A method of simulating a space image

Abstract

A spatial image simulation method includes the following steps: constructing a DMD-based optical system simulation model; uniformly sampling the angle and intensity of illumination light within the illumination numerical aperture, and selecting a simulation area; for each illumination angle, simulating the complex amplitude distribution of the micromirror in the open state and the complex amplitude distribution of the micromirror in the closed state; obtaining the interference data of the micromirror at the entrance pupil plane for each illumination angle; obtaining the spatial frequency spectrum at the exit pupil plane for each illumination angle; simulating the corresponding light intensity distribution based on the complex amplitude distribution for each illumination angle, and superimposing the light intensities corresponding to all illumination samples to obtain the final light spot result. Based on the actual working scenario of the DMD, and considering that the tilt angle of the DMD micromirrors has a significant impact on its diffraction, the introduction of various tilt-induced phase differences and tilt factors results in more accurate simulation effects.

Description

Technical Field

[0001] This invention relates to the field of laser direct writing technology, and in particular to a method for simulating the spatial image of a laser direct writing device using digital micromirror devices. Background Technology

[0002] In laser direct writing technology, digital micromirror devices (DMDs) are often used to transfer digital mask images onto the substrate surface. Through simulation and analysis of the spatial image, image quality can be predicted and evaluated at the initial design stage, reducing material consumption. However, existing simulation methods analyze the DMD in isolation, treating it as a single two-dimensional grating, or even simply understanding the DMD's micromirrors as individual micromirrors, considering only the effects of reflection. This undoubtedly ignores the unique factors arising from the diffraction of individual micromirrors, further detaching it from practical application scenarios and failing to consider the actual working conditions of the DMD in real-world applications, leading to large simulation errors. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide a spatial image simulation method to improve the accuracy of simulation.

[0004] To address the above problems, this invention provides a method for simulating spatial images, comprising the following steps: S1. Construct a simulation model of an optical system based on DMD; S2. Uniformly sample the angle and intensity of the illumination light within the numerical aperture of the illumination, select the simulation area, that is, determine the micromirror area participating in the simulation in the DMD, and determine the state corresponding to each micromirror in the simulation area. S3. For each illumination angle, simulate the complex amplitude distribution of the micromirror in the on state and the complex amplitude distribution of the micromirror in the off state. S4. For the same illumination angle, the complex amplitude distribution of the micromirror in the open state and the complex amplitude distribution of the micromirror in the closed state are superimposed to obtain the interference data of the micromirror at the entrance pupil surface at each illumination angle, that is, the spatial frequency spectrum formed at the entrance pupil surface of the optical system at each illumination angle. S5. Based on the spatial frequency spectrum formed at the entrance pupil of the optical system for each illumination angle, the imaging numerical aperture, and the imaging magnification of the projection system, obtain the spatial frequency spectrum at the exit pupil of each illumination angle. S6. After introducing Zernike aberration phase and defocus phase on the exit pupil surface, perform inverse Fourier transform on the spatial frequency spectrum of each illumination angle on the exit pupil surface to obtain the complex amplitude distribution corresponding to each illumination angle on the imaging surface. Simulate the corresponding light intensity distribution based on the complex amplitude distribution corresponding to each illumination angle, and superimpose the light intensity corresponding to all illumination samples to obtain the final light spot result.

[0005] In one embodiment, in step S3, when simulating the complex amplitude distribution of the micromirror in the open state and the complex amplitude distribution of the micromirror in the closed state for the same illumination angle, the micromirror located at the origin of the coordinate system is used as the reference mirror. The diffraction complex amplitude of the reference micromirror in the open state and the diffraction complex amplitude of the reference micromirror in the closed state are simulated respectively. Then, the diffraction complex amplitude of the micromirrors in the same state in the simulation area is obtained according to the Fourier transform phase shift theorem.

[0006] In one embodiment, in step S3, when simulating the complex amplitude distribution of the open and closed states of the reference micromirror, a three-dimensional spatial direction vector modeling method is adopted. The incident light in each direction, the normal of the micromirror plane, and the rotation axis of the micromirror are all represented by direction vectors. The direction vector of the reflected light corresponding to the incident light in each direction is calculated based on the law of reflection, and the diffraction complex amplitude simulation of the open and closed states of the reference micromirror is performed based on the Fresnel-Kirchhoff diffraction formula.

[0007] In one embodiment, in step S3, the complex amplitude distribution of the micromirror corresponding to the on state and the complex amplitude distribution of the micromirror corresponding to the off state are simulated. The simulation method is as follows: S31. Perform uniform sampling in the spatial domain on the reference micromirror to obtain the three-dimensional coordinates of each sampling point of the reference micromirror. Based on the three-dimensional coordinates of each sampling point, obtain the phase difference of different sampling points of the reference micromirror corresponding to the same illumination angle. S32. Based on the three-dimensional coordinates of the spatial domain of the reference micromirror, according to the incident ray vector and the normal vector of the reference micromirror in the open state, obtain the vector of the reflected ray in the open state of the reference micromirror. Based on the vector of the reflected ray, perform diffraction calculation to obtain the complex amplitude of the reference micromirror in the open state. According to the incident ray vector and the normal vector of the reference micromirror in the closed state, calculate the vector of the reflected ray in the closed state of the reference micromirror. Based on the vector of the reflected ray, perform diffraction calculation to obtain the complex amplitude of the reference micromirror in the closed state. S33. Perform Fourier transform on the obtained complex amplitudes of the open-state and closed-state of the reference micromirror. Based on the Fourier transform results of the open-state complex amplitude of the reference micromirror, calculate the complex amplitudes of all micromirrors in the open-state within the DMD simulation region according to the Fourier transform phase shift theorem. Based on the Fourier transform results of the closed-state complex amplitude of the reference micromirror, calculate the complex amplitudes of all micromirrors in the closed-state within the DMD simulation region according to the Fourier transform phase shift theorem.

[0008] In one embodiment, in step S32, based on the state of the DMD during operation, the diffraction calculation is performed using the paraxial approximation, Fresnel approximation, and Fraunhofer approximation to obtain the diffraction formula for a single micromirror. ; The rectangular coordinate system established by the aperture plane is (x1, y1), and the rectangular coordinate system established by the observation plane is (x, y). In a DMD system, λ refers to the complex amplitude of light waves after reflection from illumination incident at various angles onto the surface of a single micromirror. i is the imaginary unit, and λ is the wavelength of the light wave. The unit vector representing the direction of the reflected light; is the unit vector of the normal to the diffraction aperture surface; Let Q be the vector from any point Q to the observation point P, and let ∆z be the z-axis difference between different sampling points of the same micromirror.

[0009] In one embodiment, step S31, which calculates the phase difference of a single micromirror sampling point corresponding to the same illumination angle, specifically involves the following steps: S311, by and Calculate the normals to the coplanar surfaces of the two objects. ,pass Calculation, where Let the incident light direction be the unit vector. The unit vector of the normal to the reflecting surface; S312. Calculate the projection of each sampling point on the micromirror onto the coplanar plane, i.e. , The three-dimensional coordinates of a sampling point with the center of a single micromirror as the origin. These are the coordinates corresponding to the projection; S313, Calculate the projected coordinates In the incident wave The projection along the direction is the optical path difference at each sampling point. ; S314, exp(ikq) represents the phase difference introduced by the oblique incidence of the incident light, where i is the imaginary unit and k is the wave number.

[0010] In one embodiment, the complex diffraction amplitude of individual micromirrors at different positions is calculated via the incident direction. DMD reflector normal direction The optical path difference ∆d between each micromirror and the phase difference introduced by the oblique incidence of the incident light are calculated using the center coordinates of each micromirror. The object-side complex amplitude of the DMD diffracted along the z-axis can be expressed as: .

[0011] For individual micromirrors at different locations, the diffraction formula becomes ; The rectangular coordinate system established by the aperture plane is (x1, y1), and the rectangular coordinate system established by the observation plane is (x, y). It refers to the complex amplitude of the incident light within the diffraction aperture plane, including the phase difference exp(ikq) within a single micromirror introduced by the oblique incidence of the incident light; ∆z is the z-axis difference between different sampling points of the same micromirror, i is the imaginary unit; λ is the wavelength of the light wave; The unit vector representing the direction of the reflected light; The normal vector of the diffraction aperture surface; Let Q be the vector from any point Q to the observation point P.

[0012] In one embodiment, in step S32, the formula for calculating the vector of the reflected ray is: ; in Let the incident light direction be the unit vector. The unit vector representing the direction of the reflected light. is the unit vector of the normal to the reflecting surface.

[0013] In one embodiment, the DMD-based optical system includes a front-end illumination system, a mid-end DMD, and a rear-end projection system. A simulation model of the DMD optical system is constructed by setting the optical parameters of each system.

[0014] In one embodiment, in step S6, the imaging numerical aperture is converted into spatial frequency, the spatial frequency spectrum of the entrance pupil of the projection system is extracted in the frequency domain based on the imaging numerical aperture, and the spatial frequency spectrum of the entrance pupil of the projection system is converted into the spatial frequency spectrum of the exit pupil according to the imaging magnification of the projection system.

[0015] Compared with existing technologies, the technical solution of this invention is based on the actual working scenario of the DMD. It incorporates the significant impact of the tilt angle of the DMD micromirrors on their diffraction, introducing various tilt-induced phase differences and tilt factors, resulting in more accurate simulation effects. Furthermore, by analyzing individual micromirrors as units, the influence of different patterns on the DMD can be calculated, taking into account the interference effects of different patterns on the DMD in the simulation. This more closely approximates the actual application of the DMD in the entire system, thus improving the accuracy of the simulation results. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the lighting light sampling.

[0017] Figure 2 This is a schematic diagram of the DMD simulation area.

[0018] Figure 3 This is a schematic diagram of a spatial image simulation method.

[0019] Figure 4 This is a schematic diagram of spherical wave diffraction in the aperture plane.

[0020] Figure 5 This is a schematic diagram of the diffraction of a perpendicularly incident monochromatic plane wave by the aperture plane Σ.

[0021] Figure 6 This is a schematic diagram of the operation of a single micromirror.

[0022] Figure 7 This is a schematic diagram of micromirrors as aperture plane Σ diffraction.

[0023] Figure 8 This is a schematic diagram of incident light from a micromirror.

[0024] Figure 9 This is a schematic diagram of the spatial image simulation results. Detailed Implementation

[0025] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be described below with reference to specific embodiments shown in the accompanying drawings.

[0026] In the field of direct-write exposure technology, digital micromirror devices (DMDs) are typically used to output maskless images. During operation, a light source is emitted from an illumination system and incident on the DMD. The micromirrors in the DMD have two deflection angles, α and -α. When the deflection angle is α, the micromirror projects light onto the subsequent projection lens, corresponding to the digital circuit being turned on. When the deflection angle is -α, the micromirror deflects the light away from the subsequent projection lens, corresponding to the digital circuit being turned off. By controlling the deflection angles of the micromirrors in the DMD, the desired pattern is formed. Typically, the deflection angle α equals 12 degrees. After diffraction by a single micromirror and interference by multiple micromirrors, the light is incident on the projection lens and imaged on the imaging plane. The spatial image formed on the imaging plane by the DMD is simulated to analyze the imaging quality of the current optical system.

[0027] like Figures 1-9 The diagram illustrates a spatial image simulation method, which includes the following steps: S1. Construct a simulation model of the DMD-based optical system. The DMD-based optical system includes a front-end illumination system, a mid-end DMD, and a back-end projection system. The simulation model of the DMD optical system is constructed by setting the optical parameters of each system. The optical parameters include illumination numerical aperture (illumination NA), imaging numerical aperture (imaging NA), imaging magnification, and DMD-related dimensions, etc.

[0028] S2. Uniformly sample the angle and intensity of the illumination light within the numerical aperture of the illumination; select the simulation region, that is, determine the micromirror region participating in the simulation in the DMD, and determine the state corresponding to each micromirror in the simulation region. For example... Figure 1 As shown, the illumination ray 3 is conical. At the exit pupil of the illumination ray, based on the numerical aperture of the illumination ray, a sampling area 1 is obtained. Uniform grid sampling is performed to acquire the angle of each sampling ray 2 relative to the optical axis and the intensity of the sampling ray. The optical axis 4 is located at the center point of the sampling area. Figure 2 As shown, a portion of the DMD is selected as simulation region 5, and each DMD in the simulation region is set to be either on or off, with on corresponding to the number 1 and off corresponding to the number 0. The sampling of the illumination light and the selection of the simulation region are relatively independent.

[0029] S3. For each illumination angle, simulate the complex amplitude distribution of the micromirror in the open state and the complex amplitude distribution of the micromirror in the closed state. The incident light rays projected onto the micromirror correspond to multiple illumination angles. For each illumination angle, it is necessary to calculate the complex amplitude distribution of the micromirror in the open state and the complex amplitude distribution of the micromirror in the closed state. For an illumination angle, when calculating the complex amplitude distribution of the micromirror in the open state, the micromirror located at the origin is used as the reference mirror. The diffraction complex amplitude of the reference micromirror in the open state and the diffraction complex amplitude of the reference micromirror in the closed state are calculated separately. Then, the diffraction complex amplitude of the DMD micromirrors in the same state within the simulation region is obtained according to the Fourier transform phase shift theorem. Specifically, based on the diffraction complex amplitude of the reference micromirror in the open state, the diffraction complex amplitude of the micromirror in the open state is calculated in the simulation region; based on the diffraction complex amplitude of the reference micromirror in the off state, the diffraction complex amplitude of the micromirror in the off state is calculated in the simulation region.

[0030] S4. For the same illumination angle, the complex amplitude distributions of the micromirrors in the open and closed states are superimposed to obtain the interference data of the micromirrors at the entrance pupil plane for each illumination angle, i.e., the spatial frequency spectrum formed at the entrance pupil plane of the optical system for each illumination angle. The complex amplitude distributions of the micromirrors in the open and closed states for all illumination angles in the illumination sampling are superimposed to obtain the interference data of the micromirrors at the entrance pupil plane, i.e., the spatial frequency spectrum formed at the entrance pupil plane of the optical system.

[0031] S5. Based on the spatial frequency spectrum formed at the entrance pupil of the optical system for each illumination angle, the imaging numerical aperture, and the imaging magnification of the projection system, obtain the spatial frequency spectrum at the exit pupil of each illumination angle.

[0032] S6. After introducing Zernike aberration phase and defocus phase on the exit pupil plane, perform an inverse Fourier transform on the spatial frequency spectrum of each illumination angle on the exit pupil plane to obtain the complex amplitude distribution corresponding to each illumination angle on the imaging plane. Based on the complex amplitude distribution corresponding to each illumination angle, simulate the corresponding light intensity distribution. Superimpose the light intensity corresponding to each illumination angle of all illumination samples to obtain the final light spot result. The light intensity is the square of the complex amplitude modulus.

[0033] In step S3, for the same illumination angle, when simulating the complex amplitude distribution of the micromirror in the open state and the complex amplitude distribution of the micromirror in the closed state, the micromirror located at the origin of the coordinate system is used as the reference mirror. The diffraction complex amplitude of the reference micromirror in the open state and the diffraction complex amplitude of the reference micromirror in the closed state are simulated respectively. Then, the diffraction complex amplitude of the micromirrors in the same state in the simulation area is obtained according to the Fourier transform phase shift theorem.

[0034] When calculating the complex amplitude distribution of the open and closed states of the reference micromirror, a three-dimensional spatial direction vector modeling method is adopted. The incident light in each direction, the normal of the micromirror plane, and the rotation axis of the micromirror are all represented by direction vectors. Based on the Fresnel-Kirchhoff diffraction formula, the diffraction calculation of the open and closed states of the reference micromirror is performed to obtain the complex diffraction amplitude of the reference micromirror.

[0035] The simulation method for the complex amplitude distribution of the micromirror in the same state as in step S3 is as follows: S31. Perform uniform sampling in the spatial domain on the reference micromirror to obtain the three-dimensional coordinates of each sampling point of the reference micromirror. Based on the three-dimensional coordinates of each sampling point, obtain the phase difference of different sampling points of the reference micromirror corresponding to the same illumination angle.

[0036] S32. Based on the three-dimensional coordinates of the spatial domain of the reference micromirror, obtain the vector of the reflected ray in the open state of the reference micromirror according to the incident ray vector and the normal vector of the open state of the reference micromirror. Perform diffraction calculation based on the vector of the reflected ray to obtain the complex amplitude of the open state of the reference micromirror. Calculate the vector of the reflected ray in the closed state of the reference micromirror according to the incident ray vector and the normal vector of the closed state of the reference micromirror. Perform diffraction calculation based on the vector of the reflected ray to obtain the complex amplitude of the closed state of the reference micromirror.

[0037] S33. Perform Fourier transform on the obtained complex amplitudes of the open-state and closed-state of the reference micromirror. Based on the Fourier transform results of the open-state complex amplitude of the reference micromirror, calculate the complex amplitudes of all micromirrors in the open-state within the DMD simulation region according to the Fourier transform phase shift theorem. Based on the Fourier transform results of the closed-state complex amplitude of the reference micromirror, calculate the complex amplitudes of all micromirrors in the closed-state within the DMD simulation region according to the Fourier transform phase shift theorem.

[0038] The following describes in detail step S3 the sampling data based on the spatial domain of the reference micromirror, the calculation of the reflection of the reference micromirror in the open and closed states, the diffraction calculation based on the reflected light, and the complex amplitude distribution corresponding to the open state and state of the reference micromirror.

[0039] The process by which light passes through the DMD and reaches the imaging entrance pupil can be decomposed into: reflection by a single micromirror in the DMD, diffraction by a single micromirror in the DMD, and interference between different micromirrors on the DMD.

[0040] Based on a model considering the illumination of an infinitely large opaque screen by a spherical wave emitted from a monochromatic point source S, with Σ being the aperture plane, Σ1 being the opaque screen portion, Σ2 being a sphere with radius R surrounding the observation point P, S being the spherical wave emitted from the point source, and Q being an arbitrary point on the aperture plane, the Fresnel-Kirchhoff diffraction formula is obtained. ; in Σ represents the complex amplitude (including phase information) at observation point P; A represents the amplitude at a unit distance from the point source; i represents the imaginary unit; λ represents the wavelength of the light wave; and Σ represents the spatial surface (integration region) where the diffraction aperture is located. The area element on the diffraction aperture surface; exp(ikl) is the phase factor from the source to any point Q on the diffraction aperture surface, l is the distance from the source to any point Q; exp(ikl) is the phase factor from any point Q on the diffraction aperture surface to the observation point P, r is the distance from any point Q to the observation point P; k is the wavenumber, k=2π / λ; Normal vector of the diffraction aperture surface The vector pointing from any point Q to the observation point P The cosine of the angle between them Normal vector of the diffraction aperture surface The vector of the light source pointing to any point Q The cosine of the angle between them.

[0041] Considering the diffraction of a vertically incident monochromatic plane wave by an infinitely large opaque aperture Σ, since the linear dimensions of the diffraction aperture are much smaller than the distance from the observation screen to the aperture, under conventional diffraction conditions, we take... , Inclination factor . Also a constant, so ignore it.

[0042] Furthermore, the distance r from any point Q to the observation point P on the screen does not change significantly, and its variation in the denominator affects the amplitude of the spherical wavelets emitted by each wavelet source, but this effect is negligible. Therefore , where z1 is the distance between the observation screen and the diffraction screen.

[0043] However, the phase change will be very drastic, and exp(ikr) cannot be approximated as exp(ikz1), but the Fresnel approximation needs to be used.

[0044] The rectangular coordinate system established by the aperture plane is (x1, y1), and the rectangular coordinate system established by the observation plane is (x, y). r can be written in three-dimensional coordinate form and expanded by binomial terms, i.e. .

[0045] When the effect of a term on the phase is much smaller than π, that term can be ignored. Therefore, the third term and all subsequent terms can be ignored. ; Expanding the second term of the Fresnel approximation .

[0046] When z1 is very large, its effect on the phase is much smaller than π, and this term can be ignored. That is, after the Fraunhofer approximation: ; When all three of the above approximate conditions hold true, the conventional diffraction formula can be obtained as follows: .

[0047] When the DMD is working, it rotates around the diagonal axis, i.e., in a 45° direction, with a ±12° deflection to indicate its on / off state. The mirror surface has unconventional orientations. If described using methods similar to azimuth and pitch angles, subsequent coordinate transformations of the xy and yz planes would be required, which is not only difficult to understand intuitively but also unsupported by subsequent calculations. Therefore, a 3D spatial direction vector modeling method is adopted, where light in each direction, plane normals, and rotation axes are all represented using direction vectors. The reflection formula is... .

[0048] in Let the incident light direction be the unit vector. The unit vector representing the direction of the reflected light. is the unit vector of the normal to the reflecting surface.

[0049] At this point, the aperture plane Σ is the reflecting surface of the DMD, the observation plane is the entrance pupil of the projection system in the optical system, and the normal vector of the diffraction aperture plane is... The unit vector of the normal to the reflecting surface The opposite direction.

[0050] Because sampling is performed within the illumination NA, This represents a series of incident lights from different directions.

[0051] The aperture plane Σ is the reflecting surface of the DMD, and it has a certain tilt angle, causing a change in the direction of the normal. The direction of the incident wave becomes the direction of the reflected wave, i.e. .

[0052] For variations in the paraxial approximation, the normal direction leads to the tilt factor. Consequently, changes occur, but due to the small tilt angle, the problem persists. .

[0053] For the Fresnel approximation, the three-dimensional spatial coordinates of any point Q on the Σ surface change. The original z-coordinate is 0, but after tilting, the z-coordinate has a deviation of Δz, which is linearly related to the x1 and y1 coordinates. Substituting this into the Fresnel approximation expression, we get... ; Comparison of changes ; Since Δz is much smaller than z1, the above equation is approximately 0. Let's examine... Its effect on the phase is much smaller than π, therefore we have ; Compared to the untilted Σ surface, there is a phase difference due to a -Δz.

[0054] consider Its phase is ; No changes were observed for the Fraunhofer approximation.

[0055] Therefore, the diffraction formula can be rewritten as follows: ; ∆z represents the z-axis difference between different sampling points of the same micromirror, reflecting the optical path difference between different sampling points of the same micromirror relative to the entrance pupil surface of the optical system.

[0056] The diffraction process of the reference micromirror is calculated using the above formula. The on and off states of the reactive micromirror.

[0057] in, This refers to the complex amplitude of the incident light within the diffraction aperture plane. In a DMD system, it is the complex amplitude of the light reflected from the surface of a single micromirror at various angles of illumination. Therefore, a phase difference introduced by the tilted incident reflection surface needs to be introduced. The phase difference at each sampling point on the reflection surface needs to be calculated using the direction vector of the incident wave and the normal vector of the reflection surface. The specific steps are as follows: S311, by and Calculate the coplanarity of the two planes to obtain the normal to that plane. ,pass calculate; S312. Calculate the projection of each sampling point on the micromirror onto the coplanar plane, i.e. , The three-dimensional coordinates of a sampling point with the center of a single micromirror as the origin. These are the coordinates corresponding to the projection; S313, Calculate the projected coordinates In incident light The projection along the direction is the optical path difference at each sampling point. ; S314 and exp(ikq) represent the phase difference introduced by the oblique incidence of the incident light. This is the phase difference between different sampling points within a single micromirror, contained within the complex amplitude of the incident light on the diffraction aperture plane.

[0058] For light incident at an angle, there is also an optical path difference between the micromirrors in the DMD. Therefore, for a sampling point of a certain DMD micromirror, the phase difference caused by the angled incident wave consists of two parts, specifically: The three-dimensional coordinates of each sampling point of a single micromirror are represented as PositionSingle with its center point as the origin; For DMDs at different positions participating in the calculation, the coordinate position of each micromirror can be obtained with the center position of the central micromirror as the origin, denoted as PositionCenter; The sampling points of different micromirrors are represented in a unified coordinate system, with the center of the central micromirror as the origin. Then the three-dimensional coordinates of each sampling point are PositionSingle + PositionCenter.

[0059] The optical path difference caused by PositionSingle is as described above. The optical path difference caused by PositionCenter is the theoretical basis for deriving the grating equation. Similar to the reference micromirror, it can be determined through the incident direction. DMD reflector normal direction Calculate the optical path difference ∆d and phase difference between each micromirror and the reference micromirror using the center coordinates of each micromirror. The incident complex amplitude of the DMD can be expressed as .

[0060] For individual micromirrors at different locations, the diffraction formula becomes .

[0061] By calculating the FFT (Fast Fourier Transform) of only one micromirror, the complex amplitudes of the diffraction of different micromirrors are transformed by the phase shift theorem to obtain the complex amplitude of each micromirror in the entire DMD. The sum of the complex amplitudes of the diffraction of different micromirrors in the DMD is the interference of the micromirrors at the pupil plane in the DMD.

[0062] Through the above methods, the technical solution of this invention, based on the actual working scenario of the DMD, and considering the significant impact of the tilt angle of the DMD micromirrors on their diffraction, introduces various tilt-induced phase differences and tilt factors, resulting in more accurate simulation effects. Furthermore, by analyzing individual micromirrors as units, the influence of different patterns on the DMD can be calculated, taking into account the interference effects of different patterns on the DMD in the simulation, thus more closely approximating the actual application state of the DMD in the entire system. This improves the accuracy of the simulation results.

Claims

1. A method for simulating spatial images, characterized in that: Includes the following steps: S1. Construct a simulation model of an optical system based on DMD; S2. Uniformly sample the angle and intensity of the illumination light within the numerical aperture of the illumination, select the simulation area, that is, determine the micromirror area participating in the simulation in the DMD, and determine the state corresponding to each micromirror in the simulation area. S3. For each illumination angle, simulate the complex amplitude distribution of the micromirror in the on state and the complex amplitude distribution of the micromirror in the off state. S4. For the same illumination angle, the complex amplitude distribution of the micromirror in the open state and the complex amplitude distribution of the micromirror in the closed state are superimposed to obtain the interference data of the micromirror at the entrance pupil surface at each illumination angle, that is, the spatial frequency spectrum formed at the entrance pupil surface of the optical system at each illumination angle. S5. Based on the spatial frequency spectrum formed at the entrance pupil of the optical system for each illumination angle, the imaging numerical aperture, and the imaging magnification of the projection system, obtain the spatial frequency spectrum at the exit pupil of each illumination angle. S6. After introducing Zernike aberration phase and defocus phase on the exit pupil surface, perform inverse Fourier transform on the spatial frequency spectrum of each illumination angle on the exit pupil surface to obtain the complex amplitude distribution corresponding to each illumination angle on the imaging surface. Simulate the corresponding light intensity distribution based on the complex amplitude distribution corresponding to each illumination angle, and superimpose the light intensity corresponding to all illumination samples to obtain the final light spot result.

2. The spatial image simulation method according to claim 1, characterized in that: In step S3, for the same illumination angle, when simulating the complex amplitude distribution of the micromirror in the open state and the complex amplitude distribution of the micromirror in the closed state, the micromirror located at the origin of the coordinate system is used as the reference mirror. The diffraction complex amplitude of the reference micromirror in the open state and the diffraction complex amplitude of the reference micromirror in the closed state are simulated respectively. Then, the diffraction complex amplitude of the micromirrors in the same state in the simulation area is obtained according to the Fourier transform phase shift theorem.

3. The spatial image simulation method according to claim 2, characterized in that: In step S3, when simulating the complex amplitude distribution of the open and closed states of the reference micromirror, a three-dimensional spatial direction vector modeling method is adopted. The incident light in each direction, the normal of the micromirror plane, and the rotation axis of the micromirror are all represented by direction vectors. The direction vector of the reflected light corresponding to the incident light in each direction is calculated based on the law of reflection. The diffraction complex amplitude simulation of the open and closed states of the reference micromirror is performed based on the Fresnel-Kirchhoff diffraction formula.

4. The spatial image simulation method according to claim 2, characterized in that: In step S3, the complex amplitude distribution of the micromirror in the on-state and the complex amplitude distribution of the micromirror in the off-state are simulated. The simulation method is as follows: S31. Perform uniform sampling in the spatial domain on the reference micromirror to obtain the three-dimensional coordinates of each sampling point of the reference micromirror. Based on the three-dimensional coordinates of each sampling point, obtain the phase difference of different sampling points of the reference micromirror corresponding to the same illumination angle. S32. Based on the three-dimensional coordinates of the spatial domain of the reference micromirror, according to the incident ray vector and the normal vector of the reference micromirror in the open state, obtain the vector of the reflected ray in the open state of the reference micromirror. Based on the vector of the reflected ray, perform diffraction calculation to obtain the complex amplitude of the reference micromirror in the open state. According to the incident ray vector and the normal vector of the reference micromirror in the closed state, calculate the vector of the reflected ray in the closed state of the reference micromirror. Based on the vector of the reflected ray, perform diffraction calculation to obtain the complex amplitude of the reference micromirror in the closed state. S33. Perform Fourier transform on the obtained complex amplitudes of the open state and the closed state of the reference micromirror. Based on the Fourier transform results of the complex amplitudes of the open state of the reference micromirror, calculate the complex amplitudes of all micromirrors in the open state within the DMD simulation area according to the Fourier transform phase shift theorem. Based on the Fourier transform of the complex amplitude of the off-state of the reference micromirror, the complex amplitude of the off-state micromirrors in the DMD simulation region is calculated according to the Fourier transform phase shift theorem.

5. The spatial image simulation method according to claim 4, characterized in that: In step S32, based on the state of the DMD during operation, the diffraction calculation is performed using the paraxial approximation, Fresnel approximation, and Fraunhofer approximation to obtain the diffraction formula for a single micromirror. ; The rectangular coordinate system established by the aperture plane is (x1, y1), and the rectangular coordinate system established by the observation plane is (x, y). In a DMD system, the complex amplitude of light after illumination from various angles is reflected off the surface of a single micromirror, i is the imaginary unit, and λ is the wavelength of the light wave. The unit vector representing the direction of the reflected light; is the unit vector of the normal to the diffraction aperture surface; Let Q be the vector from any point Q to the observation point P. This represents the z-axis difference between different sampling points of the same micromirror.

6. The spatial image simulation method according to claim 4, characterized in that: Step S31 calculates the phase difference of a single micromirror sampling point corresponding to the same illumination angle. The specific steps are as follows: S311, by and Calculate the normals to the coplanar surfaces of the two objects. ,pass Calculation, where Let the incident light direction be the unit vector. The unit vector of the normal to the reflecting surface; S312. Calculate the projection of each sampling point on the micromirror onto the coplanar plane, i.e. , The three-dimensional coordinates of a sampling point with the center of a single micromirror as the origin. These are the coordinates corresponding to the projection; S313, Calculate the projected coordinates In the incident wave The projection along the direction is the optical path difference between each sampling point. ; S314, This is the phase difference introduced by the oblique incidence of the incident light, where i is the imaginary unit and k is the wave number.

7. The spatial image simulation method according to claim 6, characterized in that: Calculate the complex diffraction amplitude of a single micromirror at different locations. via the incident direction DMD reflector normal direction Calculate the optical path difference between each micromirror using the center coordinates of each micromirror. The phase difference introduced by the oblique incidence of the incident light is calculated, and the center coordinates are... The object-side complex amplitude of the DMD diffracted along the z-axis can be expressed as: ; For individual micromirrors at different locations, the diffraction formula becomes ； The rectangular coordinate system established by the aperture plane is (x1, y1), and the rectangular coordinate system established by the observation plane is (x, y). The complex amplitude of the incident light within the diffraction aperture plane includes the phase difference within a single micromirror introduced by the oblique incidence of the incident light. ; λ represents the z-axis difference between different sampling points of the same micromirror, where i is the imaginary unit and λ is the wavelength of the light wave. The unit vector representing the direction of the reflected light; The normal vector of the diffraction aperture surface; Let Q be the vector from any point Q to the observation point P.

8. The spatial image simulation method according to claim 2, characterized in that: In step S32, the formula for calculating the vector of the reflected ray is: ,in Let the incident light direction be the unit vector. The unit vector representing the direction of the reflected light. is the unit vector of the normal to the reflecting surface.

9. The spatial image simulation method according to claim 1, characterized in that: The DMD-based optical system includes a front-end illumination system, a mid-end DMD, and a back-end projection system. A simulation model of the DMD optical system is constructed by setting the optical parameters of each system.

10. The spatial image simulation method according to claim 1, characterized in that: In step S6, the imaging numerical aperture is converted into spatial frequency, and the spatial frequency spectrum of the entrance pupil of the projection system is extracted in the frequency domain based on the imaging numerical aperture. Then, according to the imaging magnification of the projection system, the spatial frequency spectrum of the entrance pupil of the projection system is converted into the spatial frequency spectrum of the exit pupil.

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