TOWARDS A HIGH RESOLUTION VERTICAL SCANNING INTERFEROMETER: APPLICATIONS FOR FLUID-SOLID-MICROBE INTERACTIONS

We present a method for increasing the resolution of vertical scanning interferometer (VSI) measurements of the topography of mineral surfaces. Current methods acquire images with lateral pixel spacing of ~500 nm. While there are methods for acquiring higher resolution images of surfaces, none have the non-destructive character of VSI. This is highly desirable for imaging surfaces in situ and/or involving living organisms.

Our method is based on the use of current VSI methods, but exploiting the addition of a more precise (sub-pixel) sample positioning stage. We acquire multiple overlapping images of the sample surface, offset by sub-pixel spacing offsets. These images, all with the original resolution of the interferometer, are then assembled into a single image with finer pixel spacing. The resulting image is equivalent to a higher resolution, but blurred or defocused image. We apply numerical focusing algorithms to correct the latter problem.

Using synthetic examples, we show that with perfect data (full floating point resolution in three dimensions, and known point spread function), several methods of numerical focusing work well. However, we also recognize that the VSI data fall short of perfection. The basic images from the VSI have very good, but limited, vertical resolution. Because focusing methods involve taking numerical derivatives of the sample surface height, the methods are very sensitive to rounding errors and noise. We find that this will define the limit to which techniques of this sort may be used to increase resolution. We also identify numerical focusing methods that are best for working with VSI data. The methods vary according to the assumptions that are made about the properties of the data or of the desired result. Numerical experimentation with VSI data is used to determine which work best under different circumstances. These tests take the form of numerically defocusing test data, introducing uncertainties characteristic of the VSI system, numerically focusing the data, and comparing the result with the original test data. This is done seeking progressively higher resolution until the method fails to achieve additional improvement.

The new high resolution non-destructive technique has broad applications in various fields, e.g., fluid/solid and fluid/solid/microbe interactions.