Particle Distribution in a Medium

The invention relates to a method for determining a three- dimensional particle distribution, preferably a bacteria dis tribution, in a medium.

The background of this invention lies in the field of ob serving colloids such as bacteria in a medium, for example to study bacterial onset of urinary tract infections. Moreover, plastic particles in ocean water, impurities in liquid foods or pharmaceuticals, or cells in bodily fluids could be observed. For bacteria distributions, it is known to observe the movement of bacteria in a medium by means of digital holographic micros copy. In such methods, a sample containing said bacteria is ir radiated with coherent light to obtain an interference image thereof. From this, in turn a three-dimensional model of the bacteria distribution can be computed by applying a reconstruc tion algorithm onto the interference image, for example a back propagation or back projection algorithm. However, experiments have shown that the three-dimensional model obtained in this way is often qualitatively unsuited for a detailed analysis.

To overcome this problem, in the state of the art it is known to perform spatial filtering or time averaging steps on the interference image to generate a background image. This im age contains information on fringes related to objects that are not of interest and that can be removed from the interference image by division or by subtraction of said background image. Thereafter, the reconstruction algorithm is performed on the thus "cleansed" interference image to determine the three- dimensional particle distribution. However, these processing steps have the disadvantage that the overall quality of the three-dimensional model is still insufficient in some cases. The problem arising here is that objects that scatter much light have fringes, which are easily mistaken for less brightly scattering objects. It is therefore an object of the invention to provide a method for determining a three-dimensional particle distribu tion with a qualitatively high output that is furthermore com putationally easy to perform.

This aim is achieved by means of a method for determining a three-dimensional particle distribution, preferably a bacte ria distribution, in a medium, comprising:

providing a sample of the medium containing said parti cles ;

emitting a coherent light beam by means of a light source to irradiate the sample with said light beam, wherein a first part of the light beam is scattered by the particles to create a scattered light beam;

recording, with a camera, an interference image of the scattered light beam and a second part of the light beam that has not been scattered;

computing with a processor, from the interference image, for each one of a plurality of virtual planes lying within the sample, a reconstructed image of the sample at the respective virtual plane, each reconstructed image having a plurality of pixels with an intensity value and a phase value,

generating with said processor, for each reconstructed im age, a presence image having a same layout of pixels as the re constructed image, wherein a value is assigned to each pixel of the presence images if the corresponding pixel of the recon structed image has an intensity value exceeding a threshold value and if the corresponding pixel of the reconstructed image has a phase value with a predetermined sign, and wherein no value is assigned if at least one of said two conditions is not met, and

identifying the three-dimensional particle distribution from those pixels of the presence images that have assigned values .

This method has the advantage that the quality of the de termined three-dimensional particle distribution is increased by applying a special filter algorithm on each reconstructed image, i.e., not on the interference image subject to the re construction algorithm but on the "slices" of the reconstructed sample .

It has been found that each particle causes an intensity pattern with multiple maxima in the reconstructed images. The two inventive filtering steps allow to delete those intensity values that cause the "outer" maxima, i.e., those intensity maxima that do not correspond to the actual particle. This makes the particle appear clearer as its edges are less blurred in the three-dimensional particle distribution, allowing for an improved statistical analysis, for example. The method thus manages to remove second, third, et cet . intensity maxima around the particle by means of a computationally efficient al gorithm, only needing to compute two values for each pixel in a straightforward manner.

Preferably, the method comprises the step of, after scat tering and before recording, directing the scattered light beam onto the camera by means of an optical device having a focal point lying outside of the sample. By having an optical device whose focal point lies outside of the sample, a large volume of the sample can be depicted in the interference image. Further more, the optical device allows the interference image (holo graphic image) to be magnified to a certain degree, which al lows for a more detailed computational analysis. If the focal point alternatively lies within the sample, the phase values of the reconstructed images are only present outside of a plane of the focal point .

In this embodiment, it is further preferred if said prede termined sign is dependent on the side, seen in the direction of the light beam, of the sample said focal point is located on as well as on the refractive index of the medium in relation to the refractive index of the particles. In an exemplary sce nario, the predetermined sign is positive if the focal point lies between the camera and the sample and if the refractive index of the medium is lower than the refractive index of the particles. Each change of one of these criteria causes the sign to flip once. This has the advantage that the predetermined sign can be determined before performing the method, i.e., no trial and error is needed to determine the sign.

Further preferably, the virtual planes are each spaced apart with a predetermined interval and cover the whole sample. This causes the reconstructed images and thus the presence im ages to be located in equal distances from each other such that each pixel of the presence image can be assigned a predeter mined "height" (corresponding to the third dimension in the particle distribution) that equals the predetermined intervals.

The sample, light source, and camera could be embodied as any interferometer known in the state of the art. For example, a part of the emitted light beam could be branched off, by means of a beam splitter, and combined with the scattered light beam before recording with the camera. However, experiments have shown that beam- splitting is prone to vibrations. Prefera bly, the method includes providing an inline interferometer comprising the light source, the sample, and the camera.

The camera can be embodied in any type known in the state of the art capable of recording interference images. However, it is especially preferred if the camera is a digital camera, preferably a Complementary Metal-Oxide Semiconductor (CMOS) or a Charge Coupled Device (CCD) . This allows an especially effi cient computational analysis of the recorded interference image as it can easily be processed digitally. Furthermore, CMOSs and CCDs are readily available with high resolutions.

Preferably, the method comprises using an inverse Radon transformation to compute the reconstructed images. The inverse Radon transformation is preferred as it has been optimised for similar purposes. Generally, other reconstruction algorithms such as an iterative reconstruction algorithm or a Fourier- domain reconstruction algorithm can be used for determining the reconstructed images too. To determine a movement of the particles in the medium, the method can comprise repeating the steps of emitting, irra diating, recording, generating, and identifying to determine a first and a second particle distribution, and correlating at least one particle in the first particle distribution to the same particle in the second particle distribution to track a movement of said particle. Thus, two three-dimensional particle distributions are determined and the individual particles are tracked between the two distributions. To correlate one parti cle to the same particle in the other distribution, additional constraints can be set, such as a maximum particle speed.

Preferably, the method comprises the step of projecting the three-dimensional particle distribution onto a two- dimensional plane corresponding to the plane of the interfer ence image. This allows to obtain a two-dimensional image that corresponds to the view of the interference image. In other words, through computing the reference images, generating the presence images through the two filtering conditions, and pro jecting back to a two-dimensional plane, the interference image is cleared from the effects of interference and is then avail able in a form in which each particle is easily identifiable.

Favourably, the threshold value is computed for each pixel of at least one of the reconstructed images as a predetermined percentage of the average intensity values of pixels within a predetermined range of said pixel. This allows for adjusting the threshold value to a level that is in line with the local intensity level . By computing the threshold for each pixel of one of the reconstructed images, a "threshold map" is gener ated. Since the threshold map depicts the scattering strength of the particles, samples can be analysed that contain both strongly and weakly scattering particles. Thus, the quality of the output of the method is not affected even if a part of one reconstructed image has low intensities and a different part has high intensities. In another preferred embodiment, the method comprises the step of determining the threshold value to lie between a second and a third maximum intensity value of a reference intensity distribution. The predetermined threshold is thus chosen in such a way that it lies between the second and third intensity maxima such that this criterion allows for the deletion of the third, forth, et cet . intensity maxima. The predetermined sign then corresponds to the phase value of the second intensity maximum and this allows for its deletion.

The invention shall now be explained in more detail below on the basis of preferred exemplary embodiments thereof with reference to the accompanying drawings, in which:

Fig. 1 shows an inline interferometer used for the inven tive method in a schematic side view;

Fig. 2 shows a graph of an intensity distribution and a phase progression of a particle due to interference; and

Fig. 3 schematically shows an interference image, a plu rality of reconstructed images, and a three-dimensional parti cle distribution as an output of the method of Fig. 1.

Fig. 1 shows an inline interferometer 1 comprising a light source 2, a sample 3, an optical device 4, and a camera 5. The sample 3 comprises a medium M containing (microscopic) parti cles P. In one embodiment, the particles P could be bacteria and the medium M could be water, blood, a solution, or the like. In a different embodiment, the particles P could be charged particles in water or oil to study, e.g., electrophore sis .

The inline interferometer 1 is used to determine a three- dimensional particle distribution 6 (Fig. 3), which can be de termined by means of a processor 7 connected to the camera 5 by means of an interface 8.

Based on the examples depicted in Figs. 2 and 3, the method for determining said three-dimensional particle distri bution 6 will be detailed in the following. At the outset, the light source 2 emits a coherent light beam 9 to irradiate the sample 3 with said light beam 9. In the present method, the coherence length can be fine-tuned as too many speckles can occur in the three-dimensional particle dis tribution 6 if the coherence length is chosen to be too small. The light source 2 can be of any kind that is capable of emit ting a coherent light beam 9, for example a laser diode.

Once the light beam 9 irradiates a sample 3, a first part of the light beam 9 is scattered by the particles P to create a scattered light beam 10. Depending on the choice of medium M and particles P, the percentage of scattered light can vary. In the example of bacteria and water, approximately five percent of the light beam 9 is scattered. In the shown embodiment, a second part of the light beam 9 has not been scattered by the particles P and traverses the sample 3 as a non-scattered light beam 11. In the present specification, scattering can mean dif fracting, refracting, or reflecting, and is dependent on the choice of interferometer 1 used, which in turn may depend on the nature of the particles, e.g., their transparency, reflec tivity, or refractivity .

After the light beam 9 has traversed the sample 3 as a scattered light beam 10 and a non-scattered light beam 11, the scattered light beam 10 can be magnified by means of the opti cal device 4, which is optional in some embodiments. The opti cal device 4, as known in the state of the art for inline in terferometers 1, can be construed to make the scattered light beam 10 interfere with the non-scattered light beam 11. For this purpose, the optical device 4 can have a focal point F ly ing outside of the sample 3 at a predetermined distance d thereto, which also helps to further magnify the interference image 12. The focal point F can lie on any side of the sample 3, seen in the direction of the light beam 9.

The interferometer 1 can also be embodied as another type of interferometer than an inline interferometer, for example as an interferometer 1 utilizing beam-splitters. For example, one beam-splitter could be arranged between the light source 2 and the sample 3 to branch off a part of the un- scattered light beam 9, which could at a later stage be merged with the scat tered light beam 10 such that the two beams 10, 11 interfere.

At the end of the path of the light beam 9, the camera 5 records an interference image 12 of the scattered light beam 10 and the non-scattered light beam 11. The camera 5 can for this purpose be any analogue or digital camera, for example, a Com plementary Metal-Oxide Semiconductor (CMOS) or a Charge Coupled Device (CCD) . However, other cameras 5 such as cameras with an active pixel sensor (APS) could be used alternatively.

After the camera 5 records the interference image 12, the camera 5 forwards the interference image 12 to the processor 7 via the interface 8, and processing is performed to obtain the three-dimensional particle distribution 6 from the interference image 12. The camera 5 records the interference image 12 as a purely two-dimensional image. However, this interference image 12 encodes intensity as well as phase information. This infor mation allows the processor 7 to "reconstruct" the three- dimensional sample 3 in a first step Si.

As shown in Fig. 3, in step Si a plurality of virtual planes 13i, 13 ₂ , ..., generally 13 _i can be defined within the sample 3. Preferably, the virtual planes 13i are each spaced apart with a predetermined interval IV (Fig. 1) and cover the whole sample 3, which alleviates processing. Each virtual plane 13i thus has a different distance to the camera 5.

Alternatively, the virtual planes 13i could be spaced apart with different intervals IV. The three-dimensional parti cle distribution 6 could then be generated by incorporating different factors for the different intervals IV.

A reconstruction algorithm can now be applied onto the in terference image 12 to compute a reconstructed image 14i, 14 ₂ , ..., generally 14i, for each virtual plane 13i. In the state of the art, multiple variants of reconstruction algorithms exist, some of which are known in the state of the art as back propa- gation or back projection algorithms, e.g., an inverse Radon transformation .

While in the interference image 12 usually only intensi ties are recorded, it is possible to therefrom determine both intensity and phase information for each reconstructed image 14i . Each reconstructed image 14i is thus computed to have a plurality of pixels 15 with an intensity value I and a phase value F.

After computing the reconstructed images 14 _i the proces sor 7 generates in a second step S ₂ for each reconstructed im age 14i a presence image 16i, 16 ₂ , ..., generally 16±, wherein each presence image 16± has the same layout of pixels 17 as the corresponding reconstructed image 14i. This means that the presence images 16± have the same amount of pixels 17 arranged in the same manner, i.e., arranged in the same array. A pixel 17 of the presence image 16± corresponds to a pixel 15 of the reconstructed image 14i if it has the same position in the ar ray. While the pixels 15 of the reconstructed image 14i have stored intensity information I as well as phase information F, the pixels 17 of the presence image 16± have either a value as signed or no value assigned, depending on two criteria. Spe cifically, the processor 7 assigns a value to each pixel 17 of the presence images 16± if the corresponding pixel 15 of the reconstructed image 14i has an intensity value I exceeding a predetermined threshold value TH and if the corresponding pixel 15 of the reconstructed image 14i has a phase value F with a predetermined sign SG. The processor 7 assigns no value if at least one of said two conditions is not met.

Fig. 2 shows the purpose of the two above-mentioned condi tions. The dashed line 18 shows an idealized graph of the in tensity I of an interference pattern, wherein the vertical axis shows the intensity I of a scattered light beam 11 in the re constructed image 14i and the horizontal axis shows a distance x to a point of scattering. The solid curve 19 shows an ideal ized graph of the phase F of an interference pattern, wherein the vertical axis shows the phase F of the scattered light beam 11 in the reconstructed image 14i and the horizontal axis shows a distance x to a point of scattering. As can be seen, the graph 18 of the intensity has multiple maxima Mi, M ₂ , M ₃ , ..., and the phase graph 19 has extreme values at the same distance x, however where the intensity I has the second maximum M ₂ , the phase F has a first minimum.

It is an aim of the two above-mentioned criteria to ex clude intensity values I other than those corresponding to the first maximum M _c . Therefore, the predetermined threshold TH is preferably chosen to lie between the intensity value I of the second and third maximum M ₂ , M ₃ . The reason for not choosing a higher threshold TH, i.e., between the first and the second maximum M ₁ M ₂ is that this would exclude intensity values of particles of smaller sizes. To also exclude the second maximum M ₂ , the second criterion of excluding pixels with a predeter mined sign SG of the phase value F is introduced. In the em bodiment of Fig. 2, said predetermined sign SG is a negative sign to exclude the second intensity maximum M ₂ .

Furthermore, said threshold value TH can optionally be predetermined "on the fly" to account for locally varying maxi mum intensities. To this end, the threshold value TH can be computed for each pixel 15 of the reconstructed image 14i as a predetermined percentage of the average intensity values of pixels within a predetermined range to said pixel 15, e.g., only pixels surrounding said pixel 15 or additionally also in cluding pixels surrounding said surrounding pixels 15. In this context, average also includes mean, mode, or any other statis tical function.

The value assigned can be either a constant value, e.g., "1", or the intensity value I of the corresponding pixel of the reconstructed image 14 i . Assigning no value either means as signing a "0" value or an empty string or another placeholder.

In Fig. 2, the phase graph 19 is depicted to have a posi tive value F at the distance x = 0. The predetermined sign SG is thus negative to exclude the second intensity maximum M ₂ . However, the phase graph 19 could also have a negative phase value F at the distance x = 0. This is dependent on two fac tors: Firstly on the side, seen in the direction of the light beam 9, of the sample 3 said focal point F of the optical de vice 4 is located on and secondly on the refractive index of the medium M in relation to the refractive index of the parti cles P. If the focal point F lies between the camera 5 and the sample 3, and the refractive index of the medium M is lower than the refractive index of the particles P, the phase value F is positive at the centre of a corresponding particle P such that the predetermined sign SG will be negative. If any one of those two factors change, the predetermined sign SG will have to be changed too.

Once the processor 7 has assigned a value or no value to all pixels 17 of all presence images 16i, the three-dimensional particle distribution 6 can be identified from those pixels 17 of the presence images 16 that have assigned values. To this end, the assigned values can be stored together with the coor dinates (position of the respective pixel 17 within the array and relative position of the virtual plane 13i of the corre sponding reconstructed image 14i) or plotted as a three- dimensional view of the sample 3.

During or after assigning values to pixels 17 of the pres ence images 16±, additional criteria can be used, too. For ex ample, if a pixel 17 would be assigned a value but there are no surrounding pixels 17 that were or will be assigned values, also for this pixel 17 no value can be assigned even if the above mentioned criteria of intensity threshold TH and prede termined sign SG of the phase value F yield a value. This cri terion is used, e.g., when particles are expected to occupy an area that is larger than one single pixel 17.

Once the three-dimensional particle distribution 6 has been determined, the method can be repeated after a predeter mined amount of time to generate a second particle distribution 6. From the previous (first) particle distribution 6 and the second particle distribution 6, a movement of one or more par ticles P can be tracked. This can be done by correlating at least one particle P in the first particle distribution 6 to the same particle P in the second particle distribution 6. The correlation of particles P can either be performed manually or computationally by determining if one particle P has a similar position in the second particle distribution 6. The maximum de viation distance can be restricted by a maximum speed of parti cles, for example.

As another application the three-dimensional particle dis tribution 6 can be projected onto a two-dimensional plane cor responding to the plane of the interference image 12. By means of this, an "alternative" image can be generated that shows the particle distribution 6 in a front-view, just like the inter ference image 12 but without the influences of interference. Furthermore, similar projections could be made to planes other than the plane of the interference image 12 to generate differ ent (virtual) views.

The invention is thus not restricted to the specific em bodiments described in detail herein but encompasses all vari ants, combinations and modifications thereof.