Introduction
Several types of microscopes are available for studying and analyzing the surfaces of coated papers. The most common microscopes are optical microscopes which can give a 2-dimensional resolution of approximately 1 micron. The primary advantages of the optical microscope are its ease of use and low cost. For higher resolution imaging, less than 1 micron, a scanning electron microscope (SEM) is typically used. The SEM can resolve surface features as small as a few nanometers. However, the SEM does not give high contrast images on flat samples, requires a vacuum, and often requires substantial sample preparation. The most common type of sample preparation is sputter coating a metal on the surface, which can cause the surface topography of the sample that will be imaged to change. Most recently the Atomic Force Microscope (AFM) is being applied for imaging the surfaces of coated papers. Advantages of the AFM are that it directly gives 3- Dimensional magnification, works in ambient air, requires no sample preparation, and the AFM has a resolution at the nanometer scale. In an AFM a very fine stylus is scanned over a surface in a raster pattern. By monitoring the motion of the stylus, a 3-Dimensional image of the surface can be created. Images may be displayed in 2-Dimensional or 3-Dimensional representations. Further, line profiles can be extracted from the image. The height and width of surface features are measured from line profiles.  Figure 1: Left - 2-Dimensional image of the surface of a commercially available photo quality inkjet paper. The scan size is 30 microns and the scale indicates the height of the features on the paper's surface. Right: Line profile showing the width of one of the pores in the paper. Central to the AFM is a force sensor that measures the force between the stylus and the surface. Typically, the force sensor design is based on a light lever. In the light lever a laser beam is reflected off the backside of a cantilever into a two-section photo-detector. (Figure 2) On the bottom side of the cantilever is a stylus. Interactions between the stylus and the surface cause the cantilever to bend and the reflected light to move across the photo-detector. In this type of AFM force sensor, the cantilever is typically 40 microns wide, 100 microns long, and less than a micron thick. With such a small cantilever, forces as low as a nano-newton (10-9 Newtons) are measurable with the light lever force sensor. Thus, very small probes, less than 50 nm, can be used in the AFM and not be broken by interactions with a surface.  Figure 2: Illustration of a light lever force sensor used in atomic force microscope. The laser is reflected from the cantilever into a two-section photo-detector. The horizontal resolution in an AFM depends on the geometry of the probe and the type of sample being analyzed. On very smooth surfaces only the very end of the probe interacts with the surface and the resolution of the image depends only on the probe diameter. If the specimen has large features, more of the probe than the very end interacts with the surface and the image resolution depends on the macroscopic geometry of the probe. (Figure 3)  Figure 3: Left - On a smooth surface only the very end of the probe interacts with the surface. Right - On a rough surface more of the probe interacts with the surface and the resolution depends on more than the probe diameter.
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