article turbidimètre

Turbidimeter based on a refractometerusing a charge-coupled device

Bo HouPhilippe GrossoZong Yan WuJean-Louis de Bougrenet de la Tocnaye

Turbidimeter based on a refractometer usinga charge-coupled device

Bo HouPhilippe GrossoZong Yan WuJean-Louis de Bougrenet de la TocnayeTélécom BretagneOptics Department, Technopôle Iroise 29238Brest, FranceE-mail: [email protected]

Abstract. Salinity and turbidity are two important seawater properties inoceanography. We have studied the use of a high resolution refractometerto measure the salinity of seawater. The requirement of a multifunctionalsensor makes the turbidity measurement based on our refractometer valu-able. We measure turbidity according to the attenuation of the laser beamcaused by the scattering. With the configuration of our refractometer, sev-eral issues impact the laser beamattenuationmeasurement,while themea-surement of salinity is impacted by the scattering as well. All these issuesmake light distribution nonsensitive sensors such as position sensitivedevices unsuitable for building the refracto-turbidimeters. To overcomethese issues, a charge-coupled device combined with a new location algo-rithm is used to measure both the refractive index and the attenuation.Several simulations and experiments are carried out to evaluate this newmethod. According to the results, the way to improve the resolution is dis-cussed aswell. The validation of ourmethod is proved by comparison to thenephelometer specified by the nephelometric turbidity unit standard. © 2012Society of Photo-Optical Instrumentation Engineers (SPIE). [DOI: 10.1117/1.OE.51.2.023605]

Subject terms: charge-coupled device; turbidity; turbidi-meter; formazin;refractometer.

Paper 111268 received Oct. 11, 2011; revised manuscript received Dec. 21, 2011;accepted for publication Dec. 23, 2011; published online Mar. 12, 2012.

1 IntroductionThe turbidity of water is mostly due to the existence of sus-pended undissolved solid particles. When light is incident on aparticle, several processes occur, including reflection, refrac-tion, diffraction, and absorption. For particles that are of theorder of the wavelength in size or smaller, these processes arereferred to as “scattering.”1 Usually, the measurement of tur-bidity is not a direct measurement of these suspended parti-cles, but rather a measurement of the scattering caused bythese particles. International standard ISO 7027 provides2

two different methods to measure the turbidity by computingthe diffuse radiation and the attenuation of a radian flux.Respectively, two different turbidity units, namely formazinnephelometric unit (FNU) and formazin attenuation unit(FAU), are used for both methods. Another turbidity unit,Nephelometric Turbidity Unit (NTU), defined by US EPA(U.S. Environmental Protection Agency) method 180.1,measures3 the light diffused at an angle of 90� 30 deg tothe incident light beam with a tungsten lamp.

Since the measurement of turbidity is a measurement ofthe scattering effect caused by particles, the light scatteringand its application have been investigated for many years. In1907, Gustav Mie4 gave an analytical solution of Maxwell’sequations for the scattering of electromagnetic radiation by asingle spherical particle, which is called Mie theory. Toreduce the complexity of Mie theory, several approximationshave been proposed.5–7

The study of oceanography requires different high-resolution measurement equipment to measure different phy-sical quantities of the seawater, e.g. turbidity, salinity, tem-perature, and pressure.8 A set of these quantities at different

geographical positions is most valuable for oceanography.This makes the research of in situ multisensors valuable.Our previous work involved developing an optical refract-ometer to measure the salinity of seawater based on laserbeam deviation measurement with a 1-D position sensitivedevice (PSD).9,10 The resolution for measuring salinityreaches 0.002 g∕kg with the measurement range from 0to 40 g∕kg. Further researching to replace PSD with acharge-coupled device (CCD) gives us an improvement ofresolution of nearly 1.5 times that of a PSD-based refract-ometer.11 The CCD records the location, shape, and intensitydistribution of the laser spot. This provides the possibility tomeasure physical quantities other than refraction index.

In this paper, we demonstrate how our refractometer canbe used to measure turbidity. A brief summary of our opticalrefractometer is given in the next section. In Sec. 3, the pro-blems of measuring turbidity with our optical refractometerare discussed according to the scattering theory. Solutionsare also introduced in this section. The simulations andexperiments are first carried out in a parallel slab to operateat normal incidence and then with our optical refractometer,which can be found in Secs. 5 and 6. Finally, the perfor-mance in highly turbid case and calibrated water samplesare given by a series of experiments.

2 Principle of Optical RefractometerOur optical refractometer used for salinity measurement isdepicted in Fig. 1. The refractometer consists of two prismswith different refractive indices. The laser beam first illumi-nates the lefthand side prism and reaches a mirror AB. Afterthe reflection at AB, the laser beam is redirected to thesurface between the medium and the prism, CD. It is thenrefracted and propagates a distance d in the medium.0091-3286/2012/$25.00 © 2012 SPIE

Optical Engineering 51(2), 023605 (February 2012)

Optical Engineering 023605-1 February 2012/Vol. 51(2)

The laser beam is then refracted at surface DE and enters therighthand side prism. The mirror FG finally reflects the laserbeam to the top of the prism, where a laser beam positiondetection device is used to detect the position of the laserspot xp. With this configuration, the refractive index of thewater can be calculated very accurately from the position ofthe laser spot.9 With a CCD instead of a PSD, the positionof the laser spot can be calculated with different locationalgorithms, and it is shown that the resolution is comparableto the system that uses a PSD.11 By using a CCD, the dis-tribution of the light intensity changed by the scattering ofthe particles in the medium is also recorded, giving us thepossibility to retrieve the turbidity of the medium.

3 Principle of Turbidity Measurement

3.1 Theoretical Aspects

When light meets a particle, a portion of light flux isabsorbed by the particle, while another portion is diffusedin all directions. These two processes cause the light attenua-tion. For an incident light I0, which traverses a distance d in aturbid medium with the particle density ρ, it is attenuated toI tr by the following equation:12

I tr ¼ I0e−ρ½σaðλÞþσdðλÞ�d; (1)

where σa and σd are called absorption cross section and diffu-sion cross section, respectively, which are the functions of theincident light wavelength λ. Since the part ρ½σaðλÞ þ σdðλÞ�causes the attenuation of the incident beam, it is a good candi-date to describe the optical properties of a turbid medium. Tosimplify the formula, ρ½σaðλÞ þ σdðλÞ� is expressed as T ,attenuation coefficient.

For a volume of turbid medium as shown in Fig. 2, theincident flux I0 can be separated into three portions. One por-tion of light denoted as Id is diffused out of the transmissiondirection, another portion keeps propagate along the trans-mission direction, which traverses a distance l, and thethird portion of light, which is caused by multiple scatteringinside the medium, is first diffused out of the transmissiondirection and then diffused back. This portion of light,denoted as Ims, has a longer light path than the nondiffusedlight and increases the transmitted light flux I tr, which can beexpressed as

Im ¼ I 0tr ¼ I0e−Tl þ Ims; (2)

where Im is the light intensity measured in the transmissionpath out of the volume. Therefore, the attenuation coefficientT can be calculated from

T ¼ lnðIm − ImsÞ − lnðI0Þl

. (3)

The flux intensity of multiscattered light in propagationdirection is related to the density of the particles and thelength of the light path. The higher the density of the parti-cles, the more multiscattering occurs. A longer light pathgives more light scattered into the propagation directionas well. In this paper, the impacts caused by the multiscat-tered light are evaluated in the analysis of the experimentresults.

3.2 The Resolution of Turbidity Measurement

The resolution of the turbidity measurement can be estimatedfrom Eq. (3). The multiscattering part is ignored here andwill be discussed later from the experiment results. Sincethe incident light intensity I0 can be measured with nonturbidwater in advance, the equation can be modified as

T ¼ −�lnðImÞ

l− C

�(4)

The derivative of T can be expressed as

T 0 ¼ dTdIm

¼ −1

l × Im(5)

Thus, the sensitivity of the measurement of turbidity St is

St ¼ kt × dT ¼ −dIml × Im

; (6)

where kt is a constant coefficient to convert the attenuationcoefficient into other turbidity units, for example NTU. Fromthis equation, it is obvious that the resolution of turbiditymeasurement is proportional to the resolution of the lightintensity sensor dIm, but inversely proportional to thelength of the light path l in the turbid medium. A longerlight path can provide better turbidity measurement resolu-tion. Another interesting phenomenon resulting from thisequation is the resolution depending on the measurement

Fig. 1 Principle of the refractometer. Dotted line shows the laser pathaccording to two different refraction indices of water.

Fig. 2 Theoretical aspects of turbidity measurement.

Hou et al.: Turbidimeter based on a refractometer using a charge-coupled device


range. With the same sensitivity of the light intensity sensorand the same light path length, the larger the measured inten-sity, the better the resolution obtained. Considering that themeasured light intensity decreases as the turbidity increases,it is easy to conclude that the resolution is better in the lowturbid medium than in the high turbid medium when lightpath and sensor sensitivity are the same.

3.3 Issues in Measuring Turbidity with Refractometer

As discussed in Sec. 3, the attenuation coefficient T can becalculated from the attenuation of the incident laser beamaccording to Eq. (3). When applying this theory to therefractometer demonstrated in Sec. 2, several issues arise.

The first issue is that light path changes as the refractionindex of the medium changes. In Fig. 1, OM and ON are twodifferent light paths according to different refraction indicesof the medium. This makes the measured flux intensity quitedifferent when measuring two different medium samples thatwhich have the same turbidity but different refractive indices.According to the configuration of the refractometer, the lightpath length in the medium named l in Eq. (3) can beexpressed as a function of the laser spot position, whichis shown in Fig. 3. The laser spot position is countedfrom the H point shown in Fig. 1. A quadratic fitting givesus an approximate equation to calculate the length of lightpath according to the laser spot position, which is expressedin Eq. (7).

l ¼ f ðxpÞ ¼ 6.338340 − 0.000284xp þ 0.000185x2p: (7)

With Eq. (7), the relative length of the light path compared tothe length of the light path in pure water is calculated andused as the length in Eq. (3) to obtain the attenuation coeffi-cient. In practice, the laser beam width cannot be ignored.This leads to another problem: the width of the collimatedbeam causes the different parts inside the beam to propagatethrough the medium with different lengths. As shown inFig. 4, for a wide beam, the upper parts of the beam haveshorter light paths OM than the bottom of the beamO 0M 0, and this difference varies as the refractive index ofthe medium changes. A solution to this problem is to use

the maximum of the intensity, instead of the entire intensity,to calculate the attenuation coefficient T .

Another problem raised by the refractometer is thataccording to the theory, the intensity Im is measured bythe sensor located far away from the medium, where thelight in propagation direction is well separated from the scat-tered light. However, with the refractometer, the height Lshown in Fig. 1 limits the distance between the sensorand the medium, making it difficult to measure the separatedlight beam intensity. Figure 5 depicts the difference of lightintensity measurement while locating the light intensitysensor at different distances of the medium. Besides thelight propagated along the transmission direction, anotherportion of light is scattered out of the medium. The sensorlocated near the medium, shown in position A, captures notonly the transmitted radiation but also the scattered radiationwith an angle α, while at the distant position B, the sensoraccepts the transmitted radiation and the scattered radiationwith the angle β, smaller than α. Therefore, B receives lessscattered light than A.

Besides the difficulty of separating the scattered radiationand the transmission radiation, the use of laser as the sourceleads to interference while the laser beam propagates throughthe particles. As a result, speckle is observed in the sensorplane. Figures 6(a) and 6(b) show the laser spots captured at5 cm far from the medium along the light propagationpath. Figure 6(a) depicts the laser spot with pure waterand Fig. 6(b) shows the laser spot with the turbid waterof 444.4 NTU. It is obvious that the laser spot capturedwith turbid water mixes the Gaussian spot and interferencespeckle. Both the scattered part of flux and the speckle cre-ated by the interference cause inaccurate measurement of tur-bidity, and need to be eliminated. One possible way to avoidinterference is to use LED as the light source instead of laser.With a collimator, the collimated light emitted from an LEDwith a filter to narrow the band of wavelength not only devi-ates due to the refractive index change but also avoids theinterference in turbidity measurement.

Furthermore, since our method measures the attenuationof propagated light as shown in Eq. (3), it is easy to find outthat the light intensity Im decreases when the turbidityincreases, which can be found by comparing Figs. 6(a)and 6(b). This results in another issue: the light intensitybecomes so weak that it cannot be measured in a highlyturbid case.

6.34

6.35

6.36

6.37

6.38

6.39

6.4

7 8 9 10 11 12 13 14 15 16 17 18

leng

th o

f the

ligh

t pat

h in

the

med

ium

(m

m)

laser spot position (mm)

Light path length vs spot position

Fig. 3 The relationship between the length of the light path in themedium and the laser spot position. The laser spot position is the dis-tance from the H to px in Fig. 1.

Fig. 4 Different parts inside the beam pass different lengths in themedium.

Fig. 5 The difference of light intensity measurement by locating thelight intensity sensor at different distances of the medium.



The above problems raised by the configuration of therefractometer impact the resolution of the measurement ofturbidity. Meanwhile, the measurement of turbidity itselfimpacts the accuracy of the refractometer, which needs tobe addressed in the design of the turbidimeter.

The first problem related to the resolution of the refractiveindex measurement is caused by the light path difference asshown in Fig. 4. According to Eq. (3), in a turbid case, thisdifference of light path leads to different attenuation insidethe laser spot, which further causes the change of the laserbeam position when applying the mass-center-related laserspot location methods, for example, using PSD or CCDcombined with the centroid algorithm.

Another problem that leads to the asymmetric laser spot isthe divergence of the laser beam. Both the refraction surfaceand the sensor surface are not perpendicular to the laserbeam. When a Gaussian beam is projected to the sensorsurface at a nonnormal angle, the Gaussian spot becomesasymmetric, while different refractive index changes thesize of the laser spot. Figure 7 is generated by the simulationin ZEMAX with the configuration of our refractometer. Itpresents four laser spots with different laser beam diver-gences, but with the same refractive index of the medium.It is easy to observe that the width of the laser spot increasesas the divergence of laser spot increases. The asymmetry ofthe laser beam can be noticed from the center of these laserspots calculated by the centroid algorithm, which is depictedin Fig. 8 (The solid line with mark ‘x’). The center of thelaser spots moves more than one pixel from the divergenceof 0.5 mrad to 2 mrad.

Similarly with the divergence of the laser beam, theturbidity of the medium diffused the laser beam out of itspropagation direction and makes the divergence of the laserbeam much larger. Figure 9 is the result of the simulation inZEMAX with the collimated laser beam (no divergence) and

different densities of particle. The scattering model used inthe simulation is the Mie scattering. It is noticed that theposition calculated by the centroid algorithm has a deviationof 2.5 pixels with the particle density from 0∕cm2

to 8 × 106∕cm2.

3.4 Using CCD to Measure the Turbidity with aRefractometer

One of our previous work used a PSD to measure the devia-tion of the laser beam. PSD has a single active area formedby a P-N junction. The two parts that originated from thelaser spot to the two electrodes form two lateral resistancesfor the photocurrents running toward the electrodes. Thephotocurrents are collected through the resistances by theoutput electrodes, which are inversely proportional to the dis-tance between the electrode and the center of the incominglight beam. This relationship is expressed as follows13:

x ¼ L2

I2 − I1I2 þ I1

; (8)

where I1 and I2 are the electrode photocurrents, L is thelength of the PSD active area, and x stands for the laserspot position. From the principle of PSD, the light intensitycan be calculated from I1 þ I2. However, since PSD isplaced not far from the medium due to the dimension limita-tion of the prisms, the intensity it measures mixes the scat-tered radiation so that it cannot give an accurate result. Fromthe principle of PSD, the center is the mass center of the inci-dent light. Since the divergence and turbidity make the laserspot asymmetric, the mass center cannot be used to indicatethe laser beam position. What is more, when the light inten-sity is very weak in a highly turbid medium, I1 and I2 will beso small that they cannot be retrieved. These problems,which exist for all the light intensity distribution insensitive

Fig. 6 (a) The original image with pure water. (b) The original image with turbid water of 444.4 NTU. (c) The resulting image with pure water afterpassing through the low pass filte. (d) The resulting image with turbid water of 444.4 NTU after passing through the low pass filter.



sensors, make the PSD a poor candidate to measure turbiditywith the refractometer.

To solve these problems, PSD will be substituted to aCCD. The resolution of measuring the deviation of laserbeam with CCD combined with a centroid algorithm hasbeen proven to be better than the configuration withPSD.11 Since CCD can be controlled to operate with differentexposure times, the transmitted radiation in a high turbidmedium can be measured with high exposure time. Theattenuation coefficient T can be represented by calculatingwith the transmitted radiation in a unit time period, whichcan be expressed as

T ¼ −ln�Imt

�− ln

�I0t0

�lðxpÞ

; (9)

in which t is the exposure time and t0 stands for the exposuretime used to measure the incident light intensity. As thelength of light path l changes with the deviation of thelaser beam, it is noted as lðxpÞ according to Eq. (7).

To separate the transmitted radiation with the scatteredradiation, the Fourier transformation of the laser spot in dif-ferent turbidities has been studied (depicted in Fig. 10), andgives us the profile of the laser spot Fourier transformationin pure water and turbid water of 444.4 NTU. Since a laseris used in the refractometer, the ideal Fourier transformationof the laser spot should be Gaussian too, which can be found inthe low frequency (between the spatial frequency −20 and 20approximately). By comparing the Fourier transformation fordifferent turbidities in Fig. (10), a low pass filter can be usedto remove the scattered radiation. The result of a low passfilter can be found in Figs. 6(c) and 6(d). For pure water, theresulting image does not differ much from the original image,which can be foreseen since there is no scattering in this case.Figure 6(d) shows that this method correctly retrieves theoriginal Gaussian spot from the original image that mixed thetransmitted radiation, the scattered radiation, and the specklescaused by interference. For the wide beam, the maximumvalue of the spot is used to avoid the asymmetric spot causedby the different light paths inside the beam. By applying allthese settings to Eq. (9), the attenuation coefficient is

Fig. 7 The laser spots for different laser beams with different divergence. The image is obtained from the ZEMAX simulation.



T ¼ −ln�If ct

�− ln

�I0t0

�lðxpÞ

; (10)

where If c is the maximum value of the filtered image. In prac-tice, N images will be captured for one measurement to avoidaccidental errors, and the attenuation coefficient can thus be

obtained by the formulaP

N1Ti

N , in which Ti is the attenuationcoefficient calculated from Eq. (10) with the i’th image.

As discussed in Sec. 3.3, the measurement of turbidityand the divergence of the laser beam can cause the laserspot shape to be asymmetric, which leads to the centroidalgorithm inaccuracy in showing the position of the laserspot. To solve this problem, a new algorithm is proposed,which is insensitive to the distribution of the laser spot.Figure 11 describes this algorithm, which tracks the peakof the Gaussian source shown as the dash line. This dashline divides the divergent laser beam into two parts, namedleft part and right part respectively. Since the source laserbeam can be considered as a perfect Gaussian beam, the

mass of the left part Mleft is equal to the right one Mright andthis relationship holds after the refraction of the beam, eventhough the shape is asymmetric. This beam is quantized intopixels, which is shown as the bars in Fig. 11, by a CCD. Themass in the left part M 0

left can be expressed as

M 0left ¼

Xi

0

Pi þMΔx; (11)

where MΔx is the mass shown as the shadow area, and Pi isthe value of i’th pixel. Similarly, the right part M 0

right can bewritten as

M 0right ¼

Xwidth−1j

Pj −MΔx: (12)

With Eqs. (11) and (12), the area in the shadow is obtainedby

-0.2-0.1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1 1.1 1.2 1.3 1.4 1.5

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2

the

cent

er o

f the

lase

r sp

ot (

pixe

l)

the divergence of the laser beam (mrad)

centroid algorithmnew algorithm with no filter

new algorithm with filter

Fig. 8 The positions obtained by the different algorithms for differentdivergence of the laser beam (simulated in ZEMAX).

-0.5

0

0.5

1

1.5

2

2.5

3

0 1 2 3 4 5 6 7 8

the

posi

tion

calc

ulat

ed

particle density (M)

centroid algorithmnew algorithm

Fig. 9 The positions obtained by the different algorithms for differentdensity of particles in the medium (simulated in ZEMAX).

00.0005 0.001

0.0015 0.002

0.0025 0.003

0.0035 0.004

-600 -400 -200 0 200 400 600

frequency

0 NTU444.4 NTU

00.0005 0.001

0.0015 0.002

0.0025 0.003

0.0035 0.004

-200 -150 -100 -50 0 50 100 150 200

frequency

0 NTU444.4 NTU

Fig. 10 The Fourier transformation profile of the laser spot with dif-ferent turbidities. The upper diagram shows the profiles with purewater (shown in red) and turbid water of 444.4 NTU (shown inblue); the bottom diagram is the zoom of the profiles from −200 to200 spatial frequency.

Fig. 11 The principle of new laser spot location algorithm.



MΔx ¼P

width−1j Pj −

Pi0 Pi

2(13)

and the subpixel position is calculated as

xp ¼MΔx

Pjþ i: (14)

In a turbid medium, the attenuation is not uniform inside the

beam. For a standard Gaussian beam f ðxÞ ¼ I0e−ðx−xpÞ2

2σ2 , afterthe attenuation, the beam changes to

I ¼ I0e−ðx−xpÞ2

2σ2 e−Tuðx−xpÞ−Tl ¼ e−

�x−xpþTσ2

u

�2

2σ2 I0eT2σ2

2u2−Tl; (15)

in which T is the attenuation coefficient, l is the light path ofthe center, u is a coefficient that describes the differentattenuation inside the beam, xp is the original peak position,and σ is the laser beam size. From this equation, it is easy toconclude that the new laser spot is still a Gaussian spot butwith a peak shift of − Tσ2

u compared to the original spot. The

peak value of the Gaussian spot attenuates to eT2σ2

2u2−Tl of the

original one.Thus, the mass of the left part and the right partof the peak can be calculated from the following equations:

M 0 0left ¼ I0

Zxp−Tσ2

u

−∞e−

�x−xpþTσ2

u

�2

2σ2 eT2σ2

2u2−Tldx ¼ M 0 0

right

¼ I0

Z þ∞

xp−Tσ2u

e−

�x−xpþTσ2

u

�2

2σ2 eT2σ2

2u2−Tldx: (16)

As in the divergence case, the center calculated by Eq. (14) isxp − Tσ2

u . To obtain the laser spot position xp, the deviation

part − Tσ2u needs to be calculated first. To simplify the discus-

sion, the coefficient σ2

2u2 is noted as v, thus the maximum value

measured is I0evT2−Tl. According to the principle discussed

in Sec. 3, we obtain the following equation:

vT2 − Tl ¼ lnðImÞ − lnðI0Þ: (17)

By solving this equation, the attenuation coefficient T isexpressed as

T ¼ l −ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffil2 þ 4v½lnðImÞ − lnðI0Þ�

p2v

: (18)

Combined with Eq. (14), (16), and (18), the laser spot posi-tion xp in the turbid medium is calculated by

xp ¼ w

�MΔx

Pjþ i

�þ k

�l −

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffil2 þ 4v½lnðImÞ − lnðI0Þ�

q ;

(19)

where w is the size of the pixel.

4 New Algorithm for Turbidity Measurementwith CCD

4.1 Simulation

To evaluate the performance of the new algorithm, two simu-lations, divergence simulation and turbidity simulation, arecarried out in ZEMAX, in which the configuration of therefractometer is simulated, while the scattering model chosenfor the simulation of turbidity is the Mie scattering. Thedivergence simulation takes four images with four differentlaser beam divergences from 0.5 to 2 mrad. The new algo-rithm is applied to both the original image and the filteredimage. The calculated center can be found in Fig. 8. To sim-plify the comparison, the reference center used here is thecenter calculated for 0.5 mrad, which is labeled as position0. From Fig. 8, it is clear that the new algorithm obtainsbetter stability than the centroid algorithm when applyingdifferent divergences. Table 1 gives more detail of the centercalculated by the new algorithm, which shows a maximumerror of 0.028 pixel.

The turbidity of the medium is simulated by changing thedensity of the particles. The reference image is the imagesimulated in a nonturbid case here. four different particledensities (2 × 106∕cm3, 4 × 106∕cm3, 6 × 106∕cm3, 8×106∕cm3) are simulated and the result is depicted inFig. 9. Since the turbid medium diffuses the light out ofthe beam, a threshold is used to eliminate those light inten-sities that are diffused out of the laser spot but captured bythe CCD. Combined with the threshold, the new algorithmprovides a much more accurate result than the centroid algo-rithm, which gives a deviation of 2.4 pixels. In Table 2, theerror of the new algorithm can be found as about 0.069 pixel.

Table 2 Center calculated with different algorithms for differentturbidity.

Density ofparticles(per cm3) (0 × 106) (2 × 106) (4 × 106) (6 × 106) (8 × 106)

Centroid algorithm(pixel)

0 0.6117 1.2273 1.8364 2.4439

New algorithm(pixel)

0 −0.0552 −0.0550 −0.0149 0.0695

Table 1 Center calculated with different algorithms for differentdivergences.

Divergence (mrad) (0.5) (1.0) (1.5) (2.0)

Centroid (pixel) 0 0.1684 0.5612 1.0754

New algorithm withoutfilter (pixel)

0 0.0087 0.0014 −0.0286

New algorithm withfilter (pixel)

0 0.0013 0.0078 −0.0205



4.2 Experiments

In our last paper,11 several experiments were carried out toevaluate the performance of the centroid algorithm with amircopositioner, which can move with a step of 0.1 μm.To compare the performance of the centroid algorithmwith the new algorithm, the same image set is chosen,and the two algorithms are applied. The centers calculatedby these two algorithms are depicted in Fig. 12. Furthermore,the result for the new algorithm with the filter is included inthis figure too. It is obvious that the curve of the new algo-rithm is much smoother than the centroid algorithm. Theerror of these methods can be calculated by a linear fitting.Centroid algorithm obtains a maximum error of 0.1 pixelwith the standard deviation of 0.0784 pixel, while thenew algorithm with and without the filter get a maximumerror about 0.06 pixel (the standard deviations are 0.0348and 0.0352 pixel respectively). For an image with M × Npixels, the two algorithms have the same time complexityof OðMNÞ. All the results above make the new algorithma good alternative to the centroid algorithm even in anonturbid case. Also, according to the simulation resultsand the algorithm analysis, the new algorithm is insensitiveto the divergence and can be applied to the turbid medium.

5 Simulation and Experiment in a Parallel Slab

5.1 Simulation

To test the principle of turbidity measurement, the simulationin parallel slab are carried out, first in ZEMAX. The turbidityof the medium is changed by adjusting the density of theparticles from 1 × 106∕cm3 to 1 × 107∕cm3. The scatteringmodel used in the simulation is the Mie scattering. Thedimension of the parallel slab follows the size of the parallelslab used in the real experiment. A CCD is placed 10 cm

from the parallel slab along the laser beam propagation direc-tion. Table 3 depicts the attenuation coefficient T calculatedby Eq (3). By doing a linear fitting, the attenuation coeffi-cient given by the method correctly describes the densityof the particles, which is theoretically proportional to theturbidity in the simulation. The error standard deviation ofthe calculated attenuation coefficient T according to the lineis 8.2 × 10−4. This result means the multiscattered light Ims

can be ignored in Eq (3) due to the short light path in theturbid water.

5.2 Experiments in High Turbid Medium

In addition to the simulation, an experiment was carried outin the parallel slab. Figure 13 shows the setup of the experi-ment. A red diode laser at 635 nm is mounted perpendicu-larly to the horizontal plane. A 45-deg mirror redirects thelaser beam to a parallel slab with a width of 16 mm. Another45-deg mirror is used to redirect the propagating beam into aDALSA CCD camera,14 with a 1280 × 960 resolution and asmall 3.75 × 3.75 μm pixel size. The turbidity reference usedin the experiment is the 4000 NTU Formazin standard. Sincethe scattering is sensitive to the size of the formazin particles,which change according to temperature, the setup was estab-lished in the presence of a thermostat to keep the temperaturestable. To obtain different turbidity, 1 ml 4000 NTU Forma-zin standard was added N times to the parallel slab, whichcontained 40 ml pure water at the beginning. The turbidity ofdiluted turbid water can be calculated by

ti ¼ti−1 × Vi−1 þ ΔV × 4000

Vi−1 þ ΔV; ðt0 ¼ 0;V0 ¼ 40Þ;

(20)

where ΔV is the added volume of 4000 NTU Formazin stan-dard each time, and ti and Vi are the turbidity and the totalvolume after adding the ΔV of 4000 NTU Formazin for i’thtime. 10 images are captured for each turbidity with a suffi-cient exposure time to make sure the peak of the spot reachesmore than 100 (maximum 255 for the CCD). Since thediluted formazin is not stable for longtime storage, all experi-ments are carried out in a dark room and in less than one hourto obtain the best performance.

Figure 14 shows the experimental result. The light inten-sity I0 is premeasured with pure water as the reference lightintensity. For each turbidity, according to Eq (3), threeattenuation coefficients are calculated by using the powerof the image, the max value of the image, and the pixelvalue in the position obtained from the new algorithm asIm, respectively. All three curves show linearity to the turbid-ity that is in the range from 0 to about 234.1 NTU, asexpected. The average error of these three methods is esti-mated by a linear fitting, which gives three similiar slopesof −0.0085, −0.0084, −0.0086, respectively. By using themax value of the image, the standard deviation of error is

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centroid algorithmnew algorithm with no filter

new algorithm with filter

Fig. 12 The calculated center provided by the centroid algorithm, newalgorithm with and without filter.

Table 3 Simulation results with the parallel slab

Density of particles (106∕cm3) 0 1 2 3 4 5 6 7 8 9 10

Attenuation coefficient 0 −0.015 −0.029 −0.044 −0.059 −0.073 −0.088 −0.104 −0.118 −0.133 −0.150



the largest of the three, which reaches �4.87 NTU, while thestandard deviation of error obtained by using the power ofthe image is �3.17 NTU. The standard deviation of errorgiven by the new algorithm is the smallest: �2.82 NTU.From Eq. (3), it is easy to conclude that the resolution ofthe turbidimeter is proportional to the sensitivity of thelight sensor and inversely proportional to the light pathlength. It is believed that the resolution in the experimentcan be improved by simply extending the width of the slab.

5.3 Experiments in Low Turbid Medium

As discussed in Sec. 3.2, the resolution of the turbidimeter isbetter in the low turbid medium than in the high turbid onewith the same light path and light sensor sensitivity. Todemonstrate that, another experiment was carried out withthe same parallel slab. All the configurations in this experi-ment are the same as the one for the high turbid mediumdiscussed in the last section. 40 ml pure water is pouredinto the slab as the base volume of water. 1 ml diluted turbidwater with the turbidity of 78.43 NTU is added to the slab

nine times. For each time, 24 images are captured within onesecond. According to Eq. (20), the range of the turbidity forthe nine media varies from 1.91 to 14.41 NTU. Figure 15expresses the attenuation coefficient calculated by usingthe power of the image, the maximum of the image, andthe pixel value given by the new algorithm, respectively.All of them show a linearity with respect to the turbidity.Even in this small range of turbidity, it is clear that the higherturbid medium gives larger error than the low turbid medium.For these three methods, the maximum value gives a largedeviation in higher turbidity medium than the other two.The standard deviation of error for the three methods canbe estimated by a linear fitting, which shows that the stan-dard deviation of error of using the power of the image isabout �0.5 NTU, while the new algorithm provides a stan-dard deviation of �0.6 NTU. Compared with the standarddeviation of error obtained in the last section, the resolutionof the turbidity is better in a low turbid medium than in a highturbid one.

6 Simulation and Experiment with a Refractometer

6.1 Simulation

The simulation of measuring the turbidity with our refract-ometer was carried out in ZEMAX. The turbidity of the med-ium was changed by modifying the particle density of themedium from 1 × 106∕cm3 to 1 × 107∕cm3. The divergenceof the laser beam is set to 1 mrad, the same as the source usedin the experiment. A CCD of 1280 × 960 pixels is simulatedby a rectangular detector. Table 4 expresses the attenuationcoefficient calculated from the simulation. Similarly to theparallel slab case, the attenuation coefficient given by thealgorithm discussed in this paper shows a good linearityto the density of the particles in the medium, which is the-oretically proportional to the turbidity of the medium.

Fig. 13 The experiment setup for the experiments carried out in aparallel slab.

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Fig. 14 Experimental results for the parallel slab for high turbidmedium.

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Fig. 15 Experimental results for the parallel slab for low turbidmedium.

Table 4 Simulation results with the refractometer

Density of particles (106∕cm3) 0 1 2 3 4 5 6 7 8 9 10

Attenuation coefficient 0 −0.018 −0.036 −0.053 −0.071 −0.090 −0.107 −0.126 −0.144 −0.165 −0.185



6.2 Experiments in High Turbid Medium

Figure 16 shows the setup of the experiment with the refract-ometer. The refractometer is used instead of the parallel slab.The diode laser and CCD used in this experiment are thesame as those used in the parallel slab experiment. Therefractometer is set up in a small tank, in which 100 mlpure water is used as the base water. 0.5 ml 4000 NTU for-mazin solution was added to the small tank 11 times and isdiluted to different turbid water levels. The turbidity can becalculated according to Eq. (20). All the experiments arecarried out in the presence of a thermostat to make surethe temperature of the turbid medium does not change.

The experimental results are shown in Fig. 17. Theattenuation coefficients are calculated by two different quan-tities, the power of the image and the pixel value given by thenew algorithm, as the measured intensity Im in Eq. (18). Thereference light intensity I0 is premeasured in pure water withthe same configuration. As the turbidity increases, bothmethods give a trend of decrease for the attenuationcoefficient. The average error of these two methods can beevaluated by a linear fitting. The method using the power ofthe image as the measured intensity provides an error withstandard deviation of �8.09 NTU, while the standarddeviation of error for the method using the newalgorithm is about �7.96 NTU. As we have discussed inSec. 3.2, the sensitivity of the measurement of turbidityis inversely proportional to the light path in the medium.

Compared to the error obtained in the parallel slab with15.91 mm, the error obtained with the refractometer fitsthis analysis. From Eq. (7), the light path distance can becalculated as about 6.36 mm. The ratio of the errors betweenparallel slab and refractometer is about 2.7, while the ratiobetween the light path in the parallel slab and the one in therefractometer is about 2.5. It is believed that the differencebetween both ratios is caused by the setup error of the lasersource, which makes the laser beam not exactly perpendicu-lar to the horizontal plane. This setup error makes the actuallight path distance shorter than the theoretical one.

6.3 Experiments in Low Turbid Medium

The performance of the turbidity measurement with therefractometer in a low turbid medium is tested with anotherexperiment. The experiment setup is the same as the experi-ment in high turbid medium discussed in the last section.100 ml pure water is used as the base medium, while dilutedformazin of 190 NTU is added into the base medium11 times to generate different turbid water from 0 toabout 19 NTU. The attenuation coefficients calculatedfrom the power of the image and the pixel value obtainedby the new algorithm are plotted in Fig. 18. The power ofthe image shows a better linearity than the new algorithm.The reason is that in a low turbid case, the attenuation ofthe light is very small so that the nonuniqueness of theattenuation inside the beam is not significant. Thus, themore pixels of the spot used as the measured intensity Im,the more accurate the result is. However, the new algorithmonly tracks the intensity in one location, which divides thethe mass of the spot into two identical parts. Therefore, ithighly depends on the sensitivity of the light intensity sensor.In a low turbid case, the attenuation of the light intensity forone pixel is so small that the CCD cannot detect it; thisexplains why in the low turbid case shown in Fig. 18, theattenuation coefficient calculated from the new algorithmdoes not hold a linearity, especially in ultralow turbid med-iums. The experimental results with parallel slab prove thisas well, in which the standard deviation of new algorithm(�0.6 NTU) is larger than the standard deviation of usingthe image power (�0.5 NTU). With the refractometer, thestandard deviation of using the power of the image is

Fig. 16 Experiment setup for the experiments carried out with therefractometer.

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Fig. 17 Experimental results with the refractometer in high turbidmedium.

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Fig. 18 Experimental results with the refractometer in low turbidmedium.



obtained from a linear fitting, which is about �1.15 NTU.The ratio between this error and the error obtained in theparallel slab (�0.5 NTU) is 2.3, which fits the ratio betweenthe light paths (about 2.5).

7 Compare to the NephelometerA nephelometer, which measures the diffusion of the lightat 90 deg from the light propagation direction, is a stationaryor portable instrument for measuring suspended particulatesin a liquid or gas colloid. It has been proven to be an accurateand reliable method to measure turbidity from scattering.To test the performance of our method mentioned in thispaper, the experimental result is compared to the resultobtained from a nephelometer. The test sample is 100 mldiluted formazin turbidity solution. The turbidity of the sam-ple is first measured in the nephelometer HACH 2100N,15

which gives a result of 109� 2 NTU. The experimentsetup is the same as in Sec. 6.2. The turbidimeter is first cali-brated by adding 1 ml 4000 NTU formazin turbidity solutioninto 100 ml pure water three times. Each time, 24 images arecaptured by the CCD within one second. Since the test sam-ple is not in low turbid range, the new algorithm is used tocalculate the attenuation coefficient. The attenuation coeffi-cients calculated for the calibration are shown in Fig. 19. Alinear fitting is made from the calibration results, which has aslope of −0.0055. With this calibrated configuration, theexperiment with test sample is carried out as well. Theattenuation coefficient obtained by the new algorithm is−0.6054. According to the slope of the fitting line, theturbidity of the test sample can be calculated ast ¼ ðT∕kÞ ¼ ð−0.6054∕ − 0.0055Þ ¼ 110.07, which fitsthe result obtained from the nephelometer.

8 ConclusionSalinity and turbidity are two important properties of sea-water for oceanography. Our previous work has studied ahigh resolution optical refractometer to measure salinity.The integration of the salinity and turbidity measurementinto one compact sensor is a very interesting topic in ocea-nography. Based on our refractometer, the attenuation of thelight intensity caused by the scattering is measured by usinga CCD. The attenuation coefficient, which is proportional tothe absorption, diffusion, and particle density of the medium,

is chosen as the description of the turbidity. According to theanalysis of the attenuation coefficient computation, the reso-lution of this method is proportional to the sensitivity of thelight intensity sensor, and inversely proportional to the lightpath in the medium and the measurement range.

With the configuration of our refractometer, the measure-ment of turbidity has to face several issues. The interferenceof the laser is observed in a turbid medium, which formsspeckles that lead to unexpected results. In our configurationof the refractometer, different refractive indexes will result ina different light paths. The width of the laser beam and therefraction result in the nonuniform attenuation inside thebeam, which disturbs measurement of the attenuationfrom the laser spot power. In contrast to refractive index mea-surement, the attenuation measurement requires that the laserintensity is stable during the measurement as a referenceintensity. Besides the laser beam, the light diffused out ofthe beam is received by the light intensity sensor, which dis-turbs the power of the spot. Furthermore, attenuation makesthe light intensity too weak to measure, which causes badperformance in a high turbid medium. All these problemsdetermine that a simple light instensity sensor such asPSD cannot afford to measure the turbidity in a refract-ometer. To overcome these problems, a CCD is used todeal with these issues. With recording the light intensitydistribution, an image captured by CCD can be treatedwith a low pass filter to eliminate speckle, and the diffusedlight can be eliminated by applying a proper threshold. Thelaser intensity is automatically controlled to keep it stableduring all the measurement. By playing with a longer expo-sure time, weak light can be captured as well. To avoid thenonuniform light path inside the laser beam, only one ray oflight is traced and used to calculate turbidity.

In addition to the issues of measuring the turbidity with arefractometer, the turbid medium impacts the measurementof the refractive index as well. Due to the convergence of thelaser beam, the laser spot becomes asymmetric, when it iscaptured by a CCD that is nonperpendicular to the laserbeam. What is more, turbidity makes this phenomenonmuch more obvious. In addition to the symmetry of thelaser spot, the turbidity results in a shift of the laser spotpeak, which is proportional to the attenuation coefficient.This shift needs to be corrected when applying a mass-cen-ter-based algorithm to locate the laser spot. A CCD recordsall the distribution information of the laser spot, whichmakes it possible to retrieve the position informationmore accurately. A new algorithm, which tracks the locationthat divides the mass of the spot into two equal parts, is intro-duced in this paper, and is proved to be more accurate thanthe centroid algorithm in both the non-turbid environmentand turbid environment.

Through the simulations and various experiments, theaverage accuracy of our method based on the current refract-ometer reaches 8 NTU in a range from 0 to 200 NTU and1.15 NTU in a range from 0 to 20 NTU. We compared ourmethod with the nephelometer specified by the NTU stan-dard. The result computed by our method well fits the resultobtained from a nephelometer. The sensitivity can beimproved by increasing the length of the light path in themedium, which is very useful to guide the design of anew refracto-turbidimeter. According to the results, themethod introduced in this paper provides the capability to

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measure seawater refractive index and turbidity simulta-neously. Further more, since our method evaluates turbidityfrom the sum of the scattering coefficient and absorptioncoefficient, which are two significant properties in biologicaldomain, it is possible and an interesting topic to apply thismethod to the relevant areas.

AcknowledgmentsThanks to Marc Le Menn of SHOM (Service Hydrographi-que et Océanographique de la Marine) for providing thecalibrated formazin sample, and fruitful discussion aboutthe application.

References

1. A. R. Jones,“Light scattering for particle characterization,” Progr.Energ. Combus. Sci. 25(1), 1–53 (1999).

2. ISO7027: Water quality-determination of turbidity, InternationalStandard (1999).

3. EPA. Environmental Monitoring Systems Laboratory, Method180.1: Determination of turbidity by nephelometry; revision 2.0,(August 1993).

4. G. Mie, “Beiträge zur optik trüber medien, speziell kolloidaler metal-lösungen, Leipzig,” Ann. Phys. 330(3), pp. 377–445 (1908).

5. L. C. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,”Astrophys. J., 93, 70–83 (1941).

6. W. M. Cornette and J. G. Shanks, “Physically reasonable analyticexpression for the single-scattering phase function,” Appl. Opt.31(16), 3152–3160 (1992).

7. W. M. Irvine, “Multiple scattering by large particles,” Astrophys.4, 1563 (1956).

8. M. le Menn, “Instrumentation et métrologie en océanographie,”Hermès-Lavoisier (2007).

9. D. Malardé et al., “High-resolution and compact refractometer forsalinity measurements,” Meas. Sci. Tech. 1(20) (2009).

10. M. Le Menn et al., “Advances in measuring ocean salinity with an opti-cal sensor,” Meas. Sci. Technol. 22(11), 115202 (2011).

11. B. Hou et al., “Charge-coupled devices combined with centroidalgorithm for laser beam deviation measurements compared to a posi-tion-sensitive device,” Opt. Eng. 50(3), 033603 (2011).

12. A. Ishimaru,Wave Propagation and Scattering in RandomMedia, IEEEPress Series on ElectromagneticWave Theory,Wiley IEEE Press (1999).

13. I. Edwards, “Using photodetectors for position sensing,” SensorsMagazine (Dec. 1988).

14. DALSA Corporation. Genie m1280 datasheet, http://www.dalsa.com/prot/mv/datasheets/genie_m1280_1.3.pdf.(2009).

15. Hach Company. 2100 series laboratory turbidimeters data sheet, http://www.hach.com/asset-get.download-en.jsa?id=7639982021.(2010).

Bo Hou is a PhD student at TelecomBretagne, France. He received his mastersdegree in computer science from BeijingUniversity of Posts and Telecommunica-tions. He has worked for IBM China Devel-opment Laboratory, researching anddeveloping Business Intelligence systems.His research interests include informationsystems, image processing, and high-precision instrumentation.

Biographies and photographs of the other authors are not available.



http://dx.doi.org/10.1016/S0360-1285(98)00017-3

http://dx.doi.org/10.1016/S0360-1285(98)00017-3

http://dx.doi.org/10.1002/(ISSN)1521-3889

http://dx.doi.org/10.1086/144246

http://dx.doi.org/10.1364/AO.31.003152

http://dx.doi.org/10.1086/148436

http://dx.doi.org/10.1088/0957-0233/20/1/015204

http://dx.doi.org/10.1088/0957-0233/22/11/115202

http://www.dalsa.com/prot/mv/datasheets/genie_m1280_1.3.pdf






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