WO2011039118A1

WO2011039118A1 - Method for determining the inner structure of a sample

Info

Publication number: WO2011039118A1
Application number: PCT/EP2010/064166
Authority: WO
Inventors: Carsten Glasenapp; Werner Pöltinger
Original assignee: Carl Zeiss Ag
Priority date: 2009-09-29
Filing date: 2010-09-24
Publication date: 2011-04-07
Also published as: DE102009045130B3

Abstract

The invention relates to a method for determining the inner structure of a sample, wherein sectional views in at least one first plane extending into the sample are generated by means of images capturing optical path lengths, wherein along a first imaging direction a first sectional view of the sample is generated, which is located in the plane extending into the sample, along a second imaging direction a second sectional view of the sample is generated, which is likewise located in the plane extending into the sample, first optical coordinates of at least one structural element are determined in the first sectional image and second optical coordinates of the at least one structural element are determined in the second sectional image, and the refractive index effective for the images is determined from the first and second coordinates, and in this way refractive index influence-corrected physical coordinates of the at least one structural element are determined.

Description

Method for determining the internal structure of a sample

The invention relates to a method for determining an internal structure of a sample, wherein images formed by optical path lengths of images are produced in at least one plane extending into the sample.

For the non-contact and non-destructive analysis of the internal structure of a sample tomographic methods are available. The confocal scanning scanning microscopy known to those skilled in the art (LSM abbreviated to their laser-assisted variant) allows a three-dimensional image of the sample. As an example, the publication Sharpe et al. (2001), "3D confocal reconstruction of gene expression in mouse", Mech. Dev. 100, 59-63. However, other optical techniques are also used, such as optical coherence tomography, e.g. In D. Huang et al. (1991), "Optical Coherence Tomography", Science, 1178-81. Optical Coherence Tomography (OCT) and Scanning Scanning Microscopy (LSM) provide a high-resolution three-dimensional image or sectional images of a sample. A disadvantage of these methods is the refractive index-dependent distortion of the measurement data in the depth of the sample, which is based on the fact that these methods always measure optical path lengths, which are the product of geometric path and refractive index of the medium.

The longest established structure elucidation is the use of X-radiation, as is done, for example, in computed tomography and described in Flannery BP et al. (1987), Three-dimensional x-ray microtomography, Science 237, 1439-44. Analogous to X-ray-based computed tomography, optical methods from projections can generate a three-dimensional sample image from different angles. In this case, as in X-ray computer tomography, the inverse radon transformation for computational image generation from the various projections is used. An example of an optical projection tomography can be found in EP 1410090 B1 or WO 02/095476 A2. Another possibility for such projection-based image acquisition can be found in the tomography phase microscopy (eg. W. Choi et al. (2007), "Tomography phase microscopy", Nat. Method 4, 717-719). This method overlays projection images of the phase shift of thin samples obtained from different angles. Also AM Zysk et al. (2003), "Projected index computed tomography", Opt. Lett 28, 701-703, describes a projection-based imaging method, the Projected Index Computed Tomography, where a three-dimensional refractive index distribution is generated from the projection of the mean refractive index of the sample.

A disadvantage of all projection methods are limited Ortsauf solutions.

For optical coherence tomography, dispersion equalization is known in F. Büchinger, "Dispersion equalization in optical coherence tomography", Diploma thesis TU Vienna, Faculty of Electrical Engineering and Information Technology, 2006. There the 1st order dispersion is corrected into OCT data, where a spatial Optical coherence tomography properties in connection with the wavelength dependence of the refractive index are exploited in order to improve an OCT image by suitable filtering.

The Diploma Thesis A. Dölemeyer, "Model-based Three-dimensional Fundus Reconstruction: A General Approach to the Integration of Multi-modal Data of the Human Ocular Background", Diploma Thesis RWTH Aachen, Faculty of Electrical Engineering and Information Technology, Aachen 2005, describes how data from different measurement methods are brought together in the correct position on the eye A three-dimensional model of the eye is used and overlapping points from different measurements are used to integrate the corresponding imaged parts of the eye in the correct position of an overall image to insert the image, a correction of image errors does not take place.

The invention has for its object to overcome the disadvantages of the prior art and to improve the aforementioned method as a high-resolution, not influenced by the refractive index distribution of the sample imaging method.

This object is achieved by a method for determining the internal structure of a sample, wherein images are generated by means of optical path length imaging images in at least a first, extending into the sample plane, wherein along a first imaging direction, a first sectional image of the sample in the a second sectional image of the sample, which is also located in the plane extending into the sample, is generated along a second imaging direction, is generated, first optical coordinates of at least one structural element or point in the first sectional image and second optical coordinates of the same structural element or point in the second sectional image are determined, and determined from first and second coordinates the effective refractive index in the images and thus Brechzahlbeeinflussungskorrigierte physical coordinates of the at least one structural element or point.

The invention therefore compensates for errors due to refractive index distribution by evaluating at least two sectional images which detect the same plane in the sample from different imaging directions. In this case, the invention is based on the finding that sectional images of optical path lengths detecting imaging method, z. B. OCT or LSM data sets, are not affected in the two Cartesian axes perpendicular to the imaging direction by the refractive index distribution in the sample, a refractive index distribution error thus occurs substantially along the imaging direction. An optical path length detecting imaging method in the sense of the invention described here is thus a method which is subject to refractive index influences along the imaging direction, but not transverse to the imaging direction, as long as no refraction effects occur. If the optical axis of the image is oriented (as usual) along a z-axis of a Cartesian coordinate system, the refractive index then influences (only) the z-coordinate and not the x and y coordinates of a measurement. Distortion at refractive index interfaces that are not traversed vertically can also interfere with optical path length measurement.

The position of each measuring point must therefore be weighted with the refractive index profile between the penetration point of the illumination radiation into the sample and the position of the object to be measured on the optical axis (z-axis). The z-axis z 'equalized with respect to the refractive index influencing can be calculated

where n (z) is the refractive index curve along the z-axis. Evidently, one needs for this type of correction the refractive index profile along the z-axis. However, he is usually unknown.

The invention therefore uses several sectional images in the same plane, wherein the sectional images are obtained from different imaging directions. The invention rotates the z-axis in the selected plane, so that a correction can be made due to the other coordinate axes not distorted by the refractive index influencing. Due to the refractive index-dependent optical path length can therefore z. B. in OCT or LSM, the optical coordinates that can be read from the optically obtained sectional image, from the physical, ie actually present in the sample, distinguish. Insofar as refractive index distribution-related coordinates are to be distinguished from actual coordinates in this description, we speak of optical coordinates or physical coordinates.

The refractive index of the sample has an effect on the entry of illumination radiation if it does not run at right angles to the sample surface. At an oblique incidence on the sample surface is a deflection of the incident illumination beam. In order to avoid the resulting correction effort, it is preferable to choose the two imaging directions so that they are perpendicular to each other and perpendicular to the sample surface in the respective images. This is an application of the invention, in which coordinate information from the two sectional images only have to be combined in order to reduce or correct refractive index-related errors. In the combination, the coordinate images are combined from the sectional images, which are subject to no or one, compared to the respective other sectional image, lower refractive index influence. The more distorted coordinates (axes) of a sectional image are thus replaced by a small falsified coordinates (axes) from the other sectional image. This is made possible by the different imaging directions.

However, the invention is also applicable to cases where such a choice of imaging direction is not possible, for example because of the lack of accessibility of the sample or due to the structure of the sample surface. For such cases, a development is preferred in which the course of an interface of the sample, in particular of the sample surface, is determined for both sectional images. Furthermore, the entry point at which the illumination radiation passed through the interface during the respective imaging is determined for each sectional image. From the entry point, the course of the interface and the optical path length of the illumination radiation to the structural element or point in question, the physical coordinates of the structural element / point can also be determined by the correction of the refractive index.

This embodiment therefore makes use of the fact that the angle of incidence of the illumination radiation into the sample can be determined from the entry point and the course of the interface. Thus, the refraction effects occurring at the surface can be easily detected and taken into consideration, and together with the optical path length of the illumination radiation, the physical coordinates of the feature are obtained. With this method, it is also possible to determine iteratively the shape and position of further, lower-lying structural elements or refractive index interfaces, so that any samples with arbitrary refractive index distributions can be measured in terms of their physical dimensions.

The concept according to the invention can also be extended to the three-dimensional structure determination if at least one second plane extending into the specimen is selected for cross-sectional images which intersect the at least one first plane. A further supplement to the method according to the invention results from the fact that a plurality of mutually parallel first and optionally also second planes are used, so that a tomographic elucidation of the sample structure is achieved by a large number of sections while the refractive index influences are adjusted.

The adjustment of the imaging direction can be obtained particularly easily by rotating the sample.

It is understood that the features mentioned above and those yet to be explained below can be used not only in the specified combinations but also in other combinations or alone, without departing from the scope of the present invention.

The invention will be explained in more detail for example with reference to the accompanying drawings, which also disclose characteristics essential to the invention. 1 shows schematically a section through a sample with four embedded particles,

2 is a sectional view of the sample of FIG. 1, as it results from a first imaging direction by means of optical coherence tomography, FIG. 3 is a further illustration similar to FIG. 2, but from a different imaging direction, FIG.

4 shows a schematic representation of the sample of FIG. 1 for clarifying a refractive index distribution-related error and its correction, FIG.

Fig. 5 is another illustration similar to Figure 4 for a sample me not straight surface and 6 is a schematic representation of a device for carrying out the measurements for the correction method described with reference to FIGS. 1 to 5.

FIG. 1 schematically shows a section through a sample P which contains particles a, b, c and d for explanatory purposes. The sample P has an optical refractive index n which is not constant over the sample. To simplify the explanation, a two-dimensional section in a z / x plane is shown here. In this section, the particles have corresponding coordinates (χ ,, z,) which indicate the physical position of the particles. For the particle a, the coordinates (x _a , z _a ) are shown by way of example.

If the sample is formed using an optical method, the refractive index of the sample P causes a distortion along the imaging axis. This situation is illustrated in FIG. 2, which schematically shows the image of the sample P by means of optical coherence tomography (OCT). The section shown in FIG. 1 is then distorted along the z-axis due to the refractive index distribution n (z) of the sample P. As a result, instead of the coordinate z, the coordinate z 'occurs. Knowing the refractive index distribution, the equalized z-axis can be easily calculated from the optical values along the distorted z'-axis by the equation mentioned at the outset. The equation also shows that at constant refractive index n (z) = n ₀ , z = z7n ₀ . However, if there is a non-constant course of the refractive index n, which is generally the case, the integral of the equation has to be evaluated for each measuring line along the z axis in order to obtain the z coordinates for the particles a, b, c, d to equalize.

However, since the refractive index characteristic along the z-axis is usually not known, a second OCT measurement along the other coordinate of the section, namely the x-axis in Figures 1 and 2 is performed. Then the ratios shown schematically in FIG. 3 are established. Because of the imaging direction of the second OCT image, which is rotated by 90 degrees relative to FIG. 2 and is illustrated in FIG. 3 by the double arrow labeled OCT2, the z-axis is undistorted, since it lies perpendicular to the recording direction OCT2. Distorted, however, is the x-axis.

The x-coordinate of the individual particles a, b, c, d can now be determined from the first sectional image, which was imaged along the imaging direction OCT1. The second, rectangular figure shows the z-coordinate of the particles. As a result, the physical, ie the refractive-index-free, coordinates of the particles a, b, c, d are now determined from two optical sectional images. Of course, the reference to particles is to be understood as exemplary for the correction of coordinates. The prerequisite for this procedure is that, on the one hand, the imaging directions of the two optical images for generating the sectional images are parallel to the main axes of the selected coordinate system. If it is a Cartesian coordinate system as in Figures 2 and 3, the imaging directions must be perpendicular to each other. On the other hand, it is desirable that the two imaging directions are perpendicular to the surface of the sample P in order to avoid diffraction effects due to the refractive index jump when entering the sample. The described method thus requires correspondingly shaped or prepared samples P. Of course, a vertical position of the sample P in the area in which the OCT imaging is sufficient, is sufficient.

Figure 4 shows a correction for the case that only one of the two imaging directions can be perpendicular to the sample surface. In the representation of FIG. 4, this is the imaging direction OCT1. The imaging direction OCT2, however, is at an angle α to the solder L on the surface of the sample P.

When imaging along the imaging direction OCT1, the x-coordinate (the coordinate system is selected as in FIG. 2) is free from influences due to the refractive index distribution, as already explained above. The problem is, however, the depth of a particle in the imaging direction OCT1. It is therefore shown in Figure 4 for clarity, only the particle a. Here, a denotes the particle at its physically correct position, the optical position of the particle as viewed from the imaging direction OCT1, a ₂ the optical position of the particle as viewed from the imaging direction OCT 2 taking into account the refractive index of the medium and a ₃ the optical position of the particle when viewed from the imaging direction OCT3 taking into account the refractive index of the sample P and the Schnell'schen refraction in the sample with the refractive index n. Next is the abbreviation OPD for the optical path difference (Optical Path Difference) and the abbreviation PPD for the geometric length (Physical Path difference).

By imaging the cross-sectional image of two spatial directions, with only one must be aligned perpendicular to the surface of the sample ß, now both the physical morphology (ie the internal structure) and the refractive index of the sample can be determined.

From the first measurement along the imaging direction OCT1, the x-coordinate of the particle a is surely determined. The z-coordinate is distorted by the factor of the refractive index, since this is not known, the exact position of the particle a in the z-coordinate from the sectional image along the imaging direction OCT1 can not be determined. In the second measurement, the coordinates (x _2: z ₂ ) are determined from the angle of incidence α. Both coordinates are optical coordinates and do not reflect the physical position of the particle a, because due to the refraction of the optical interface of the sample P, the light rays are deflected in imaging along the imaging direction OCT2. In addition, the optical path length in the material is increased by the effective refractive index of the medium by the effective refractive index factor n.

The impact point of the radiation along the imaging direction OCT2 at the surface can be calculated in the x-direction by x ₂₀ = x ₂ / cosa directly from the measured value x ₂ and the (known) angle of incidence to the perpendicular of the surface (angle a). The physical path length PPD = p ₂ = (z ² _a + (x _a - x ₂₀₎ ° ⁵ is distorted by the factor n of the measured optical path length OPD Since x _a = X is known from the figure along the imaging direction _OCT1.! follows

z ₂ = OPD = PPD ■ n = n ■ p ₂ . Since z _a = z ^ n and x _a = xt are known from the first measurement, the refractive index can be determined by n ² = (z ₂ ² -z) 1 (x 1-x ₂₀ ) ² . If the refractive index is thus known, the physical coordinates (x, z) of the structural element a can be determined directly from the optical path lengths ζ and * _\ .

Of course, this approach applies not only to a particular structural element a, but for each point in the sample P. Further, the refractive index n described in the above approach is the effective refractive index along the radiation propagation, thus also takes into account a varying refractive index in the sample P.

The approach of Figure 4 assumes that the surface in the region in which the radiation of the imaging direction OCT1 and the radiation of the imaging direction OCT2 incident, is sufficiently flat and is perpendicular to the imaging direction OCT1. With an arbitrary surface course this is often not the case. In order to be able to determine the position of a particle (or point) without the boundary condition that the sample has a certain orientation and surface for imaging, the approach shown schematically in FIG. 5 can be used. In FIG. 5, three imaging directions OCT1, OCT2 and OCT3 are shown, which may be necessary when measuring three-dimensionally structured samples. For simplicity, however, the principle is described here for two dimensions, which means that OCT3 measurement is not required.

In Figure 5, which follows with respect to the coordinate system of the convention of Figures 1 to 4, the points ST and S ₂ (as well as S ₃ ) denote the entry points of the radiation used for the imaging OCT1, OCT2 (and OCT3) on the surface of the sample P. , for the sake of simplicity in Figure 3, the interface between two refractive index regions, namely refractive index n and refractive index n ', registered, the position of the entry points S, can without related to the refractive index from each sectional drawing. If the refractive index n, ie the refractive index from which the radiation is incident along the imaging directions 0CT1-3, is known, the shape and position of the interface (eg the surface on entry into the sample) can be determined by translation of the sample P. From this automatically follow the angles ψι, φ ₂ (and φ ₃ ), which denote the angle between the surface normal at the entry point S ^ S ₂ (and S ₃ ) and the z-space axis. If we denote the distances S, - a as vectors Pi, then the vector relations (x _a , y _a , z _a ) = S, + p, (with i = 1, 2 or 3), where (x _a , y _a , z _a ) describe the physical coordinates of the point a in three-dimensional space. In the two-dimensional case of exemplifying below, the y coordinate is omitted.

The angles α, α, α ₂ and α ₃ represent the angles of incidence to the solder on the sample surface at the respective entry point. The angles αΊ, α ' ₂ and α' ₃ denote the angles following the refraction in the medium with the refractive index n ', ie in the sample P. The sign convection of the angles used in the drawing is based on the z-axis in a clockwise direction positive sign.

Consequently, the following relationships apply:

1 . (x _{a "} z _a ) = S ₁ + p _!

2. (x _a z _a ) = S ₂ + p ₂

The vectors p ^ ₂ = | ρ, | ^* (sin (cpi + α,), cos (cpi + a,) = | Zi / n '| ^* (sin (cpi + a,. ₂ ), cos (cpi + a,)) can be calculated from the angles of the Determine the measuring beam with respect to the z-axis in the medium of the refractive index n 'and the optical path length z from the sectional image (with i = 1, 2) The angles a, can according to Snell's law n' sin α ' = n sin a and the addition theorems sin (cp + a) = sin (cp) cos (a) + sin (a) cos (cp)

cos (cp + a) = sin (cp) sin (a ') - cos (cp) cos (a) by the angle of incidence α and the refractive index n. The two equations summarized result:

2. (χ ₃ , ζ ₃ ) = (8χ ₂ , 8ζ ₂ ) + | ζ ₂ / η '| * (5ίη (φ ₂ + α ₂ ), 005 (φ ₂ + α ₂ )

The 3 unknowns x _a z _a and n 'existing in this system of equations can thus be reliably determined from the 4 equations. Consequently, coming from a medium 1 coming with a known refractive index n, the shape and the position of an optical interface to the medium 2 of the refractive index n 'can be determined exactly. With the method described above, the position of particles (or coordinate correction) in the medium 2 and the refractive index n 'is determined exactly. Consequently, the shape and the position of a further optical interface to a medium 3 with the refractive index n ", since n 'is known, can also be measured by means of this ray tracing with the aid of refractive index distributions to their physical dimensions.

The invention has been described above with reference to optical coherence tomography. An example of a construction suitable for this purpose is shown in FIG. 6 with a Michelson interferometer construction known to the person skilled in the art for optical coherence tomography, using a detector 1 which detects a measurement signal and a radiation source 2 which emits, for example, short-coherent radiation. a depth profile of the sample (commonly referred to as A-scan) won. In this case, the Michelson interferometer structure has a beam splitter 4 and a reference beam path 6. Radiation coming from the radiation source 3 is split by the beam splitter 4 into the reference beam path to the reflector 6 and into a detection beam path to the sample P. From the reference beam path, d. H. Reflecting from the reflector 6 reference radiation and reflected back from the sample P or scattered Me ßstrahlung is superimposed on the beam splitter 4 and passed to the detector 1. If the optical path length for a reflection or a backscatter within the optical coherence length of the radiation of the radiation source 3 after passing between the reference beam path and the measuring beam path is the same, interference occurs at the detector. The measurement principle of optical coherence tomography is known to the person skilled in the art, for example from one of the aforementioned publications.

In order to realize the different imaging directions, a relative rotation between sample P and measurement beam path can be performed. This is illustrated by a corresponding arrow in FIG. Optionally, a relative displacement between sample P and measurement beam path can also be carried out, for example in order to set a surface region on the sample P as the incidence region for the measurement radiation, which satisfies the conditions mentioned above.

However, the method according to the invention is not restricted to optical coherence tomography as an image. It is also suitable for other imaging methods which are subject to a refractive index influence in the depth direction in the image, but not in the perpendicular spatial directions. An example of such an imaging method is, for example, the raster scanning microscopy already mentioned at the outset, which therefore likewise comes into question as an imaging method for generating the sectional images.

Claims

claims

1 . Method for determining the internal structure of a sample, wherein images formed by optical path lengths of images are produced in at least one first plane extending into the sample, characterized in that

along a first imaging direction, a first slice image of the sample lying in the plane extending into the sample is generated, along a second imaging direction a second slice image of the sample, which also lies in the plane extending into the sample, is generated,

first optical coordinates of at least one structural element or point in the first sectional image and second optical coordinates of the same structural element or point in the second sectional image are determined, and

the effective refractive index of the images is determined from first and second coordinates and thus physical coordinates of the at least one structural element or point which are corrected for refractive index influence are determined.

2. The method according to claim 1, characterized in that the two imaging directions are chosen so that radiation incident on the sample perpendicular to the sample.

3. The method according to claim 1 or 2, characterized in that for each coordinate axis, the cross-sectional image is selected, the image of the lowest refractive index influencing is subject and that the coordinate data from the selected sectional images are combined to a Brechzahlbeeinflussungskorrigierten coordinate set.

4. The method according to claim 1, characterized in that in the first and second sectional image in each case the course of an interface of the sample, in particular the sample surface is determined, and

in each case coordinates of an entry point are determined at which, during the respective imaging, an illumination beam incident on the structural element or the point passes through the interface, and

from the coordinates of the entry points, from the course of the boundary surface and from an optical path length of the illumination beams, the refractive-index-corrected physical coordinates of the structural element or of the point are determined.

5. The method according to claim 4, characterized in that the iterative layers of several, in the depth direction of the optical images consecutive interfaces and structural elements or points are determined.

6. The method according to any one of the above claims, characterized in that for determining the three-dimensional structure of the sample, the method of claim 1 is also carried out for at least a second, extending into the sample level, which intersects the at least one first level.

7. The method according to any one of the above claims, characterized in that the sample is rotated to set the imaging directions.

8. The method according to any one of the above claims, characterized in that the imaging is carried out by optical coherence tomography or confocal scanning scanning microscopy.