Design of the instrument
The CCD-LADS includes several main components: a high-power continuous laser
emitter, two CCD cameras, optical filters and fisheye lenses. The laser and
CCD cameras are mounted on tripods and controlled by a laptop. Each
component is portable and on a scale of a few cubic decimetres.
The emitting system of the CCD-LADS is mainly built with a solid continuous
laser emitter. Nd : YAG is used as the solid laser material as the
wavelength of the emitter is 532 nm. The transverse mode is near TEM00. The
M2 factor is less than 2.0 while the divergence of the beam is less than
2.0 mrad. The diameter at the aperture is 3.0 mm. The power of the laser is
1 W. To change the polarisation state of the laser from linear to circular,
a quarter-wave plate was mounted in front of the laser emitter. During the
exposure time (a few minutes) of the image, the circular-polarisation light can
be assumed to be unpolarised.
The receiving system of CCD-LADS has three main parts, the CCD cameras, the
optical filters and the fisheye lenses. The SBIG model STF-8300 CCD imaging
camera, which has the KAF-8300 CCD sensor (ON Semiconductor, Phoenix, AZ,
USA) is used. The area array (17.96 × 13.52 mm) of pixels has
8.3 million (3326 × 2504) effective pixels, while each pixel is a
square 5.4 µm on a side. The exposure time is from 0.1 s to 1 h.
The A/D converter is 16 bit. Due to its outstanding performance, this
product is often used in astronomical measurements and also measurements in
the other research areas (Coenen et al., 2015). The quantum efficiency of the
CCD is about 55 % at 532 nm, while the linearity error is about
10 %. This camera has an air-cooling unit to control the temperature of
CCD.
The fisheye lens (Sigma Corp., Japan) has a 10 mm focus length and a F2.8
aperture. When this lens is used with a Nikon camera, the field of view can
be 180∘. Because of the size of the CCD arrays, when this lens is
used with the STF-8300 camera, the field of view is about 120∘. The
equisolid projection, which means that the solid angle of the object is
directly proportional to the area on the CCD arrays, is used by this lens
(Miyamoto, 1964). The modulation transfer function of the lens shows that,
according to the size of the CCD sensor, the difference of the sensitivities
from the centre to the corner is less than 5 %
(http://www.sigma-photo.co.jp/english/lens/wide/10_28/#/data).
To filter out the background noise from the sky radiation, an optical filter
(Thorlabs, Newton, NJ, USA) is mounted between the CCD camera and the lens.
The filter has a 532 ± 2 nm wavelength, and a 10 ± 2 nm full
width at half maximum, while the minimum transmission at the peak is
70 %.
Figure 1a is the sketch map of the geometric relationship of CCD-LADS. The
laser is emitted horizontally, while a beam trap is used to receive the laser
beam on the other side. Besides the laser beam, two CCD cameras with fisheye
lenses are installed at the same altitude with the laser to capture the
scattering signal from the laser beam, while the directions of the cameras
are forward and backward. With the mounted lens, there is a one-to-one
correspondence between the image of the laser beam captured by CCDs and the
laser beam object according to the principle of image formation by lenses.
When two CCD cameras are used in this system, the detective angle can be
expanded to 10–170∘. The angle resolution can reach 0.1∘ per
pixel. The scattering signal from 0 to 10 and 170 to 180∘ cannot be
detected, because the signal to noise ratio is significantly lower than the
value needed to estimate the quantities effectively.
Sketch map of the geometric relationship and the sampling image of
CCD-LADS.
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To decrease the total area of the instrument, the distance between the CCD
cameras and the laser beam should be less than 1 m. Therefore the CCD-LADS system
covers an area 12 m long and 1 m wide. When the instrument is set up, the
first step is to measure the relative position of the CCD cameras, the
laser beam and the laser emitter. From the geometric relationship shown in
Fig. 1, we can know that the light scattered at different position on the
laser beam will be collected by different pixels on the CCD, so that the
scattering light at different angles can be retrieved from the image captured
by CCD. Due to the open path structure of the CCD-LADS, the background noise
is much higher in the daytime than at night-time. Currently, the CCD-LADS system
can only estimate the nocturnal aerosol scattering phase function.
Methodology
Data acquisition and preprocessing
The data acquisition of CCD-LADS involves obtaining the angle-resolved
scattering signals from images captured by two independent CCD systems and
then merging the signals. Firstly, the CCD-LADS is set up as shown in
Fig. 1a. The geometric relationships between the CCDs, laser emitter and
light trap are measured by tape. Then the scattering angle of laser in the
image should be calibrated. The direction of the CCD cameras are adjusted to
make sure that the image from the laser goes through the centre of the pixel
arrays of CCD. By using a beam block, the backscattering light is blocked
from going into the CCD and the pixel related to the 90∘ scattering
angle can be referred from the calibrated image (Fig. 1d). Because of the
equisolid projection is used by the lens, the distance from a point on the
image on the CCD to the centre of the pixels can be calculated as R=2f×sinθ/2, where θ is the angle in rad between
a point in the real world and the optical axis, which goes from the centre of
the image through the centre of the lens, f is the focal length of the lens
(Miyamoto, 1964). Therefore, the scattering angle, which is related to the
centre of the image, can be
calculated by introducing the distance between the centre of the pixels and the pixel related to the
90∘ scattering angle in the calibrated
image into the equation of the equisolid projection. In this way,
each pixel on the image of laser will be associated with a scattering angle.
At the beginning of the measurement, the CCDs are cooled down to
-15 ∘C to minimise the noise from dark current. Then a test image
with a 10 s exposure time is captured to fix the exposure time of the
measurement by evaluating the signal intensity of this image. Generally, the
maximum of the signal intensity is tuned to about 214 because the
limitation is 216. If the maximum increased to the limitation in an
image, the exposure time will also be changed in the next image
automatically. The exposure time of these two CCDs that were always about
5–60 s in the past observations and should be in complete accordance for
the comparison. After the test image, a dark frame image is captured for each
CCD by using a shutter in front of the lens. The dark current noise from the
process and transmission of the signal can be subtracted during the procedure
of image configuration by subtracting the dark frame image from the regular
image (Fig. 2a). The images are captured automatically after these steps.
Noise subtraction of CCD-LADS: (a) dark current noise
subtraction, (b) background noise subtraction.
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After the image has been captured, the scattering light of the laser beam is separated
from the background noise in the image as in the following steps. Firstly, the
central axis of the scattering signals of laser beam is fitted in the programme
(the red line shown in Fig. 2b). Then the intensities of image on the
perpendicular of this central axis (the blue line shown in Fig. 2b) are
fitted with a normal distribution:
fx=I0+I×12πσexp-x-μ22σ2,
where I0 is the intensity of the background noise, I is the
intensity of the scattering signal of the laser beam related to one
scattering angle, x represents the distance between the pixels on the
perpendicular and central axis of the scattering signals. σ
and μ are the fitting parameters of the normal distribution. By combining
this with the calibrated one-to-one correspondence between the image of the laser and
the scattering angle, the angle-resolved scattering signals is obtained with
the above steps of data acquisition.
When the angle-resolved signals from two CCDs are obtained, the change of
signals with angles can be merged by following the steps below. Firstly, the
minimum angle θ1 and maximum angle θ2 of the overlap
angular region of signals from two CCDs are set as the boundary angle of data
merging (shadow zone in Fig. 3). θ1 and θ2 are always
around 50 and 80∘, respectively. In this region, a transform
coefficient with scattering angles Tθ is calculated:
Tθ=I1θI2θ.
I1θ is the signal with the scattering angleθ captured by the first CCD while I2θ is
that of the second CCD. The lifted signal I2′θ can
be calculated by multiplying I2θ with the average
of Tθ (Fig. 3). For the regions where θ< θ1 or θ>θ2, the signal I1θ or I2′θ are used as the merged scattering
signal Iθ, respectively. For the overlap region, a
linear weighting average is calculated between I1θ and
I2′θ,
Iθ=I1θ,θ<θ1θ2-θθ2-θ1×I1θ+θ-θ1θ2-θ1×I2′θ,θ1≤θ≤θ2I2′θ,θ>θ2.
Using the method above, the merged signals with scattering angles Iθ can be estimated.
The retrieval algorithm to determine aerosol phase function
Figure 4 shows the flow chart of the retrieval algorithm used to determine pθ from CCD-LADS measurements. According to the
geometric structure of the CCD-LADS, the echo equation of CCD-LADS can be
figured first:
Iθ=N0τZτRβθ,
where βθ is the scattering function of atmospheric
air molecules and aerosols, τZ and τR are the transmittances
on the optical paths of laser emitting and scattering respectively, N0 is the calibration factor that depends on the optical efficiency
of the instrument. Depending on the area that the CCD-LADS covers, the
longest distance between CCD cameras and the laser beam is less than 8 m. In
this range, an assumption that τZ=τR=1 can be
established with a threshold that the visibility should be larger than
1.5 km. The correlation between the visibility and extinction coefficient
kex can be expressed as kex=3/visibility(km) (Chen et al., 2012) which means that the
assumption can be established if kex is smaller than
2 km-1. In some extreme pollution processes with high concentrations of
both aerosol and gaseous pollutants (Ma et al., 2011; Xu et al., 2011),
the scattering and
absorption of aerosols and gases (NO2, Dixon, 1940, O3, Burrows et
al., 1999, etc.) may lead to
extreme kex values. If the kex is more than
2 km-1, the assumption cannot be applied while the transmittance can be
calculated with the measurement of visibility. With the assumption, Eq. (4)
can be transformed to Iθ=N0βθ.
Signal merging of two CCD cameras. Besides the signals captured by
the first CCD (blue dotted line) and the second CCD (red solid line), the
lifted signal from the second CCD (red dashed line) is also shown in the left
drawing. The merged signal is shown in the right drawing.
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Scattering phase function pθ is the normalised
angular distribution of the scattering function:
pθ=4πβθ∫4πβθdΩ=2βθ∫0180βθsinθdθ=2Iθ∫0180Iθsinθdθ.
Consequently, the scattering phase function can be calculated directly from
Iθ measured by CCD-LADS. If the scattering function of
aerosols βaeroθ is known, the pθ can be calculated. Therefore, a retrieval algorithm is built
to separate the scattering signals with angles into the scattering of
aerosols and air molecules (shown in the dashed box in Fig. 4).
Flow chart of the retrieval algorithm used to determine aerosol phase
function from CCD-LADS measurements (the processes in the dashed box are used
to subtract the scattering signal of air molecules from the total scattering
signal).
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As the first step, the scattering coefficient of air molecules at near-surface
level ksc-air is calculated with the density of
atmosphere by a Rayleigh scattering model:
ksc-air=8π3m2-123nairλ4,
where nair is the number density of air molecules, which depends
on the surface pressure and temperature measured by the weather station. m
is the index of refraction of atmosphere, which depends on nair
and the wavelength of the laser λ. The hemispheric backscattering
coefficient of air molecules kbsc-air is a half of
ksc-air (Bohren and Huffman, 2008).
To resolve the ratio between the air molecules and the total hemispheric
scattering Rair=kbsc-airkbsc-air+kbsc-aero,
the hemispheric backscattering coefficient of aerosols
kbsc-aero is measured with an integrating nephelometer here.
To solve the intensity of the total hemispheric backscattering scattering
signals Ibsc, the angle-resolved scattering signals should be
integrated from a 90 to 180∘ scattering angle. Because of the detective
angular range of CCD-LADS is 10–170∘, the angular truncation
correction is necessary to resolve the hemispheric scattering intensity. For
the backward angular truncation, the scattering intensity in that range is
assumed to be equal to the scattering intensity at the largest scattering
angle that CCD-LADS can measured. After the correction above, the corrected
intensity I′θ is used to obtain Ibsc:
Ibsc=∫02π∫π/2πI′θsinθdθdφ.
Then the angle-resolved scattering signals of air molecules can be
calculated with a molecular phase function (Bohren and Huffman, 2008):
Iairθ=31+cos2θ4×Ibsc×Rair2π,
where Iairθ is the calculated angle-resolved
scattering signals of air molecules. According to Eq. (5), the aerosol phase
function paeroθ can be estimated as
paeroθ=2Iθ-Iairθ∫0180Iθ-Iairθsinθdθ.
Error analysis
Two types of uncertainties determine the error of the retrieved aerosol
phase function: the measurement errors caused by the processes of obtaining
the angle-resolved signals and an error introduced by the retrieval
algorithm.
There are two sources of measurement errors in the data acquisition processes
introduced in Sect. 2.2.1. Firstly, the measurement error of CCD used in the
CCD-LADS is 10 % according to the related manual. The relative difference
between the fitted normal distribution introduced in Eq. (1) and the measured
signal in the laboratory study is 8.8 % ± 1.5 %, which can also
certify the 10 % measuring error on I introduced by the manual of CCD.
Secondly, the measurement of the geometric relationship will lead to a relative error
of 5 % at the most on the scattering angle θ introduced by the
resolution and accuracy of the used tools.
The relative errors on the merged angle-resolved signals Iθ can be derived by applying a standard propagation of errors to
Eq. (3) (Bevington and Robinson, 2003):
ΔII2=FI1ΔI1I12+FI2′ΔI2′I2′2+FθΔθθ2,
where Δ means the standard deviation of variables, Δxx is equal to the relative error of x and the propagation factor
Fx is defined as Fx=xI∂I∂x2. By substituting the relative errors and the average signals in
Eq. (10), the uncertainties on Iθ are calculated as a
distribution with an angle-resolved distribution shown in Fig. 5. The values
of uncertainties on Iθ are between 10 and 19 %, and
they vary with angle.
Uncertainties of the merged angle-resolved signal from CCD-LADS
measurement.
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The uncertainties of the retrieval algorithm are introduced by the
uncertainties of the input parameters. There are three groups of input
parameters in the retrieval algorithm: merged angle-resolved signals, aerosol
hemi-backscattering coefficient and temperature/pressure. The errors of the
temperature and pressure are about 0.1 K and 0.1 hPa (Box and Steffen,
2001), which will lead to a 0.02 % uncertainty on
kbsc-air. Combined the 10 % uncertainties on the measured
kbsc-aero (Heintzenberg et al., 2006), the uncertainty of
Rair can be calculated as 7 % with the algorithm in
Sect. 2.2.2. According to the algorithm shown in Fig. 4, the uncertainty of
the retrieved aerosol phase function are mainly dominated by the
uncertainties of the merged signal shown in Fig. 5, and also influenced by
the uncertainty of Rair in a way.