Background

Diffraction Gratings

Any object that is either very small or has a very sharp edge is capable of diffracting light, and any repetitive array of these objects is known as a diffraction grating. A replica of such a diffraction grating was used to calibrate the TEM; that particular replica is shown at the right. In the figure, the parallel ridges are evenly spaced, and for that reason they were used as a length standard during the calibration of the TEM. 2,160 ridges like the ones shown are contained in one millimeter of this replica.

Latex Beads

The dark circles shown in the figure are latex beads. At high magnifications, the spacing between adjacent ridges is larger than the available image size, so the beads, which are smaller, can be used to determine distance in the image. These latex beads had an average diameter or 0.261 microns.

Catalase Crystals and Fourier Analysis

Consider the image of a catalase crystal shown below. Note that the crystal is regular, which means that the spacing between adjacent crystals can be used as a length standard.

Now consider the image at the lower right. This is the Fourier transform of the crystal image. The spacing between the amplitude maxima is equal to the reciprocal of the spacing between the crystals in the real image; notice that it is easier to measure distances in the Fourier-transformed space than in real space. For this reason, measurements were taken in Fourier space and then converted to actual dimensions. The dimensions of the catalase crystals displayed in the analysis section were calculated using this Fourier transform method.

Catalase Crystal	Fourier Transform

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