The present invention relates to a making method of random uneven data, an optical element, and an optical apparatus.
In light diffusion by a regularly array shape, diffusion characteristics are easily controlled using a pitch of an uneven surface, but a steep intensity peak is generated at a specific angle corresponding to each order. Thereby, a two-wire blur occurs. Moreover, in the diffusion by the regularly array shape, color unevenness occurs due to wavelength dependency of a diffraction angle. To improve the above harmful effects, applying a random uneven shape to a light diffusing element has been recently considered.
In light diffusion by a random uneven shape, a steep intensity peak is moderated, but controlling diffusion characteristics is difficult. Japanese Patent No. 4845290 discloses a making method of random uneven data introducing irregularity by a specific position shifting parameter with respect to a regularly array shape. Additionally, Japanese Patent Laid-Open No. 2014-119552 discloses a method to make random uneven data by performing a filter operation in a frequency space with respect to random data.
However, as the making method of Japanese Patent No. 4845290 introduces the irregularity with respect to the regularly array shape, deviation is generated in a shape position. When the deviation is generated in the shape position, undesirable unnatural light falloff occurs. Furthermore, when a random parameter increases, desired diffusion angle distribution cannot be obtained.
In addition, in the method for making the random uneven data of Japanese Patent Laid-Open No. 2014-119552, the filter operation in the frequency space cannot be performed to a divided necessary area, and thus need to be performed to the necessary area in a lump. Accordingly, for example, when random uneven data is formed on the whole area of a full size (36 mm×24 mm) image sensor, a large capacity memory is needed. Besides, as performing the batch operation to the whole area, the method for making the random uneven data of Japanese Patent Laid-Open No. 2014-119552 cannot make the random uneven data by non-linear filter processing, which varies characteristics continuously for each region.
In view of the foregoing, the present invention provides a making method of random uneven data capable of making random uneven data having a desired frequency component and randomness without deviation in a two-dimensional space.
A making method of random even data as one aspect of the present invention includes a step of making random uneven data by performing a filter operation in a real space using a filtering function with respect to random array data obtained using a random number or random array data obtained by randomly arranging a predetermined shape part.
Further features of the present invention will become apparent from the following description of exemplary embodiments with reference to the attached drawings.
Exemplary embodiments of the present invention will be described below with reference to the accompanied drawings. In each of the drawings, the same elements will be denoted by the same reference numerals and the duplicate descriptions thereof will be omitted.
In this embodiment, random array data is obtained by using a random number or by randomly arranging a predetermined shape part. Performing a filter operation in a real space using a filtering function with respect to the obtained random array data, which is digital data, makes random uneven data. The random uneven data made in this way has a desired frequency component and randomness without deviation in a two-dimensional space. A random uneven shape that is formed on the basis of the random uneven data made by a method explained in this embodiment is used for an optical element such as a light diffusion element.
In this example, a description will be given of a method for making random uneven data, which is one example of the present invention, by performing a filter operation in a real space using a filtering function having bandpass performance with respect to random array data obtained using a random number. Table 1 shows one example of set values of parameters and values of conditional expressions regarding this example.
In this example, a description will be given of the filter operation using data a(x,y) of an array length Na×Na, and data b(x, y) of an array length Nb×Nb having a size smaller than that of the data a(x,y). An output of the filter operation is data of (Na−Nb+1)×(Na−Nb+1) which is cut from a central part of data c(x,y) obtained by a convolution between grid data represented by the following expression (1). x and y are respectively coordinates in the x direction and the y direction, and are not continuous values but discrete values.
c(x,y)=a(x,y)*b(x,y) (1)
In this example, the filtering function 102 is expressed as a function g(r) of the following expression (4), which corresponds differences between values obtained by multiplying two sine functions fH(r) and fL(r) of the following expressions (2) and (3) by a constant number. r is a distance from a central position, that is, (x2+y2)0.5, and α and β are constants. In this example, coefficients PH and PL are respectively 8.5 and 9.5.
fH(r)=[sin(Πr/PH)]/(Πr/PH) (2)
fL(r)=[sin(Πr/PL)]/(Πr/PL) (3)
g(r)=fH(r)/α−fL(r)/β (4)
α=∫|fH(r)|dr (5)
β=∫|fL(r)|dr (6)
As mentioned above, the random uneven data 105 has the desired frequency components, and has the randomness without deviation in the two-dimension.
In this example, to perform the filter operation in the real space, the array length of the filtering function 102 can be set to be shorter than that of the random array data 101. When the filter operation in the real space is performed, the filtering function 102 may be cut in a proper length, that is, the array length can be set to be short. Accordingly, operation memory necessary for the operation can be decreased.
Meanwhile, a filter operation in a frequency space is performed using the following expression (7).
C(kx,ky)=F[a(x,y)]·F[b(x,y)] (7)
Herein, F[a(x,y)] and F[b(x,y)] are respectively Fourier transformation of the data a(x,y) and the data b(x,y). kx and ky are respectively a discrete value representing a coordinate on the frequency space. As the expression (7) includes multiplication of matrix elements, the array length of the filtering function cannot be shortened.
In a filter operation in real space, too short array length increases deviations from desired frequency characteristics. Meanwhile, too large array length uses operation memory unnecessarily. Thus, the expression represented by the array lengths Nfx and Nfy of the filtering function 102 and the weighted average frequency <f> preferably satisfies the following conditional expression (8) to determine whether or not the array length is set appropriately.
4.0<(Nfx/Nfy)0.5·<f><100.0 (8)
When the midst member of the expression (8) is smaller than the lower limit, the array length is too short, and thus filtering cannot be performed to have the desired frequency. When the midst member is larger than the upper limit, the array length is too long, and thus large operation memory is required. In this example, the midst member (Nfx/Nfy)0.5·<f> is 11.2 and satisfies the expression (8). More preferably, the lower and upper limits are set to be 6.5 and 20, respectively.
Furthermore, the filtering function 102 need to have the lowpass performance or the bandpass performance to make the random uneven data 105 having the desired frequency components. When Cmax is a maximum value of absolute values of the filtering function 102 and rmin is the shortest distance from a coordinate corresponding to the maximum value Cmax to a coordinate corresponding to the absolute value Cmax/2, the shortest distance rmin preferably satisfies the following conditional expression (9).
0.4<rmin<1000.0 (9)
The performance of the filtering function 102 is evaluated using the expression (9). When the shortest distance rmin is smaller than the lower limit, the filtering function 102 has the highpass performance and thus is undesirable to be used for making the random uneven data 105. When the shortest distance rmin is larger than the upper limit, the grid size of the data is not appropriate, and memory and an operation time are required unnecessarily. More preferably, the upper limit of the expression (9) is set to be 40.
In addition, the randomness of the random uneven data 105 can be evaluated using the autocorrelation function 301. When I0 and I1 are respectively intensity of a maximum peak and intensity of a second peak in the autocorrelation function of the random uneven data 105 and Δr is a distance from the origin to a coordinate corresponding to the second peak, a peak intensity ratio I0/I1 preferably satisfies the following conditional expression (10).
0.05<11/10<1−2.5·Δr/(Nox·Noy)0.5 (10)
The randomness of the random uneven data 105 is evaluated using the expression (10). Having the peak intensity close to the dotted lines 302 and 303 in
d(r)=1−2.5·r/(Nox·Noy)0.5 (11)
Herein, r is a distance from the center. When the distance Δr from the origin to the coordinate corresponding to the second peak is substituted for the distance r, the expression (11) corresponds to the right member of the expression (10). When the peak intensity I1 corresponding to the distance Δr is smaller than the dotted lines 304 and 305, the random uneven data 105 has the shape with high randomness.
Accordingly, when the peak intensity ratio I1/I0 is larger than the upper limit in the expression (10), the randomness of the random uneven data 105 is insufficiency. Using the random uneven shape formed on the basis of the random uneven data 105 for a surface shape of a light diffusion element causes influence of diffraction due to a regularly pitch, and thus is undesirable. Besides, when the peak intensity ratio I1/I0 is smaller than the lower limit, the randomness of the random uneven data 105 becomes too high. Using the random uneven shape formed on the basis of the random uneven data 105 for the surface shape of the light diffusion element cannot obtain the desired diffusion characteristics, and thus is undesirable. In this example, according to
Moreover, after dividing the random array data into a plurality of predetermined unit areas (unit random array data), the filter operation in the real space may be performed for each unit random array data. Performing the filter operation in the real space for each unit random array data can release operation memory after operating the unit random array data. Accordingly, large area random uneven data, which cannot be made by a batch operation due to limitation of capacity of operation memory, can be made.
When the filter operation is performed by dividing the random array data, the unit random array data preferably has a part (common area) overlapping with the adjacent unit random array data by the distance Nfx/2 in the x direction and the distance Nfy in the y direction. When the array lengths Nfx and Nfy are odd numbers, a length in the x direction and a length in the y direction of the overlapped part are preferably (Nfx−1)/2 and (Nfy−1)/2, respectively. Providing the overlapped part can connect the plurality of pieces of the unit random array data continuously. In this example, the length in the x direction and the length in the y direction of the overlapped part are respectively Nfx/2 and Nfy/2, but the present invention is not limited to this.
Referring to
First, performing the filter operation in the real space using a filtering function 502 having array lengths of Nf×Nf with respect to unit random array data 501 having array lengths of Nr×Nr can obtain unit random uneven data 503 having array lengths of No×No. The array length No of the unit random uneven data 503 is Nr−Nf+1. After performing the filter operation, operation memory is released before performing next filter operation.
Next, performing the filter operation with respect to unit random array data 504 adjacent to the unit random array data 501 can obtain unit random uneven data 505. As illustrated in
As mentioned above, performing the filter operation in the real space with respect to each unit random array data, which is divided from the random array data and has the overlapped part, can make unrepeated and large area random uneven data without limitation of operation memory.
Referring to
Herein, the case where the array lengths Nrx and Nry of the random array data are respectively 240000 and 360000 will be explained. As mentioned above, performing the filter operation in the real space with respect to each of the plurality of the unit areas divided from the random array data can make unrepeated and large area random uneven data without limitation of capacity of operation memory. The randomness of the random uneven data is higher than that of the random unevenness data 105 obtained on the basis of the random array data 101 having array lengths of 200×200. When the grid data of the random uneven data has the shape by 100 nm, large area random uneven shape of 24 mm×36 mm can be made on the basis of the random uneven data. That is, unrepeated random uneven shape can be formed on the whole area of a full-size image sensor. Using large area and unrepeated random uneven shape for the surface shape of the light diffusion element can suppress diffraction components due to the repetitive pitches.
Furthermore, the random uneven shape is formed on the surface of the optical element on the basis of the random uneven data using the method according to this example, an average pitch <Ps> calculated from the frequency characteristics of the random uneven shape preferably satisfies the following conditional expression (12).
0.8(μm)<<Ps><100(μm) (12)
The average pitch <Ps> is calculated from the weighted average of the frequency characteristics of uneven shape data obtained from the grid less than or equal to 200 nm detected by a measuring method such as Atomic Force Microscope (AFM) and Scanning Electron Microscope (SEM). When the average pitch <Ps> is larger than the upper limit, the shape is too large to use for the optical element and unnecessarily reflection easily occurs. When the average pitch is smaller than the lower limit, the shape has a size nearly equal to a wavelength in visible wavelength band and obtaining the effect of diffusion is difficult. More preferably, the upper limit and the lower limit of the expression (12) are respectively 40 μm and 1.5 μm.
In addition, when the random uneven shape is formed on the surface of the optical element on the basis of the random uneven data made by the method according to this example, a ratio of the average value (average height) <hs> of heights of the random uneven shape to the average pitch <Ps> desirably satisfies the conditional expression (13).
0.01<<hs>/<Ps><2.0 (13)
The average value <hs> of heights is calculated from the weighted average of heights of uneven shape data obtained from the grid less than or equal to 200 nm detected by the measuring method such as AFM and SEM. When the aspect ratio of <hs>/<Ps> is larger than the upper limit, the aspect ratio is too large and total reflection strongly occurs in using as the light diffusion element in addition to difficulty of making. When the aspect ratio <hs>/<Ps> is smaller the lower limit, the shape is too small with respect to a wavelength in visible wavelength band and obtaining the effect of diffusion is difficult.
Besides, the random uneven shape on the basis of the random uneven data made by the method according to this example is preferably formed using a gray scale lithography technology and a nanoimprint technology. An organic material may be used, but using an inorganic material is preferable in the light of warpage and durability. Moreover, the forming method is one example, and does not limit an effect of the present invention. The random uneven shape may be formed using an appropriate method as usage.
Random array data according to this example are obtained by arranging circles on the basis of a predetermined array regulation. In this example, a description will be given of a method to make random uneven data by performing a filter operation in a real space using a filtering function having bandpass performance with respect to the obtained random array data. Table 2 shows one example of set values of parameters and values of conditional expressions regarding this example.
As mentioned above, the random uneven data 704 has the desired frequency components, and has the randomness without deviation in the two-dimension. In this example, the array length is set to be relatively small, the present invention is not this. Moreover, in this example, the random array data is obtained by arranging the circle on the basis of the predetermined random array regulation, but the present invention is not limited to this. The random array data may be obtained by arranging a predetermined shape part on the basis of a predetermined random array regulation.
In this example, a description will be given of a method to make random uneven data by performing a filter operation in a real space using filtering function, which has bandpass performance continuously changing according to a position, with respect to random array data given by a random number. For example, a random uneven shape, which is used for a focus plate, preferably changes its characteristics according to a position. The focus plate, where a random uneven shape formed on the basis of the random uneven data made by the method according to this example is applied, can have characteristics which are different for each image height, and thus can improve performance. Table 3 shows one example of set values of parameters and values of conditional expressions regarding this example.
Referring to
In this example, a description will be given of the case of changing coefficients of the filtering function according to a distance r from a central position 905 as one example to change characteristics of the filtering function according to a position. The filtering function is represented by the expressions (2) to (6). In this example, setting the coefficients PH and PL to functions PH(r) and PL(r) of the distance r can characteristics of the filtering function according to a position. To continuously change characteristics of the filtering function from a center to a periphery, the functions PH(r) and PL(r) are represented by the following expressions (14) and (15) to be small dependent on the distance r.
PH(r)=9/(1+2r/((Nrx−Nfx+1)·(Nry−Nfy+1))0.5) (14)
PL(r)=11/(1+2r/((Nrx−Nfx+1)·(Nry−Nfy+1))0.5) (15)
Besides, when characteristics of the filtering function are changed according to a position, a frequency spectrum at a local area preferably fully changes for each local area. Specifically, when an average pitch calculated from the frequency spectrum of the random uneven data is <P>, a local average pitch <P1> calculated from each frequency spectrum of a plurality of areas of the local area of 4<P>×4<P> is preferably 1.3 times or more different. When the local average pitch <P1> is at least 1.3 times or more different, the random data used for the light diffusion element can give diffusion characteristics suitable for each image height.
In this example, in
As mentioned above, the random uneven data 902 has the desired frequency components, and has the randomness without deviation in the two-dimension. The random uneven data 902 also has the desired frequency components which are different in the central local area and the peripheral area. In this example, the array length is set to be relatively small, the present invention is not limited to this.
In this example, a description will be given of a light diffusion element 1201 which is one example of an optical element. The light diffusion 1201 has mainly light diffusion performance.
Accordingly, as the average pitch <Ps> of the random uneven shape 1301 is 1.8 μm, the light diffusion element 1201 according to this example has diffusion characteristics to concentrate in a relatively high angle region, and thus is preferably used for a diffraction type lowpass filter. In this example, a size of the random uneven shape 1301 is set to be relatively small, the present invention is not limited to this. Moreover, approximately constant multiplication of the random uneven shape 1301 is preferably performed according to the desired diffusion angle distribution.
In this example, a description will be given of a light diffusion element 1201 which is one example of an optical element. The light diffusion 1201 has mainly light diffusion performance.
Accordingly, as the average pitch <Ps> of the random uneven shape 1401 is 20.0 μm, the light diffusion element 1201 according to this example has diffusion characteristics to concentrate in a low angle region, and thus is preferably used for a diffraction type lowpass filter. In this example, a size of the random uneven shape 1401 is set to be relatively small, the present invention is not limited to this. Additionally, approximately constant multiplication of the random uneven shape 1401 is preferably performed according to the desired diffusion angle distribution.
In this example, a description will be given of a light diffusion element 1201 which is one example of an optical element. The light diffusion 1201 has mainly light diffusion performance.
In this example, the grid size of the random uneven data 802 is 4000 nm and the maximum value of the shape height is 2.4 μm. In the random uneven shape according to this example, the average pitch <Ps> is calculated to be 20.0 μm and satisfies the expression (12). As the average height <hs> according to this example is also calculated to be 1.2 μm, the aspect ratio <hs>/<Ps> is 0.06, and thus satisfies the expression (13).
Characteristics of the focusing plate is preferable to be optimized for each image height. The focusing plate has diffusion characteristics having a low angle at its center and a high angle at its periphery, and thus can improve take-in light quantity into the finder. The local average pitches are different for each local area, and a random uneven shape 1301 formed on the entire surface of the light diffusion element 1201 has diffusion characteristics having a low angle at its center and a high angle at its periphery. Accordingly, as having the above characteristics and the random uneven shape including the average pitch <Ps> of 20.0 μm, the light diffusion element 1201 is preferably used for the focusing plate of the optical apparatus.
In this example, the size of the random uneven shape is set to be comparatively small, but the present invention is not limited to this. Furthermore, approximately constant multiplication of the random uneven shape is preferably performed according to the desired diffusion angle distribution.
In this comparative example, a description will be given of a making method of random uneven data by performing a filter operation in a real space using a filtering function, which fails to satisfy the expression (8), with respect to random array data given by a random number. Table 4 shows one example of set values of parameters and values of conditional expressions regarding this comparative example.
b are explanatory views of the making method of the random uneven data according to this comparative example.
Random uneven data 1702 illustrated in
As mentioned above, when the filtering function fails to satisfy the expression (8), the desired frequency characteristics cannot be realized.
In this comparative example, a description will be given of a light diffusion element as an optical element using a regularly uneven shape formed on the basis of periodic data, which fails to satisfy the expression (8). The light diffusion element according to this comparative example mainly has performance to diffuse light. On a surface of the light diffusion element according to this comparative example, a regularly uneven shape 1901 illustrated in
U(r)=sin2 r (16)
r represents a distance from the center.
While the present invention has been described with reference to exemplary embodiments, it is to be understood that the invention is not limited to the disclosed exemplary embodiments. The scope of the following claims is to be accorded the broadest interpretation so as to encompass all such modifications and equivalent structures and functions.
This application claims the benefit of Japanese Patent Applications No. 2016-152533, filed on Aug. 3, 2016, which is hereby incorporated by reference herein in its entirety.
Number | Date | Country | Kind |
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2016-152533 | Aug 2016 | JP | national |