Analysis

Length measurements obtainable with the TEM were calibrated using a replica of a diffraction grating with 2,160 lines per millimeter. An image of this replica was taken at several magnifications and the distance between adjacent ridges was measured in pixels using the NIH Image software. (High magnification measurements were taken using the Fourier transform of a catalase crystal.) Results are displayed in the graph below.

As shown above, the distance per pixel varies linearly with the reciprocal of the magnification. To see this more clearly, consider the following graph.

Pixel Size vs. 1/Magnification

To summarize this data quantitatively, the above results are also included in the table below.

Magnification	Pixel Size (nm)	95% confidence
500x	34.42	0.06
660x	26.72	0.08
870x	20.51	0.04
1150x	15.66	0.04
1500x	11.72	0.02
1500xLM	12.32	0.02
2000x	8.99	0.03
2750x	6.70	0.05
3800x	4.82	0.03
5000x	3.63	0.02
6600x	2.85	0.02
8800x	2.15	0.02
11500x	1.58	0.03
15000x	1.34	0.06
20000x	1.00	0.03
27500x	0.74	0.02
38000x	0.55	0.02
50000x	0.41	0.01
66000x	0.31	0.01

Again, the pixel size varies linearly with the reciprocal of the magnification. The 95% confidence level is equal to twice the standard deviation between measurements of the same image; 95% of all measurements made at a given magnification will deviate less than this amount from the pixel value quoted.

This table is also intended as a calibration table for the TEM. At any of the magnifications shown, measurements made in pixels can be converted to distance in nanometers using the data provided here.

Catalase Crystal Calibration Check

To confirm the accuracy of the above data, the pixel length was measured using a beef liver catalase crystal as a length standard instead of a diffraction grating replica. This catalase crystal was imaged at most of the higher magnifications. The left image below shows the 38,000x image.


Catalase Crystal	Fourier Transform

Next, the two-dimensional Fourier transform of the crystal image was taken using NIH Image's FFT function. The transformed image is shown at the right of the crystal image. In the transformed image, the distance between consecutive intensity maxima is the reciprocal of the distance between consecutive molecules in the crystal image.

To obtain the distance between crystals, the spacing between adjacent maxima in Fourier space was measured in 1/pixels using NIH Image software. This number was normalized by dividing by the size of the sample used in the FFT, compared with the actual distance of 206 angstroms, and then averaged with several other measurements.

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