JP2006242746A - Device and method for visualizing fine sample, and device and method for visualizing disturbance of fine lattice - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a technology capable of visualizing a fine sample by observation using light without using a complicated expensive device. <P>SOLUTION: This device for visualizing the fine sample is equipped with a mounting plate having a mounting surface capable of mounting the sample and having a distribution of a light transmission characteristic changing in a lattice shape, a light source for irradiating the mounting plate with light, an image data acquisition means for acquiring image data of an image formed on an imaging surface approximately parallel to the mounting surface, and a restoration device for restoring the acquired image data. The restoration device treats the acquired image data as an image deteriorated by being transferred through an optical system, and performs restoration processing into an original image. The restoration device grasps a distribution of the deteriorated image and a distribution of the original image as a distribution of a probability density function, and grasps a transfer function as the probability density function of a probability with a condition. A distribution of the original image which is most probable to the distribution of the deteriorated image is calculated by repeated calculation from a relational expression based on the theory by Bayes relative to the probability density function. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to an apparatus and a method for visualizing disturbance of a fine sample or a fine lattice. Specifically, the object having a lattice-like light transmission characteristic is irradiated with light, an image formed by diffraction is acquired as image data, and restoration processing is performed on the image data, so that the object is placed on the object. The present invention relates to an apparatus and a method for visualizing a disturbance of a lattice inherent to a specimen and its object.

  In recent years, with the progress of digitalization in the electrical industry field, the integration degree of semiconductor integrated circuits has been actively improved. How to provide such a highly integrated semiconductor integrated circuit efficiently and at low cost is an important issue that will affect the future development of the digital electrical industry.

In a semiconductor integrated circuit, a circuit pattern is formed using a photomask. As the degree of integration increases, circuit patterns have been miniaturized, and the shape of a photomask used to form the circuit pattern has also been miniaturized.
In order to efficiently produce a semiconductor integrated circuit at a low cost, it is important to quickly and accurately detect problems that occur during the manufacturing process. For this reason, there is an increasing demand for a technique capable of accurately observing a fine pattern such as the shape of a photomask and inspecting soundness.

  A technique for observing such a fine structure is also expected in other technical fields. For example, in the field of biochemistry, research on biopolymers such as peptides and proteins has been actively conducted. When evaluating the characteristics of a biopolymer, it is necessary to accurately grasp the composition of the polymer, and a technique for observing a fine molecular structure of about several nanometers is awaited.

  As an observation apparatus having a high resolution, one using a scanning electron microscope (SEM), an atomic force microscope (AFM), or the like is known. However, these scanning electron microscopes and atomic force microscopes are inconvenient to handle because they require a vacuum for observation. In addition, since a certain amount of time is required for one observation, there is a problem that it takes a long time, for example, when the entire semiconductor device is inspected or when a sample containing a biopolymer is comprehensively observed. Furthermore, the apparatus itself is expensive, and there is a drawback that the cost required for observation is high.

  From such a background, an optical observation apparatus such as an optical microscope has attracted attention. An optical observation apparatus has an advantage that non-destructive observation can be performed, a vacuum is not required, and non-contact inspection can be performed. In recent years, a solid-state laser that emits ultraviolet light by converting the wavelength of a YAG laser or the like using a nonlinear optical crystal has been developed. Using this solid-state laser as an illumination light source, an illumination optical system using an objective lens with a high NA Therefore, there is a great expectation that an optical microscope can obtain a resolution that is thin compared to a scanning electron microscope or the like.

  In the case of the above-described optical observation apparatus, it is required to improve the resolution. In observation using an optical observation device, in principle, a resolution exceeding the wavelength of light cannot be realized. The wavelength of light is several hundred nm. Therefore, a resolution of several nm to several tens of nm could not be realized.

The present inventors conceived that an image obtained from an optical observation device is regarded as a deteriorated image in which information on a minute part is lost, and the image before deterioration is restored based on the theory of probability statistics. did. The deterioration of the image in the observation using light does not occur in the first eye, but depends on the light transmission characteristics. Therefore, based on the theory of probability statistics, it is possible to estimate the most likely image before deterioration from the deteriorated image. In this way, the inventors have conceived that it is possible to substantially improve the resolution of an optical observation apparatus by estimating an image before deterioration including information on a minute part.
Hereinafter, an actually acquired image in which information on a minute part is lost is referred to as a degraded image, and an ideal image in which information on a minute part is not lost is referred to as an original image. . The process of restoring the original image from the degraded image based on the theory of probability statistics is described in detail in Patent Application Nos. 2004-300206 and 2004-300207 filed earlier by the present applicant. However, it should be noted that these patent applications have not been published at the time of filing this application.

Photomasks as described above often have a fine lattice pattern. With respect to such a photomask, if the disturbance of the lattice pattern can be visualized, the soundness can be evaluated. Biopolymers such as proteins can be handled as disordered lattice patterns by placing them on a fine lattice pattern. By visualizing the disorder of the lattice pattern, it is possible to observe the molecular structure.
The present invention provides a technique capable of visualizing disturbance of a fine sample or a fine lattice by observation using light without using a complicated and expensive apparatus.

The apparatus embodied in the present invention is an apparatus for visualizing a fine sample. The apparatus includes a mounting plate having a mounting surface on which a sample can be mounted and a distribution of light transmission characteristics that change in a lattice shape along the mounting surface, a light source that irradiates the mounting plate with light, and a mounting plate. An image data acquisition means for acquiring image data of an image formed on the image pickup surface by light diffracted by the mounting plate, and a restoration device for restoring the acquired image data ing.
The restoration device is
(A1) processing for converting acquired image data into a distribution of degraded images;
(B1) a process of specifying the initial estimated distribution of the original image;
(C1) a process of specifying an initial estimated distribution of the impulse response of the transmission system;
(D1) updating the estimated distribution of the impulse response based on the distribution of the degraded image, the estimated distribution of the original image, and the estimated distribution of the impulse response;
(E1) processing for updating the estimated distribution of the original image based on the distribution of the degraded image, the estimated distribution of the original image, and the estimated distribution of the impulse response;
(F1) A process of alternately repeating the processes (D1) and (E1),
(G1) a process of converting the estimated distribution of the updated original image into image data;
To implement.
The process of updating the estimated distribution of the impulse response of (D1) is as follows:
(D1-1) a process of obtaining a spectral distribution of the estimated distribution of the original image by performing Fourier transform on the estimated distribution of the original image;
(D1-2) a process of obtaining a first function by performing Fourier transform on the estimated distribution of the impulse response;
(D1-3) a process of obtaining a second function by multiplying the first function by a spectral distribution of the estimated distribution of the original image;
(D1-4) processing for obtaining a third function by performing inverse Fourier transform on the second function;
(D1-5) a process of dividing the degraded image distribution by the third function to obtain a fourth function;
(D1-6) A process of obtaining a fifth function by performing a Fourier transform on the fourth function;
(D1-7) A process of obtaining a sixth function by multiplying the fifth function by an inversion function of a spectral distribution of the estimated distribution of the original image;
(D1-8) Processing for obtaining a seventh function by performing inverse Fourier transform on the sixth function;
(D1-9) Multiplying the estimated distribution of the impulse response by the seventh function to obtain a next estimated distribution of the impulse response;
(D1-10) Processing for replacing the next estimated distribution of the impulse response with the estimated distribution of the impulse response is provided.
The process of updating the estimated distribution of the original image of (E1) is as follows:
(E1-1) processing for obtaining an estimated distribution of the frequency response of the transmission system by Fourier-transforming the estimated distribution of the impulse response;
(E1-2) processing for obtaining an eighth function by performing Fourier transform on the estimated distribution of the original image;
(E1-3) a process of multiplying the eighth function by the estimated distribution of the frequency response to obtain a ninth function;
(E1-4) processing for obtaining a tenth function by performing inverse Fourier transform on the ninth function;
(E1-5) a process of obtaining the eleventh function by dividing the distribution of the deteriorated image by the tenth function;
(E1-6) A process of obtaining a twelfth function by performing a Fourier transform on the eleventh function;
(E1-7) A process of obtaining a thirteenth function by multiplying the twelfth function by an inversion function of the estimated distribution of the frequency response;
(E1-8) Processing for obtaining a fourteenth function by performing an inverse Fourier transform on the thirteenth function;
(E1-9) Multiplying the estimated distribution of the original image by the fourteenth function to obtain the next estimated distribution of the original image;
(E1-10) A process of replacing the next estimated distribution of the original image with the estimated distribution of the original image is provided.

  The impulse response referred to in this specification indicates a distribution of a point spread function (PSF) when an original image is transmitted through an optical system to form a deteriorated image. The frequency response referred to in this specification is the ratio of the spectral distribution of the degraded image to the spectral distribution of the original image, that is, the distribution of the optical transfer function (OTF) of the optical system. Point to.

When light is applied to the mounting plate from the light source, the light is diffracted by the mounting plate and forms an image on the imaging surface of the image data acquisition means. At this time, an image that depends on the lattice-like light transmission characteristics of the placement plate and the light transmission characteristics of the sample placed on the placement surface is formed on the imaging surface. When the sample is fine, an image of a lattice having fine disturbance is formed on the imaging surface. Since the disturbance of the lattice image is caused by the sample placed on the placement surface, the fine features of the sample can be visualized by visualizing the disturbance.
The image formed on the imaging surface is blurred due to various factors in the process of transmission, and information on minute parts is lost. That is, it has deteriorated. Therefore, even if the image formed on the imaging surface is handled as it is, it is impossible to observe details in detail. In the visualization apparatus according to the present invention, the degraded image data is restored to image data that can be observed in detail in detail.

An image data restoration process performed by the visualization apparatus of the present invention will be described. First, image restoration based on Bayes's theory will be described. In the following, a case where the original image is a black and white image and the original image is transmitted via a certain optical system to form a black and white deteriorated image will be described. In the following, the original image and the deteriorated image have the same size, and the position of a point in the image can be expressed by coordinates (x, y), and the illuminance distribution of the original image is f _r ( x, y), and the illuminance distribution of the deteriorated image is expressed by g _r (x, y).

Distribution g _{r (x,} y) of the distribution f _{r (x,} y) and the degraded image of the original image, by performing a two-dimensional Fourier transform shown below, and the spatial frequency s in the x-axis, y-axis A spectrum for the spatial frequency t can be obtained.

OTF of the optical system, the spatial spectrum _F r of the original image of the distribution _{f r (x, y) (} s, t), spatial spectrum _G r (s distribution of the degraded image _{g r (x, y),} t ) Is a complex function H _r (s, t) that satisfies the following relationship.

In the case of a general optical system, for any original image distribution f _r (x, y), H _r (s, t), which is an OTF determined by the optical system and the photographing conditions, is used. Image g _r (x, y) can be obtained.

The OTF which is a complex function includes an amplitude transfer function (MTF; Modulation Transfer Function) M _t (s, t) representing the magnitude of a complex amplitude and a phase transfer function (PTF; Phase Transfer Function) P _t ( _Pt ( s, t) is expressed by the following equation.

  By using the above OTF, it is possible to accurately evaluate the characteristics related to the phase of the optical system. The above OTF can be calculated from the characteristic parameters of the optical system.

In the apparatus of the present invention, the distribution of the original image and the distribution of the deteriorated image are handled as a probability density function, and the original image is estimated based on the Bayes theory. The original image distribution f _r (x, y) and the deteriorated image distribution g _r (x, y) set as described above can be handled as a probability density function by performing the following normalization.

In accordance with the above normalization, the optical transfer function H _r (s, t) is also normalized. H _r (s, t) is normalized using the value at the point where the spatial frequency is zero.

  Since the normalized distribution f (x, y) of the original image and the degraded image g (x, y) are non-negative functions and the integral value in the defined region is 1, the probability density function Can be handled. In the above case, f (x, y) is a probability density function of an event of image formation at the coordinates (x, y) of the original image. g (x, y) is a probability density function of an event of image formation at the coordinates (x, y) of the deteriorated image.

When the distribution of the original image and the deteriorated image can be regarded as a probability density function, the distribution of the original image causing the deteriorated image can be estimated from the distribution of the deteriorated image based on the Bayes theory. it can.
An event in which light is imaged at the coordinates (x, y) of the original image can be treated as an event in which a point light source exists at the coordinates (x, y). V (x ₁ , y ₁ ) represents an event in which a point light source exists at the coordinates (x ₁ , y ₁ ) of the original image, and A () represents an event that a point image is formed at the coordinates (x ₂ , y ₂ ) of the deteriorated image. x ₂ , y ₂ ), the probabilities P (V) and P (A) of each event are expressed as follows.

In addition, when a point light source exists at the coordinates (x ₁ , y ₁ ) of the original image, the probability of forming an image at the coordinates (x ₂ , y ₂ ) of the deteriorated image is the event V (x ₁ , y ₁ ) Is a probability of occurrence of event A (x ₂ , y ₂ ) on condition of occurrence. The above probabilities are expressed below using h (x, y) which is the PSF of the optical system.

Based on Bayes' theory, the distribution P (V (x, y) | A (x ₂ , y ₂ )) of the original image when a point image is formed on the point (x ₂ , y ₂ ) in the deteriorated image. Is estimated below.

When Expression (8) and Expression (10) are substituted into P (V (x, y)) and P (A (x ₂ , y ₂ ) | V (x, y)) on the right side of the above expression, Get.

The left side of the above expression represents the distribution of the estimated original image when a point image is formed in the degraded image. The original image distribution f (x, y) for realizing the deteriorated image distribution g (x, y) can be obtained by multiplying the above expression by the deteriorated image distribution g (x, y) and integrating. it can.
Multiplying both sides of the above equation by P (A (x ₂ , y ₂ )) = g (x ₂ , y ₂ ) and integrating over all (x ₂ , y ₂ ) yields the following equation:

  When Expression (9) is substituted into the left side of the above expression, the result of the integration is P (V (x, y)), which is equal to f (x, y). Therefore, based on Bayes' theory, the following relationship holds.

The above relationship is considered to hold when the distribution f (x, y) is a true original image distribution. That is, calculating the distribution f (x, y) that satisfies the above expression corresponds to restoration of a deteriorated image.
In the distribution f (x, y) satisfying the above relationship, f (x, y) on the right side of the equation (14) is set to f _k (x, y), and f (x, y) on the left side of the equation (14). the _{f k + 1 (x, y} ) as _to perform an iterated computations on f k _(x, y), you can be calculated by obtaining a converged value of f k (x, y). The convergence value of f _k (x, y) obtained by the above iterative calculation corresponds to the estimated distribution of the original image based on the Bayes theory.

  In the above description, the original image distribution f (x, y) and the deteriorated image distribution g (x, y) have been normalized. However, in the actual iterative calculation, these distributions are normalized. It can be used as it is without.

In the above iterative calculation, the initial estimated distribution f ₀ (x, y) of the original image is set before performing the iterative calculation. An arbitrary distribution can be set as the first estimated distribution f ₀ (x, y). In general, the distribution g (x, y) of the deteriorated image does not greatly differ from the distribution f (x, y) of the original image. Therefore, the first estimated distribution f ₀ (x, y) is the deteriorated image. It is preferable to use the distribution g (x, y).

The right side of Expression (14) includes a convolution integral using h (x, y) which is PSF. In general, it is difficult to accurately evaluate the PSF including the phase characteristics of the optical system, and it is difficult to perform the above iterative calculation including the accurate phase characteristics. An iterative calculation using PSF that does not include an accurate phase characteristic results in erroneous convergence, thus preventing accurate restoration of the original image.
Therefore, it is possible to restore the original image more accurately by using OTF that can easily include accurate phase characteristics instead of PSF. Further, in order to accurately evaluate the phase characteristics in the process of restoration, the estimated distribution f _k (x, y) (k = 0, 1, 2,...) Of the original image is expanded to a complex function, and its real part Are treated as expressing the image distribution. By using the Fourier transform and the inverse Fourier transform on the right side of the above equation, it can be changed to a format using OTF. When the Fourier transform is expressed by FT () and the inverse Fourier transform is expressed by FT ⁻¹ (), Expression (14) is expressed as follows.

By repeatedly performing the above iterative calculation until f _k converges, the original image can be estimated. determining whether f _k has converged, for example, been set the number of iterations in advance, it may be determined by the number of times of iterative calculation, and calculating a difference between f _k and f _{k + 1,} calculated It may be determined whether or not the sum of the absolute values of the differences to be obtained is equal to or less than a threshold value.

The restoration method using the above principle is realized by sequentially performing the following steps. In the following, it is assumed that the distribution of the original image estimated by repeated calculation is f _k (k = 0, 1,...). The estimated distribution f _k of the original image is treated as a complex function in order to accurately evaluate the phase-related characteristics during the restoration process.
First, H (s, t), which is an OTF, is specified based on the characteristics of the transmission system.
Next, as the first estimated distribution of the original image, the real part of f ₀ (x, y) is set to g (x, y), and the imaginary part of f ₀ (x, y) is set to 0.
Next, the following calculation is repeatedly performed until f _k (x, y) converges. Here, FT () represents a two-dimensional Fourier transform, and FT ⁻¹ () represents a two-dimensional inverse Fourier transform. H ^# (s, t) is an inversion function of H (s, t), and H ^# (s, t) = H (-s, -t).

The above iterative calculation is repeatedly performed to obtain a final estimated distribution _fk of the original image. The real part of the estimated distribution f _k (x, y) of the original image finally obtained corresponds to the restored image f (x, y) of the original image.

  By performing the above processing, if the deteriorated image distribution and the OTF distribution are known, the unknown original image distribution can be restored. Based on the same principle as described above, when the OTF distribution is unknown, the OTF distribution can be restored if the deteriorated image distribution and the original image distribution are known.

In the equation (12), when x ₂ −x is newly set as x ′ and y ₂ −y is newly set as y ′, the following equation is obtained.

When both sides of the above formula are multiplied by P (A (x ₂ , y ₂ )), the following formula is obtained.

The left side of the above formula is P (A (x ₂ , y ₂ ) | V (x ₂ −x ′, y ₂ −y ′)) × P (V (x ₂ −x ′, y ₂ −y ′)), the following equation is obtained.

  Substituting Equation (8), Equation (9), and Equation (10) into the above equation yields the following equation:

When both sides of the above equation are integrated with respect to (x ₂ , y ₂ ), the following equation is obtained.

  Since the integral on the left side of the above equation is equal to 1, the following relationship is established based on Bayes' theory.

  When h (x, y) satisfying the relationship of the above equation is calculated, the OTF distribution H (s, t) can be estimated by Fourier transforming the calculated h (x, y).

In the method according to the present invention, h (x, y) on the right side of Expression (14) is set to h _k (x, y), and h (x, y) on the left side of Expression (24) is set to h _{k + 1} (x, y). ) as _to perform an iterated computations on h k (x, _y), obtaining the convergence value of h k (x, y). This iterative calculation is expressed by the following equation.

The convergence value of h _k (x, y) obtained by the above iterative calculation can be Fourier transformed to obtain an estimated distribution H _k (x, y) of OTF based on Bayes' theory. This relationship is expressed by the following equation.

The OTF estimation method using the above principle is realized by sequentially performing the following steps. In the following, it is assumed that the PSF distribution estimated by repeated calculation is h _k (k = 0, 1,...). The estimated distribution h _{k of the} PSF is treated as a complex function in order to accurately evaluate the characteristics regarding the phase in the process of iterative calculation.
First, a degraded image distribution g (x, y) and an original image distribution f (x, y) are specified. In the method of the present invention, the real part of g (x, y) is set as the illuminance distribution in the deteriorated image, and the imaginary part of g (x, y) is set to 0. In addition, the real part of f (x, y) is set as the illuminance distribution in the original image, and the imaginary part of f (x, y) is set to 0.
Next, the original image distribution f (x, y) is Fourier-transformed to calculate the spectral distribution F (s, t) of the original image distribution.
Next, the first estimated distribution h ₀ (x, y) of the PSF is specified. The initial estimated distribution h ₀ (x, y) of the PSF may be any distribution. For example, the first estimated distribution h ₀ (x, y) of the PSF has a real part as 1 and an imaginary part as 0.
Next, the following calculation is repeatedly performed until h _k (x, y) converges. Here, FT () represents a two-dimensional Fourier transform, and FT ⁻¹ () represents a two-dimensional inverse Fourier transform. F ^# (s, t) is an inversion function of F (s, t), and F ^# (s, t) = F (−s, −t).

The determination of the convergence of h _k (x, y) may be made based on, for example, whether or not the number of iterations has reached a predetermined number, or h _k (x, y) and h _{k + 1.} A difference distribution of (x, y) may be calculated, and a determination may be made based on whether the absolute value of the difference is equal to or less than a certain threshold value for all (x, y), The difference between f _k and f _{k + 1} may be calculated, and the absolute value of the calculated difference may be determined based on whether or not the value obtained by integrating (x, y) is less than or equal to a certain threshold value.
When h _k (x, y) converges, it is Fourier transformed to calculate an estimated distribution H _k (s, t) of OTF.

  By using the above method, the OTF of the transmission system can be estimated appropriately. When the method of the present invention is used, OTFs for all frequency bands can be estimated even when the original image distribution does not include a specific frequency band.

As described above, if the degraded image and the OTF are known, the original image can be restored, and if the degraded image and the original image are known, the OTF can be estimated.
By combining these, it is possible to estimate the OTF based on only the degraded image and restore the original image.
That is, an appropriate distribution is assumed for each of the original image and the PSF, and the above-described PSF estimation (that is, OTF estimation) and original image estimation are alternately performed repeatedly, thereby obtaining the original image. To restore.
With respect to OTF, a more improved estimated distribution can be obtained by calculation based on Bayes's theory using the distribution of the degraded image and the estimated distribution of the original image. As the estimated distribution of the original image used for OTF estimation is closer to the true original image distribution, an estimated distribution closer to the true OTF distribution can be obtained.
With respect to the original image, a further improved estimated distribution can be obtained by calculation based on Bayes's theory using the distribution of the degraded image and the estimated distribution of OTF. As the estimated distribution of the OTF used for estimating the original image is closer to the true OTF distribution, an estimated distribution closer to the true original image distribution can be obtained.
Accordingly, by alternately and repeatedly performing the above-described OTF estimation and original image estimation, the estimated distribution of the original image approaches the distribution of the true original image, and the estimated distribution of the OTF becomes more true OTF. As a result, it is possible to obtain both a well-reconstructed original image and a well-estimated OTF.

In the apparatus of the present invention, the original image can be restored only from the degraded image by sequentially performing the following steps.
First, the first estimated distribution of the original image and the first estimated distribution of the PSF are set. Any distribution may be used as the initial estimated distribution of the original image. In general, since the distribution of the deteriorated image does not differ greatly from the distribution of the original image, it is preferable to use the distribution of the deteriorated image as the initial estimated distribution of the original image. Any distribution may be used as the initial estimated distribution of the PSF.
Next, calculation of Expressions (27) to (29) is performed to obtain an improved PSF estimated distribution h _k (s, t), and the obtained h _k (s, t) is Fourier transformed. The OTF estimated distribution H _k (s, t) is obtained by conversion. By performing the above estimation, an estimated distribution of OTF closer to the true OTF distribution can be obtained.
Next, calculations of Expressions (16) to (18) are performed to obtain a further improved estimated distribution f _k (x, y) of the original image. By performing the above estimation, an estimated distribution of the original image closer to the true original image distribution can be obtained.
By alternately and repeatedly performing the above OTF estimation and original image estimation, the estimated original image distribution approaches the true original image distribution, and the estimated OTF distribution is true. It approaches the distribution of OTF. Therefore, the original image can be restored by performing the above iterative calculation.

  By performing the above-described image restoration process on the image formed on the imaging surface, even if the image acquired by the image data acquisition unit is blurred, the image can be restored to a non-blurred image. it can. The image formed on the imaging surface can be restored to details clearly. As a result, a fine sample can be visualized as a disturbance of the lattice image, and details can be observed in detail.

In the above-described visualization device, any material may be used as the mounting plate as long as the property of transmitting light changes in a lattice shape. For example, a general photomask formed of a light transmitting portion and a light shielding portion, in which the light shielding portions are distributed in a lattice shape, and the light transmitting portions are distributed in the eyes of the lattice may be used. Alternatively, a so-called phase shift mask in which the phase delay characteristic of transmitted light changes in a lattice shape may be used.
Further, the shape of the lattice is not limited to a quadrangle, and may be a triangular lattice or a hexagonal lattice.
The size of the grid of the mounting plate used in the present invention can be adjusted so that characteristics at a desired size can be visualized when the sample is visualized. According to the principle of the present invention, it is considered possible to use a naturally existing crystal lattice as a mounting plate. In this case, since the lattice spacing is from several angstroms to several nanometers, it is considered possible to visualize even the same minute sample.

  In the above-described visualization apparatus, it is preferable that the light source is a point light source close to a mounting plate, and the imaging surface is located on a Fourier plane corresponding to a distribution of light transmission characteristics of the mounting plate.

  The light emitted from the light source to the mounting plate is diffracted by the mounting plate, and forms a lattice image array similar to the distribution of light transmission characteristics of the mounting plate on the rear side of the mounting plate as viewed from the light source. . The image formed in this way is called a Fourier image. The Fourier image is formed on a surface separated from the placement surface by a distance z. The distance z is calculated by the following equation.

  Here, a is the distance from the light source to the placement surface, and z is the distance from the placement surface to the rear side. λ is the wavelength of the irradiated light. n is an arbitrary natural number. d is the repetition period of the grating in the distribution of the light transmission characteristics of the mounting plate. In this specification, a plane on which a Fourier image is formed (that is, a plane that is parallel to the mounting surface and has a distance z from the lattice) is referred to as a Fourier plane. There are an infinite number of Fourier planes corresponding to the distribution of the light transmission characteristics of the mounting plate, corresponding to an arbitrary natural number n.

  When the light source is a point light source, an image having a shape similar to a lattice in the distribution of light transmission characteristics of the mounting plate is formed as a Fourier image. The magnification of the image formed relative to the grid of the mounting plate is given below.

Therefore, according to the above-described visualization apparatus, an image obtained by enlarging the grid of the mounting plate to a desired magnification can be obtained without using a lens. If the lattice image is disturbed due to the sample being placed, the disturbance can be magnified and observed. However, the grid of the mounting plate has a finite size, and a complete Fourier image cannot be obtained. The image actually formed on the imaging surface of the image data acquisition unit is an image in which higher-order wavelength components are lost. Further, it is difficult to accurately match the Fourier plane and the imaging plane of the image data acquisition unit, and the formed image is blurred even when the position is slightly shifted. That is, it is usually impossible to clearly visualize the details of the enlarged image. However, by performing the image restoration process described in detail on the image obtained in this way, it is possible to visualize the disturbance present in the fine lattice image. It is possible to suitably visualize the characteristics of a fine sample.
According to this visualization apparatus, it is possible to enlarge and visualize the characteristics of the sample without using a lens. Such a visualization apparatus can be realized with a simple configuration and can be manufactured at low cost.

  The visualization device further includes a sample image detection device, and the sample image detection device includes image data restored from image data acquired in a state where the sample is placed on the placement plate, and a sample on the placement plate. It is desirable to detect the difference in the image data restored from the image data acquired in a state where no image is placed.

  The image data acquired with the sample placed is an image of a distorted lattice due to the distribution of the light transmission characteristics of the placement plate and the light transmission characteristics of the sample placed on the placement surface. I have. On the other hand, the image data acquired in a state where the sample is not placed has a lattice image without any disturbance due to the distribution of the light transmission characteristics of the placement plate. Therefore, by calculating the difference between the image data restored from the former image data and the image data restored from the latter image data, an image similar to the grid of the mounting plate is removed from the image data, and the sample Only features can be visualized.

  Alternatively, the above-described visualization device further includes a lens that forms an image on the imaging surface of light diffracted by the mounting plate, and the light source emits light having an optical axis as an axis that is oblique to the mounting surface. It is preferable that the lens forms an image of the higher-order light irradiated and diffracted by the mounting plate on the imaging surface.

  When the mounting plate is irradiated with light, the irradiated light is diffracted and dispersed in different directions for each wavelength component. By declining the optical axis of the light source in advance, only high-order light generated by diffraction can enter the lens and form an image on the imaging surface. When a sample is placed on the placement surface and there is a disturbance in the formed grating image, high-order light having a wavelength corresponding to the disturbance is incident on the lens and imaged on the imaging surface. The position where the disturbance exists can be emphasized and visualized. The high-order light component is light having a short wavelength and includes information on a minute part. Therefore, even when enlarged by a lens, details can be clearly visualized. By performing the above-described image restoration processing on the image formed on the imaging surface in this manner, a clear image in which the disturbance of the lattice image is emphasized can be acquired. Therefore, the characteristics of the sample placed on the placement surface can be clearly visualized. Even if the sample is extremely fine and the lattice image in the image formed on the imaging surface is extremely fine, it is possible to highlight and clearly visualize the site where the disturbance exists. .

The principle of the visualization device can also be embodied as a method.
The method of the present invention is a method for visualizing a fine sample. The method includes a step of placing a sample on a placement plate having a placement surface on which the sample can be placed and a distribution of light transmission characteristics that change in a lattice pattern along the placement surface, and a light on the placement plate. , A step of acquiring image data of an image formed on an imaging surface substantially parallel to the mounting surface by light diffracted by the mounting plate, and a step of restoring the acquired image data .
The process to restore is
(A3) converting the acquired image data into a distribution of degraded images;
(B3) identifying an initial estimated distribution of the original image;
(C3) identifying an initial estimated distribution of the impulse response of the transmission system;
(D3) updating the estimated distribution of the impulse response based on the distribution of the degraded image, the estimated distribution of the original image, and the estimated distribution of the impulse response;
(E3) updating the estimated distribution of the original image based on the distribution of the degraded image, the estimated distribution of the original image, and the estimated distribution of the impulse response;
(F3) a step of alternately repeating the steps (D3) and (E3),
(G3) converting the updated estimated distribution of the original image into image data.
The step of updating the estimated distribution of the impulse response of (D3) is as follows:
(D3-1) Fourier transforming the estimated distribution of the original image to obtain a spectral distribution of the estimated distribution of the original image;
(D3-2) obtaining a first function by Fourier-transforming the estimated distribution of the impulse response;
(D3-3) multiplying the first function by a spectral distribution of the estimated distribution of the original image to obtain a second function;
(D3-4) obtaining a third function by performing inverse Fourier transform on the second function;
(D3-5) dividing the degraded image distribution by the third function to obtain a fourth function;
(D3-6) Fourier transform of the fourth function to obtain a fifth function;
(D3-7) obtaining a sixth function by multiplying the fifth function by an inversion function of a spectral distribution of the estimated distribution of the original image;
(D3-8) obtaining a seventh function by performing an inverse Fourier transform on the sixth function;
(D3-9) multiplying the estimated distribution of the impulse response by the seventh function to obtain a next estimated distribution of the impulse response;
(D3-10) A step of replacing the next estimated distribution of the impulse response with the estimated distribution of the impulse response is provided.
The step of updating the estimated distribution of the original image of (E3) is as follows:
(E3-1) Fourier transforming the estimated distribution of the impulse response to obtain an estimated distribution of the frequency response of the transmission system;
(E3-2) Fourier transform of the estimated distribution of the original image to obtain an eighth function;
(E3-3) multiplying the eighth function by the estimated distribution of the frequency response to obtain a ninth function;
(E3-4) obtaining a tenth function by performing inverse Fourier transform on the ninth function;
(E3-5) dividing the distribution of the deteriorated image by the tenth function to obtain an eleventh function;
(E3-6) Fourier transform of the eleventh function to obtain a twelfth function;
(E3-7) obtaining a thirteenth function by multiplying the twelfth function by an inversion function of the estimated distribution of the frequency response;
(E3-8) obtaining a fourteenth function by performing an inverse Fourier transform on the thirteenth function;
(E3-9) multiplying the estimated distribution of the original image by the fourteenth function to obtain the next estimated distribution of the original image;
(E3-10) replacing the next estimated distribution of the original image with the estimated distribution of the original image;
It has.

According to the above-described visualization apparatus or method, a fine sample can be visualized using a mounting plate having a lattice-like light transmission characteristic. In this case, the sample to be observed is visualized as a fine disturbance of the lattice image. By applying the principle of the present invention, it is possible to visualize not only the disturbance of the lattice image caused by the sample but also the disturbance of the lattice image caused by the irregular shape of the original lattice. .
For example, in the manufacturing process of a semiconductor device, a photomask having a regular lattice pattern is used. In such a photomask, if the irregular shape inherent in the lattice pattern can be visualized, the soundness of the photomask can be accurately evaluated.

Another device of the present invention is a device for visualizing fine lattice disturbances. The apparatus includes a light source that irradiates light to a grating, an image data acquisition unit that includes an imaging surface that is substantially parallel to the surface of the grating, and that acquires image data of an image formed on the imaging surface by light diffracted by the grating; And a restoration device for restoring the acquired image data.
The restoration device is
(A2) a process of converting the acquired image data into a distribution of degraded images;
(B2) a process of specifying the initial estimated distribution of the original image;
(C2) a process of specifying an initial estimated distribution of the impulse response of the transmission system;
(D2) processing for updating the estimated distribution of the impulse response based on the distribution of the degraded image, the estimated distribution of the original image, and the estimated distribution of the impulse response;
(E2) processing for updating the estimated distribution of the original image based on the distribution of the degraded image, the estimated distribution of the original image, and the estimated distribution of the impulse response;
(F2) a process of alternately repeating the processes (D2) and (E2);
(G2) processing for converting the estimated distribution of the updated original image into image data;
Is to implement.
The process of updating the estimated distribution of the impulse response of (D2) is as follows:
(D2-1) Fourier transform of the estimated distribution of the original image to obtain a spectral distribution of the estimated distribution of the original image;
(D2-2) processing for obtaining a first function by Fourier-transforming the estimated distribution of the impulse response;
(D2-3) processing for multiplying the first function by a spectral distribution of the estimated distribution of the original image to obtain a second function;
(D2-4) processing for obtaining a third function by performing inverse Fourier transform on the second function;
(D2-5) processing for dividing the distribution of the degraded image by the third function to obtain a fourth function;
(D2-6) a process of obtaining a fifth function by performing a Fourier transform on the fourth function;
(D2-7) a process of obtaining a sixth function by multiplying the fifth function by an inversion function of a spectral distribution of the estimated distribution of the original image;
(D2-8) processing for obtaining a seventh function by performing inverse Fourier transform on the sixth function;
(D2-9) Multiplying the estimated distribution of the impulse response by the seventh function to obtain a next estimated distribution of the impulse response;
(D2-10) Processing for replacing the next estimated distribution of the impulse response with the estimated distribution of the impulse response is provided.
The process of updating the estimated distribution of the original image of (E2) is as follows:
(E2-1) processing for obtaining an estimated distribution of the frequency response of the transmission system by performing Fourier transform on the estimated distribution of the impulse response;
(E2-2) processing for obtaining an eighth function by Fourier-transforming the estimated distribution of the original image;
(E2-3) a process of multiplying the eighth function by the estimated distribution of the frequency response to obtain a ninth function;
(E2-4) a process of obtaining a tenth function by performing an inverse Fourier transform on the ninth function;
(E2-5) a process of obtaining the eleventh function by dividing the distribution of the deteriorated image by the tenth function;
(E2-6) a process of obtaining a twelfth function by performing a Fourier transform on the eleventh function;
(E2-7) a process of obtaining a thirteenth function by multiplying the twelfth function by an inversion function of the estimated distribution of the frequency response;
(E2-8) Processing for obtaining a fourteenth function by performing an inverse Fourier transform on the thirteenth function;
(E2-9) processing for multiplying the estimated distribution of the original image by the fourteenth function to obtain the next estimated distribution of the original image;
(E2-10) a process of replacing the next estimated distribution of the original image with the estimated distribution of the original image;
It has.

The principle of visualizing the disturbance of the grating by the above-described visualization apparatus is the same as the principle of visualizing the disturbance of the image of the grating in the apparatus for visualizing a fine sample that has already been described in detail.
According to the above-described visualization apparatus, it is possible to visualize a minute lattice disturbance inherent in a lattice pattern. For example, when applied to a photomask having a lattice pattern, the soundness of the photomask can be evaluated quickly and accurately using an inexpensive apparatus.

  In the above-described visualization apparatus, it is preferable that the light source is a point light source close to a lattice, and the imaging surface is located on a Fourier plane of the lattice.

  The above-described visualization device further includes a lattice disturbance detection device, and the lattice disturbance detection device includes image data restored from image data acquired in a state where the lattice is disturbed, and in a state where the lattice is not disturbed. It is further preferable to detect a difference in the restored image data from the acquired image data.

  Alternatively, the visualization device described above further includes a lens that forms an image of light diffracted by a grating on the imaging surface, and the light source irradiates light having an optical axis as an axis oblique to the plane of the grating, It is desirable that the lens forms high-order light diffracted by a grating on the imaging surface.

The principle of the visualization device can also be embodied as a method.
Another method of the present invention is a method for visualizing fine lattice disturbances. The method includes a step of irradiating light on a grating, a step of acquiring image data of an image formed on an imaging surface in which light diffracted by the grating is substantially parallel to a surface of the grating, and a step of restoring the acquired image data It has.
The process to restore is
(A4) converting the acquired image data into a degraded image distribution;
(B4) identifying an initial estimated distribution of the original image;
(C4) identifying an initial estimated distribution of the impulse response of the transmission system;
(D4) updating the estimated distribution of the impulse response based on the distribution of the degraded image, the estimated distribution of the original image, and the estimated distribution of the impulse response;
(E4) updating the estimated distribution of the original image based on the distribution of the degraded image, the estimated distribution of the original image, and the estimated distribution of the impulse response;
(F4) a step of alternately repeating the steps (D4) and (E4),
(G4) converting the updated estimated distribution of the original image into image data.
The step of updating the estimated distribution of the impulse response of (D4) is as follows:
(D4-1) Fourier transforming the estimated distribution of the original image to obtain a spectral distribution of the estimated distribution of the original image;
(D4-2) Fourier transforming the estimated distribution of the impulse response to obtain a first function;
(D4-3) obtaining the second function by multiplying the first function by the spectral distribution of the estimated distribution of the original image;
(D4-4) a step of performing inverse Fourier transform on the second function to obtain a third function;
(D4-5) dividing the degraded image distribution by the third function to obtain a fourth function;
(D4-6) Fourier transform of the fourth function to obtain a fifth function;
(D4-7) obtaining a sixth function by multiplying the fifth function by an inversion function of a spectral distribution of the estimated distribution of the original image;
(D4-8) obtaining a seventh function by performing inverse Fourier transform on the sixth function;
(D4-9) multiplying the estimated distribution of the impulse response by the seventh function to obtain a next estimated distribution of the impulse response;
(D4-10) A step of replacing the next estimated distribution of the impulse response with the estimated distribution of the impulse response is provided.
The step of updating the estimated distribution of the original image of (E4) is as follows:
(E4-1) a step of Fourier transforming the estimated distribution of the impulse response to obtain an estimated distribution of the frequency response of the transmission system;
(E4-2) Fourier transform of the estimated distribution of the original image to obtain an eighth function;
(E4-3) obtaining an ninth function by multiplying the eighth function by the estimated distribution of the frequency response;
(E4-4) obtaining a tenth function by performing an inverse Fourier transform on the ninth function;
(E4-5) dividing the degradation image distribution by the tenth function to obtain an eleventh function;
(E4-6) Fourier transform of the eleventh function to obtain a twelfth function;
(E4-7) obtaining a thirteenth function by multiplying the twelfth function by an inversion function of the estimated distribution of the frequency response;
(E4-8) obtaining a fourteenth function by performing an inverse Fourier transform on the thirteenth function;
(E4-9) multiplying the estimated distribution of the original image by the fourteenth function to obtain the next estimated distribution of the original image;
(E4-10) replacing the next estimated distribution of the original image with the estimated distribution of the original image;
It has.

By using the visualization apparatus or method of the present invention, it is possible to visualize the characteristics of a fine sample. For example, nano-level structures of biopolymers such as peptides and proteins can be visualized. Furthermore, the dynamics of the biopolymer can also be visualized by acquiring changes over time in the characteristics of the visualized fine sample.
Further, according to the visualization apparatus or method of the present invention, it is possible to visualize a minute shape irregularity originally provided in the lattice pattern. For example, the inspection of the soundness of a photomask having a lattice pattern used for manufacturing a semiconductor device can be performed with high accuracy.

  Hereinafter, embodiments embodying the present invention will be described with reference to the drawings.

(First embodiment)
The visualization apparatus 102 according to the present embodiment will be described with reference to the drawings.
FIG. 1 is a schematic diagram showing the configuration of the visualization apparatus 102 of this embodiment. The visualization device 102 according to the present embodiment includes a plate 112 on which a sample 114 can be placed, a light source 104, an image sensor 106, and a restoration device 108.

  The light source 104 is a point light source that emits coherent light, and irradiates the plate 112 with light. As the light source 104, for example, a light emitting diode can be used.

The sample 112 can be placed on the plate 112.
FIG. 2 is an enlarged view of the plate 112 as viewed from above. The plate 112 includes a transmission part 204 that transmits the irradiated light and a shielding part 202 formed in a lattice shape that shields the irradiated light. Accordingly, the plate 112 serves as a diffraction grating for the light emitted from the light source 104. In the visualization apparatus 102 of the present embodiment, the horizontal width d1 and the vertical width d3 of the transmission part 202 are each 5 nm. Moreover, in the visualization apparatus 102 of the present embodiment, the horizontal width d2 and the vertical width d4 of the lattice of the shielding unit 204 are each 5 nm.

When the sample 114 is placed on the plate 112, it is observed as a disorder of the lattice pattern of the shielding portion 202 of the plate 112. By comparing this disordered lattice pattern with an undisturbed lattice pattern, the fine features of the sample 114 on the plate 112 can be visualized. Further, by examining the temporal change in the disturbance of the lattice pattern described above, it is possible to observe the minute feature change of the sample 114.
In the visualization apparatus 102 of the present embodiment, for example, a fine structure can be visualized using a biopolymer such as a peptide or protein as a sample 114.

The image sensor 106 includes an imaging surface 110 that is parallel to the surface of the plate 112. The image sensor 106 includes a plurality of imaging devices on the imaging surface 110, recognizes an image formed on the imaging surface 110 through the imaging device, and converts the image signals into electrical signals indicating the illuminance distribution of each color component of RGB. The data is transmitted to the restoration device 108. The image sensor 106 can adjust the distance from the surface of the plate 112 to the imaging surface 110.
In the visualization apparatus 102 of the present embodiment, the size of one image sensor is 10 μm × 10 μm.

  The restoration device 108 performs restoration processing on the data transmitted from the image sensor 106. Details of the restoration process performed by the restoration device 108 will be described later.

The operation of the visualization apparatus 102 of this embodiment will be described.
The light emitted from the light source 104 is diffracted by the plate 112 and the sample 114, partly scattered and partly transmitted.
The light transmitted through the plate 112 is diffracted to form an image row similar to the grating on the rear side of the plate 112. The image formed in this way is called a Fourier image. The Fourier image is formed at a position z specified below. However, a is the distance from the light source 104 to the plate 112, and z is the distance from the plate 112 to the rear side. λ is the wavelength of the irradiated light. n is an arbitrary natural number. d is the repetition period of the grating of the plate 112, and in the case of the visualization apparatus 102 of the present embodiment, d = d1 + d2 = 10 nm.

  The image formed behind the plate 112 has a shape similar to the lattice of the plate 112. The magnification of the grating image to be formed relative to the grating of the plate 112 is given below.

Therefore, an image of the plate 112 and the sample 114 enlarged at the magnification m is formed on the imaging surface 110 of the image sensor 106. In the visualization apparatus 102 of the present embodiment, the distance from the light source 104 to the plate 112 is set to a = 10 μm and z = 999,990 μm. In this case, the magnification m = 100,000. On the imaging surface 110 of the image sensor 106, an image of the plate 112 and the sample 114 enlarged at a magnification of 100,000 times is formed.
The image formed on the imaging surface 110 is read by the image sensor 106 and transmitted to the restoration device 108 as data.

In order to accurately form the above-described Fourier image on the imaging surface 110, the distance between the plate 112 and the imaging surface 110 must be exactly matched to the focal length z described above. Such position adjustment is very difficult. In many cases, the distance between the plate 112 and the imaging surface 110 is slightly deviated from the focal length z. Further, since the lattice pattern of the plate 112 has a finite size, a complete Fourier image cannot be formed. Therefore, the image formed on the imaging surface 110 is blurred because the magnification is enlarged but the details are not completely reproduced. The details cannot be observed in detail.
The visualization apparatus 102 according to the present embodiment regards the image acquired on the imaging surface 110 described above as an image that has deteriorated due to the transmission of the optical system, performs restoration processing by the restoration apparatus 108, and performs details from the degraded image. Restore the image expressed up to.

The restoration device 108 receives the image data transmitted from the image sensor 106 and performs restoration processing of the image data. The restoration device 108 treats the image data obtained by the image sensor 106 as a degraded image, and performs restoration processing from the degraded image to the original image, assuming that both the characteristics of the optical system and the original image are unknown.
Hereinafter, the restoration process performed by the restoration device 108 will be described.

FIG. 3 shows a flowchart of the restoration process performed by the restoration device 108.
First, in step S302, the illuminance distributions gr (x, y), gg (x, y), and gb (x, y) of RGB color components are specified from the image data received by the restoration device 108. The illuminance distributions gr (x, y), gg (x, y), and gb (x, y) of each color component are variables representing the illuminance of each color component as a real number. The restoration device 108 according to the present exemplary embodiment performs the processing from step S304 onward for each of the illuminance distributions gr (x, y), gg (x, y), and gb (x, y) of each color component described above. , Restore the image. Hereinafter, as an example, processing for restoring the distribution of gr (x, y) will be described. The restoration processing for gg (x, y) and gb (x, y) is the same as that for gr (x, y), and thus the description thereof is omitted.

  In step S304, the distribution g (x, y) of the deteriorated image is specified. The degraded image distribution g (x, y) is a complex function that describes the distribution of the illuminance of light including the phase characteristics. In the visualization apparatus 102 of the present embodiment, the real part of g (x, y) is matched with the distribution of gr (x, y), and all imaginary parts of g (x, y) are set to zero.

In step S306, the initial estimated distribution f ₀ (x, y) of the original image is set. An arbitrary distribution can be set for the initial estimated distribution f ₀ (x, y) of the original image. In the method of the present embodiment, the degraded image distribution g (x, y) is used as the initial estimated distribution f ₀ (x, y) of the original image. In general, it is considered that the distribution of the original image and the distribution of the deteriorated image are not significantly different. Therefore, the original image is restored by setting the initial estimated distribution f ₀ (x, y) of the original image as described above. It is possible to reduce the number of iterative calculations involved.
In step S306, the first estimated distribution h ₀ (x, y) of the point spread function PSF, which is an impulse response of the optical system, is set. An arbitrary distribution can be set as the first estimated distribution h ₀ (x, y) of the PSF. In the method of the present embodiment, as the first PSF estimated distribution h ₀ (x, y), a function having a real part of 1 and an imaginary part of 0 for all (x, y) is used.
In step S306, the number of iterations k is set to zero.

  In step S308, the iteration number k of the iterative calculation is increased by one.

In step S310, the PSF estimated distribution h _k (x, y) is calculated, and the PSF estimated distribution is updated. This calculation will be described later.

In step S312, the PSF estimated distribution h _k (x, y) is Fourier transformed to calculate the OTF estimated distribution H _k (s, t).

In step S314, the estimated distribution f _k (x, y) of the original image is calculated, and the estimated distribution of the original image is updated. This calculation will be described later.

In step S316, the difference between the estimated distribution f _k (x, y) of the original image updated in step S314 and the estimated distribution f _k−1 of the original image before being updated is calculated. It is determined whether or not (x, y) is below a certain threshold value ε. If the difference is greater than or equal to the threshold ε for (x, y) (NO in step S316), it is determined that the estimated distribution f _k (x, y) of the original image has not yet converged. Then, the process proceeds to step S308, and the processes from step S308 to step S314 are repeated again. If the difference is less than the threshold value ε for all (x, y) (YES in step S316), the estimated distribution f _k (x, y) of the original image is determined to have converged. The process proceeds to step S318.

In step S318, the estimated distribution f _k (x, y) of the original image obtained as a result of the iterative calculation is set to the restored distribution f (x, y) of the original image. In the method of the present embodiment, the distribution describing an image in the process of iterative calculation is treated as a complex function, so the distribution f (x, y) of the original image set as described above is generally a complex function. In the method of this embodiment, the real part of the restored original image distribution f (x, y) represents the illuminance distribution in the original image. When the real part of the degraded image distribution g (x, y) is the illuminance distribution gr (x, y) of the R component of the image data, the actual distribution f (x, y) of the restored original image Represents the irradiance distribution fr (x, y) of the R component in the original image.
The R component illuminance distribution fr (x, y) is restored from the R component illuminance distribution gr (x, y) by the series of processes from step S304 to step S318. By performing the above processing for gg (x, y) and gb (x, y), the illuminance distributions fg (x, y) and fb (x, y) are also restored. Image data can be obtained from the restored fr (x, y), fg (x, y), and fb (x, y).
The fr (x, y), fg (x, y), and fb (x, y) restored by the above method may be displayed on a display or printed on paper using a printing device. It may be stored in a storage device such as a hard disk or transmitted to another computer via a communication line.

Hereinafter, estimation of h _k (x, y) in step S310 will be described in detail. In the method of the present embodiment, steps S402 to S426 shown in the flowchart of FIG. 4 are performed as h _k (x, y) estimation.

In step _{S402, h k (x, y} ) initial estimated distribution _h ^k 0 (x, y) of setting a. In the method of the present _{embodiment, h k-1 (x,} y) that has already been _acquired, and initial estimated _h ^k 0 (x, y) of h k (x, y) to. In step S402, the iteration number m of the iteration calculation related to the estimation of h _k (x, y) is set to zero.

In step S404, an estimated distribution F (s, t) of the spectrum of the original image is set. In the method of this embodiment, the estimated distribution f _k-1 (x, y) of the already acquired original image is Fourier transformed, and the result is F (s, t).

In step _{S406, h k (x, y} ) estimated distribution _h ^k m (x, y) of the Fourier transform, the result is set to the function _K 1 (s, t). The function K ₁ (s, t) corresponds to the first function.

In step S408, the function K ₁ (s, t) calculated in step S406 is multiplied by the estimated distribution F (s, t) of the spectrum of the original image calculated in step S404 to obtain the function K ₂ (s, t ) Is calculated. The function K ₂ (s, t) corresponds to the second function.

In step S410, the function K ₂ (s, t) calculated in step S408 is subjected to inverse Fourier transform, and the result is set as the function L ₃ (x, y). The function L ₃ (x, y) corresponds to the third function.

In step S412, the degraded image distribution g identified in step S304 in FIG. 3 (x, y), by dividing the functions _L 3 calculated in step S410 in FIG. 4 (x, y), the function _L 4 ( x, y) is calculated. The function L ₄ (x, y) corresponds to the fourth function.

In step S414, the function L ₄ (x, y) calculated in step S412 is Fourier transformed, and the result is set to the function K ₅ (s, t). The function K ₅ (s, t) corresponds to the fifth function.

In step S416, the function K ₅ (s, t) calculated in step S414 is multiplied by F ^# (s, t) to calculate the function K ₆ (s, t). The function K ₆ (s, t) corresponds to the sixth function. F ^# (s, t) is an inversion function of the estimated distribution F (s, t) of the spectrum of the original image calculated in step S404, and F ^# (s, t) = F (-s, -t). Satisfy the relationship.

In step S418, the function K ₆ (s, t) calculated in step S416 is subjected to inverse Fourier transform, and the result is set to the function L ₇ (x, y). The function L ₇ (x, y) corresponds to the seventh function.

In step _{S420, h k (x, y} ) estimated distribution _h ^k m (x, y) of the, set function _L 7 (x, y) in step S418 is multiplied by, the result _h k (x, Set the improved estimated distribution h _k ^{m + 1} (x, y) of y).

In step S422, the number m of iterations for estimating h _k (x, y) is incremented by one.

In step S424, it is determined whether or not the number m of iterations for estimating h _k (x, y) is equal to or greater than a threshold value. In this embodiment, the number of iterative calculations performed for estimating h _k (x, y) is five. If the repetition number m is less than 5 (NO in step S424), the process proceeds to step S406, and the processes from step S406 to step S422 are performed again. If the repetition number m is 5 or more (YES in step S424), the process proceeds to step S426.

In step S426, the distribution h _k ⁵ (x, y) obtained as a result of the above iterative calculation is set as the estimated distribution of h _k (x, y).
The above iterative calculation corresponds to estimating the PSF distribution h _k (x, y) from the deteriorated image distribution g (x, y) and the original image distribution f _k−1 (x, y). The closer the original image distribution f _k−1 (x, y) is to the true original image distribution f (x, y), the h _k (x, y) estimated by the above iterative calculation is the true PSF. It approaches the distribution h (x, y).

Hereinafter, estimation of f _k (x, y) in step S314 of FIG. 3 will be described in detail. In the method of the present embodiment, steps S502 to S524 shown in the flowchart of FIG. 5 are performed as the estimation of f _k (x, y).

In step _{S502, f k (x, y} ) initial estimated distribution _f ^k 0 (x, y) of setting a. In the method of this embodiment, already set acquired by that _{f k-1 (x, y} ) _and, f k _(x, y) initial estimated distribution _f ^k 0 (x, y) as a. In step S502, the iteration number n for iterative calculation for estimating f _k (x, y) is set to zero.

In step _{S504, f k (x, y} ) estimated distribution _f ^k n (x, y) of the Fourier transform, the result is set to the function _K 1 (s, t). The function K ₁ (s, t) corresponds to the first function.

At step S506, the function _K 1 (s, t) calculated in step S504, the multiplied by the estimated distribution _H k (s, t) of the OTF calculated in the step S312 of FIG. 3, the function _K 2 (s, t) is calculated. The function K ₂ (s, t) corresponds to the second function.

In step S508, the function K ₂ (s, t) calculated in step S506 is subjected to inverse Fourier transform, and the result is set as the function L ₃ (x, y). The function L ₃ (x, y) corresponds to the third function.

At step S510, the degraded image distribution g identified in step S304 in FIG. 3 (x, y), by dividing the functions _L 3 calculated in step S508 of FIG. 5 (x, y), the function _L 4 ( x, y) is calculated. The function L ₄ (x, y) corresponds to the fourth function.

In step S512, the function L ₄ (x, y) calculated in step S510 is Fourier-transformed, and the result is set as the function K ₅ (s, t). The function K ₅ (s, t) corresponds to the fifth function.

In step S514, the function K ₅ (s, t) calculated in step S512 is multiplied by H _k ^# (s, t) to calculate a function K ₆ (s, t). H _k ^# (s, t) is an inversion function of the estimated distribution H _k (s, t) of OTF calculated in step S312 of FIG. 3, and H _k ^# (s, t) = H _k (−s , −t).

In step S516, the function K ₆ (s, t) calculated in step S514 is subjected to inverse Fourier transform, and the result is set to the function L ₇ (x, y). The function L ₇ (x, y) corresponds to the seventh function.

In step _{S518, f k (x, y} ) estimated distribution _f ^k n (x, y) of the, multiplied by the function _L 7 calculated in step _{S516 (x, y), f} k (x, y) of An improved estimated distribution f _k ^{n + 1} (x, y) is calculated.

In step S520, the iteration number n of the iteration calculation for estimating f _k (x, y) is incremented by one.

In step S522, it is determined whether or not the number n of iterations for estimating f _k (x, y) is equal to or greater than a threshold value. In this embodiment, the number of iterative calculations performed for estimating f _k (x, y) is five. If the number of repetitions n is less than 5 (NO in step S522), the process proceeds to step S504, and the processes from step S504 to step S520 are performed again. If the number of repetitions n is 5 or more (YES in step S522), the process proceeds to step S524.

In step S524, the distribution f _k ⁵ (x, y) obtained as a result of the above iterative calculation is set as the estimated distribution of f _k (x, y).
The above iterative calculation corresponds to estimating the original image distribution f _k (x, y) based on the deteriorated image distribution g (x, y) and the OTF distribution H _k (s, t). As the OTF distribution H _k (s, t) is closer to the true OTF distribution H (s, t), the f _k (x, y) estimated by the above iterative calculation is the true original image distribution f ( approaches x, y).

  The restoration device 108 includes an image restored from image data obtained with the sample 114 placed on the plate 112, and an image restored from image data obtained without the sample 114 placed on the plate 112. The difference is calculated. The calculated distribution of differences is a visualization of the lattice disturbance caused by the presence of the sample 114. The calculated difference distribution is enlarged by the visualization apparatus 102 to a magnification of m = 100,000 times. By observing this difference distribution, the fine structure of the sample 114 can be visualized.

  By observing the disturbance of the visualized lattice as described above and recording changes over time, it is possible to know the state of transformation of the sample 114. For example, when the sample 114 is a protein in the modification process, it is possible to visualize the microscopic dynamics of the protein in the modification process by using the visualization device 102.

  In the above embodiment, the example in which the estimated distribution of the OTF is updated first and then the estimated distribution of the original image is updated in the process of the iterative calculation. The update of the estimated distribution of the OTF and the update of the estimated distribution of the original image may be performed repeatedly, so the estimated distribution of the original image may be updated first, and then the estimated distribution of the OTF may be updated. .

  In the above-described embodiment, an example in which the sample 114 placed on the plate 112 is visualized has been described. However, using a device having a similar configuration, shape irregularities in a photomask having a distribution of light transmission characteristics in a lattice shape are visualized. You can also

(Second embodiment)
A visualization apparatus 602 according to the present embodiment will be described with reference to the drawings. The same components as those in the first embodiment are denoted by the same reference numerals and description thereof is omitted.
The visualization device 602 includes a mask 612 having a lattice-like light transmission pattern, a light source 604, a lens 614, an image sensor 106, and a restoration device 108.

FIG. 7 is a view of the mask 612 as seen from above. The mask 612 includes a transmitting portion 802 that transmits the irradiated light and a shielding portion 804 that is formed in a lattice shape that blocks the irradiated light. Accordingly, the mask 612 serves as a diffraction grating for light emitted from the light source 604.
The mask 612 is a photomask used when manufacturing a CCD device, and has a lattice pattern formed by irradiation with an electron beam. When the lattice pattern is formed in this way, a step may be generated in the lattice at the turn-back point or the repetition point. Such a step is a kind of photomask defect and is called an EB striping defect or an EB step defect. The mask 612 of this embodiment is a photomask having a lattice pattern having a transmission portion width of 9.9 μm and a shielding portion width of 1.1 μm, and has EB steps 808 and 810 in the vertical and horizontal directions.

  A light source 604 in FIG. 6 is a light source that emits coherent light. The optical axis LB of the light source 604 is inclined with respect to the surface of the mask 612. In order to simplify the description, a single light source is shown as the light source 604 in FIG. 6, but the light source 604 may be a plurality of light sources. In such a case, the light sources 604 irradiate light with the same oblique angle with respect to the surface of the mask 612 from different directions.

  The lens 614 forms an image of the high-order light diffracted by the mask 612 on the imaging surface 110 of the image sensor 106. In the visualization device 602 of this embodiment, the numerical aperture NA of the lens 614 is adjusted so that an image formed on the imaging surface 110 has a desired magnification. The position of the lens 614 is adjusted so that only desired high-order light among the high-order light diffracted by the mask 612 is incident.

  The restoration device 108 performs restoration processing on the data transmitted from the image sensor 106. Since the restoration process performed by the restoration apparatus 108 is the same as the restoration process performed by the restoration apparatus 108 of the first embodiment, the description thereof is omitted.

The operation of the visualization device 602 according to the present embodiment will be described with reference to FIG.
The light source 604 irradiates light along the optical axis LB oblique to the mask 612. The light applied to the mask 612 is diffracted by the lattice pattern of the mask 612 and dispersed behind the mask 612 when viewed from the light source 604. In FIG. 8, the light having the same wavelength as the irradiated light is L ₀ , and the primary light, the secondary light,... Of the light having a higher order wavelength than the irradiated light is represented by L ₁ , L ₂ ,. In this figure, −1st order light, −2nd order light,... Are expressed as L ₋₁ , L _−2,.

Of the light diffracted by the mask 612, only higher-order components enter the lens 614. In the example illustrated in FIG. 8, only high-order light from the fifth-order component L ₅ to the seventh-order component L ₇ is incident on the lens 614 and the other components are not incident on the lens 614. The high-order light incident on the lens 614 is refracted by the lens 614 and enlarged and imaged on the imaging surface 110 of the image sensor 106 at a desired magnification.
High-order light incident on the lens 614 can be adjusted by changing the position and numerical aperture of the lens 614. For example, only the 19th-order light may be incident on the lens 614 and other components may not be incident on the lens 614.

The image formed on the imaging surface 110 is composed only of higher-order light components in the diffracted light. By entering light having a wavelength shorter than the spatial frequency in the lattice pattern of the mask 612 as a high-order light component, an image in which the disturbance of the lattice pattern of the mask 612 is emphasized can be formed on the imaging surface 110. The image formed on the imaging surface 110 is composed only of higher-order light components, and even when the image is enlarged and formed by the lens 614, it is possible to visualize the details.
FIG. 9 shows an image 906 formed on the imaging surface 110 when the mask 612 shown in FIG. 7 is used. The image 906 is acquired with the position of the lens 614 and the numerical aperture adjusted so that only the 19th-order light among the light diffracted by the mask 612 is incident.
Although the image 906 is blurred and the lattice pattern of the mask 612 can hardly be identified, it can be seen that the line 908 appears highlighted at a position corresponding to the step 808 and the line 910 appears at a position corresponding to the step 810.
By capturing the image 906 obtained on the imaging surface 110 as an image that has deteriorated due to transmission through the optical system, and performing restoration processing, it is possible to visualize such disturbance of the lattice more clearly.
The restoration device 108 performs restoration processing based on the image data transmitted from the image sensor 106 and creates restored image data. Since the restoration process performed by the restoration device 108 is the same as that of the first embodiment, description thereof is omitted.

  According to the visualization device 602 described above, it is possible to obtain an image that visualizes the disturbance of a minute lattice existing in the lattice pattern of the mask 612. Even a very small defect can be clearly visualized by emphasizing a site where the defect exists. The soundness of the mask 612 can be evaluated quickly and accurately using an inexpensive apparatus.

  In the above, an example in which a minute defect of the mask 612 is visualized has been described. However, instead of the mask 612, a plate having an accurate grid-like light transmission characteristic distribution is used, and an apparatus having a similar configuration is used. It is also possible to clearly visualize the characteristics of the fine sample placed on the top.

As mentioned above, although embodiment of this invention was described in detail, these are only illustrations and do not limit a claim. The technology described in the claims includes various modifications and changes of the specific examples illustrated above.
In addition, the technical elements described in the present specification or the drawings exhibit technical usefulness alone or in various combinations, and are not limited to the combinations described in the claims at the time of filing. In addition, the technology illustrated in the present specification or the drawings achieves a plurality of objects at the same time, and has technical utility by achieving one of the objects.

FIG. 1 is a diagram illustrating a configuration of the visualization apparatus 102. FIG. 2 is a top view of the plate 112 having a lattice pattern. FIG. 3 is a flowchart for explaining processing performed by the restoration device 108. FIG. 4 is a flowchart for explaining an OTF distribution estimation process performed by the restoration apparatus 108. FIG. 5 is a flowchart for explaining the estimation process of the original image distribution performed by the restoration device 108. FIG. 6 is a diagram illustrating a configuration of the visualization device 602. FIG. 7 is a view of the mask 612 as viewed from above. FIG. 8 is a diagram illustrating the principle of the visualization device 602. FIG. 9 is a diagram illustrating an image 906 formed on the imaging surface 110.

Explanation of symbols

102 ... Visualization device 104 ... Point light source 106 ... Image sensor 108 ... Restoration device 110 ... Imaging surface 112 ... Plate 114 ... Sample 202 ... Shielding unit 204 ... Transmission unit 602 ... Visualization device 604 ... Light source 612 ... Mask 614 ... Lens 802 ... Transmission unit 804 ... Shielding unit 808, 810 ... Stage 906 ... Image 908, 910 ···line

Claims (10)

An apparatus for visualizing a minute sample,
A mounting plate having a mounting surface on which a sample can be mounted, and a distribution of light transmission characteristics that change in a lattice shape along the mounting surface;
A light source for irradiating the mounting plate with light;
An image data acquisition means comprising an imaging surface substantially parallel to the mounting surface, and acquiring image data of an image formed on the imaging surface by the light diffracted by the mounting plate;
It has a restoration device that restores the acquired image data.
The restoration device
(A1) processing for converting acquired image data into a distribution of degraded images;
(B1) a process of specifying the initial estimated distribution of the original image;
(C1) a process of specifying an initial estimated distribution of the impulse response of the transmission system;
(D1) updating the estimated distribution of the impulse response based on the distribution of the degraded image, the estimated distribution of the original image, and the estimated distribution of the impulse response;
(E1) processing for updating the estimated distribution of the original image based on the distribution of the degraded image, the estimated distribution of the original image, and the estimated distribution of the impulse response;
(F1) A process of alternately repeating the processes (D1) and (E1),
(G1) a process of converting the estimated distribution of the updated original image into image data;
Is to implement
The process of updating the estimated distribution of the impulse response of (D1) is as follows:
(D1-1) a process of obtaining a spectral distribution of the estimated distribution of the original image by performing Fourier transform on the estimated distribution of the original image;
(D1-2) a process of obtaining a first function by performing Fourier transform on the estimated distribution of the impulse response;
(D1-3) a process of obtaining a second function by multiplying the first function by a spectral distribution of the estimated distribution of the original image;
(D1-4) processing for obtaining a third function by performing inverse Fourier transform on the second function;
(D1-5) a process of dividing the degraded image distribution by the third function to obtain a fourth function;
(D1-6) A process of obtaining a fifth function by performing a Fourier transform on the fourth function;
(D1-7) A process of obtaining a sixth function by multiplying the fifth function by an inversion function of a spectral distribution of the estimated distribution of the original image;
(D1-8) Processing for obtaining a seventh function by performing inverse Fourier transform on the sixth function;
(D1-9) Multiplying the estimated distribution of the impulse response by the seventh function to obtain a next estimated distribution of the impulse response;
(D1-10) comprising a process of replacing the next estimated distribution of the impulse response with the estimated distribution of the impulse response,
The process of updating the estimated distribution of the original image (E1) is as follows:
(E1-1) processing for obtaining an estimated distribution of the frequency response of the transmission system by Fourier-transforming the estimated distribution of the impulse response;
(E1-2) processing for obtaining an eighth function by performing Fourier transform on the estimated distribution of the original image;
(E1-3) a process of multiplying the eighth function by the estimated distribution of the frequency response to obtain a ninth function;
(E1-4) processing for obtaining a tenth function by performing inverse Fourier transform on the ninth function;
(E1-5) a process of obtaining the eleventh function by dividing the distribution of the deteriorated image by the tenth function;
(E1-6) A process of obtaining a twelfth function by performing a Fourier transform on the eleventh function;
(E1-7) A process of obtaining a thirteenth function by multiplying the twelfth function by an inversion function of the estimated distribution of the frequency response;
(E1-8) Processing for obtaining a fourteenth function by performing an inverse Fourier transform on the thirteenth function;
(E1-9) Multiplying the estimated distribution of the original image by the fourteenth function to obtain the next estimated distribution of the original image;
(E1-10) a process of replacing the next estimated distribution of the original image with the estimated distribution of the original image;
With
Visualization device characterized by that. The light source is a point light source close to the mounting plate,
The visualization apparatus according to claim 1, wherein the imaging surface is located on a Fourier plane corresponding to a distribution of light transmission characteristics of the mounting plate. A sample image detecting device;
The sample image detection device is based on image data restored from image data acquired in a state where the sample is mounted on the mounting plate, and image data acquired in a state where the sample is not mounted on the mounting plate. The visualization apparatus according to claim 2, wherein a difference between restored image data is detected. A lens that images the light diffracted by the mounting plate onto the imaging surface;
The light source emits light having an optical axis as an axis inclined with respect to the mounting surface,
The lens forms high-order light diffracted by a mounting plate on the imaging surface,
The visualization device according to claim 1. A device for visualizing fine lattice disturbances,
A light source that illuminates the grating;
An image data acquisition means comprising an imaging surface substantially parallel to the surface of the grating, and acquiring image data of an image formed on the imaging surface by the light diffracted by the grating;
It has a restoration device that restores the acquired image data.
The restoration device
(A2) a process of converting the acquired image data into a distribution of degraded images;
(B2) a process of specifying the initial estimated distribution of the original image;
(C2) a process of specifying an initial estimated distribution of the impulse response of the transmission system;
(D2) processing for updating the estimated distribution of the impulse response based on the distribution of the degraded image, the estimated distribution of the original image, and the estimated distribution of the impulse response;
(E2) processing for updating the estimated distribution of the original image based on the distribution of the degraded image, the estimated distribution of the original image, and the estimated distribution of the impulse response;
(F2) a process of alternately repeating the processes (D2) and (E2);
(G2) processing for converting the estimated distribution of the updated original image into image data;
Is to implement
The process of updating the estimated distribution of the impulse response of (D2) is as follows:
(D2-1) Fourier transform of the estimated distribution of the original image to obtain a spectral distribution of the estimated distribution of the original image;
(D2-2) processing for obtaining a first function by Fourier-transforming the estimated distribution of the impulse response;
(D2-3) processing for multiplying the first function by a spectral distribution of the estimated distribution of the original image to obtain a second function;
(D2-4) processing for obtaining a third function by performing inverse Fourier transform on the second function;
(D2-5) processing for dividing the distribution of the degraded image by the third function to obtain a fourth function;
(D2-6) a process of obtaining a fifth function by performing a Fourier transform on the fourth function;
(D2-7) a process of obtaining a sixth function by multiplying the fifth function by an inversion function of a spectral distribution of the estimated distribution of the original image;
(D2-8) processing for obtaining a seventh function by performing inverse Fourier transform on the sixth function;
(D2-9) Multiplying the estimated distribution of the impulse response by the seventh function to obtain a next estimated distribution of the impulse response;
(D2-10) comprising a process of replacing the next estimated distribution of the impulse response with the estimated distribution of the impulse response,
The process of updating the estimated distribution of the original image of (E2) is as follows:
(E2-1) processing for obtaining an estimated distribution of the frequency response of the transmission system by performing Fourier transform on the estimated distribution of the impulse response;
(E2-2) processing for obtaining an eighth function by Fourier-transforming the estimated distribution of the original image;
(E2-3) a process of multiplying the eighth function by the estimated distribution of the frequency response to obtain a ninth function;
(E2-4) a process of obtaining a tenth function by performing an inverse Fourier transform on the ninth function;
(E2-5) a process of obtaining the eleventh function by dividing the distribution of the deteriorated image by the tenth function;
(E2-6) a process of obtaining a twelfth function by performing a Fourier transform on the eleventh function;
(E2-7) a process of obtaining a thirteenth function by multiplying the twelfth function by an inversion function of the estimated distribution of the frequency response;
(E2-8) Processing for obtaining a fourteenth function by performing an inverse Fourier transform on the thirteenth function;
(E2-9) processing for multiplying the estimated distribution of the original image by the fourteenth function to obtain the next estimated distribution of the original image;
(E2-10) a process of replacing the next estimated distribution of the original image with the estimated distribution of the original image;
With
Visualization device characterized by that. The light source is a point light source close to the grid,
The visualization device according to claim 5, wherein the imaging surface is located on a Fourier plane of a lattice. It further comprises a lattice disturbance detection device,
The lattice disturbance detection device detects a difference between image data restored from image data obtained in a state where the lattice is disturbed and image data restored from image data obtained in a state where the lattice is not disturbed. The visualization apparatus according to claim 6, wherein: A lens for imaging the light diffracted by the grating onto the imaging surface;
The light source emits light having an optical axis as an axis inclined with respect to the plane of the grating,
The lens forms high-order light diffracted by a grating on the imaging surface;
The visualization device according to claim 5. A method for visualizing a fine sample,
A step of placing the sample on a placement plate having a placement surface on which the sample can be placed and having a distribution of light transmission characteristics that change in a lattice shape along the placement surface;
Irradiating the mounting plate with light;
A step of acquiring image data of an image formed on an imaging surface in which light diffracted by the mounting plate is substantially parallel to the mounting surface;
It has a process to restore the acquired image data,
The restoring step includes
(A3) converting the acquired image data into a distribution of degraded images;
(B3) identifying an initial estimated distribution of the original image;
(C3) identifying an initial estimated distribution of the impulse response of the transmission system;
(D3) updating the estimated distribution of the impulse response based on the distribution of the degraded image, the estimated distribution of the original image, and the estimated distribution of the impulse response;
(E3) updating the estimated distribution of the original image based on the distribution of the degraded image, the estimated distribution of the original image, and the estimated distribution of the impulse response;
(F3) a step of alternately repeating the steps (D3) and (E3),
(G3) converting the updated estimated distribution of the original image into image data,
The step of updating the estimated distribution of the impulse response of (D3) is as follows.
(D3-1) Fourier transforming the estimated distribution of the original image to obtain a spectral distribution of the estimated distribution of the original image;
(D3-2) obtaining a first function by Fourier-transforming the estimated distribution of the impulse response;
(D3-3) multiplying the first function by a spectral distribution of the estimated distribution of the original image to obtain a second function;
(D3-4) obtaining a third function by performing inverse Fourier transform on the second function;
(D3-5) dividing the degraded image distribution by the third function to obtain a fourth function;
(D3-6) Fourier transform of the fourth function to obtain a fifth function;
(D3-7) obtaining a sixth function by multiplying the fifth function by an inversion function of a spectral distribution of the estimated distribution of the original image;
(D3-8) obtaining a seventh function by performing an inverse Fourier transform on the sixth function;
(D3-9) multiplying the estimated distribution of the impulse response by the seventh function to obtain a next estimated distribution of the impulse response;
(D3-10) comprising replacing the next estimated distribution of the impulse response with the estimated distribution of the impulse response,
The step of updating the estimated distribution of the original image of (E3) is as follows:
(E3-1) Fourier transforming the estimated distribution of the impulse response to obtain an estimated distribution of the frequency response of the transmission system;
(E3-2) Fourier transform of the estimated distribution of the original image to obtain an eighth function;
(E3-3) multiplying the eighth function by the estimated distribution of the frequency response to obtain a ninth function;
(E3-4) obtaining a tenth function by performing inverse Fourier transform on the ninth function;
(E3-5) dividing the distribution of the deteriorated image by the tenth function to obtain an eleventh function;
(E3-6) Fourier transform of the eleventh function to obtain a twelfth function;
(E3-7) obtaining a thirteenth function by multiplying the twelfth function by an inversion function of the estimated distribution of the frequency response;
(E3-8) obtaining a fourteenth function by performing an inverse Fourier transform on the thirteenth function;
(E3-9) multiplying the estimated distribution of the original image by the fourteenth function to obtain the next estimated distribution of the original image;
(E3-10) replacing the next estimated distribution of the original image with the estimated distribution of the original image;
With
A visualization method characterized by that. A method for visualizing fine lattice disturbances,
Irradiating the grating with light;
Obtaining image data of an image formed on an imaging surface in which light diffracted by the grating is substantially parallel to the surface of the grating;
It has a process to restore the acquired image data,
The restoring step includes
(A4) converting the acquired image data into a degraded image distribution;
(B4) identifying an initial estimated distribution of the original image;
(C4) identifying an initial estimated distribution of the impulse response of the transmission system;
(D4) updating the estimated distribution of the impulse response based on the distribution of the degraded image, the estimated distribution of the original image, and the estimated distribution of the impulse response;
(E4) updating the estimated distribution of the original image based on the distribution of the degraded image, the estimated distribution of the original image, and the estimated distribution of the impulse response;
(F4) a step of alternately repeating the steps (D4) and (E4),
(G4) converting the updated estimated distribution of the original image into image data,
The step of updating the estimated distribution of the impulse response of (D4) is as follows.
(D4-1) Fourier transforming the estimated distribution of the original image to obtain a spectral distribution of the estimated distribution of the original image;
(D4-2) Fourier transforming the estimated distribution of the impulse response to obtain a first function;
(D4-3) obtaining the second function by multiplying the first function by the spectral distribution of the estimated distribution of the original image;
(D4-4) a step of performing inverse Fourier transform on the second function to obtain a third function;
(D4-5) dividing the degraded image distribution by the third function to obtain a fourth function;
(D4-6) Fourier transform of the fourth function to obtain a fifth function;
(D4-7) obtaining a sixth function by multiplying the fifth function by an inversion function of a spectral distribution of the estimated distribution of the original image;
(D4-8) obtaining a seventh function by performing inverse Fourier transform on the sixth function;
(D4-9) multiplying the estimated distribution of the impulse response by the seventh function to obtain a next estimated distribution of the impulse response;
(D4-10) comprising replacing the next estimated distribution of the impulse response with the estimated distribution of the impulse response,
The step of updating the estimated distribution of the original image of (E4) is as follows:
(E4-1) a step of Fourier transforming the estimated distribution of the impulse response to obtain an estimated distribution of the frequency response of the transmission system;
(E4-2) Fourier transform of the estimated distribution of the original image to obtain an eighth function;
(E4-3) obtaining an ninth function by multiplying the eighth function by the estimated distribution of the frequency response;
(E4-4) obtaining a tenth function by performing an inverse Fourier transform on the ninth function;
(E4-5) dividing the degradation image distribution by the tenth function to obtain an eleventh function;
(E4-6) Fourier transform of the eleventh function to obtain a twelfth function;
(E4-7) obtaining a thirteenth function by multiplying the twelfth function by an inversion function of the estimated distribution of the frequency response;
(E4-8) obtaining a fourteenth function by performing an inverse Fourier transform on the thirteenth function;
(E4-9) multiplying the estimated distribution of the original image by the fourteenth function to obtain the next estimated distribution of the original image;
(E4-10) replacing the next estimated distribution of the original image with the estimated distribution of the original image;
With
A visualization method characterized by that.