This invention pertains in general to the field of optical analysis. More particularly the invention relates to optical analysis of scattering media and even more particularly to quantitative measurements of the optical properties of disperse elastic and/or inelastic scattering media. This invention, called Modulated Illumination

Imaging, allows up to three-dimensional measurements and is applicable to

inhomogeneous turbid media.

BACKGROUND

It is known that electromagnetic radiations, generated for example by a laser, can be used to measure properties of a scattering sample. US 2002/01 13136 Al discloses a method of determining mass distribution within an ensemble of particles, comprising directing a beam of excitation light into the ensemble. However, this method does not allow for direct two-dimensional measurements, since only a single beam of light is utilized. In addition no correction for the scattering and multiple light scattering intensity is employed in this approach.

Several planar laser imaging techniques have been developed using a laser sheet for two-dimensional measurements of, for example, spray characteristics.

Although these techniques use different properties of light scattering (e.g. Mie scattering, laser induced fluorescence etc), they are all based on the single scattering approximation, assuming that the detected photons have experienced a maximum of only one scattering event prior to arrival at the detector. This assumption remains valid when the free photon path length is larger than the dimensions of the probed medium. However, within optically dense media, a large amount of photons are in fact scattered several times and the single scattering assumption is no longer valid. As a result of this successive light-particle interaction, three phenomena are observed:

First, the incident light radiation is attenuated along its initial direction when it traverses the disperse medium due to scattering and/or absorption. This effect is called Light Extinction. Depending on the position along the line-of-sight propagation, particles are not illuminated with the same intensity. Second, the radiation scattered (elastically or inelastically) from the incident beam (single scattering) is also attenuated between the position of the first scattering event and the detector. This effect is called Signal Attenuation.

Finally, the singly scattered light might interact with a number of particles within the sample, a phenomenon called Multiple Scattering. When detected, this so- called "extraneous light" introduces errors in the measurement. The degree of error is directly related to the optical density of the probed medium.

US 6184989 Bl discloses a method of extracting the two-dimensional probability density function of local extinction coefficient using laser sheet tomography. The principle of the technique is based on transmission measurement and the system is able to account for laser extinction and signal attenuation due to the tomographic procedure. However, multiple scattering remains still the main factor strongly limiting the accuracy of the measurement.

Conventional attenuation/extinction method (called transmission measurement) measure experimentally the ratio 7/7 7, in order to extract the optical properties of a scattering/absorbing sample from the Beer-Lambert derivation such that:

Eq. 1

I

f exp(-/ · a _e ^■ C) with a _e = σ + σ, a

I, Eq. 2

I

f

e pH - /0 with μ _£ = σ · C

I,

Eq. 3

I

exp(-OZ ⁾ ) with OD = l - μ _(!

I, Eq. 4

wherein:

It : incident intensity - before light crosses the sample,

I/ : final intensity - after light crosses the sample,

/ : path length through the sample,

C : concentration (number density) of particles/molecules,

a _s : scattering cross-section averaged over a distribution of particles/molecules, σ _α : absorption cross-section averaged over a distribution of particles/molecules, a _e : extinction cross-section averaged over a distribution of particles/molecules, p _e : extinction coefficient averaged over a distribution of particles/molecules,

OD: optical depth, and wherein C, σ ₅ , σ _α , σ _β , μ _ε and OD may be referred to as optical properties.

However, if the medium has an OD > 1 , then a light intensity contribution I _ms from scattering and multiple scattering is introduced into the measurement such that:

I _f = /, exp(-OZ)) + /„„

Eq. 5

In this case, the use of the conventional Beer-Lambert law, without taking into account I _ms within the equation will provide an underestimation of OD from the experimental transmission measurement.

A method to take into account the multiply scattered light contribution in images recorded with planar laser imaging has been disclosed in a published article by E. Berrocal, E. Kristensson, M. Richter, M. Linne and M. Alden, "Multiple scattering suppression in planar laser imaging of dense sprays by means of structured

illumination," ILASS 2008, Sep. 8-10, 2008, Como Lake, Italy. The method, Structured Laser Illumination Planar Imaging (SLIPI), is based on using spatially modulated excitation light in order to remove a part of the multiple light scattering intensity I _ms detected after adequate image post-processing. The results show that by removing a part of I _ms , a better contrast may be obtained, providing qualitative images with enhanced contrast. However, as only a part of I _ms was removed according to this article, the process was not optimal/designed to provide quantitative measurement.

Hence, an improved method and system for accurate measurement of optical properties in disperse scattering media, where the single scattering regime is no longer valid (OD>\) would be advantageous. More specifically, a method and system allowing for increased accuracy/quality and extended capability of the measurement of optical properties in turbid media is desired.

SUMMARY

Accordingly, the present invention preferably seeks to mitigate, alleviate or eliminate one or more of the above-identified deficiencies in the art and disadvantages singly or in any combination and solves at least the above mentioned problems by providing a method, a system and a computer-readable medium for measuring (in one, two or three-dimensions) optical properties of an elastic or inelastic scattering medium, according to the appended patent claims. An elastic scattering medium is a medium, in which a photon changes direction due to a scattering event and conserves its incident energy (e.g. Rayleigh, Mie scattering). As a result, the wavelength of the scattered radiation is conserved.

An inelastic scattering medium is a medium, in which a photon changes direction due to a scattering event and loose (or gain) some energy (e.g. Raman scattering, fluorescence). As a result, the wavelength of the scattered radiation is shifted.

In a first aspect, there is provided a method for measuring optical properties of an elastic or inelastic scattering medium, comprising: directing a first light beam towards the scattering medium along a first line; directing a second light beam towards the scattering medium along a second line which is substantially parallel with the first line but off-set a predetermined distance from the first line; whereby the light beams form an illumination having a substantially sinusoidal intensity pattern; measuring intensity of the light passing through the scattering medium at at least three positions, a first intensity, (Ιβ) at a first position related to the first line, a second intensity (7#) at a second position related to the second line and a third intensity (I _ms ) at a third position intermediate of the first and the second positions; obtaining input intensities (/, _/ and hi) of the light entering the scattering medium; calculating at least a local extinction coefficient of the scattering medium from said at least three intensity measurements and said at least two input intensities.

In an embodiment, the measured intensities may be measured at the end of the medium opposite to the input side, i.e. intensities of light passing straight through the medium in transmission mode. Alternatively or additionally, the measured intensities may be measured from the side along the light beams, i.e. intensities of light scattered from the light beams in side mode.

In another embodiment, the intensities may be measured simultaneously in time for the same medium. Alternatively, the intensities may be measured separately in time for the same medium.

In a further embodiment, the method may comprise, in transmission mode when the measurement is made on transmitted light at the end of the medium, the intermediate intensity measurement (I _ms ) is an estimation of scattered light, whereupon the desired non-scattered intensity may be obtained by subtracting the scattered intensity (I _ms ) from the measured intensity (I/i or Ι _β ), and/or, in side mode when the measurements is made from the side of the medium, the intermediate intensity measurement is an estimation of light scattered more than one time, i.e. multiple scattered light, whereupon the desired singly scattered intensity may be obtained by subtracting the multiple scattered intensity (I _ms ) from the measured intensity (fy or Ip).

In a still further embodiment, the singly scattered intensities and/or the multiple scattered intensities may be obtained by Fourier transformation of the measured intensities.

In a yet further embodiment, several light beams may be arranged in a line (Y- axis) forming a light sheet beam with a substantially sinusoidal intensity in a direction which is perpendicular to the light beam direction (X-axis) and/or wherein several light beams may be arranged in a matrix in two directions (Y-axis and Z-axis) forming a matrix having substantially sinusoidal intensities in the two directions perpendicular to the light beam direction.

In still another embodiment, several measurements may be made with the medium in different angular rotational positions, and the measurements may be combined to provide a tomographic image of the medium.

In yet another embodiment, the light may be substantially monochromatic having a predetermined wavelength and wherein at least two measurements of the optical properties may be made with light having different wavelengths.

In a still further embodiment, each modulated image may be post-processed by frequency filtering, for example low-pass-filtering.

In a yet further embodiment, images may be recorded with two illuminations at two positions having a distance (AT) from each other and detected from two sides resulting in four intensity measurements; and wherein the extinction coefficient may be calculated according to the formula:

In a still yet further embodiment, there is provided a method for quantitative

measurements of the optical properties in a disperse scattering medium, comprising the steps of: directing a spatially modulated light sheet towards a sample of the medium, which light sheet has a sinusoidal spatial modulation in a direction perpendicular to the light direction; obtaining a signal (S _pi ), which is related to the light power of the incident light; obtaining a signal (¾ ^■ ), which is related to the light power of the final transmitted light; obtaining a SLITI intensity measurement (¾ ) corresponding to the incident light intensity without the sample; measuring a SLITI signal (S _t / )

SUBS 11 1 U I b SHEET (TCULETZB) corresponding to the final transmitted light intensity after crossing the sample;

measuring a SLIPI signal (S _mei j) corresponding to the light intensity scattered from the sample; calculating at a given depth (O) within the medium, an extinction coefficient e(m,n) f° ^{r eacn} voxel V( _mi „) according to the formula

wherein

l _v is the width of the voxel, seen from the detector; and

d _v is the depth of the voxel, seen from the detector.

In another aspect, there is provided a system for calculating a number of extinction coefficients of a disperse scattering media, comprising: a light unit arranged to illuminate a sample of disperse scattering medium; a detection unit arranged to detect images comprising side scattered light from the sample and/or transmission light through the sample; and a processor arranged to perform the calculating steps mentioned above.

In a further aspect, there is provided a computer-readable medium having embodied thereon a computer program for processing by a computer, wherein said computer program comprises code segments for performing the steps mentioned above.

Further embodiments of the invention are defined in the dependent claims. The present invention has the advantage over the prior art that it provides more accurate measurements and characterization of elastic and/or inelastic scattering media. A further advantage is that it provides the possibility to perform measurements at higher optical depth, where conventional techniques are limited. In addition, the invention allows for three-dimensional measurements which are of fundamental importance for the complete characterization of inhomogeneous media. BRIEF DESCRIPTION OF THE DRAWINGS

These and other aspects, features and advantages of which the invention is capable of will be apparent and elucidated from the following description of

embodiments of the present invention, reference being made to the accompanying drawings, in which

Fig. 1 is a schematic showing the classification of the techniques based on the Modulated Illumination Imaging method;

Fig. 2 is an illustration of intensity modulation. The upper portion shows how two beams form a sinusoidal intensity pattern. The lower portion shows how several beams are arranged to form a sinusoidal pattern in both the vertical and horizontal direction;

Fig. 3 is a schematic illustration of the different systems that are based on the Modulated Illumination Imaging method;

Fig. 4 is a schematic top view illustration showing a system according to an embodiment;

Fig. 5 is a procedure to deduce the extinction coefficient of a scattering medium based on the recording of a single modulated image according to an

embodiment. Here, a modulated light sheet crosses a sample of polystyrene spheres in suspension in distilled water, and the scattered light intensity is detected from the side (Single-SLIPI);

Fig. 6 is an alternative to the procedure described in Fig. 5 where a Fourier transform analysis is employed to deduce the amplitude of the modulation for each pixel column of the modulated image (Single-SLIPI);

Fig. 7 is a schematic top view illustration showing a system according to another embodiment;

Fig. 8 is a schematic top view illustration showing a system according to another embodiment;

Fig. 9 is an illustration showing another system (Mil-Scan) according to an embodiment;

Fig. 10 is a side view illustration of the system (Mil-Scan) of Fig. 9;

Fig. 1 1 is a top view schematic illustration showing two positions of the modulated laser sheet crossing an inhomogeneous scattering medium and being imaged by a camera;

Fig. 12 illustrates the resultant three-dimensional matrix of voxels formed by a number of two stacked images. This illustration, together with Fig. 11, describe the _{! Γ} , ... „„.. _ ,_

8

system (Mil-Scan) used for the correction calculation of signal attenuation and laser extinction, according to an embodiment;

Fig. 13 is a perspective view showing a magnification of a single voxel imaged by a single pixel on the detector array;

Fig. 14 is a series of nine images where the incident modulated laser sheet crosses an inhomogeneous scattering medium, which is, here, an aerated water spray. The phase shift of the sinusoidal modulated illumination is in this case Δ(Φ) = 2π/9;

Fig. 15 the upper part shows the conventional image built up from the nine images given in Fig. 14 when applying Eq. 8. The middle part shows the resultant image built up from the nine images given in Fig. 14 when applying Eq. 7. The lower shows the extinction coefficient of the spray built up after correcting for signal attenuation and laser extinction using Eq. 6;

Fig. 16 illustrates the resultant two-dimensional mapping of the extinction coefficients between position 0 (central axis of the spray) to position 7 (edge of the spray). The positions have a 1 mm distance separation between each other;

Fig. 17 illustrates the optical depth OD, i.e. the integral of j ^~ u _{e{m n)} along the path travelled by the photons for a given direction. On the left side a two-dimensional mapping of OD between the central axis of the spray and the camera is shown. On the right side the OD mapping is related to the laser beam transmission of trough the spray;

Fig. 18 is a flow chart describing the Mil-Scan procedure;

Fig. 19 is a schematic top view illustration showing a system (Dual-SLIPI) according to an embodiment;

Fig. 20 is a schematic top view illustration showing an alternative imaging approach for a system (Dual-SLIPI) according to an embodiment;

Fig. 21 is a schematic illustration of three different computer tomography reconstruction algorithms;

Fig. 22 is a schematic illustration of the Tomo-SLITI procedure according to an embodiment;

Fig. 23 is a comparison between uncorrected and corrected images. By using a correction procedure, implemented in the improved process, it is seen that the residual lines induced by laser intensity fluctuation are suppressed. For comparison purpose, a single image of the modulated laser sheet crossing the spray is also shown on the top; DESCRIPTION OF EMBODIMENTS

Several embodiments of the present invention will be described in more detail below with reference to the accompanying drawings in order for those skilled in the art to be able to carry out the invention. The invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. Furthermore, the terminology used in the detailed description of the particular embodiments illustrated in the accompanying drawings is not intended to be limiting of the invention.

1) Mil - Modulated Illumination Imaging

The invention described here is called Modulated Illumination Imaging (Mil) and includes the use of:

- a spatially modulated incident light radiation (which can be generated by a Laser, a Laser diode, an LED, a Tungsten lamp etc)

- a image post-processing algorithm

- a theoretical derivation based on the Beer-Lambert relation

Mil is a quantitative imaging technique capable of extracting the optical properties of turbid media. As depicted in Fig. 1 , the Mil family includes approaches based on SLIPI (Structured Laser Illumination Planar Imaging) and on SLITI (Structured Laser

Illumination Transmission Imaging). Depending on the approach employed, results can be extracted up to three-dimensions.

An illustration of the modulated illumination used to operate Mil is depicted in Fig. 2, viewed from both the front and the side. In Fig. 2 (I) the minimum spatially modulated pattern to operate Mil is shown. By duplicating this pattern, a new profile in two dimensions can obtain as exemplified in Fig. 2 (II). Depending on the

source/detector configuration and the medium of interest different Mil systems can be utilized. A summary of all systems representing the Mil family is depicted in Fig. 3.

The main optical property extracted from the Mil method is the extinction coefficient, i _e , averaged over a number of particles/molecules. Based on this measurement other optical properties can be derived such as:

- the extinction cross section, a _e = fi ^~ C

- the particle/molecule concentration, C = J _e I cr, ,

- the optical depth OD = / · /J _e , Also, by operating Mil measurements of i _e at different wavelengths, the scattering cross-section, σ ₅ , and absorption cross-section, σ _α , can be extracted from the extinction cross section, <r _e - σ + σ _α .

2) SLIPI - Structured Laser Illumination Planar Imaging

SLIPI is an imaging technique which has demonstrated, both experimentally and by simulation, capabilities for multiple scattering suppression in planar imaging of sprays, thereby improving visualization (qualitative imaging).

The principle of the technique is to use a laser sheet which is spatially modulated in intensity. This modulation, which may have a sinusoidal pattern, acts as a "finger print" allowing the singly scattered photons to be recognized, as they will scatter according to the sinusoidal pattern. In contrast, photons which, after a first scattering event, deviate from their trajectory will appear as a position-dependent intensity noise on the recorded image and will not follow the sinusoidal modulation pattern. These photons have been scattered more than once. To extract the single scattering intensity from the detected intensity, which contains both singly and multiply scattered light, the method comprises extracting the amplitude of the modulated components in the recorded images, which can be estimated by the difference between the maximum intensities and the minimum intensities divided by two.

However, by using a single modulated laser sheet illumination, parts of the probed sample are not illuminated i.e. the parts wherein the sinusoidal pattern is zero or small. This may be compensated for by shifting the line-pattern vertically, inducing a shift on the position of the single scattering events, while the contribution from multiply scattered light remains mostly unaffected. When vertically shifting the modulation (N, - 1) times, N, images are recorded with an angular shift of Δ(Φ) = 2JI//V, between each image as shown in Fig. 14 with N, = 9.

Finally, the resulting SLIPI images S, as well as the conventional image Conv. , shown in Fig. 15, are constructed from the Ni modulated images according to the following equations:

Eq. 8 wherein 7, and are intensity values and the subscript j and k denotes the different recordings of the modulated images.

In Eq. 7, the pair-wise subtraction [I _j - /*] removes similar image features (introduced by the multiply scattered light) while unique image features (from the singly scattered light) are kept. When averaging the N _t images the conventional image Conv. is extracted using Eq. 8. This image is, in theory, equal to the one acquired by using a homogeneous laser sheet, thus allowing the two techniques to be easily compared. Note that the construction of a SLIPI image requires a minimum of three vertically shifted images, in order to preserve the spatial resolution of the detector. Note also that the SLIPI image S corresponds to the amplitude of the modulation related to the recorded modulated images. This is calculated, here, on a pixel-to-pixel basis by means of Eq. 7.

Note that Eq. 7 also holds for transmission measurement (SLITI) and will be referred in the text as the general structured illumination equation.

In an embodiment applicable to homogeneous scattering disperse media, a SLIPI image is obtained based on the use of a single modulated image (instead of N _t >3 as described in Eq. 7), with a system 40 according to Fig. 4.

The system 40, comprises an optical unit 420, which produces a sinusoidal modulated light sheet arranged to irradiate, at a given position, a scattering sample 410. The scattered light is detected from the side by a camera 430 arranged to detect two- dimensional images comprising the side scattered light 440.

A single image of a modulated laser sheet crossing a homogeneous scattering medium is seen in Fig. 5 (I). The scattering medium is, here, a homogeneous solution of polystyrene particles of 0.5 micron in suspension in distilled water which is contained within a glass cuvette. Each pixel represents a number of photon counts, as a function of the horizontal distance along the axis M and the vertical distance along the axis O in [mm]. Based on this image, the maximum and minimum values of the modulation along O may be extracted, as shown in Figs. 5 (II), for all pixel columns along the horizontal distance M.

Figs. 5(11) are illustrations showing maximum and minimum values of the modulation at horizontal distance =0.4 mm and =9.3 mm, respectively. It is seen that the amplitude of the modulation is strongly reduced between the two positions. The maximum values (or peaks) are interconnected by a line called I _max and the minimum values (or valleys) are interconnected by a line called /,„,„. The intensities /,„,„ represent the light introduced by multiple scattering (I _m j„~lMs)- Next, the corrected intensity is calculated by taking the difference between curve corresponding to the peaks I _max and the curve corresponding to the valleys I _min . This corrected intensity corresponds to the amplitude of the modulation only (without the off-set value corresponding to I _min ) and is what we refer to as a Structured Illumination signal. For this reason we will denote this corrected intensity, S. The calculations are carried out for each column of pixels along M and a corrected intensity S is obtained for each M and O value, which is plotted in a diagram shown in Fig. 5 (V). Finally, from Fig. 5 (V), the intensity profile S (integrated along O) is compared with a single exponential decay as shown in Fig. 5 (VI). Based on Eq. 3 the averaged extinction coefficient μ _ε is extracted from the best exponential fitting, as a function of the horizontal distance. In this example ju _e - 0.361 mm ^"1 and as / = 10 mm the optical depth OD = 3.61.

Another approach to extract the loss of light based on a single modulated image is to study the information stored within the image in the frequency domain rather than in the spatial domain. Every image is built up by a certain combinations of sinusoidal waves, with different directions, magnitudes and frequencies. This information can be accessed through the Fourier transform. With SLIPI a sinusoidal component is superimposed onto the illumination and the magnitude of this spatial frequency therefore becomes very prominent in the Fourier transform. However, as this illumination travels through a scattering and/or absorbing medium, the magnitude of the sinusoidal structure weakens. This reduction of magnitude can be measured through the process illustrated in Fig. 6. First, a single image of the modulated light sheet is recorded Fig. 6 (I). Second, a cross section for each column of the image is extracted. This process is illustrated, in Fig. 6 (II), for four different positions along the direction of the light sheet. Similar to Fig. 5 (II), it is noticeable how the amplitude of the modulation decreases with distance. The Fourier transform is then calculated for each cross section in Fig. 6 (III). The ±1 interference orders, whose magnitude describes the strength of the incident spatial sinusoidal modulation, are seen in Fig. 6 (IV). Finally, for each column the magnitude of the sinusoidal component is measured and plotted as a function of distance. An example of a result is presented in Fig. 6 (V). An exponential fitting routine is then used together with the Beer-Lambert law to extract the averaged extinction coefficient as previously explained.

Note that the two processes (spatial and Fourier peaks detection) which are based on a single modulated image, are approximations of the process operated in Eq. 7 (with Nj > 3 modulated images). 3) SLITI - Structured Laser Illumination Transmission Imaging

In a further embodiment applicable to homogeneous scattering disperse media, images using SLITI are obtained with a system 70 according to Fig. 7.

The system 70 comprises an optical unit 720, which produces a sinusoidal modulated light sheet/beam arranged to irradiate a scattering sample 710. The transmitted light 740 is detected by a camera 730 to produce two-dimensional images of the transmitted light intensity. Similar to SLIPI, a SLITI image is obtained based on the general structured illumination equation (Eq. 7) where the minimum number of modulated images is N, >3.

In an embodiment suitable for detection of the transmitted modulated light, the camera may be arranged in conjunction with a dye cell, i.e. on the side of the dye cell, as shown in the system described in Fig. 3 (II). The Dye cell can be, for example, a liquid solution in a cuvette, containing Rhodamine 6G which can be excited at wavelength λ=532 nm and is fluorescent at longer wavelengths.

In an embodiment suitable for detection of modulated light beams, the camera may be arranged in conjunction with a screen, i.e. behind the screen, as shown in the system described in Fig. 3 (I).

In an embodiment applicable to homogeneous scattering disperse media, a SLITI image is obtained based on the use of a single modulated image (instead of N, >3 as described in Eq. 7), with a system 70 according to Fig. 7. The maximum and minimum peaks of the modulation are calculated as shown previously (see Fig. 5 and 6). If a light beam, which is modulated in both the vertical and horizontal direction (see Fig. 2 (II)), is used - instead of a modulated light sheet which is modulated along the vertical direction only (see Fig. 2 (I)) - the process described above must be operated along both the horizontal and vertical directions in order to extract the incident and final intensity profiles /, and 1/ . These data are introduced in the Beer-Lambert relation given in Eq. 3 and ]2 _e is directly deduced. Note that, here, J _e is extracted from the measurement of an intensity ratio given at distance M= I while the side technique describe previously extract I _e from an exponential fitting of the curve along M.

4) Mil - Scan

According to Fig. 8, a system 80 is provided. The system 80 comprises an optical unit 820, which produces a sinusoidal modulated laser sheet arranged to irradiate a scattering sample 810. The system further comprises a detection unit 830 and 850 _ _vv .. ,..„ , ,

14

arranged to detect a succession of two-dimensional images comprising respectively the side scattered light 840 from the sample, and the transmitted light 860 through the sample. The system further comprises a processor 870 arranged to perform the SLIPI image post-processing and the calculating steps according to an aspect.

The following embodiment is suitable for inhomogeneous disperse scattering media and combines SLIPI with SLITI. The following detailed description focuses on embodiments applicable to the calculation of extinction coefficients for each voxel based on a number of SLIPI images. The embodiments encompass a method, system, and a computer readable medium.

Experimental Setup

In an embodiment, according to Fig. 9, a system 90, viewed from the top, is provided. A modulated laser sheet is formed by a laser source (not shown), e.g. a frequency doubled Nd:YAG laser, λ = 532 nm, operating at 10 Hz repetition rate. A small portion of the central Gaussian beam is selected and spatially filtered to create an initial near top hat intensity distribution i.e. a laser beam with a near-uniform fluence (energy density) within a circular disk. The line structures are formed using a transmission Ronchi grating (not shown, a constant-interval bar and space square wave optical target) and were shifted vertically by tilting a 1 mm glass plate (not shown). The laser beam was expanded in the vertical dimension and focused in the other direction, into a laser sheet 420 by combining two oppositely orientated (rotated 90 degrees around the optical axis in relation each to each other) positive cylindrical lenses (not shown) and was 3.3 cm high in the measurement region and in the order of a few tenth of a millimeter thick. The resulting spatial period of the modulation is 1.15 mm

(distance between the lines). Such a laser sheet generating system is shown in for example the above-mentioned published article, the entire contents of which is incorporated in the present specification by reference. Other methods of forming a laser sheet modulated in the vertical direction may be used.

The modulated laser sheet 420 was vertically shifted 8 times with a

displacement of 128 μηι between images to produce nine modulated images (see Fig.

14). At each of the nine positions an average over 500 images were recorded by a 14-bit Electron Multiplying CCD camera 910 (iXon-897, 512 X 512 pixels, not shown). The camera field of view is marked by a dotted line in Fig. 10. To keep the contribution of multiple scattering as low as possible the full angle of the collection optics was fixed as small as possible such that Q _co = 1.35°. This was obtained by choosing a f-number F# = ^

8 on a Nikkon 200 mm focal length objective. The imaged area was situated at 2.3 cm below a nozzle tip, which generate a disperse scattering cloud of fine droplets 920. In this embodiment, a dye cell 930, i.e. a cuvette containing a solution of Rhodamine 6G, was located next to the spray system 920. The dye cell was illuminated by the laser sheet after crossing the spray providing a measurement of the light transmission, which was recorded by the camera 910. Thus, the camera works here as both a first detector and, together with the dye cell, as a second detector (see Fig. 2). Furthermore, a portion of the incident beam 940 was extracted and guided by mirrors 950 around the spray to the dye cell in order to monitor the pulse-to-pulse intensity fluctuation of the laser sheet.

In Fig. 10, a side view of the system according to Fig. 9 is shown. The nozzle

1010 is a Delavan AL-45 of tip diameter equal to 3 mm, producing a narrow angle spray pattern with a nominal angle of 15°-20° in ambient air. This air assisted nozzle, is an internal mixing nozzle, where a change in air or liquid injection pressure results in a change of flow or atomization. An increase of air pressure decreases flow and increases atomization while an increase of liquid pressure increases flow and decreases atomization. The investigated spray was running in steady state at 3 bar water pressure and 4.2 bar air pressure delivering a liquid flow rate of 21 1/hour and an air flow rate of 175 1/min in ambient air. Due to the internal mixing, breakups occur already at the nozzle tip exit producing a dense elongated cloud of fine droplets of -15 μτη nominal diameter (droplet size provided by the manufacturer). The camera field of view 1020 is shown with a dotted line.

To obtain the value of the extinction coefficient in three dimensions, SLIPI images of the spray 920 and the dye cell 930 are calculated based on Eq. 7 (using 9 modulated images as shown in Fig. 14) for 30 successive planes, where the spray nozzle was translated perpendicularly to the laser sheet with a step of 500 μηι between each image as principally shown in Fig. 1 1. This scanning process was performed from the spray edge closest to the camera to the centre of the spray (corresponding to a total distance of 1.5 cm), resulting in an increase of the signal attenuation at each translation step.

Note that the probed sample may be any kind of dispersed medium, such as a scattering and/or absorbing, a homogeneous or inhomogeneous, a monodisperse or polydisperse medium. Correction for Signal Attenuation and Light Extinction

To extract the extinction coefficient distribution within each of the 30 SLIPI planes obtained above, the following calculations were performed. A single SLIPI image represents the light intensity which is close to the pure single light scattering intensity. However, these images are still affected by the attenuation of the emitted signal between the light sheet and the camera and by the extinction of the light sheet as it propagates through the spray along the incident direction. As a result, the SLIPI images must be adequately processed in order to obtain valuable quantitative information regarding the optical properties of the sample, and more specifically, to extract the value of the extinction coefficient. The mathematical procedure to correct for signal attenuation and light extinction is based on the Beer-Lambert law and is described as follows:

Fig. 1 1 is a top- view schematic illustration showing two positions of the modulated laser sheet crossing an inhomogeneous scattering medium and being imaged by a camera. At each position, nine modulated images were recorded to form one SLIPI image according to Eq. 7. Figure 12 illustrates the resultant three-dimensional matrix of voxels formed by a number (here, only two) of stacked SLIPI images. These illustrations describe the system used for the correction calculation of signal attenuation and light extinction.

S _me d defines the calculated SLIPI signal/image (according to Eq. 7) of the probed medium;

S _t i defines the calculated SLITI signal/image (according to Eq. 7)

corresponding to the incident light intensity, for transmission measurement. This signal is measured without the probed medium. It is recorded, here, from the side by recording the light fluorescing from a Dye cell;

S,f defines the calculated SLITI signal/image (according to Eq. 7)

corresponding to the final transmitted light intensity after crossing the scattering medium. It is recorded, here, from the side by recording the light fluorescing from a Dye cell;

Spj is the signal related to the laser power of the incident light intensity. This information is used to monitor laser power fluctuations.

S _p f is the signal related to the laser power of the final transmitted light transmitted. This information is used to monitor laser power fluctuations between ¾ and S _t f.

Vfm.n.o) is a voxel, at position (m, n, o) within the probed volume; l _v is the length of a voxel, seen by a single pixel of the detector array;

d _v is the depth of a voxel, which is equal to the distance interval between two successive laser sheets;

h _v is the height of a voxel, seen by a single pixel of the detector array;

A is the side area of a single voxel. Here A = h _v -d _v

Each illuminated voxel V( _m „ _i0 ) is assumed to be homogeneous and contains a collection of particles/droplets of different size. The resultant averaged extinction coefficient J2 _e equals:

where N _P (D) is the number of particle of diameter D, C is the number density of particles, a _s is the scattering cross-section and σ _α is the absorption cross-section.

An illustration of a single voxel with its characteristics is shown Fig. 13. The methodology employed, here, is governed by two equations - Eq. 12 and Eq. 13 - and is derived at given vertical distance O in a (MNO) coordinate system.

First, the equation respecting the conservation of energy: The final power P(m+i _, n) from a voxel V( _mi „j equals the initial power minus the power loss ΔΡ( _Μι „) such that:

P = P - A ^P (m,») £q | Q

AP(m,n) corresponds to the radiant power of light scattered/absorbed by the voxel V( _m< n). By converting the previous equation in term of light intensity, instead of radiant power, the side area A of the illuminated voxel (see Fig. 13) must be considered such that:

/ . A - I . A— AP

and then:

- / - A P A Eq. 12

Second, the Beer-Lambert law describing the exponential reduction of light intensity across a voxel: The final intensity, I( _m +i ) from a single voxel V _mi „j, equals the initial intensity exponentially reduced along the length l _v as a function of the averaged extinction coefficient of the voxel Ji _{c[ n m)} : _^

I(m+\,n) ^~ I(m,n) ^{' ex} P( e(m,n) ' >) Eq. 13

By combining Eq. 12 and Eq. 13 the following equations may be obtained:

Equation 14 is the general expression describing the extinction coefficient within a single voxel as a function of the the radiant power AP( _mi „). Now, the variable must be calculated for each voxel

Based on the Beer-Lambert law, and assuming the that the multiple light scattering intensity is suppressed, the SLIPI signal S _me d( _m ) of the scattering medium, detected at pixel m (in the horizontal axis) and corresponding to voxel (m,n) equals:

where P( _mi „ is the radiant power emitted by voxel V( _{m n} ) and K( _{m> n} is a coefficient containing the solid angle of detection and the collection efficiency of the camera. Term (a) corrects for the exponential loss of light as the signal crosses the sample towards the camera (signal attenuation), along the N axis. At «=0, this term equals 1. Note that, here, N is a variable incrementing in the summation from N=0 to N=n-1. From the equation above we obtain Eq. 16:

The sum of the radiant power AP( _m ,„) loss/scattered from each voxel along the same row (along the axis) is equal to the difference between the incoming and exiting laser power, as Eq. 17: Eq. 17 Note that, here, M is a variable incrementing in the summation from M=0 to M-m _max . If ₍ „ ₎ is the final transmitted intensity (see Fig. 1 1 ). By combining Eq. 16 and Eq. 17 and assuming the coefficient K _(mi „ to be constant (K) for every voxel along M and N it may be moved outside of the summation and expressed as Eq. 18:

By combining Eq. 18 and Eq. 16, Eq. 19 is obtained:

Equation 19 is the general expression describing the power radiant from a single voxel as a function of the SLIPI signal of the medium S _me d and the initial /, and final intensity lf( _n Now the variable A _(m „ ₎ must be calculated for each voxel V _{(m ιΠ)} .

Including Eq. 19 in Eq. 14, the area A cancels out and we obtain:

Eq. 20

SUBSTITUTE SHEET (RULE-26) Based on the Beer-Lambert law, and assuming the that the multiple light scattering intensity is suppressed, the signal / ₍ ,„ _, „ ₎ detected at pixel m (in the horizontal axis) and corresponding to voxel V( _mi „) equals:

M=m-\

iH,«) ^{= / - e} (- ∑¾)W ^' 'v )

M=0 Eq. 21

where & is a constant related to camera efficiency/response, the collection angle and the efficiency of the dye (note that k which corresponds to the fluorescing dye cell differs from K related to the scattering medium). with Ifl„) - k ^■ (Spj I SpA„)) ^■ S _t j{„) ; and by inserting Eq. 21 in Eq. 20 we finally obtain:

Note that this equation corresponds to Eq. 6 and has been presented in the summary section.

By performing the method according to an aspect a three-dimensional mapping of the local averaged extinction coefficient μ is extracted over the spray, following the procedure described above.

- The initial nine modulated images of the spray recorded by the camera are shown in Fig. 14.

- The resultant conventional and SLIPI images according to Eq. 7 and Eq. 8 respectively, are shown in Fig. 15.

- Finally, Fig. 16 shows the results of the calculated extinction coefficient for 8 planes, from the centre toward the edge of the spray, with 1 mm step between images. _{■memaT Wtl A}

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This succession of images clearly shows the reduction of the extinction coefficient as the plane of consideration is getting closer to the spray edge. It can be seen that the maximum i _e equals 0.45 mm ^"1 and is, as expected, located in the region the closest to the nozzle tip. On the opposite, the minimum fi ^~ _e equals -0.01 mm ^"1 and is located on the spray edge.

- In addition to these data, the optical depth OD is shown in Fig. 17, for both the path between the laser sheet and the camera and along the laser sheet. Note that OD corresponds to the integration of J _e along the path travelled by the photons for a given direction.

Additional improvements

Depending on the characteristics of the detection system, and/or on the level of turbidity some additional improvement of the Mil-Scan are required for higher measurement accuracy.

In the above embodiment the collection angle of the objective is assumed to be zero. In this way the calculations of the signal attenuation can be done along a single line between the scattering voxel and the camera. However, to more realistically model the detection system, the effect due to the acceptance angle of the collecting lens must be included in the algorithm. These effects are particularly important when the collecting lens is close from the probed medium (large detection acceptance angle of the camera) and can result in too large inaccuracies on value the calculated extinction coefficient. A procedure to take into account "non-zero" detection acceptance angles is presented below:

The scattered light from each voxel is divided into Q rays evenly distributed within the cone of light collected by the objective of the camera. Each ray now experiences an individual attenuation based on the extinction coefficients and path length in the voxels that they intersect. The total attenuation a _to t of the light scattered from a voxel becomes, hence, the average of the attenuation of all the Q rays according to the following equation: Eq. 22 where l _p (M,N, 0) is the propagation distance of ray p through voxel located at (Μ,Ν, Ο) determined from entering position and angle.

Substituting in Eq.19 the signal attenuation term (term (a) given in Eq.15) by citot(m,n,o) the following expression of the radiant power is obtained:

The final expression of the extinction coefficient using this approach is written as:

Eq. 24

In the Mil-Scan embodiment it is assumed that the structured illumination process is entirely removing the multiple light scattering intensity. However, at certain level of turbidity, multiple scattering intensity residuals still remain on the S images. In order to increase the accuracy of the measurement, such residuals must be quantified and suppressed. Due to the strong capability of SLIPI in removing complex multiple scattering contributions, it can be assumed that the magnitude of these unwanted residuals is linearly related to the total number of scattering events and therefore to the sum of the extinction coefficient along photon path. With the knowledge of this relationship the multiple scattering residuals could be removed from the initial SLIPI data. One quantity that provides a good indication about the remaining multiple scattering intensity in each image, is the camera function K _{(m ).} As explained previously, K _(m: „ ₎ is related to the solid angle of the collection optics, the property of the detection lenses as well as the quantum efficiency and fill factor of the camera. Since neither the position nor the settings of the camera or collection optics are altered during the recordings (i.e. same distance between the laser sheet and the camera and constant camera gain), Κ ₍ „„ ₎ should remain constant at each position O of the laser sheet in the spray. According to Eq. 18, the camera function K( _m, „) is calculated from the relationship between the recorded scattered light S _me d and the extinction measurements (7, - 1/). Thus, an increased value of S _mec j due to multiple scattering residuals also results in an increased value of K( _m, „). By plotting K( _m, „ ₎ as a function of the sum of the extinction coefficient along the photon path, the variations of the camera function from a constant value can be visualized, providing indication about multiple scattering residuals contained in the S _me d images. Using this information the correction of the original SLIPI data can be performed. As a result, an iterative procedure between the corrected SLIPI data and the newly calculated extinction coefficient can be operated until results converge. This approach taking into account multiple scattering residuals allows an increase in measurement accuracy.

5) Dual-SLIPI

In another embodiment suitable for inhomogeneous disperse scattering media, a system 1900 according to Fig. 19 is used to detect two SLIPI images on opposite sides of the scattering medium. In Fig. 19 a system consisting of two cameras is demonstrated while, in Fig. 20, a system 2000 with only one camera is demonstrated.

Intensity is obtained by camera 1 according to Eq. 25: and Eq. 26:

wherein

is the final intensity reaching camera 1 (C I ), position 1 ; is the final intensity reaching camera 2 (C2), position 1 ; ' is the actual signal generated at position 1, regarded as "initial intensity": same for both camera 1 and camera 2;

7 _e i is the mean extinction coefficient over l ;

/7 _e! is the mean extinction coefficient over / ₂ ;

7 _e is the extinction coefficient of interest, between position 1 and position 2;

/ _] is the distance between position 1 and camera 1 ;

l ₂ is the distance between position 2 and camera 2; and

I is the distance between l _x and / ₂ . Similarly, the intensity is obtained by camera 1 according to Eq. 27: and Eq. 28: r(2)

lC2 ₀ - exp(-// _e2 - / ₂ ) Eq. 28 wherein additionally,

iff is the final intensity reaching camera 1 (CI), position 2; is the final intensity reaching camera 2 (C2), position 2; and

7 ₍ j ²⁾ is the actual signal generated at position 2, regarded as "initial intensity": same for both camera 1 and camera 2 - but not same as due to sample inhomogeneity. To extract /7 _e , the unknown variables 7 _el and j _e 2 must first be removed. This is achieved by deriving an expression for the unknown ' and based on the four measurements. With Eqs. 25 and 27 the following expressions are obtained: ₇ (D_ / ⁽²⁾

I ⁽²⁾ = 'ci

exp(- _> " _e i -h) and e p(-/« _e l " -Me ^'Al )

With Eqs.26 and 28 the following expressions are obtained:

Dividing the two former expressions with each other yields:

• exp(- _e · Δ/)

Similarly, dividing the two latter expressions with each other gives:

With these mathematical expressions two formulas both describing the ratio //g* are obtained:

From Eq.29 and Eq.30 we obtain Eq.31 : Eq.31

/ / exp- _e -A/ where the variables and are removed. Equation 31 can be rearranged according to: /(l) r(2)

exp(-2 · μ _ε · Δ/) =

C2 ⁷ C1 which gives Eq. 32 from which we obtain μ _β

6) Tomo-SLITI

In an embodiment suitable for quantitative measurements of inhomogeneous disperse scattering and/or absorbing media, a system 70 is used to detect one- or two- dimensional SLITI data of a sample 710. With this configuration several SLITI measurements are performed, between which the sample is rotated around its central axis (alternatively the camera and illumination is rotated around the sample), as illustrated in Fig. 3 (IV). Before further processing, the Beer-Lambert law is applied on each recording according to:

ΟΟ _φ = - \η[ΐ _ίφ ΙΙ _ί \ Eq. 33 wherein;

ii is the incident beam profile.

Ι/ is the final intensity, SLITI image recorded at a degree of φ.

ΟΩψ is the optical depth, at the corresponding angle φ. This set of data (Οϋφ) is commonly referred to as a sinogram and, although built up from line-of-sight information, holds information regarding the spatial distribution of the optical properties of the medium. If the sinogram is built up from ID SLITI measurements a 2D mapping of the optical properties can be reconstructed. If the sinogram is built up from 2D SLITI measurements, the data is treated as many stacked ID SLITI measurements, thus allowing a 3D mapping of the optical properties to be reconstructed. Various standard computer tomography algorithms can be employed to obtain this final result. Some examples are; back projection, filtered-back projection, Fourier reconstruction and iterative reconstruction. ...

27

Figure 21 (I) and (2) illustrates the basic principle for the two first algorithms, respectively. Common for both approaches is that reconstructed image is created by "smearing" the SLITI values back through an image matrix in the direction the SLITI measurement was originally acquired (as can be seen in the example with 3 views in Figure 21 (I)). The difference between the two approaches is that filtered-back projection utilizes a spatial filter to reduce the blurring seen in the back projected image.

With Fourier reconstruction the Fourier transform (i.e. the spectrum of the spatial frequencies) of each transmission measurement is first extracted. This spectrum is then placed in an image matrix, arranged with an angle equal to the viewing angle of that specific recording. Figure 21 (III) demonstrates how the different ID spectra are stored in the matrix for two and 18 viewing angles. The reconstructed image is then formed by first interpolating the values within the matrix and then calculating its inverse Fourier transform.

With iterative reconstruction, a matrix M is filled with an initial guess of the spatial distribution of the optical properties. A set of (computerized) transmission data is then extracted from M and the results are compared with the actual measurements. Based on observed differences between these transmission data from M and the actual transmission measurements, the values in M are altered and a reconstructed image of the object is formed by repeating the procedure in an iterative fashion.

Computer tomographic (CT) imaging relies on accurate transmission data of the unperturbed (non-scattered) light. However, when performing transmission imaging of a turbid sample with visible light some of the detected photons may have been scattered, either once or a multiple number of times. Including these photons in the CT process renders an error and the sample is not accurately reconstructed. By using tomo- SLITI, this error is significantly reduced.

Tomo-SLITI can be achieved with several different optical arrangements as well as with different reconstruction algorithms. The most sophisticated optical arrangement, that provides a 3D reconstruction of the optical properties, involves the use of a modulated light beam (see Fig. 2 (II)). The full procedure of tomo-SLIPI is explained in Fig. 22. The concept tomo-SLITI does, however, include other

tomographic approaches based on a modulated illumination scheme. 7) Improvements of the SLIPI and SLITI images

Apart from the requirement of recording more than three images to preserve the vertical spatial image resolution, another issue with the structured illumination technology, concerns the presence of residual lines in the S images (see Eq. 7). These artefacts arise mostly because of spatial changes in the intensity profile between the modulated images. This is a problem, because such lines introduce errors while performing quantitative measurements. A general improvement of structured

illumination, adequate for quantitative measurement is obtained by one or several of the following features:

- By increasing the number TV, of images, which leads to a more narrow line displacement.

- By using a small detection acceptance angle and, if possible, applying spatial filtering before detection on the detector array.

- By applying a correction procedure which aims to adequately normalize the raw data and take into account temporal and spatial intensity fluctuations of the incident intensity profile. With time this profile undergoes some small and "smooth" changes. These changes can be seen in the raw data by extracting, in the Fourier domain, the low frequency information. By extracting the variations of the low frequency information between each modulated images, a 2D normalizing procedure can be performed, correcting for intensity fluctuations. Such correction procedure of the individual modulated images results in a structured illumination image containing almost no residual lines, which is of importance for quantitative measurements. A comparison between a SLIPI non-corrected and a SLIPI corrected image is shown as an example in Fig. 23.

- By using a high frequency, i.e. narrow lines, of the intensity modulation, close to the resolution limit of the detection system.

- By illuminating the sample with a pure sinusoidal intensity modulation. This can be achieved by illuminating a Ronchi ruling with a laser beam and selecting only the first (±1) interference orders. The presence of higher and lower interference orders will induce residual line patterns in the final S image.

8) Multi-color Mil

As introduced in Eq. 2 and Eq. 3 the extinction coefficient equals the sum of the scattering and the absorption coefficient such as, fi ^~ _e = Ji _s + μ _α . The independent extraction of μ _α and 7 _V at a given wavelength can be extracted by means of a multicolor Mil method. The method can be described as follow:

Measuring from the side, (with Single-SLIPI - see Fig.5), /2 _e , with a first wavelength of interest where both scattering and absorption occur

Measuring from the side and in the same medium, /J _e2 , at a second wavelength where only scattering occurs ( μ _ε2 = μ ^~ and μ _α2 = 0 ).

For the two chosen wavelengths the extinction coefficients should very close to each other « /7 _el ).

- The two extracted intensity curve will, then, have the same intensity decay (see Fig. 5 (VI)). However the absolute intensity of the second curve (where only scattering occurs - at the second wavelength) will be K times higher than absolute intensity of the first curve (where scattering and absorption occur - at the first wavelength). This coefficient K corresponds then to the ratio in scattering cross-section between the two measurements ( a _s2 / σ _$| ).

- The scattering coefficient 7 ₍₁ is then deduced from /7 _cl by the relation:

- Finally, the absorption coefficient μ _α is deduced from μ _Λ and μ _Δ by the relation: μ _Λ = μ _Λ - μ _Λ

Although the present invention has been described above with reference to specific embodiments, it is not intended to be limited to the specific form set forth herein. Rather, the invention is limited only by the accompanying claims and, other embodiments than the specific above are equally possible within the scope of these appended claims.

In the claims, the term "comprises/comprising" does not exclude the presence of other elements or steps. Furthermore, although individually listed, a plurality of means, elements or method steps may be implemented by e.g. a single unit.

Additionally, although individual features may be included in different claims, these may possibly advantageously be combined, and the inclusion in different claims does not imply that a combination of features is not feasible and/or advantageous. In addition, singular references do not exclude a plurality. The terms "a", "an", "first", "second" etc do not preclude a plurality. Reference signs in the claims are provided merely as a clarifying example and shall not be construed as limiting the scope of the claims in any way.