Magnification/spatial calibration

Calculation

The width of an image in µm taken with the DSG is
width = 10^((-0.9948 × log(displayed magnification)) + 5.1426)
where displayed magnification is the magnification set on the SEM.

The spatial calibration can either be

calibration in µm/pixel = width in µm / width in pixel

calibration in pixel/µm = width in pixel / width in µm

calibration for commonly used magnifications
displayed magnification	width measured	width extrapolated	640×480		1280×960
displayed magnification	width measured	width extrapolated	µm/pixel	pixel/µm	µm/pixel	pixel/µm
10 000	14.38	14.57	0.02	43.92	0.01	87.84
5000	29.53	29.04	0.05	22.04	0.02	44.08
4000	36.46	36.26	0.06	17.65	0.03	35.30
2000	73.94	72.25	0.11	8.86	0.06	17.72
1000	146.22	143.98	0.22	4.45	0.11	8.89
500	283.28	286.91	0.45	2.23	0.22	4.46
450	316.31	318.61	0.50	2.01	0.25	4.02
400	354.98	358.22	0.56	1.79	0.28	3.57
300	471.04	476.90	1.75	1.34	0.37	2.68
250	562.30	571.73	0.89	1.12	0.45	2.24
200	708.86	713.83	1.12	0.90	0.56	1.79
120	1174.31	1186.54	1.85	0.54	0.93	1.08
100	1412.80	1422.49	2.22	0.45	1.11	0.90
60	2410.53	2364.48	3.69	0.27	1.85	0.54
30	4758.36	4711.82	7.36	0.14	3.68	0.27

getting the width of an image taken at 5000 ×
10^((-0.9948 × log(5000)) + 5.1426) = 29.04 µm

making a scale bar

calculate the length of a scale bar for 2 commonly used image resolutions
image size (pixel)	calibration (pixel/µm)	scale bar (µm)	length of scale bar (pixel)
640×480	640 ÷ 29.04 = 22.04	1	22.04 × 1 = 22.04
1280×960	1280 ÷ 29.04 = 44.08	1	44.08 × 1 = 44.08

a grating replica with 2160 line/mm i.e., a "d" spacing of 0.4629 µm was used for higher magnification and a 1 mm scale with 10 µm divisions for lower magnification
640×480 pixel or 1280×960 pixel images were acquired between 30K and 30 × at 15 KV and working distance setting of 39 mm
- the specimen was rotated to have the grids or division marks aligned with the edge of the image during acquistion and fine tuned afterward in ImageJ
- position of grid bars or division marks were obtained from an average intensity profile using a Matlab peak finding routine by Billauer
- selected area of an image of the grating replica taken at 5000 × and the corresponding average intensity profile with grid bars indicated
- selected area of an image of the 1 mm scale taken at 200 × and the corresponding average intensity profile with division marks indicated
log-log plot of magnification vs image width (physical dimension of the image as calculated using the "d" spacing or the mm scale) to obtain the slope and intercept of the straight line represented by the data