Self-calibrated global rainbow refractometry:
a dual-wavelength approach
Xuecheng Wu (吴学成)
1,
*, Haoyu Jiang (姜淏予)
1
, Kailin Cao (操凯霖)
1
,
Yingchun Wu (吴迎春)
1,2
, Can Li (李 灿)
1
, Gérard Gréhan
2
, Sawitree Saengkaew
2
,
and Kefa Cen (岑可法)
1
1
State Key Lab of Clean Energy Utilization, Zhejiang University, Hangzhou 310027, China
2
CNRS UMR 6614/CORIA, Saint Etienne du Rouvray BP12 76801, France
*Corresponding author: wuxch@zju.edu.cn
Received November 24, 2016; accepted January 13, 2017; posted online February 14, 2017
Calibration of the relationship between the scattering angle and the CCD pixel is a key part of achieving accurate
measurements of rainbow refractometry. A novel self-calibrated global rainbow refractometry system based on
illumination by two lasers of different wavelengths is proposed. The angular calibration and refractive index
measurement of two wavelengths can be completed simultaneously without extra measurement devices.
The numerical and experimental results show the feasibility and high precision of the self-calibration method,
which enables the rainbow refractometry to be implemented in a more powerful and convenient way. The
self-calibrated rainbow system is successfully applied to measure the refractive indices of ethanol-water solutions
with volume concentrations of 10% to 60%.
OCIS codes: 290.5820, 120.4820, 120.6780, 290.5820, 290.3030.
doi: 10.3788/COL201715.042902.
Liquid atomization and spray have a broad range of ap-
plications in energy, chemical, and many other industrial
fields. Accurate measurements and control of the key
parameters of droplets in the complex atomization or a
spray flow field play an instructive role in mechanism
studies of multiphase flows and in the optimization of spe-
cific industrial processes. Among the advanced optical
measurement techniques
[1–4]
for characterizing droplets,
rainbow refractometry
[5–7]
has been shown to be a powerful
tool for its advantages in simultaneously measuring the
size/size distribution (individual droplet/polydispersed
droplet cloud) and refractive index. Thereafter, the tem-
perature
[8]
, concentration
[9]
, solution components
[10]
, and
other characterization parameters can be determined on
the basis of prior knowledge of their relationships with
the measured refractive index.
By analyzing the distribution of scattered light around
the primary rainbow angle, the rainbow technique extracts
the absolute angular location and fits the shape of the
rainbow pattern to the inverse of the refractive index
and the droplet size. Roth et al.
[11]
first presented the stan-
dard rainbow technique (SRT) to measure a single spheri-
cal droplet or individual monodispersed droplets in a line.
Later, Van Beeck et al.
[12–14]
improved the SRT to the global
rainbow technique (GRT) for measuring spray droplets.
GRT employs a larger-sized pinhole and longer exposure
time of the CCD camera than SRT to get the superposition
of the rainbows from numerous droplets that are illumi-
nated by a laser. This superposition of rainbows suppresses
the effects of the non-sphericity of the droplets and
eliminates the high-frequency ripple component of the
rainbow signals to obtain a steady and smooth Airy
rainbow structure. Recently, Wu et al.
[15]
proposed a
one-dimensional rainbow technique (ORT-1) that ex-
tended a point volume measurement to a one-dimensional
segment measurement by using slit apertures. Then,
Wu et al.
[16]
developed an alternative optical design of
the one-dimensional rainbow technique (ORT-2) which
aims to facilitate the angular calibration in the full image
field by using Fourier domain filtering.
Since the information on the refractive index contained
in the rainbow intensity distribution is highly sensitive to
the scattering angle, precise calibration of the relationship
between the scattering angle (θ) and the CCD pixel (pix) is
the key part of guaranteeing the measurement accuracy.
One of the calibration methods involves acquiring global
rainbow images of a set of sprays with known tempera-
tures
[17]
, but it is susceptible to environmental perturba-
tions, such as tempe rature changes. The calibration
process usually involves rotating a mirror mounted in
the measurement volume
[18,19]
, which we call the mirror
calibration method. However, errors caused by manual
operation and additional precision instruments are
unavoidable in the mirror calibration method. When it
comes to harsh industrial environments, such as sprays
in containers, the calibration of the mirror in inaccessible
occasions represents a challenge. To solve the problem,
we propose a self-calibration method based on dual-
wavelength lasers for global rainbow refractometry. This
method enables us to calibrate the scattering angle along
with the refractive index measurement under two wave-
length illuminations.
As the material’s natural property, the refractive index
changes with the wavelength of light, while other condi-
tions remain the same. The refractive indices of common
liquids, such as water and alcohol, decrease with the
COL 15(4), 042902(2017) CHINESE OPTICS LETTERS April 10, 2017
1671-7694/2017/042902(5) 042902-1 © 2017 Chinese Optics Letters