JPH0989720A - Imagery evaluating device for optical system - Google Patents

Abstract

PROBLEM TO BE SOLVED: To obtain the imagery evaluating device for an optical system, which can obtain the intensity distribution of the image of a body by an imagery optical system at a high speed in high accuracy and can obtain the performance of the imagery optical system readily in high accuracy. SOLUTION: A memory means 2, which stores various kinds of data with regard to light sources, bodies and imagery optical systems, a central processing means 1, which divides the light source into a plurality of point light sources and obtains the intensity distribution at the specified surface of the body with the luminous fluxes from a plurality of the point light source, and an output means, which outputs the result of the operation from the central processing means, are provided. The central processing means 1 divides the image of the light source formed on the pupil surface of an imagery optical system into the equal-distance rectangular lattice shape the same as a pupil dividing method, divides the light source to be obtained when the divided image is reversely projected on the light source and replaces the Fourier transform of the body corresponding to the position of the individual point light source, which is obtained by the division, by the Fourier transform of the body, which is obtained for the point light source at a certain specified position, by deviating the position at the Fourier transform surface of the body in correspondence with the position of the individual light source. Thus, the intensity distribution of the image of the body is obtained.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an image forming evaluation apparatus for an optical system, and is particularly suitable for evaluating the performance of an optically designed image forming optical system by obtaining the intensity distribution of an object image.

[0002]

2. Description of the Related Art Conventionally, a so-called partially coherent image forming optical system includes a microscope, various projectors, a semiconductor exposure apparatus, and the like. Design of these imaging optics,
Alternatively, a method of calculating the intensity distribution of an object image under partial coherent illumination is known as a means for evaluating optical performance. Especially, in a semiconductor exposure apparatus, such a calculation means is indispensable for its design and evaluation, and it is also used in the semiconductor production factory to set the optimum exposure condition to help improve the yield. There is.

Well-known basic analytical formulas used for these calculations are the HHHopkins formula and the formula recently used by M. Yeung. Formerly HHHo
The method based on the pkins formula was the mainstream, but recently FF
M.Yeung's method, which uses a lot of Fourier transforms, has become widely used due to the higher speed of T (fast Fourier transform), and commercial software also employs this method.

FIG. 7 is a sectional view of an entire partially coherent optical system which has been generally used conventionally. As a feature of this optical system, when it is assumed that the light source 28 is a surface light source, the light source surface 28 is located on the front focal plane of the condenser lens 29, so that the light emitted from one point on the light source surface 28 is the object 30. Is a plane wave at the time of illuminating, and if there is no object (also a planar object) on the object plane 30, an image of the rear focal plane 28 of the imaging lens 31 is imaged. There are two points.

The rear focal plane 3 of the imaging lens 31
Since an aperture stop (not shown) is installed at 2, it can be considered as the exit pupil of the imaging lens 31, and the light source imaged there is considered as an effective light source introduced by HH Hopkins.

Further, since the object illumination light is a plane wave, the exit pupil plane 32 is also a Fourier transform plane of the object plane 30.

The method of M. Yeung is to calculate the object image intensity distribution for each point on the assumption that each point on the light source surface is incoherent, and take the sum as the total intensity distribution of the light source. And the overall intensity distribution I (x,
y) is given. (Proc. Kodak Microelectronics Sem
inar INTERFACE'85,115 (1986))

[0008]

[Equation 1] Here, A (ξ ', η') is the intensity distribution on the light source plane 28, Fa (f, g) is the Fourier transform on the exit pupil plane 32 of the object to be evaluated, and (f, g) is the spatial frequency.
P (ξ, η) is the pupil function, and (p, q) is (ξ ′,
η ′) is the x ′ and y ′ components of the direction cosine representing the traveling direction of light when the point light source illuminates the object, λ is the wavelength, and z is the distance between the exit pupil 32 and the image plane 33.

In the equation (1), the Fourier transform of the object Fa (fp /
Since λ, gq / λ) depends on the position (ξ ′, η ′) of each point of the light source through the direction cosine (p, q), it is necessary to calculate the Fourier transform of the object for each point light source . Here, if the object used for evaluation is a combination of figures such as a triangle, a quadrangle, and a circle for which a Fourier transform formula is analytically obtained, the Fourier transform of the object can be calculated from the formula. This method is hereafter called analytical Fourier transform, and its calculation process is shown in FIG.

In FIG. 8, the light source is divided and held in step 34, the pupil function is calculated in step 35, and the position of the point light source is extracted in step 36. In step 37, one element graphic forming the object is extracted, in step 38 the Fourier transform of the element graphic is calculated analytically or by analytical Fourier transform, and in step 39 it is judged whether or not the element graphic remains. In step 40, the intensity distribution by the point light source is calculated, in step 41, it is determined whether or not the point light source remains, and in step 42, the intensity distribution of the object image is calculated.

[0011]

In the case of an object in which many figures are combined in this analytic Fourier transform, calculation using the analytic expression of the Fourier transform is required for each figure, and the object shape However, there is a problem that the calculation time increases even if the number of light source divisions is roughened due to an increase in the number of element figures when the number becomes complicated.

FIG. 9 is a flow chart when the Fourier transform of the object is calculated using FFT. In FIG. 9, the light source is divided and held in step 43, the pupil function is calculated in step 44, the position of the point light source is extracted in step 45, and the Fourier transform of the object is calculated by FFT in step 46.
In step 47, the intensity distribution by the point light source is calculated, in step 48, it is judged whether or not the point light source remains, and in step 49
Calculates the intensity distribution of the object image.

In the case of calculation based on the flowchart shown in FIG. 9, in order to obtain sufficient calculation accuracy for an object having a complicated shape, it is necessary to increase the number of divisions of the object, which requires a lot of calculation time. become. In particular, in order to determine the performance of the semiconductor exposure apparatus, the shape of the light source, the shape of the object, the wavelength used, the position in the optical axis direction to obtain the intensity distribution (defocus position), etc. can be recombined in various ways to obtain the intensity distribution under several tens of conditions. Therefore, it is strongly desired to further reduce the calculation time per condition.

The present invention solves the problem that a large amount of calculation time is required to calculate the intensity distribution of an object image,
An object of the present invention is to provide an imaging evaluation apparatus for an optical system that can obtain the intensity distribution of an object image at high speed and with high accuracy without depending on the shape of the object, and easily calculate and obtain the performance of the optical system.

[0015]

SUMMARY OF THE INVENTION An image forming evaluation apparatus for an optical system according to the present invention comprises a storage means for storing various data relating to a light source, an object and an image forming optical system, and the light source is divided into a plurality of point light sources. , A central processing means for obtaining an intensity distribution on a predetermined surface of the object based on the divided luminous fluxes from the plurality of point light sources, and an output means for outputting a calculation result from the central processing means. In the image evaluation apparatus, the central processing means obtains when the image of the light source formed on the pupil plane of the imaging optical system is divided into rectangular grids at equal intervals as in the pupil division method of the imaging optical system. The light source is divided so as to be obtained when the divided image obtained is back-projected onto the light source surface, and the Fourier transform of the object corresponding to the position of each point light source obtained by the division is calculated at a specific position. Fourier transform of the object obtained for a point light source in It is characterized in that the alternate and by performing shifting position in the Fourier transform plane of the object according to the position of the individual light sources, are required.

In particular, (1) the Fourier transform plane of the object is the pupil coordinate plane of the imaging optical system. (2) The central processing means uses an element light source configured by selecting a part of all point light sources generated by division. (3) When n is the number of the selected point light sources and N is the total number of the point light sources generated by dividing the light sources, n ≦ N / 2 is satisfied. And so on.

[0017]

DESCRIPTION OF THE PREFERRED EMBODIMENTS FIG. 1 is a block diagram of essential parts of a first embodiment of the present invention. The embodiment of FIG. 1 shows a block diagram relating to information processing for calculating the intensity distribution of an object image at high speed. In FIG. 1, IN is an input means, which is composed of, for example, a keyboard, and is used to input various numerical values related to the light source and the optical system, the relationship between the optical system and the object image, and various numerical values related to the object.

Reference numeral 1 denotes a central processing means, which performs a predetermined calculation based on data from the input means IN and data from a storage means 2 and an external storage means 3 which will be described later. Reference numeral 2 denotes a storage unit which stores various data calculated by the central processing unit 1 and data obtained in advance. An external storage unit 3 stores necessary light sources, optical system data, object data, and the like. OUT is a display means (output means), which outputs and displays the result calculated by the central processing means 1 based on the data from the central processing means 1.

Next, the features of the optical system of this embodiment will be described with reference to the optical system of FIG. In the figure, 28 is a light source surface, 29 is a condenser lens with a focal length f ', and 30 is a condenser lens.
Is an object plane, 31 is an imaging lens with a focal length f ₀ , 32 is an exit pupil position (aperture stop position), and 33 is an image plane.

In this embodiment, in the formula (1) representing the image intensity distribution by the partially coherent optical system, the light source surface 2
8 intensity distribution A (ξ ', η'), Fourier transform of the object F
Both a (fp / λ, gq / λ) and the pupil function P (-λzf, -λzf) can be considered on the exit pupil plane 32 where the aperture stop of the imaging lens 31 is located in FIG.

The origin (p / λ, q / λ) of the Fourier transform of the object 30 depending on each position coordinate (ξ ', η') of the divided point light source on the light source surface 28 is on the exit pupil plane 32. It matches the position (ξ ″, η ″) of the corresponding point light source image. Therefore, Fa, P
By performing the discretization on the exit pupil plane 32 at the same grid interval, once the Fourier transform of the object 30 in a sufficient area is obtained, the necessary Fourier transform of the object 30 is at the position of each point light source. It can be obtained by shifting by the corresponding amount, and the speed can be increased as compared with performing Fourier transform for each point light source.

In the above-mentioned method, the exit pupil plane 32 is divided into the necessary and sufficient subdivisions in order to maintain the calculation accuracy. Therefore, the light source plane 28 is also subdivided into subdivisions, and the calculation amount is still large. The next means of reducing the calculation time is to select only a part of a large number of point light sources generated by the discretization of the light source to form an element light source, and perform the calculation only on the point light sources included in the element light source. , The sum of these is obtained to obtain the intensity distribution of the image of the object 30.

According to the present embodiment, when the number of selected light sources is n and the original number of point light sources is N, if n ≦ N / 2, the calculation time can be shortened with almost no decrease in accuracy. . For example, in the present embodiment, the number of light sources is about 1/2 to 1/4 of the number of point light sources.

FIG. 2 is a flowchart of the arithmetic processing according to the first embodiment of the present invention. In this embodiment, necessary light sources, optical system data, object data, etc. are stored in the external storage device 3 and can be extracted when necessary.

The processing in this embodiment uses the following steps. First, the light source is divided and saved, step 4 is stored, step 5 is performed to extract the elemental figure of the object, and Fourier transformation is performed by the point light source on the optical axis of the imaging lens of the figure extracted in step 5 by an analytical expression. Step 6 for calculating and Step 7 for determining whether or not the element graphic remains
And step 8 of calculating the pupil function from the optical system data,
Step 9 of extracting the position of each saved light source point
Then, according to the position of the point light source extracted in step 9, the position of the Fourier transform of the object obtained in step 6 is shifted to extract the Fourier transform of the object, and from the pupil function and the Fourier transform of the object, The step 11 of calculating the intensity distribution of the object image by the point light sources, the step 12 of determining the presence or absence of the point light source that has not been calculated, and the sum of the calculated intensity distributions are used to obtain the intensity distribution of the object image by all the light sources. The calculation step 13 is used.

FIG. 3 is a schematic diagram of the object used in the first embodiment of the present invention. The object in the figure consists of a combination of 21 quadrangles and 16 triangles. Comparing the calculation times of the method shown in the flow chart of FIG. 2 and the conventional method of FIG. 8, it was 1 minute 55 seconds and 30 minutes 57 seconds, respectively. That is, in this embodiment, the calculation speed is 16 times as efficient as that of the conventional example.

FIG. 4 is a flowchart of arithmetic processing according to the second embodiment of the present invention. The flowchart of FIG. 4 shows a process of calculation using an element light source configured by a part of all point light sources generated by division.

In the present embodiment, step 14 of dividing and storing the light source, step 15 of extracting one elemental figure forming the object, step 16 of calculating the Fourier transform of the elemental figure by an analytical expression, and the elemental figure remaining. Step 17 for determining whether or not there is a step, and Step 18 for calculating a pupil function
And step 19 of extracting the position of the point light source.

Then, it is determined in step 20 whether the point light source extracted in step 19 is an element light source, and the processing in steps 21 and 22 is performed only when the point light source is an element light source. That is, in step 21, the Fourier transform of the object considering the position of the point light source is extracted, and in step 22, the intensity distribution by the point light source is calculated. Then, in step 23, it is determined whether or not the point light source remains, and in step 24, the intensity distribution of the object image is calculated.

FIG. 5 is an explanatory diagram of a method of dividing a light source and a method of constructing element light sources according to the second embodiment of the present invention. In the figure, reference numeral 25 is an aperture stop projected on a light source surface 28, 26 is a light source, and 27 is a projection of an equally-spaced rectangular grid which is a pupil division method. The figure shows an example of a method of dividing the light source 26 (shaded portion) and a method of configuring the element light source (hatched portion) when the number of selected point light sources is about ¼ of all the point light sources.

According to the present embodiment, the intensity distribution of the object shown in FIG. 3 is calculated so that the number of element light sources is about 1/4 of the total number of point light sources.
In addition, the calculation time when the method of FIG. 4 is used is 34 seconds, which is 3.4 times faster than 1 minute 55 seconds in the first embodiment. Further, it is possible to calculate 55 times faster than 30 minutes 57 seconds when the method of FIG. 8 is used.

Next, a third embodiment of the present invention will be described. An infinitely long bar having a width of 0.5 μm is used as an evaluation object, and five bars are arranged in parallel at intervals of 0.5 μm. The calculation time in this case is 21 seconds when calculated for all point light sources (no thinning), whereas it is 1/4 thinned when calculated with the number of element light sources being about 1/4 of all point light sources) Is 6 seconds, which is reduced to 29%.

FIG. 6 is an explanatory diagram showing the difference between these two calculation results. Here, the solid lines of the five rectangles represent the intensity distribution of light immediately after passing through the object, that is, the shape of the object. The other solid line represents the intensity distribution on the image plane in the case of 1/4 thinning, and is referred to as the solid line below. The broken line shows the absolute value of the difference in intensity distribution between the case without thinning and the case with quarter thinning magnified 100 times. In this figure,
If the solid line and the broken line overlap, it means that the difference (error) between the intensity distributions calculated without thinning and that calculated with 1/4 thinning is 1% of the actual intensity distribution. It can be said that the error is 1% or less in the entire area.

Further, when the intensity distribution is large, 0.
Since the error is about 2%, it can be seen that the contrast, which is one of the important parameters, can be suppressed to about 0.2% between the non-thinning and the 1/4 thinning. When the contrast is actually calculated from these intensity distributions, the difference is 0.250, which is 0.95017 in the case of no thinning and 0.95038 in the case of 1/4 thinning, which is sufficient even if calculation is not performed for all point light sources. Accuracy is obtained.

[0035]

As described above, according to the present invention, the calculation of the intensity distribution of an object image can be performed several times to several tens of times that of the conventional method without impairing the calculation accuracy in practice and even in the case of a complicated object shape. Thus, it is possible to achieve an image forming evaluation apparatus for an optical system, which can be calculated at extremely high speed, and the performance of the image forming optical system can be easily and highly accurately obtained.

[Brief description of drawings]

FIG. 1 is a block diagram of a main part of a first embodiment of the present invention.

FIG. 2 is a flowchart of a calculation method according to the first embodiment of the present invention.

FIG. 3 is a schematic diagram of an object according to the first embodiment of the present invention.

FIG. 4 is a flowchart of a calculation method according to the second embodiment of the present invention.

FIG. 5 is an explanatory diagram of a light source dividing method according to a second embodiment of the present invention.

FIG. 6 shows an intensity distribution calculated with the number of element light sources of Embodiment 3 of the present invention being about ¼ of the number of all point light sources, and an absolute value of a difference between the intensity distribution and the intensity distribution calculated with all point light sources. Figure

FIG. 7 is a schematic diagram of a conventional imaging optical system.

FIG. 8 is a flowchart when a conventional analytical Fourier transform is used.

FIG. 9 is a flowchart when a conventional analytical Fourier transform is used.

[Explanation of symbols]

 1 Central Processing Means 2 Storage Means 3 External Storage Means IN Input Means OUT Output Means

Claims (4)

[Claims] 1. A storage means for storing various data relating to a light source, an object and an imaging optical system, the light source being divided into a plurality of point light sources, and the object based on the luminous fluxes from the plurality of divided point light sources. A central processing means for obtaining an intensity distribution on a predetermined surface of, and an output evaluation means for outputting a calculation result from the central processing means.
The central processing means divides a divided image obtained when the image of the light source formed on the pupil plane of the imaging optical system is divided into rectangular grids at the same intervals as the pupil division method of the imaging optical system. The light source is divided so as to be obtained when back-projecting onto a light source surface, and the Fourier transform of the object corresponding to the position of each point light source obtained by the division is converted into a point light source at a specific position. An image formation evaluation apparatus for an optical system, which is obtained by performing a Fourier transform of the object obtained with respect to the object and a position shift on the Fourier transform surface of the object according to the position of each light source, and performing the substitution. . 2. The image formation evaluation apparatus for an optical system according to claim 1, wherein the Fourier transform plane of the object is a pupil coordinate plane of the image formation optical system. 3. The image forming evaluation apparatus for an optical system according to claim 1, wherein the central processing means uses an element light source configured by selecting a part of all point light sources generated by division. 4. The optical system according to claim 3, wherein n ≦ N / 2 is satisfied, where n is the number of the selected point light sources and N is the total number of the point light sources generated by dividing the light sources. Imaging evaluation device.