meters. However, extension to the nano and micro scales has met with limited success due to distortion in high magnification image systems such as the atomic force microscope (AFM) and scanning electron microscope (SEM)).

Our work has shown that AFM and SEM images are distorted due to both time-dependent effects (drift distortion) and position-dependent effects (spatial distortion). They cannot be modeled adequately using parametric models common to light optics systems. We have therefore constructed an approach incorporating a new model that identifies and removes both types of distortion.

General spatial distortion correction—the procedure will work in all types of imaging systems—employs a non-parametric approach.¹ The effect of spatial distortions at each location is extracted using simple translations of the object. Similarly, general drift distortion is extracted from sequential images of an untranslated specimen. For motions due to image distortions, methods have been developed to apply a random pattern to specimen surfaces as small as 50nm.²

Figure 1. Scanning electron microscope images of Au thin films patterned on aluminum and silicon substrates at 120°C.

Our procedures for general image distortion correction procedures provide ease of use in high magnification imaging applications.^3,4 Figure 2 presents a schematic of the process. To correct for drift distortion, pairs of images of the specimen are first acquired without imposing additional change in position. To correct for spatial distortions, small translations are performed and pairs of images are acquired before and after each translation. The set of images consisting of pairs from the translation sequence and from the actual experiment represents the basic data required to correct for distortions and extract accurate measurements.

Figure 2. Schematic of the overall process for correcting images and extracting deformation fields using high magnification images.

DIC and image processing are employed once the experment is complete. DIC is used to locate the position of each subset so that the image motion can be determined and used to correct for both drift and spatial distortion.

Figure 3. Measured horizontal and vertical spatial distortion fields in an FEI Quanta-200 SEM at 10,000×.

Figure 4. Measured horizontal and vertical drift distortion fields after 30 minutes of imaging in an FEI Quanta- 200 SEM at 10,000×.

Figure 5. Measured axial strain (ε_xx· 10⁻⁶) with and without distortion corrections.

Typical drift and spatial distortions obtained using images acquired at 10000× magnification in an FEI Quanta SEM are shown in Figures 3 and 4. For a simple uniaxial tension experiment performed in an SEM, a comparison between uncorrected and corrected results, shown in Figure 4, confirms the importance of correcting for distortions when attempting to extract material parameters such as the elastic modulus.

Modern digital image correlation methods for rapid sub-pixel pattern matching have been combined with novel image correction algorithms to develop a simple and effective approach for full-field deformation measurements at high magnification using either SEM or AFM for imaging. These methods have been shown to be effective in reducing strain variability by nearly two orders of magnitude, providing scientists and engineers with the ability to accurately measure deformations at the micro and nano scales. Issues yet to be addressed include the presence of embedded image shifts during SEM imaging that could affect accuracy when extending method to 50000× or higher, and, in addition, the presence of noise in AFM images that may require feedback control or other approaches to reduce effects.

The support of the National Science Foundation, NASA Langley Research Center, Intel Corporation, and the University of South Carolina Research Foundation are gratefully acknowledged.