6.4 Complex Methodology for Reverse Engineering …
565
This parameter is usually determined solely by the quality of the lens used. In
order to assess the quality of a lens, the criterion of the modulation transfer function
(MTF) is used. MTF is the relationship between the contrast in an object image and
the spatial frequency. The contrast in the image in this case can be determined from
the expression:
E =
E max − E min
/
E max + E min
where E max and E min are the maximum and minimum illumination of the image
elements.
During photography, contrast of the image is reduced due to aberrations, diffractions, and errors in the production of optics and lens mechanics. As the spatial
frequency increases, the contrast decreases until the image finally becomes gray,
and even the difference between black and white stripes cannot be seen. Modulation
transfer function allows for a continuous check of resolution and contrast.
Moreover, it is possible to use another formula, in which the contrast B is determined by the relationship of the difference between the brightness of the observation
object B 1 and the background B 2 to one of these brightness values:
B = (B 1 − B 2 )/B
When the object has the absolute contrast, then B − 1; in case of its absence (the
object merges with the background) B = 0 (Fig. 6.41).
Another method of increasing the quality of image processing, which allows for a
more successful topology analysis, is the brightness alignment between frames. Not
only correct group alignment of frames, but also uniformity of illumination of each
frame and the minimum difference between frame brightness values influence the
successful analysis of topology of IC chips. In order to eliminate the effect of frame
brightness difference, the brightness alignment procedure is used. Automatic global
and local brightness alignment is used to eliminate brightness and color differences
between the aligned images.
Figure 6.42 shows a mosaic composed of nine source fragments without brightness
alignment and after performance of this procedure [10].
Global alignment brings luminance and color characteristics of individual images
to a certain reference value. Both brightness and color array of separate images and
their average value can be used as such reference.
Local alignment aligns brightness and color characteristics along the lines of
conditional cuts. Its effect is gradually reduced from the borders of the section to
the center of images. Combination of global and local alignment, as well as the
possibility of smoothing the alignment lines make it possible to obtain a visually
uniform mosaic (Fig. 6.42).
Just as important is the accuracy of aligning two adjacent topology fragments
(Fig. 6.43).
As practice shows, the value of the alignment error for accurate interpretation of
IC chip topologies shall not exceed half of the observed object width. Therefore, it is
565
This parameter is usually determined solely by the quality of the lens used. In
order to assess the quality of a lens, the criterion of the modulation transfer function
(MTF) is used. MTF is the relationship between the contrast in an object image and
the spatial frequency. The contrast in the image in this case can be determined from
the expression:
E =
E max − E min
/
E max + E min
where E max and E min are the maximum and minimum illumination of the image
elements.
During photography, contrast of the image is reduced due to aberrations, diffractions, and errors in the production of optics and lens mechanics. As the spatial
frequency increases, the contrast decreases until the image finally becomes gray,
and even the difference between black and white stripes cannot be seen. Modulation
transfer function allows for a continuous check of resolution and contrast.
Moreover, it is possible to use another formula, in which the contrast B is determined by the relationship of the difference between the brightness of the observation
object B 1 and the background B 2 to one of these brightness values:
B = (B 1 − B 2 )/B
When the object has the absolute contrast, then B − 1; in case of its absence (the
object merges with the background) B = 0 (Fig. 6.41).
Another method of increasing the quality of image processing, which allows for a
more successful topology analysis, is the brightness alignment between frames. Not
only correct group alignment of frames, but also uniformity of illumination of each
frame and the minimum difference between frame brightness values influence the
successful analysis of topology of IC chips. In order to eliminate the effect of frame
brightness difference, the brightness alignment procedure is used. Automatic global
and local brightness alignment is used to eliminate brightness and color differences
between the aligned images.
Figure 6.42 shows a mosaic composed of nine source fragments without brightness
alignment and after performance of this procedure [10].
Global alignment brings luminance and color characteristics of individual images
to a certain reference value. Both brightness and color array of separate images and
their average value can be used as such reference.
Local alignment aligns brightness and color characteristics along the lines of
conditional cuts. Its effect is gradually reduced from the borders of the section to
the center of images. Combination of global and local alignment, as well as the
possibility of smoothing the alignment lines make it possible to obtain a visually
uniform mosaic (Fig. 6.42).
Just as important is the accuracy of aligning two adjacent topology fragments
(Fig. 6.43).
As practice shows, the value of the alignment error for accurate interpretation of
IC chip topologies shall not exceed half of the observed object width. Therefore, it is