Biomedical Engineering Reference
In-Depth Information
from each other. One reflector is mounted on a tip-tilt stage to bring the
reflectors parallel. The second reflector is mounted on a translational stage to
adjust the reflector separation. The transmission from the cavity is imaged
on an indium-gallium-arsenide (InGaAs) sensor array with 5
×
magnification
m
2
areas
and an aperture setting the NA to 0.1. With these settings, 12
×
12
µ
m
2
are imaged on the 60
×
128 pixels. The laser wavelength is swept at a rate of 0.5 nm s
−
1
while the
camera captures images at a rate of 30 fps. Images are digitized to 12 bits
(4,096 gray-levels) and transferred to a PC.
These data are transferred to Matlab and fit using several different meth-
ods. There is a trade-off between the accuracy and the speed with which the
data can be fit. A more accurate (noise-resilient) curve fitting method is to fit
the data to resonant line shape given by (6.1), which models a simple resonant
cavity where
×
60
µ
pixels of the sensor array, which has 128
2
t
2
e
jkd
n
i
n
f
T
=
,
(6.1)
1
− r
2
e
−
2
jkd
n
i
and
n
f
are the refractive indices in and beyond the cavity,
t
and
r
are
the transmission and reflection coe
cients, respectively, of the reflectors,
k
is
the wavenumber inside the cavity, and
d
is the reflector separation (Fig. 6.5).
Further image processing subtracts the curvature inherent to the reflectors.
Finally, a surface profile of small height variations on the SiO
2
surface can be
obtained.
6.2.3 Experimental Results
The system sensitivity was tested by imaging etched features on the oxide
surface (Fig. 6.6). The reflector that has a SiO
2
layer on top is used as the
Fig. 6.5.
Resonant curve recorded and fitting to this data using (6.1).
