Biomedical Engineering Reference
In-Depth Information
determine the phase signal in the presence of a DC background and various low-frequency
noises. In contrast, these undesired signals can be effectively avoided by introducing a large
phase bias
Δ
L
PR
, which shifts the interferometric signal to higher spectral frequency.
Once the high-frequency interferogram is acquired, it is processed to extract the phase term
(
Δ
L
PR
1δ
L
NP
1δ
L
DIC
)
[20,22]
, where (
Δ
L
PR
1δ
L
NP
) constitutes a background constant,
and
L
DIC
represents the quantitative OPL gradient of the sample. Meanwhile, the process
also produces a signal intensity image, obtained by summing
I
t
(
k
;
x
,
y
) across the entire
spectral bandwidth at each point on the sample. The image can be interpreted as a very
close approximation of the conventional brightfield (intensity) image, representing the
reflectivity or transmission distribution across the sample.
δ
14.3.2 Characterization of USAF Resolution Target
To demonstrate the performance of the SD-DIC system for surface profiling, we imaged the
chromium (Cr) pattern of a positive USAF resolution target.
Figure 14.2A
shows the
L
DIC
image of Group 7, Element 1, with a clear shadow-cast appearance typical to DIC images.
The DIC contrast is provided by the surface step between the Cr coating and the uncoated
glass substrate. For comparison, the intensity image is shown in
Figure 14.2B
.
Figure 14.4C
and D
shows the cross-sectional profiles from both the DIC and intensity images,
respectively. In the DIC curve, the rising and falling edges are clearly indicated by the
positive and negative peaks. The unequal magnitudes suggest an oblique incident angle
possibly due to slight sample misalignment. The axial resolution of
δ
δ
L
DIC
measurement on
the coated surface is 32 pm. The transverse resolution is 0.95
μ
m, measured as the 10
90%
edge response in the intensity curve.
It is worth noting that the bars appear wider in the DIC image (
Figure 14.4A
) than in the
intensity image (
Figure 14.4B
). This is further shown in
Figure 14.4C and D
, where the
DIC peaks are not precisely located at the middle of the intensity slopes where the
differential signal is expected to be the largest; rather, they shift toward the slope bottom.
Therefore, the separation between the positive and negative DIC peaks is 5.0
μ
m, greater
than the 3.8
μ
m full width at half maximum of the intensity peak (actual bar width 3.9
μ
m).
We note that the 1.2
m discrepancy is a consequence of the drastic contrast in reflectivity
between the glass substrate and the Cr coating. As shown in the inset of
Figure 14.4C
,
where the incident beam covers more glass than coating, the reflected light and its phase
can be dominated by photons reflected from the coating. In terms of phase measurement,
this is equivalent to the situation where the entire incident beam is on the coated area,
hence extending the apparent size of the bar. It should be noted that this dimensional
artifact is a consequence of the decoupling of phase and intensity and therefore is present in
perhaps all quantitative DIC techniques, but will manifest itself only where there is steep
contrast in reflectance or transmittance. Under these conditions, the apparent transverse size
μ
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