The extinction coefficient is one of the most importantoptical properties for the characterization of an inhomo-geneous turbid medium. It describes the probability oflight–matter interaction per unit distance and equalsthe sum of the scattering and absorption coefficients. Nu-merous methods to measure this quantity can be found inthe literature, such as time-gated transmission measure-ments [1], time resolved backscattering and Raman lidar[2], side-scattering detection in combination with mea-suring transmission [3], and extinction tomography [4].Some of these examples are restricted to homogeneousvolumes, while others can measure the extinction co-efficient resolved in either one or two dimensions. Acommon obstacle when probing turbid media is the suc-cessive light scattering events known as multiple scatter-ing. The direct consequence of detecting these undesiredphotons is an underestimation of the extinction coeffi-cient [1]. In this Letter we demonstrate for the first time,to the best of our knowledge, a technique based solely onside scattering to acquire depth-resolved images of theextinction coefficient where uncertainties introducedby the detection of multiple light scattering are stronglyreduced.Laser sheet imaging is a common approach used to
record side-scattered light in dilute media [5]. When ap-plied on more turbid samples, errors in the measurementare introduced by the detection of multiply scatteredlight. In 2008, a technique—structured laser illuminationplanar imaging (SLIPI)—capable of diminishing this un-wanted contribution of light was demonstrated [6], andits suppression capabilities were investigated quantita-tively by Kristensson et al. [7]. SLIPI combines laser sheetimaging and structured illumination [8] and consists ofsuperimposing a sinusoidal pattern on the incident lasersheet. When photons are multiply scattered, they losethis structural information and will instead appear as adiffuse background on the recorded image. To extractthe singly scattered photons, which are represented bythe amplitude of the modulation, three images are re-quired between which the phase of the sinusoidal patternis shifted 2π=3. The contribution of singly scattered lightis then obtained by calculating the rms of the images [8].Based on SLIPI, the effect of signal attenuation be-
tween two laser sheets is measured here, allowing the
average extinction coefficient to be calculated usingthe Beer–Lambert law. The proposed technique, nameddual SLIPI, simultaneously views the sample from bothsides of the laser sheet and takes advantage of the sym-metrical scattering properties of light (valid for sphericalparticles or random scattering media) to allow inhomo-geneous media to be probed.
Figure 1 shows a top view of the optical arrangementin which two cameras, positioned at þ90° and −90°, re-cord the scattered light. To explain the method in detail,one can assume a scattering sample being illuminatedwith a one-dimensional laser beam that propagates alongthe x axis with an initial intensity of I0. Equations (1) and(2) describe the singly scattered light intensity recordedby each camera at an arbitrary point along the initialdirection of the laser beam (x ¼ x0):
Fig. 1. Schematic of the detection arrangement for dual SLIPI.Two cameras, positioned at �90°, are used for the two SLIPImeasurements. The dashed region between the two laser sheetsindicate the probed volume over which the average extinctioncoefficient is calculated. The laser sheets propagate along the xdirection.
Here the subscripts denote either camera, while thesuperscript indicates the recording number. S is a samplefunction defining the magnitude of the light scattered at90°, and C describes the camera functions, such as col-lection angles and optics. The former of the two exponen-tial terms in each equation describes the decay of theinitial light intensity (laser extinction), while the latteris the reduction of the generated signal as it propagatestoward the camera (signal attenuation). The laser beamis positioned at z ¼ z0, while the two cameras are posi-tioned at z ¼ 0 or z ¼ L, respectively. The beam isnow shifted to z ¼ z0 þΔz, followed by an additional re-cording. The intensities reaching each camera are nowexpressed as
Because the laser sheet is shifted in space, the samplefunction is now denoted differently (to account for inho-mogeneities). Rewriting terms A and B as the product oftwo exponential decays and dividing Eq. (1) with Eq. (2)as well as Eq. (3) with Eq. (4) leads to
I11ðx0ÞI12ðx0Þ
¼C1=C2 ·exp
�−
Rz00 μeðx0;zÞdz
�
exp
�−
Rz0þΔzz0 μeðx0;zÞdzÞ·exp
�−
RLz0þΔzμeðx0;zÞdz
�;
ð5Þ
I21ðx0ÞI22ðx0Þ
¼exp
�−
Rz00 μeðx0;zÞdz
�·exp
�−
Rz0þΔzz0 μeðx0;zÞdz
�
C2=C1 ·exp
�−
RLz0þΔzμeðx0;zÞdz
� :
ð6Þ
Equations (5) and (6) contain parts with identical infor-mation that can be divided to unity, leaving only the ex-ponential terms for the intensity decay between z ¼ z0and z ¼ z0 þΔz according to
I11ðx0Þ · I22ðx0ÞI21ðx0Þ · I12ðx0Þ
¼ exp
�2Z
z0þΔz
z0μeðx0; zÞdz
�: ð7Þ
From this relation, the average extinction coefficient cannow be calculated through Eq. (8):
�μeðx0Þ ¼ ln
�I11ðx0Þ · I22ðx0ÞI21ðx0Þ · I12ðx0Þ
�·
12Δz
: ð8Þ
In summation, the method can measure the average ex-tinction coefficient between two locations, separated byΔzmm. Although explained only in one dimension, themethod is capable of acquiring two-dimensional informa-tion, where the collection optics and number of pixelsdefine the lateral resolution, while the axial is definedby Δz. The technique relies, however, on three assump-tions. First, light scattering properties are assumed to beidentical at þ90° and −90°. According to the Mie theory,this is valid when probing spherical particles or randomscattering media. Second, to perform pixel-to-pixel calcu-lations, light is assumed to be collected at 90° only. A highcamera f-number or spatial filtering is therefore appropri-ate. Finally, as the calculations are based on the Beer–Lambert law, only singly scattered photons should be de-tected. Multiply scattered light intensity present in theSLIPI images will lead to an underestimation of the ex-tinction coefficients.
To investigate the axial resolution and to verify thetechnique, a cuvette filled with a homogeneous mixtureof scattering polystyrene microspheres (0:5 μm in diam-eter) and distilled water was probed. This provided priorknowledge, as the resulting extinction coefficientsshould be of a single value throughout the entire sample.Figure 2(a) shows an example of such a dual SLIPImeasurement with Δz ¼ 4mm, together with images ob-tained using either laser sheet imaging or SLIPI. Thegraphs below each image show an average horizontal
-0.1 0 0.1 0.2 0.3 0.40
1
0.51.01.52.03.04.05.0
Extinction coefficient [mm ]-1
Nor
mal
ized
cou
nts
[a.u
]
0.2
0.4
0.6
0.8 µ = 0.118 mm-1e
_ ∆z [mm]
0
0.1
0.15
Laser sheet imaging SLIPI dual SLIPI [mm ]-1
∆z = 4
0.05
-1Best fit:µ = 0.117 mme
-1µ = 0.118 mme
µ e
10 mm
(a)
(b)
Fig. 2. (Color online) (a) Images and average cross sections ofa homogeneous scattering sample obtained using laser sheetimaging, SLIPI and dual SLIPI with Δz ¼ 4mm. The laser sheetand SLIPI images are normalized to unity, whereas the extinc-tion coefficient values are given by the color bar. (b) Histogramsof the extinction coefficients for seven different Δz. It is seenthat the results converge to a single value of μe, confirming thehomogeneity of the probed sample.
cross section within the dashed area. The laser sheet im-age shows an increase of intensity with distance (the la-ser enters from the right), a consequence of detectingmultiply scattered light. This falsely suggests that moreparticles are situated on the leftmost side. When suppres-sing multiply scattered light using SLIPI, the image showsan exponential decay of light intensity with distance,while the homogeneity can be seen directly with dual SLI-PI. To evaluate these dual SLIPI results, the averageextinction coefficient can also be estimated by fittingan exponential curve to the SLIPI data [see Fig. 2(a)].The result—�μe ¼ 0:117mm−1
—is in accordance withthe average value obtained with dual SLIPI (�μe ¼0:118mm−1). Note that this alternative approach to ex-tract μe is only applicable for homogeneous media.Figure 2(b) shows histograms for seven dual SLIPI
images of the cuvette, with Δz values ranging from 0.5to 5mm. As is shown, a too-small Δz (for this specificsample) results in a broadened histogram, with even ne-gative values. However, all histograms converge to a sin-gle value �μe ¼ 0:118mm−1 when increasing Δz, whichindicate the homogeneity of the probed sample. Theseresults demonstrate the trade-off between axial resolu-tion and precision as the effect of signal attenuation overΔz must exceed the acquisition noise level.Figure 3 shows a comparison between laser sheet
imaging, SLIPI, and dual SLIPI when applied to inho-mogeneous turbid media. Two different atomizing air-assisted water sprays were studied: one solid cone spray(top row) and one six-hole injector (bottom row). Be-cause of the lack of specific spray structures (e.g., hollowregions) in the solid cone case, errors caused by multiplyscattered light are not directly apparent. ApplyingSLIPI does not therefore lead to any distinct image
improvements but results in an asymmetric spray image.The dual SLIPI image does, however, reveal the true sym-metry of the spray together with more accurate informa-tion regarding its inner conical structure. The six-holeinjector consists of six spray plumes and, not too fardownstream, a hollow central region. The three imagingtechniques were applied on one of the plumes, and theimages in Fig. 3 show approximately half of the spray.As seen, the hollow region becomes visible when multi-ply scattered light is suppressed using either SLIPI ordual SLIPI. Comparing the dual SLIPI results indicatesthat the solid cone spray is almost twice as dense, withvalues of μe up to ∼0:55mm−1. Also noticeable is that thedual SLIPI results are not affected by intensity variationsin the laser sheet profile.
To conclude, dual SLIPI is a technique capable of ac-quiring depth-resolved images of the extinction coeffi-cient. The method is based on side-scattering detectiononly, and because the sample is viewed from two oppo-site sides simultaneously, uncertainties related to theunknown distribution of scattering particles can be can-celed out. This allows the technique to be applied on in-homogeneous media, given that three-way optical accessis available. Multiply scattered light intensities, whichlead to an underestimation of the extinction coefficientwhen detected, are suppressed by the implementationof SLIPI instead of traditional laser sheet imaging, thusimproving both accuracy and precision. Finally, dualSLIPI does not require any calibration and can directlybe applied to the central region of an inhomogeneousscattering medium.
Finally, the authors wish to thank the Linné Centerwithin the Lund Laser Center as well as the Centre forCombustion Science and Technology through the Swed-ish Foundation for Strategic Research and the SwedishEnergy Agency for financial support. Also the EuropeanResearch Council Advanced Grant Development and Ap-
plication of Laser Diagnostic Techniques for Combus-
tion Studies is acknowledged.
References
1. L. Wang, X. Liang, P. Galland, P. P. Ho, and R. R. Alfano,Opt. Lett. 20, 913 (1995).
2. A. Ansmann, M. Riebesell, and C. Weitkamp, Opt. Lett. 15,746 (1990).
3. H. Koh, D. Kim, S. Shin, and Y. Yoon, Meas. Sci. Technol.17, 2159 (2006).
4. J. Lim, Y. Sivathanu, V. Narayanan, and S. Chang, Atomiz.Sprays 13, 27 (2003).
5. J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodt, andE. H. K. Stelzer, Science 305, 1007 (2004).
6. E. Berrocal, E. Kristensson, M. Richter, M. Linne, andM. Aldén, Opt. Express 16, 17870 (2008).
7. E. Kristensson, E. Berrocal, M. Richter, S. G. Pettersson,and M. Aldén, Opt. Lett. 33, 2752 (2008).
8. M. A. A. Neil, R. Juškaitis, and T. Wilson, Opt. Lett. 22,1905 (1997).
0
0.1
0.2
0
0.1
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0.5
Laser sheet imaging SLIPI dual SLIPI [mm ]-1
10 mm ∆z = 2
Hollowregion
Spray plume
∆z = 2
µe
Spray plume
Fig. 3. (Color online) Images obtained using either laser sheetimaging, SLIPI, or dual SLIPI. Top row, solid cone spray. Bot-tom row, single-spray plume of a six-hole injector. The lasersheet and SLIPI images are normalized to unity, whereas theextinction coefficients are given in the color bar. Δz is givenin millimeters. The laser sheet enters from the right.
