Microscope imaging system and method for emulating a high aperture imaging system, particularly for mask inspection

Abstract

An optical imaging system for inspection microscopes with which lithography masks can be checked for defects particularly through emulation of high-aperture scanner systems. The microscope imaging system for emulating high-aperture imaging systems comprises imaging optics, a detector and an evaluating unit, wherein polarizing optical elements are selectively arranged in the illumination beam path for generating different polarization states of the illumination beam and/or in the imaging beam path for selecting different polarization components of the imaging beam, an optical element with a polarization-dependent intensity attenuation function can be introduced into the imaging beam path, images of the mask and/or sample are received by the detector for differently polarized beam components and are conveyed to the evaluating unit for further processing.

Description

CROSS-REFERENCE TO RELATED APPLICATION

In a particularly advantageous construction, the optical element 5 arranged in the imaging beam path is constructed in such a way that the s-polarized beam components are not attenuated and the p-polarized beam components are attenuated corresponding to the condition described above. Only an image of the mask and/or sample 1 containing the simulated vector effects for the p-polarized beam components is received by the detector. A separate illumination with s-polarized radiation and p-polarized radiation is not required for this purpose. Further, the optical element 5 can remain in the beam path. In this case, the optical element 5 arranged in the imaging beam path is a partial polarizer with a polarization-dependent and angle-dependent intensity attenuation function.

The optical element 5 can be constructed, for example, as a diffractive optical element. It should advantageously be rotatable and/or displaceable along the optical axis for selectively inserting into the beam path.

In order to optimize the intensity-attenuating action of the optical element 6, the latter should be arranged so as to be tiltable so that the point at which the radiation impinges perpendicularly and at which, therefore, no polarization effect is to be expected can be displaced within the pupil.

The images of the mask and/or sample received by the detector for illumination with differently polarized radiation are conveyed to the evaluating unit for further processing. The images of the mask and/or sample received for differently polarized radiation are combined by the evaluating unit, e.g., a computer unit, to form a total image by summing the intensity distributions.

Method for Emulating High-Aperture Scanner Systems

In the method, according to the invention, for emulating high-aperture imaging systems, e.g., scanner systems, in a microscope imaging system particularly for mask inspection, the polarization characteristics of the images of the mask and/or sample are determined in that a quantity of differently polarized images are recorded, the degree and the direction of polarization is determined therefrom for all segments of the image, the images are subjected to a polarization-dependent weighting of their intensity distribution and are combined to form a total image containing information about the intensity and the polarization characteristics.

For this purpose, polarizing optical elements are selectively arranged in the illumination beam path and/or in the imaging beam path. In the illumination beam path, these polarizing optical elements are used to generate different polarization states of the illumination beam path corresponding to the illumination conditions and imaging conditions of a lithography scanner system or another high-aperture imaging system. In contrast, they are used in the imaging beam path to generate differently polarized images of the mask and/or sample. Differently polarized images of the mask can also be measured by illuminating them with different polarizations.

Determination of the Degree and Direction of Polarization

One or more polarization-optical elements, e.g., a linear polarizer, is/are arranged so as to be rotatable in the illumination beam path and/or imaging beam path for recording a quantity of differently polarized images of the mask and/or sample. This polarization optical element is rotated in at least three angular positions so that at least one image can be received in every angular position by the detector. For example, an image is received for the angular position of the linear polarizer of 0°, 45°, 90° and 135°. An image offset that may be caused by the polarizer can be measured and corrected by adjustment or by means of hardware or software. In order to be able to compensate for influences of the polarizer on the image quality, it is advantageous to record an unpolarized image, i.e., without the linear polarizer, in addition.

Recording of the images of the mask and/or sample with and without a polarizing optical element can be carried out at different distances from the focal plane. While the recording of the image or images with polarizing optical elements is carried out in the focal plane, the image is recorded without a polarizing optical element in several planes in front of and/or in and/or behind the focal plane. The images obtained in this way with polarizing optical elements form the basis for calculating all of the images without a polarizing optical element. Within a certain range, the degree and direction of polarization does not depend on whether or not the images of the mask and/or sample are obtained in front of, in, or behind the focus position.

The degree and direction of polarization determined from these images for a plurality of pixels of the detector are preferably displayed as a Jones vector, Stokes vector or polarization matrix.

The polarization matrix, for example, is defined as:

$P=\left[\begin{array}{cc}{P}_{\mathrm{xx}}& P_{\mathrm{xy}}\\ P_{\mathrm{yx}}& P_{\mathrm{yy}}\end{array}\right]=\left[\begin{array}{cc}\langle {A_x\left(t\right)}^2\rangle & \langle A_x\left(t\right)A_y^{*}\left(t\right)e^{i\left[\Phi \left(t\right)-\Psi \left(t\right)\right]}\rangle \\ \langle A_x^{*}\left(t\right)A_y\left(t\right)e^{-i\left[\Phi \left(t\right)-\Psi \left(t\right)\right]}\rangle & \langle {A_x\left(t\right)}^2\rangle \end{array}\right].$

This polarization matrix comprising four elements forms the basis for the emulation of vector effects in the AIMS. Different methods of polarization-dependent weighting of the intensity distributions of the images (emulation of vector effects) will be discussed in the following.

In an advantageous embodiment, the determination of the polarization characteristics of the image and the determination of the degree and direction of polarization for different pixels of the detector can be dispensed with assuming that the polarization characteristics of the image correspond to those of the illumination. Of course, the polarization characteristics of the illumination must be known for this purpose. This simplification provides sufficient accuracy particularly for simple mask structures.

Displacement Methods

Contrast in the image occurs by means of the interference of at least two orders of diffraction whose angle of incidence is θx in x-direction and θy in y-direction. For x-polarized light, a phase delay of η=+θx or −θx must be generated proceeding from the vector effects to be emulated in the pupil of the inspection microscope:
I_x+=E₀²+E₁²+E₀E₁ cos (φ+Δθx)
and
I_x−=E₀²+E₁²+E₀E₁ cos (φ−Δθx),
where φ is the phase difference between E₀ and E₁. This corresponds in a sufficient approximation to a displacement of the image by a determined amount D in the +/−x-direction.

Adding the two images and dividing by 2 gives:
I=(I_x++I_x−)/2=E₀²+E₁²+E₀E₁ cos φ cos Δθx.

The weighted intensity distribution I_x emulates the above-mentioned vector effects in sufficient approximation.

A partially polarized state can be described as an incoherent sum of two orthogonal polarization states. Accordingly, the intensity function for every pixel of the detector is also divided into a first image whose field vector E extends parallel to the polarization direction and a second image whose field vector E extends perpendicular thereto. The conditions for the two field vectors are as follows:

• • E parallel to the polarization direction:
    I_□=(1+g)/2*I_ges
  • E perpendicular to the polarization direction:
    I_⊥=(1−g)/2*I_ges,
    where g defines the degree of polarization.

In this method, the image is subjected in a polarization-dependent manner to a weighting of its intensity distribution in that the portion I_□ of the image of the mask and/or sample is displaced as an intensity function in the direction of the determined polarization direction by an amount ±D. In a corresponding manner, the portion I_⊥ of the image of the mask and/or sample is displaced perpendicular to the direction of the determined polarization direction by an amount ±D and these four intensity values are summed. The division of the intensity of the image into different portions is carried out in a polarization-dependent manner in a ratio of 1+g to 1−g, where g is the degree of linear polarization.

At least two portions of the intensity are preferably displaced in different directions. The displacement directions lie at least partially parallel and/or perpendicular to the direction of polarization.

FIG. 6 shows a diagram for illustrating the summing of the images that are offset by D. By displacing an image and subsequently summing the images, a loss in contrast caused by the vector effect is emulated.

The images are subjected in a polarization-dependent manner to a weighting of their intensity distribution in that the image of the mask and/or sample as an intensity function is shifted in the direction of the determined polarization direction by an amount ±D on the one hand and perpendicular to the determined polarization direction by an amount ±D on the other hand.

The amount D can be selected, for example, as:

$D=\frac{\lambda }{n_{\mathrm{Lack}}4\sqrt{2}}·\frac{c·\mathrm{NA}/n_{\mathrm{Lack}}/\mathrm{arc}\sin \left(c·\mathrm{NA}/n_{\mathrm{Lack}}\right)}{1/\sqrt{2}/\mathrm{arc}\sin \left(1/\sqrt{2}\right)},$
where c is a constant ≦1, e.g., c=0.9. This applies to the imaging system to be emulated. In the inspection microscope, D must be scaled by the ratio of the magnification factors of the two systems.

Consider, for example, a pixel of the detector at the location (x, y) at which the image is polarized in x-direction with a linear degree of polarization of g. This gives the corrected image:

$I_{\mathrm{corrected}}=\frac{I\left(x+D,y\right)+I\left(x-D,y\right)}{2}·\frac{1+g}{2}+\frac{I\left(x,y+D\right)+I\left(x,y-D\right)}{2}·\frac{1-g}{2}.$

For polarization directions which do not lie parallel to the x-axis and y-axis, the displacement direction is calculated in a corresponding manner.

Consider, for example, a pixel of the detector at the location (x, y) at which the image is polarized in direction φ with a linear degree of polarization of g. This gives the corrected image:

$I_{\mathrm{corrected}}=\frac{1+g}{2}·\frac{I\left(x+D\cos \left(\phi \right)x,y+D\sin \left(\phi \right)\right)+I\left(x-D\cos \left(\phi \right),y-D\sin \left(\phi \right)\right)}{2}+\frac{1-g}{2}·\frac{I\left(x-D\sin \left(\phi \right),y+D\cos \left(\phi \right)\right)+I\left(x-D\sin \left(\phi \right),y-D\cos \left(\phi \right)\right)}{2}.$

The images of the mask and/or sample in positions (x+D, y), (x−D, y), (x, y+D) and (x, y−D) are summed with or without weighting, where x and y are two determined directions or any directions orthogonal to one another.

For a polarization direction which does not lie parallel to the coordinate axes, the displacement direction is given in a corresponding manner. When the polarization state changes over the image, the displacement directions also change over the image field. Accordingly, the vector effects are emulated with sufficient accuracy.

In order to exclude influences of the polarizer on image quality, the intensity can be taken from an image that was recorded without a polarizer. The images with a polarizer then serve to determine the polarization characteristics.

The polarization characteristics can also be measured in another plane than the intensity. For example, the polarization characteristics can be measured in the focal plane and the unpolarized intensity can be measured in a plurality of planes in front of, in and behind the focal plane.

At the expense of limited accuracy, polarization measurement can be replaced by the assumption that the mask or sample does not act in a polarizing manner, that is, that the polarization of the image is identical to the polarization of the illumination and is therefore constant over the entire image.

Vector Effects in Fourier Space

In this first method in Fourier space for emulating high-aperture scanner systems in a microscope imaging system, the image is subjected in a polarization-dependent manner to a weighting of its intensity distribution in that, for all elements of the polarization matrix, Stokes vector, Jones vector, the intensities recorded with different polarization or other polarization-optical description of the image for different pixels of the detector, a two-dimensional Fourier transformation is carried out, a polarization-dependent attenuation factor is calculated, and a two-dimensional inverse Fourier transformation is carried out.

Every Fourier component corresponds to a spatial frequency occurring in the image. Accordingly, the degree and direction of the linear or total polarization is obtained for every Fourier component. The Fourier transform of the image is not identical to the intensity distribution in the pupil.

In this second method in Fourier space for the emulation of high-aperture scanner systems in a microscope imaging system, there is a different procedure for determining the pupil distribution, i.e., the Fourier components.

A method that has already been described many times is the measurement of the intensity distribution in the pupil by means of Bertrand optics and subsequent reconstruction of the image. When measuring the intensity distribution in the pupil, no information is obtained about the phase relationship between the individual Fourier components. In addition, higher orders of diffraction which contribute substantially to the fine structuring of the image are difficult to detect because of their low intensity.

Therefore, it is suggested to reconstruct a pupil distribution from the image. The pupil reconstruction is not clear-cut, i.e., different pupil distributions (intensity and phase) can generate one and the same image. In the procedure described herein to take into account the vector effects, only a reasonably small error is made in taking the vector effect into account when the pupil distribution is not correct but still allows the image to be correctly reconstructed.

When the pupil size is compared to the Fourier component distribution occurring when the image is Fourier-transformed, some Fourier components lie outside the pupil size in critical structures (structures at the limit of resolution), so that this direct approach of Fourier transformation does not lead to the desired pupil distribution, since all Fourier components must lie inside the pupil size. However, these Fourier components are suitable as starting values for a recursive optimization. In the optimization loop, the Fourier components (intensity and phase) are varied and the image is subsequently reconstructed and compared to the true image. When the difference between the true image and reconstructed image is below a selected value, the resulting pupil distribution can be used for further calculation. When a polarized image, rather than an unpolarized image, is used as a basis for this procedure, the individual polarization states of the Fourier component scan be determined in this way.

##STR00001##

The emulation of the vector effects is now carried out by means of a pupil procedure, e.g., by multiplying by a spatial frequency-dependent and polarization-dependent attenuation factor of the individual Fourier components in the pupil. This attenuation factor is determined, among others, by the angle between the spatial frequency vector and the polarization direction. Subsequently, a new image is reconstructed with this modified pupil distribution.

Another possibility consists in carrying out the weighting by means of the convolution of a suitable function in real space instead of by multiplying by an attenuation function in Fourier space. The inverse Fourier transform of the attenuation function in Fourier space is a suitable function for this purpose.

A given spatial frequency in the image is generated by at least two orders of diffraction in the pupil. The orders of diffraction at points ν_l and ν₂ have a vectorial distance Δν and the mean coordinate ν₀. Based on the condition that ν₁ and ν₂ must lie in the pupil, ν₀ must lie within a determined range. The smaller Δν, the greater this range must be.

For every spatial frequency or Fourier component, the loss in contrast caused by the vector effect is calculated as a function of ν₀. The attenuation factor is determined by the angle between the spatial frequency vector and the polarization direction and/or by the amount of the spatial frequency vector and is dependent, among other things, upon the cosine of the angle enclosed by the three-dimensional E field vectors in the image space of the high-aperture system. When there is more than one possible value of the attenuation factor for different possible values of ν₀, a weighted or unweighted average, the median, the mean value between the smallest and largest value, or some other value within the possible area of variation is formed. In an advantageous embodiment, the weighting function is formed by taking into account the degree of coherence, the illumination setting and/or the polarization of the illumination.

In this method, partially polarized Fourier components are split into a plurality of differently polarized portions and the attenuation factor is calculated individually for the portions.

When a Fourier component is partially polarized, it is divided into a polarized and an unpolarized portion. The unpolarized portion is considered to be 50% x-polarized and 50% y-polarized without a phase relation. The Fourier component can also be split into a portion that is parallel to the polarization direction F_□=(1+g)/2*F_ges and a portion that is perpendicular to the polarization direction F_⊥=(1−g)/2*F_ges, where g defines the degree of polarization. The multiplication factor T is then calculated separately for each of the portions.

In an advantageous method, the polarization characteristics are determined by recording one or more images with polarization-optical components in the illumination beam path and/or imaging beam path and the intensity is determined by recording without polarization-optical components in the illumination beam path and/or imaging beam path. The images of the mask and/or sample with and without a polarizing optical element are calculated together in Fourier space.

The polarization characteristics can also be measured in a different plane than the intensity. For example, the polarization characteristics can be measured in the focal plane and the unpolarized intensity can be measured in a plurality of planes in front of, in and behind the focal plane.

A total image is formed by image reconstruction, e.g., an inverse Fourier transformation of at least one component of the polarization-optical description and/or total intensity.

Vector Effects by Convolution with the Difference of Two Point Images

In this third method for emulating high-aperture scanner systems in a microscope imaging system, the image is subjected in a polarization-dependent manner to a weighting of its intensity distribution in that the image of the mask and/or sample is subjected to a spatial convolution with a normalized point image for every pixel of the detector.

The intensity distribution occurring when imaging a point will be referred to hereinafter as point image. In this connection, the point image formed in an image-side high-aperture system is different than that in an inspection microscope due to the vector effect.

Normalized point image refers to the function with which the point image of the inspection microscope must be convoluted in order to obtain the point image of the high-aperture system. This is obtained by means of an inverse convolution of the high-aperture point image with the point image of the inspection microscope.

FIG. 7 shows the point images and the corresponding normalized point images for s-polarized and p-polarized beam components. The spatial convolution of the image of the mask and/or sample with the normalized point image is carried out for every pixel of the detector separately for horizontally and vertically polarized beam components. Instead of this, the beam component can also be divided into a portion whose E field is parallel to the spatial polarization direction and a portion orthogonal thereto. The intensities are then divided in a ratio of 1+g to 1−g, where g is the degree of polarization.

The point image of the scanner is determined empirically or theoretically. For this method, it is desirable that the point images of a scanner are known for all field points. A partially polarized state can be described as the incoherent sum of two orthogonal polarization states. In every pixel, let the polarization matrix P(x, y) be:

$P=\left[\begin{array}{cc}{P}_{\mathrm{xx}}& P_{\mathrm{xy}}\\ P_{\mathrm{yx}}& P_{\mathrm{yy}}\end{array}\right]=\left[\begin{array}{cc}\langle {A_x\left(t\right)}^2\rangle & \langle A_x\left(t\right)A_y^{*}\left(t\right)e^{i\left[\Phi \left(t\right)-\Psi \left(t\right)\right]}\rangle \\ \langle A_x^{*}\left(t\right)A_y\left(t\right)e^{-i\left[\Phi \left(t\right)-\Psi \left(t\right)\right]}\rangle & \langle {A_x\left(t\right)}^2\rangle \end{array}\right].$
with the associated degree of polarization:

$g\left(x,y\right)=\sqrt{1-\frac{4\mathrm{de}\mathrm{tP}\left(x,y\right)}{{\mathrm{Sp}}^{2}P\left(x,y\right)}}.$
The polarized portion:

$P^{\mathrm{pol}}\left(x,y\right)=P\left(x,y\right)-\frac{\mathrm{SpP}\left(x,y\right)}{2}\left(1-g\left(x,y\right)\right)I$
can be calculated from the given polarization matrix and gives the field E₁(x, y):

${\stackrel{\rightharpoonup }{E}}_1\left(x,y\right)=\left(\begin{array}{c}{E}_x\\ E_y\end{array}\right)=\left(\begin{array}{c}\sqrt{p_{\mathrm{xx}}^{\mathrm{pol}}}{e}^{-i\Psi /2}\\ \sqrt{p_{\mathrm{yy}}^{\mathrm{pol}}}{e}^{\mathrm{i\Psi }/2}\end{array}\right)$
and the field E2(x,y) orthogonal hereto:

${\stackrel{\rightharpoonup }{E}}_2\left(x,y\right)=\left(\begin{array}{c}-E_y^{*}\\ E_x^{*}\end{array}\right)=\left(\begin{array}{c}-\sqrt{p_{\mathrm{yy}}^{\mathrm{pol}}}{e}^{-i\Psi /2}\\ \sqrt{p_{\mathrm{xx}}^{\mathrm{pol}}}{e}^{i\Psi /2}\end{array}\right)$
with the phase angle
ψ(x,y)=arg(P_xy^pol)
and the matrix elements:

$\begin{array}{c}{P}_{\mathrm{xx}}^{\mathrm{pol}}=P_{\mathrm{xx}}-\frac{P_{\mathrm{xx}}+P_{\mathrm{yy}}}{2}\left(1-g\right)=\frac{P_{\mathrm{xx}}}{2}\left(g+1\right)+\frac{P_{\mathrm{yy}}}{2}\left(g-1\right)\\ P_{\mathrm{yy}}^{\mathrm{pol}}=P_{\mathrm{yy}}-\frac{P_{\mathrm{xx}}+P_{\mathrm{yy}}}{2}\left(1-g\right)=\frac{P_{\mathrm{xx}}}{2}\left(g-1\right)+\frac{P_{\mathrm{yy}}}{2}\left(g+1\right)\\ P_{\mathrm{xy}}^{\mathrm{pol}}=P_{\mathrm{xy}}\end{array}$
P_xy^pol=P_xy

While |E₂|=0 in the completely polarized case, the condition |E₁|=|E₂| applies in the completely unpolarized case. In the partially polarized case, the ratio of the intensities of E₁ and E₂ is

$\frac{I_2}{I_1}=\frac{1-g}{1+g}.$
Accordingly, the polarization state described by the polarization matrix P is composed of

$\sqrt{\frac{1+g}{2}}$
from Ē₁
and

$\sqrt{\frac{1-g}{2}}$
from Ē₂.
Accordingly, the point image of a scanner is also composed of these parts of the point images of the two orthogonal portions.

In accordance with the methods that were already described above, the convolution of the image of the mask and/or sample is carried out separately for a plurality of pixels of the detector with the normalized point image likewise for differently polarized beam components. The convolution is carried out, for example, for two portions of the intensity of the image, wherein the division into different portions is carried out in a polarization-dependent manner and one portion is at least partially parallel and/or perpendicular to the direction of polarization.

The images are subjected in a polarization-dependent manner to a weighting of their intensity distribution in that the image of the mask and/or sample as an intensity function is convoluted in the direction of the determined polarization direction by an amount ±D on the one hand and perpendicular to the determined polarization direction by an amount ±D on the other hand, wherein the amount D corresponds, for example, to the following condition:

$D=\frac{\lambda }{n_{\mathrm{Lack}}4\sqrt{2}}·\frac{\mathrm{NA}/n_{\mathrm{Lack}}/\mathrm{arc}\sin (\mathrm{NA}/n_{\mathrm{Lack}}}{1/\sqrt{2}/\mathrm{arc}\sin \left(1/\sqrt{2}\right)},$
where c=constant≦1.

The images of the mask and/or sample that are obtained in positions (x+D, y), (x−D, y), (x, y+D) and (x, y−D) are summed with or without weighting, where x and y are two determined directions or any directions orthogonal to one another.

The images for differently polarized beam components are combined by the evaluating unit by summing the intensity distributions to form a total image. Images for differently polarized beam components can be subjected to a weighting of the intensity distribution beforehand.

The evaluation of the images is carried out while taking into account the polarization characteristics so that vector effects are taken into account at least partially.

With the solution according to the invention, it is possible to examine lithography masks for defects by means of inspection microscopes with large magnifications in spite of increasingly smaller structures and increasingly higher numerical apertures of imaging systems. Realistic images of the scanner systems can be generated by emulation in spite of occurring vector effects.

Even scanner systems which use immersion optics, for example, and therefore achieve an optional image-side NA of, e.g., 1.6, can be emulated with the proposed microscope imaging system.

It is also possible to use the inventive solution within a microscope. For example, the in-coupling device and the out-coupling device can be designed in such a way that they can be installed inside a tube lens of a microscope or can be used as a tube lens. The polarization influencing arrangement can then be provided in the area of an intermediate image inside the tube lens. The polarization influencing arrangement should be exchangeable so that different polarization states can be realized.

While the foregoing description and drawings represent the present invention, it will be obvious to those skilled in the art that various changes may be made therein without departing from the true spirit and scope of the present invention.

Claims

1. A method for emulation of high-aperture imaging systems, particularly for mask inspection, comprising the steps of:

providing imaging optics, a detector and an evaluating unit, in which different polarization states of an illumination beam or imaging beam can be selectively generated in an illumination beam path or in an imaging beam path;

determining the polarization characteristics of an image in that at least one image of a mask or sample made with or without a polarization-optical element in the illumination beam path or imaging beam path is received by a detector;

determining the degree and the direction of polarization therefrom for different pixels of the detector; and

subjecting images to a polarization-dependent weighting of their intensity distribution and combining them to form a total image.

2. The method for emulation according to claim 1, wherein a quantity of images of the mask or sample are recorded, while a linear polarizer arranged in the illumination beam path or imaging beam path is rotated stepwise.

3. The method for emulation according to claim 1, wherein at least one image of the mask or sample is recorded for at least three angular positions of a polarizing optical element.

4. The method for emulation according to claim 1, wherein an unpolarized image of the mask or sample is recorded in addition or instead.

5. The method for emulation according to claim 1, wherein the images of the mask or sample are recorded at different distances from the focal plane with and without a polarizing optical element arranged in the illumination beam path or imaging beam path.

6. The method for emulation according to claim 5, wherein the image or images is/are recorded with polarizing optical elements in front of, in, or behind the focal plane, and the image is recorded without a polarizing optical element in front of or in or behind the focal plane.

7. The method for emulation according to claim 1, wherein the degree and direction of polarization is described for a plurality of pixels of the detector as a polarization matrix, Jones matrix, Jones vector or other polarization-optical description.

8. The method for emulation according to claim 1, wherein the determination of the polarization characteristics of the image and the determination of the degree and direction of polarization for different pixels of the detector can be dispensed with, assuming that the polarization characteristics of the image correspond to those of the illumination.

9. The method for emulation according to claim 1, wherein the images are subjected in a polarization-dependent manner to a weighting of their intensity distribution in that portions of the intensity of the image of the mask or sample are displaced by a determined amount in different directions as intensity function, wherein the division into different portions is carried out in a polarization-dependent manner.

10. The method for emulation according to claim 9, wherein at least two portions of the intensity are displaced in different directions, wherein the displacement directions lie at least partially parallel or perpendicular to the direction of polarization.

11. The method for emulation according to claim 9, wherein the division into different portions is carried out in a ratio of l+g to l−g, where g is the degree of linear polarization.

12. The method for emulation according to claim 9, wherein the images are subjected in a polarization-dependent manner to a weighting of their intensity distribution in that the image of the mask or sample as intensity function is displaced in the direction of the determined polarization direction by an amount ±D on the one hand and perpendicular to the determined polarization direction by an amount ±D on the other hand, wherein D is the amount of the displacement of the image.

13. The method for emulation according to claim 12, wherein the amount D corresponds to the condition:

14. The method for emulation according to claim 9, wherein the images of the mask or sample in positions (x+D, y), (x−D, y), (x, y+D) and (x, y−D) are summed with or without weighting, where x and y are two determined directions or any directions orthogonal to one another, wherein D is the amount of the displacement of the image.

15. The method for emulation according to claim 1, wherein, proceeding from the image, this image is modified by following the alternative route of pupil distribution or reconstruction thereof, or a convolution with a suitable point image, the difference of the point image of the image-side high-aperture and low-aperture system.

16. The method for emulation according to claim 15, wherein the images are subjected in a polarization-dependent manner to a weighting of their intensity distribution in that a two-dimensional frequency component determination is carried out, a polarization-dependent attenuation factor is calculated, and a two-dimensional image reconstruction is carried out for all elements of the Jones vector, Stokes vector or polarization matrix, the images measured with different polarizing optical elements in the illumination beam path or imaging beam path, or another polarization-optical description of the image for different pixels of the detector.

17. The method for emulation according to claim 15, wherein the weighting is carried out by a convolution of a suitable function in real space instead of by multiplication by an attenuation function in frequency space, wherein the transform of the attenuation function in the image space is a suitable function.

18. The method for emulation according to claim 15, wherein the polarization-dependent attenuation factor is determined by the angle between the spatial frequency vector and the polarization direction or the amount of the spatial frequency vector.

19. The method for emulation according to claim 18, wherein the polarization-dependent attenuation factor is calculated from, among others, the cosine of the angle enclosed by the three-dimensional E field vector in the image space of the high-aperture system.

20. The method for emulation according to claim 15, wherein when there is more than one possible value of the attenuation factor a weighted or unweighted average, the median, the mean value between the smallest and largest value, or some other value within the possible area of variation is formed.

21. The method for emulation according to claim 20, wherein the weighting function is formed by taking into account the characteristics or the polarization of the illumination.

22. The method for emulation according to claim 15, wherein partially polarized frequency components are split into a plurality of differently polarized portions and the attenuation factor is calculated individually for the portions.

23. The method for emulation according to claim 22, wherein these portions are preferably polarized parallel or perpendicular to the polarization direction.

24. The method for emulation according to claim 15, wherein partially polarized frequency components are divided into a polarized portion and an unpolarized portion, the unpolarized portion is considered to be 50% x-polarized and 50% y-polarized, where x and y are two determined directions or any directions orthogonal to one another and the polarization-dependent attenuation factor is calculated individually for each of the three portions.

25. The method for emulation according to claim 15, wherein the images of the mask or sample with and without a polarizing optical element arranged in the illumination beam path or imaging beam path are calculated together in the frequency space.

26. The method for emulation according to claim 25, wherein a total image is formed by image reconstruction of at least one component of the polarization-optical description or the total intensity.

27. The method for emulation according to claim 15, wherein an optimization algorithm, a recursive optimization algorithm, is used for reconstructing the pupil distribution which can then be used for calculating and taking into account the vector effect.

28. The method for emulation according to claim 1, wherein the images are subjected in a polarization-dependent manner to a weighting of their intensity distribution in that the image of the mask or sample is subjected to a spatial convolution with a normalized point image for a plurality of pixels of the detector.

29. The method for emulation according to claim 28, wherein the inverse convolution of the high-aperture point image with the point image of the inspection microscope is used as normalized point image.

30. The method for emulation according to claim 28, wherein the spatial convolution of the image of the mask or sample for a plurality of pixels of the detector with the normalized point image is carried out separately for different polarized beam components.

31. The method for emulation according to claim 28, wherein the spatial convolution of the image of the mask or sample with a normalized point image is carried out for at least two portions of the intensity of the image, wherein the division into the different portions is carried out in a polarization-dependent manner and a portion lies at least partially parallel to or perpendicular to the direction of polarization.

32. The method for emulation according to claim 28, wherein the division into the different portions is carried out in a ratio of l+g to l−g, where g is the degree of polarization.

33. The method for emulation according to claim 1, wherein images of the mask or sample for differently polarized beam components are combined by the evaluating unit by summing the intensity distributions to form a total image, wherein images for differently polarized beam components may have been subjected beforehand to a weighting of the intensity distribution.

34. The method for emulation according to claim 33, wherein the evaluation of the images is carried out by taking into account the polarization characteristics and vector effects are taken into account at least partially.

35. A method for emulating imaging of an object by a first imaging system having a high numerical aperture na₁, the method comprising:

obtaining one or more images of the object using a second imaging system having a low numerical aperture na₂, where na₂ is less than na₁;

determining a degree of polarization and a direction of polarization for imaging light from the second imaging system used to form the one or more images of the object;

using an electronic processor, constructing one or more synthetic images based on the obtained one or more images and na₁; and

using the electronic processor, constructing an output image emulating vector effects in the first imaging system based on the one or more synthetic images, and the determined degree of polarization and direction of polarization for the imaging light from the second imaging system.