Optics and Photonics Journal, 2013, 3, 118-121
doi:10.4236/opj.2013.32B029 Published Online June 2013 (http://www.scirp.org/journal/opj)
Reducing Refractive Index Variations in Compression
Molded Lenses by Annealing
Bo Tao1, Lianguan Shen1, Allen Yi2, Mujun Li1, Jian Zhou1
1Department of Precision Machinery and Precision Instrumentation, University of Science and Technology of China,
Hefei, Anhui, China
2Department of Integrated Systems Engineering, the Ohio State University, Columbus, Ohio, USA
Received 2013
ABSTRACT
Compression molding of glass optics is gradually becoming a viable fabrication technique for high precision optical
lenses. However, refractive index variation was observed in compression molded glass lenses, which would contribute
to image quality degradation. In this research, annealing experiments were applied to control the refractive index varia-
tion in molded glass lenses. The refractive index variations pre and post annealing experiment in molded lenses were
measured by an experiment setup based on Mach-Zehnder interferometer. The experimental results showed that the
refractive index variation can be controlled providing that a proper cooling process is applied during cooling.
Keywords: Refractive Index; Mach-Zehnder Interferometer; Optical; Annealing; Compression Molding
1. Introduction
Compression molding is a thermal forming process for
precision glass optics [1, 2]. However, refractive index
variation was induced in glass during cooling when the
glass material went through its glass transition region
[3-5]. On the other hand, the variation of refractive index
in a molded glass lens will introduce distortion to the
wave-front passing through the glass lens, which leads to
image quality degradation. In order to ensure a proper
optical performance of thermally formed glass lens, it is
important to reduce the degree of refractive index varia-
tion in the molded glass lens.
Annealing has been studied for improving the quality
of glass [6-9]. Through annealing, glass can achieve ho-
mogeneous refractive index. Annealing of the compres-
sion molding of glass lenses was investigated in this re-
search. In order to identify the effects of annealing on
refractive index variations, computer tomography method
was employed to measure the refractive index distribution
in the glass lenses. The measurement was conducted by
using an optical setup based on Mach-Zehnder interfer-
ometer [4, 10]. By comparing experimental results of the
glass lens pre and post annealing, the results showed that
refractive index variation was reduced.
2. Design of Experiments
Glass lenses studied in this research were molded in a
commercial glass molding machine (GMP-211V). Ther-
mal forming was carried out at 684 °C. After forming,
the temperature was maintained until stresses in glass
caused by pressing were completely released. Two steps
cooling process was followed: the glass lens was cooled
to 520 ℃ at a rate of 0.8 ℃/s and then to 200 ℃ at a
rate of 1.6 ℃/s. When the glass lens was cooled to 200
℃, the lens was taken out of the molding machine and
cooled naturally at room temperature. Figure 1 is the
illustration of the glass lens. BK7 was chosen as the glass
material. The properties of BK7 are shown in Table 1.
Figure 1. Illustration of the compression molded glass lens.
Table 1. Properties of BK7 glass [11].
Material Properties BK7
Elastic modulus, E [MPa] 82,500
Poisson’s ratio,  0.206
Transition temperature, Tg [℃] 557
Refractive index, n 1.5148

B. TAO ET AL. 119
2.1. Refractive Index Measurement
Figure 2 shows a schematic of the experiment setup used
to measure the refractive index in glass lenses. To avoid
refraction, tested lens was placed in a box filled with
refractive index matching liquid of BK7. He-Ne laser
was used as the light source. In the experiment setup,
beam splitter 1 divides the laser beam into two. One is
used as reference beam, the other one goes through the
lens under test. These two beams interfere with each
other at beam splitter 2. Fringe pattern carried with re-
fractive index distribution in the lens was captured by a
CCD camera.
Figure 3 is the fringe pattern of the molded glass lens
at one direction. The fringe pattern was analyzed by a 2D
Fourier transform technique [12] and a least-square phase
unwrapping method [13] for unwrapped phase. Because
of the axisymmetric property of the glass lens, it is suffi-
cient to reconstruct the refractive index distribution in the
glass lens through only one fringe pattern. With the un-
wrapped phase, 3 dimensional (3D) refractive index dis-
tribution of the glass lens relative to the refractive index
of matching liquid can be reconstructed using the filtered
back-projection method [14].
(, ,)
(, ,)2 pxyz nxyz d


(1)
Figure 2. Schematic of the experiment setup for refractive
index measurement.
Figure 3. Fringe pattern of the compression molded glass
lens before annealing at one direction.
where, p(x,y,z) is the reconstructed phase distribution at
point (x,y,z), d is the pixel size in the test lens of the in-
terferogram. The reconstructed refractive index in the
middle section of the compression molded lens relative
to the matching liquid is shown in Figure 4.
2.2. Annealing
Annealing experiments were conducted in a commercial
furnace (Grieve, BF-12128-HT). Figure 5 illustrates the
time-temperature history of the annealing experiments.
At first, the molded glass lens was heated to 560 ℃,
slightly higher than the glass’s transition temperature,
and soaked for 10 minutes. After soaking, the glass lens
was cooled to 500 ℃ at a rate of 1 ℃/min. Then the
furnace was turned off. The maximum cooling rate was
about 1.29 ℃/min after turning off the furnace, because
there was no force cooling system. Once the temperature
decreased to 150 ℃, the glass lens was taken out of the
furnace and cooled to room temperature naturally. In the
experiments, the glass lens under thermal treatment was
placed on a ceramic plate in the furnace with the concave
side facing down.
Figure 4. Refractive index distribution of middle section of
the molded glass lens relative to the matching liquid.
Figure 5. Time-temperature history of annealing.

B. TAO ET AL.
120
3. Results and Discussion
Refractive index variations of the molded glass lens pre
and post annealing were both measured. Figure 6 shows
the average refractive index variations in the middle sec-
tion of the glass lens along radial direction pre and post
annealing experiment. The maximum refractive index
variation was reduced about 4 × 10-4 which was more
than half of the maximum variation before annealing.
The relations between refractive index n and density

of the glass material can be described by Lorentz–Lorenz
equation [15]:
2
2
14
3 2


A
N n
M
n

 
(2)
where NA is the Avogadro number, α is the mean polari-
zation and M is the molar weight. Differentiating Equa-
tion (2), the relations between refractive index change dn
and density change d  can be obtained by:
22
(1)( 2
6


dn nn
dn 
)
(3)
Substituting volume for the density, refractive index
change Δn can be calculated from the volume change
 V
and the original volume Vo:
22
0
(1)( 2)
6


 


nn V
nnV

V
(4)
After annealing, residual stresses inside the glass lens
were released. Values of the coefficient of thermal ex-
pansion (CTE) of the glass lens were different at differ-
ent cooling rates due to the behavior of structural relaxa-
tion when the glass went through its glass transition re-
gion. As such, the volume change was imported by both
stresses relaxation and the changes of CTE [16]:
Figure 6. Comparison of the refractive index variations in a
molded glass lens pre and post annealing.
Figure 7. Residual stresses in the glass lens pre and post
annealing in cylindrical coordinate.


11 2233
33
12()
 








oh c
o
VV
VE


(5)
where, and .
2
1
()T
hh
TTdT

1
2
()T
cc
TTdT

αh and αc are CTE during heating and cooling, respec-
tively. T1 is room temperature and T2 is soaking tem-
perature.
 is Poisson’s ratio and E is elastic modulus. 
11,

22 and

33 are the changes of normal stresses along the
axes.
The residual stresses inside the glass lens can be
measured by a circular polariscope based on the property
of birefringence when the glass is stressed [17-19]. The
maximum residual stress in the compression molded
glass lens was about 3 Mpa in cylindrical coordinate
system. Figure 7 shows residual stresses in the middle
section of the glass lens pre and post annealing. The re-
sidual stresses were significantly released after annealing.
Substituting the maximum changes of residual stresses, E
and v of the glass lens into Equation (5), the volume
change induced by stress relaxation can be calculated,
 V
= 6  10-5 Vo. The maximum refractive index change
induced by stresses relaxation was 4  10-5.
Therefore the refractive index change was mainly
caused by the changes of CTE. Basically, slower cooling
rates yield lower volumes. In order to get lower refrac-
tive index variation, lower cooling rate should be ap-
plied.
4. Conclusions
Refractive index variations in compression molded glass
lenses were investigated using an experiment setup. The
refractive index variation was induced during the cooling
due to structural relaxation of the glass material. Conse-

B. TAO ET AL.
121
quently the refractive index variation in the glass lens can
induce wave-front distortion. To control the refractive
index variation, annealing of the glass lenses were con-
ducted and the results demonstrated that the refractive
index variations were significantly reduced. This re-
search demonstrated that CTE played a critical role in
process optimization for precision compression molded
glass optics.
5. Acknowledgements
The material is partially based on work supported by
National Science Foundation under Grants No. CMMI
0547311. Any opinions, findings, and conclusions or
recommendations expressed in this material are those of
the authors and do not necessarily reflect the views of the
National Science Foundation. The work is also supported
by National Natural Science Foundation of China (No.
51075381). Bo Tao acknowledges the financial support
from China Scholarship Council.
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