JP3814252B2 - Image display device - Google Patents

Description

[0001]
BACKGROUND OF THE INVENTION
The present invention relates to an image display device using a lenticular lens or the like, and more particularly, to an image display device that displays an image without a sense of incongruity within a wide visual field range.
[0002]
[Prior art]
A stereoscopic image display apparatus using a lenticular lens is widely known. A parallax barrier may be used instead of the lenticular lens. The principle of a stereoscopic image apparatus using a conventional lenticular lens will be briefly described with reference to FIGS. FIG. 7 is a front view schematically showing an image arranged on the back surface of the lenticular lens, and FIG. 8 is a reduced cross-sectional view taken along the uppermost pixel row in FIG. The smallest square frame in the figure indicates a unit pixel. The lenticular lens L is indicated by an alternate long and two short dashes line, and has a configuration in which a cylindrically shaped cylindrical lens is arranged. In the figure, the width of one cylindrical lens coincides with the width of 4 pixels. The four pixels arranged in the arrangement direction of the cylindrical lenses are in principle taken from image data picked up from positions having different parallaxes, and a known arrangement method is obtained so that a stereoscopic image can be obtained when viewed through the lenticular lens L. It is arranged by. In the figure, four pixel groups surrounded by bold lines are arranged vertically and horizontally as a unit. In the present application, the minimum unit of pixel groups extracted from image data having different parallaxes and arranged according to a certain rule is referred to as a “unit pixel group”. Note that, at the edge of the image, the unit pixel group may include pixels in the image captured from the same parallax.
[0003]
A stereoscopic image can be obtained by dividing the unit pixel group in the middle into one pixel group for the right eye and the other pixel group for the left eye, as shown in FIG. The light and the light from the pixel that should enter the left eye El are refracted by each cylindrical lens constituting the lenticular lens and are distributed to the left and right eyes, so that parallax can be given to both eyes of the observer. It is. The point S in the figure is the principal point of the cylindrical lens constituting the lenticular lens L, and is a line segment along the cylindrical lens that is long in one direction when viewed from the front.
An image display device using such a lenticular lens is also used for morphing and animation image display in addition to stereoscopic image display.
[0004]
[Problems to be solved by the invention]
Although a stereoscopic image display device using a lenticular lens has the configuration described above, there is a problem that the viewing angle is narrow due to its properties. That is, as shown in FIG. 8, when the right eye Er is shifted to the position A in the drawing, the pixel to be viewed by the adjacent lenticular lens is seen, and stereoscopic vision is lost. That is, stereoscopic viewing is possible only at a viewing angle such that pixels other than the pixels handled by the cylindrical lens do not enter the eyes through one cylindrical lens.
Even if the position of the eye is fixed, when the line of sight Y shown in FIG. 8 is near the end of the image to be viewed, the pixels handled by the adjacent cylindrical lens can be seen through one cylindrical lens, and so-called reverse viewing occurs. Therefore, when viewing an image with a field of view within a range where such reverse viewing does not occur, stereoscopic viewing without discomfort is possible.
[0005]
The problem of reverse viewing near the edge of the image can also be dealt with by the method disclosed in Japanese Patent Laid-Open No. 8-194273. That is, it is possible to prevent reverse vision by arranging the unit lens group so that no reverse vision occurs even when the unit pixel group is positioned near the end by shifting the pitch width of the arrangement of the cylindrical lenses and the unit pixel group. However, this method has a drawback in that it is necessary to redesign the image by changing the pitch width of the arrangement of unit pixels for each lenticular lens having a different cylindrical lens pitch.
In view of the above problems, an object of the present invention is to widen the viewing angle in an image display device using a lenticular lens or the like. It is another object of the present invention to make it possible to design a rear image more flexibly in expanding the viewing angle near the edge of the image.
[0006]
[Means for Solving the Problems]
The present application for solving the above problems has the following configuration.
The invention described in claim 1 is an image display device that satisfies the following requirements (101) to (108).
(101) It has a lenticular lens.
(102) A rear image display body that displays an image in which unit pixel groups in which pixels obtained from a plurality of image data groups having parallax are arranged in a predetermined order is displayed.
(103) The lenticular lens is disposed on the rear image display body.
(104) The width of the one unit pixel group in the arrangement direction of the cylindrical lenses constituting the lenticular lens is a width of the cylindrical lens of approximately a predetermined number N (where N is an integer of 2 or more).
(105) M (where M is an integer greater than or equal to 2) types of filters each passing a specific type of light are provided on the surface of each of the adjacent M cylindrical lenses.
(106) Each unit pixel group emits or reflects only one type of light passing through each filter.
(107) M unit pixel groups adjacent in succession are simultaneously displayed so as to overlap in the longitudinal direction of the cylindrical lens .
(108) The unit pixel group that radiates or reflects the light passing through one filter is arranged so that the cylindrical lens provided with the filter is located at the approximate center of the unit pixel group.
With such a configuration, the width of the unit pixel group becomes N times the conventional width (N width of the cylindrical lens). Then, the unit pixel can be seen by the cylindrical lens located at the approximate center of each unit pixel group by a filter provided on the surface of the cylindrical lens, but the unit pixel group is covered with a filter that does not transmit light that is emitted or reflected. The unit lens group cannot be seen with the cylindrical lens.
[0007]
The invention described in claim 2 is the image display device according to claim 1, wherein M = N.
With such a configuration, a cylindrical lens provided with a filter that transmits light that is emitted or reflected by the unit pixel group that is provided in the approximate center of the unit pixel group, and a cylindrical lens that is provided with a filter that transmits other light, Each unit pixel group can be covered.
A third aspect of the present invention is the image display device according to the first or second aspect, wherein the filter is a filter that selectively allows light of M types of different wavelengths to pass therethrough.
By doing so, the unit pixel group can be handled by changing the color.
A fourth aspect of the present invention is the image display device according to the first or second aspect, wherein the filter comprises a linearly polarizing filter that selectively transmits two types of polarized light different by 90 °.
By doing in this way, it can respond by covering a unit pixel group with a corresponding linear polarization filter.
[0008]
The invention described in claim 5 is the image display device according to any one of claims 1 to 4, which further satisfies the following requirements (501) and (502).
(501) The unit pixel emits or reflects one kind of light.
(502) N unit pixel groups adjacent to each other are arranged so as not to overlap in the arrangement direction of the cylindrical lenses.
With such a configuration, it is possible to obtain an image display device that has a wide viewing angle and prevents the appearance of extra pixels even when each pixel emits or reflects only one type of light.
The invention according to claim 6 is the image display device according to any one of claims 1 to 4, further satisfying the following requirements (601) and (602).
(601) The rear image display body forms N types of unit pixel groups at one unit pixel position by simultaneously radiating or reflecting N types of light passing through the N types of filters at one unit pixel position. Unit pixels to be displayed can be displayed in an overlapping manner.
(602) N unit pixel groups adjacent to each other are arranged so as to overlap in the arrangement direction of the cylindrical lenses.
With such a configuration, N types of unit pixel groups overlap in the longitudinal direction of the cylindrical lens, and the image density in the longitudinal direction of the cylindrical lens increases.
[0012]
DETAILED DESCRIPTION OF THE INVENTION
(Embodiment 1)
FIG. 1 schematically shows an arrangement configuration of pixels of an image displayed on a rear image display body D installed on the rear surface of the lenticular lens of the image display device according to the first embodiment. Assume that an image constituted by these pixels is printed on paper as a rear image display body. A portion surrounded by a thick line shown in FIG. Each unit pixel group P is composed of 12 horizontally arranged pixels. Each unit pixel group P is arranged in a matrix with the X direction in the figure as the horizontal direction and the Y direction as the vertical direction, and constitutes one image. In the drawing, uppercase alphabets A, B, C,... In each pixel indicate the arrangement order of unit pixel groups in the X direction, and lowercase alphabets a, b,. The order of arrangement is shown.
Further, the lenticular lens L in which the two-dot chain line in the figure is arranged is shown, and two adjacent two-point difference lines in the Y direction correspond to one cylindrical lens constituting the lenticular lens L.
[0013]
In each cylindrical lens constituting the lenticular lens L, films that pass only colors of red (R), green (G), and blue (B) are attached to the surfaces of the respective cylindrical lenses so as to be arranged in this order. In addition, each pixel is configured so that one row in the X direction has the same color and is arranged in the order of red (R), green (G), and blue (B) for each row in the Y direction. The first letters R, G, and B in each pixel in FIG. 1 indicate that the color of the pixel is red, green, and blue, respectively.
The width of each unit pixel group is substantially the same as the width of three cylindrical lenses, and the color constituting each unit pixel group and the color transmitted through the film attached to the cylindrical lens located in the middle of the unit pixel group Are arranged to match. For example, in the unit pixel group in which B is displayed in FIG. 1, the cylindrical lens of B is in the middle position. When arranged in this manner, adjacent unit pixel groups in the X direction do not line up in the X direction, and one third of the width of each unit pixel group overlaps in the longitudinal direction of the cylindrical lens in the order of red, green, and blue. It will be arranged while shifting. Since unit pixel groups adjacent in the X direction are arranged using three pixels in the Y direction, the unit pixel groups are thinned out in the Y direction.
[0014]
Next, how the image is displayed on the image display device configured as described above will be described. FIG. 2 is a diagram schematically showing how the image of the image display apparatus is seen. FIG. 2 is a cross-sectional view in which three image display devices are arranged vertically, and each unit pixel group P is cut from the top by pixel rows drawn in red, green, and blue. Further, R, G, and B shown in the cylindrical lens indicate colors that are transmitted through the attached film.
Consider the image display device in which the top pixel group is drawn in red. Assuming that the width of the unit pixel group is substantially the same as the width of the cylindrical lens as in the past, when viewing a cylindrical lens with a film passing through red from directly above, the pixels at both ends in the width of the cylindrical lens can be seen. The angle α in the figure, which is the range, is the viewing angle that allows stereoscopic viewing. However, in the image display device according to the present embodiment, the unit pixel group has a width corresponding to three cylindrical lenses, so that the pixels at both ends of the unit pixel group P, which is three times as wide as the conventional one, can be seen. An angle β in a certain figure is a viewing angle at which stereoscopic viewing is possible.
[0015]
Further, for example, the line of sight y1 of the right eye Er is to see a pixel to be viewed with a cylindrical lens that transmits red, and the adjacent lenticular lens has a film that passes only green. Therefore, this pixel is actually not visible. Only the pixels constituting the unit pixel group arranged at an appropriate position drawn in green of the image display device shown second from the top can be seen with the cylindrical lens that passes only green. Similarly, only the pixels constituting the unit pixel group arranged at an appropriate position drawn in blue of the image display device shown third from the top can be seen by the cylindrical lens that passes only blue. In other words, the image display apparatus according to the present embodiment can prevent an extra pixel from being shown to the observer even though the viewing angle is widened. Note that the positions of the unit pixel groups arranged in the X direction are shifted by the width of three pixels in the Y direction, but this is not a problem because it is hardly recognized by human vision.
[0016]
(Embodiment 2)
In the first embodiment, the case where three colors of red (R), green (G), and blue (B) are used has been described. However, it is also possible to use two types of polarized light having different 90-degree directions. . FIG. 3 shows the pixels of the image displayed on the rear image display body D arranged on the rear surface of the lenticular lens of the image display device using two types of polarized light used in the image display device according to the second embodiment. An arrangement configuration is schematically shown. It is assumed that an image composed of these pixels is printed on paper as the rear image display body D. A portion surrounded by a thick line shown in FIG. Each unit pixel group P is composed of eight horizontally arranged pixels. Each unit pixel group P is arranged in a matrix with the X direction in the figure as the horizontal direction and the Y direction as the vertical direction, and constitutes one image. In the drawing, uppercase alphabets A, B, C,... In each pixel indicate the arrangement order of unit pixel groups in the X direction, and lowercase alphabets a, b, c,. The sequence of the groups is shown.
Further, the lenticular lens L in which the two-dot chain line in the figure is arranged is shown, and two adjacent two-point difference lines in the Y direction correspond to one cylindrical lens constituting the lenticular lens L.
[0017]
In each cylindrical lens constituting the lenticular lens L, a linear polarization filter that passes only polarized light in the X direction and a linear polarization filter that passes only polarized light in the Y direction are alternately attached to the surface of each cylindrical lens. In addition, each pixel has a linear polarizing filter that passes X-direction polarized light and a linear polarizing filter that passes only Y-direction polarized light for each row in the X direction so as to be alternately arranged on the rear image display body.
Further, the width of each unit pixel group is substantially the same as the width of two cylindrical lenses, so that the polarized light reflected by each unit pixel group and the polarized light transmitted by the cylindrical lens located in the middle of the unit pixel group match. Has been placed. The first letters H and V in each pixel in FIG. 3 indicate that the polarized light reflected by the pixel is in the respective X and Y directions. When arranged in this way, unit pixel groups adjacent in the X direction are not aligned in the X direction, and unit pixel groups that reflect polarized light in the X direction in the longitudinal direction of the cylindrical lens, and unit pixel groups that reflect polarized light in the Y direction, Are alternately arranged and shifted by a half of the width of each unit pixel group. In addition, since unit pixel groups adjacent in the X direction are arranged using two pixels in the Y direction, the unit pixel groups are thinned in the Y direction.
Similarly to the image display device shown in the first embodiment, the image display device configured as described above has a viewing angle of 4 pixels in the past, but extends to a viewing angle of 8 pixels, and a polarizing filter. Thus, it is possible to prevent the extra pixels from being shown to the observer.
[0018]
(Embodiment 3)
In the image display according to the first embodiment, each pixel represents only one color, but one pixel is represented by three colors of red (R), green (G), and blue (B) as in a CRT monitor. In such a case, the resolution can be increased.
FIG. 4 schematically shows an arrangement configuration of pixels of an image displayed on the rear image display body D installed on the back surface of the lenticular lens of the image display device according to the third embodiment. It is assumed that an image constituted by these pixels is displayed on a CRT monitor as the rear image display body D. FIG. 4B is an enlarged view of a portion surrounded by a thick line in FIG. Each unit pixel in FIG. 4B is composed of three colors of red (R), green (G), and blue (B), and R, G, and B are shown corresponding to each color. In addition, uppercase alphabets A, B, C,... Written for each color constituting each pixel indicate the arrangement order of the unit pixel groups in the horizontal direction, and lowercase alphabets a, b, c. The arrangement order of unit pixel groups in the direction is shown. Also, each cylindrical lens constituting the lenticular lens L is pasted on the surface of each cylindrical lens so that films that pass only the colors of red (R), green (G), and blue (B) are arranged in this order. Yes.
[0019]
The pixel arrangement shown in FIG. 4 is a combination of three pixels arranged in the Y direction in the pixel arrangement shown in FIG. For example, the upper right pixel in FIG. 4B includes RDa1, GBa1, and Bca5, which match the elements of the three pixels from the top of the corresponding M columns in FIG. Note that if three pixels arranged in the Y direction in FIG. 1 are combined into one, two rows are left behind. In the first embodiment, since the unit pixel groups adjacent in the X direction are arranged using three pixels in the Y direction, the pixels for two rows are thinned out. However, in this embodiment, one pixel is used in the Y direction. Since it is not necessary to thin out pixels in the Y direction in order to overlap three pixels, an image may be formed using the thinned pixels in the Y direction in these two empty rows in the first embodiment. That is, in the rear image display according to the present embodiment, the three pixels arranged in the Y direction in the pixel arrangement shown in FIG. 1 when the pixels are not thinned out in the first embodiment are combined into one. It can be said that. Therefore, for example, the pixels RDb1, GBb9, and BCb5 in the fourth, fifth, and sixth rows in the M column in FIG. 1 are the pixels in the fourth row in FIG. Are the same, but do not enter this pixel, but coincide with RDd1, GBd9, and BCd5, which are the pixels in the fourth row of the M column in FIG. 4B.
[0020]
Each unit pixel group arranged in this way overlaps for each color. That is, for each row, 12 pixels centering on a cylindrical lens with a film that transmits the corresponding color are each unit pixel, and each unit pixel group of each color is overlapped by 1/3. That is, the unit pixel group overlaps in the longitudinal direction and the arrangement direction of the cylindrical lens.
In the same way as in the first embodiment, the viewing angle of the image is widened to the viewing angle where the pixels having the width of three cylindrical lenses can be seen, and the appearance of extra pixels can be excluded through the filter. In addition, the resolution in the Y direction is higher than that in the first embodiment.
[0021]
Although a case where one pixel is divided and three colors are emitted is shown here, the three colors may be superimposed and displayed in one pixel as in a three-plate liquid crystal projector. The same effect can be obtained even if each color is switched at a high speed in a time series with one pixel.
In each of the above embodiments, the number of cylindrical lenses (= M) that matches the width of the unit pixel group matches the type of light that is emitted or reflected (= N). Even if you don't do it, there are certain effects. However, by setting M = N, it is almost eliminated that irrelevant pixels can be seen from the cylindrical lens within the range of the predetermined viewing angle as shown in the above embodiment.
Further, in the upper embodiments, the light type is 3 or 2, but it is theoretically possible even if the light type is 4 or more.
[0022]
(Embodiment 4)
FIG. 5 schematically shows an image display apparatus according to Embodiment 4, and FIG. 6 shows an enlarged view of a range Z in FIG. The figure shows a cross section at the position of the pixel row aligned in the arrangement direction of the cylindrical lenses. The image display device shown in the figure is also composed of a lenticular lens L and a back image display D installed on the back of the lenticular lens. The rear image display body D is an image formed by printing a plurality of pixels on paper, and pixels obtained from a group of image data having parallax in a predetermined order so that a stereoscopic image can be seen by the lenticular lens L. Are arranged in a matrix. In the figure, a portion surrounded by a thick line constitutes a unit pixel group P, and each unit pixel group P is composed of eight horizontally arranged pixels. The width of each unit pixel group P substantially coincides with the width of the cylindrical lens constituting the lenticular lens L.
[0023]
In the image display device according to the present embodiment, in the unit pixel group arranged in the arrangement direction of the cylindrical lenses constituting the lenticular lens L from the predetermined reference point O of the rear image display body D, an excess is provided at predetermined intervals. Pixels (hereinafter referred to as “additional pixels”) r1, r2, r3,... Are sandwiched between unit pixel groups. In FIG. 5, the predetermined reference point O is a position that intersects with a longitudinal line segment of the cylindrical lens located in front of the observer assumed in the rear image display body. The additional pixels r1, r2, r3,... Are sandwiched between positions where reverse vision occurs when viewed from the assumed observation position of the left eye El. As a result, each unit pixel group P moves away from the reference point O every time an additional pixel is sandwiched when viewed from the reference point O, and the unit pixel group P is shifted from the position of the cylindrical lens by the amount of sandwiched additional pixel. It will be. It should be noted that the position where the reverse view occurs does not include the position where the reverse view does not occur as a result of the deviation of the unit pixel group P.
[0024]
Each additional pixel is a pixel continuous to the unit pixel group on the reference point O side. Specifically, in the unit pixel group, normally, eight pixels obtained from an image with parallax are arranged, but when the ninth pixel is arranged away from the reference point O, the ninth pixel is It becomes an additional pixel. In the drawing, two r4 and r5 are arranged side by side, which are the ninth and tenth pixels in the unit pixel group on the reference point side. That is, if there are a plurality of pixel portions where reverse viewing occurs, additional pixels are sandwiched at all positions, and pixels that are continuous in the unit pixel group on the reference point side are selected.
In the figure, the arrangement of the pixels on the right side of the observer is described, but the pixels on the left side are arranged in the same manner.
In the image of the image display apparatus having the above-described configuration, additional pixels are arranged so that the reverse view does not occur even in a position where the reverse view occurs when the image is viewed from the assumed position. Therefore, reverse viewing does not occur and the observer can see an appropriate image.
[0025]
In the above embodiment, the rear image display body D is a paper or CRT monitor, but this may be anything as long as it can display an image, and any liquid crystal display device, plasma display device, plastic sheet, etc. may be used. Can do.
Further, in each of the above embodiments, a lenticular lens is used, but this can use a parallax barrier. In this case, each slit corresponds to each cylindrical lens of the lenticular lens.
[0026]
【The invention's effect】
From the above description, the present invention has the following effects.
According to the first aspect of the present invention, the width of the unit pixel group becomes wide, and the unit pixel group cannot be seen with a cylindrical lens covered with a filter that does not transmit light that is emitted or reflected by the unit pixel group. Even when observing at a viewing angle, the cylindrical lens located at the approximate center of the unit pixel group can see the pixels of the unit pixel group, and the irrelevant pixels are prevented from being seen by the observer via other cylindrical lenses. Is done. Therefore, an appropriate image can be observed with a wide viewing angle.
According to a second aspect of the present invention, there is provided a cylindrical lens provided at a substantially center of the unit pixel group and provided with a filter that passes light emitted or reflected by the unit pixel group, and a cylindrical lens provided with a filter that passes light other than the cylindrical lens. Since the unit pixel group can be covered by the lens, it is possible to exclude the observer from seeing pixels that are almost completely irrelevant.
[0027]
According to the third aspect of the present invention, since the unit pixel group can be dealt with by changing the color, the rear image display body can be formed very easily.
According to the fourth aspect of the present invention, since the unit pixel group can be covered by the corresponding linear polarization filter, there is no limitation on the color, and the color of each pixel can be varied.
According to the fifth aspect of the present invention, since each pixel emits or reflects only one kind of light, an image display apparatus having a wide viewing angle and suppressing the appearance of extra pixels can be obtained. It can be constituted by a rear image display body.
According to the sixth aspect of the present invention, since the N types of unit pixel groups overlap in the longitudinal direction of the cylindrical lens, and the density of the image in the longitudinal direction of the cylindrical lens increases, the resolution of the image in this direction is increased. can do.
According to the seventh aspect of the invention, since the parallax barrier can achieve the same effect as that of the lenticular lens, an image display device having the same effects as those of the above claims can be obtained.
[Brief description of the drawings]
FIG. 1 is a diagram schematically showing an arrangement configuration of pixels of an image displayed on a rear display body of an image display device according to Embodiment 1. FIG.
FIG. 2 is a diagram schematically illustrating how an image is displayed in the image display apparatus according to the first embodiment.
FIG. 3 is a diagram schematically showing an arrangement configuration of pixels of an image displayed on a rear display body of the image display device according to the second embodiment.
4A is a diagram schematically illustrating an arrangement configuration of pixels of an image displayed on a rear display body of an image display device according to Embodiment 3, and FIG. 4B is a diagram illustrating a configuration of FIG. 4A. It is an enlarged view of the part enclosed with the thick line.
FIG. 5 is a diagram schematically illustrating an image display device according to a fourth embodiment.
6 is an enlarged view of a portion of a range Z in FIG.
FIG. 7 is a front view schematically showing an arrangement configuration of pixels of an image displayed on a rear display body of a conventional image display device.
8 is a reduced cross-sectional view of the rear image display body shown in FIG.
[Explanation of symbols]
L Lenticular lens D Rear image display body P Unit pixel group

Claims (6)

An image display device that satisfies the following requirements (101) to (108).
(101) It has a lenticular lens.
(102) A rear image display body that displays an image in which unit pixel groups in which pixels obtained from a plurality of image data groups having parallax are arranged in a predetermined order is displayed.
(103) The lenticular lens is disposed on the rear image display body.
(104) The width of the one unit pixel group in the arrangement direction of the cylindrical lenses constituting the lenticular lens is a width of the cylindrical lens of approximately a predetermined number N (where N is an integer of 2 or more).
(105) M (where M is an integer greater than or equal to 2) types of filters each passing a specific type of light are provided on the surface of each of the adjacent M cylindrical lenses.
(106) Each unit pixel group emits or reflects only one type of light passing through each filter.
(107) M unit pixel groups adjacent in succession are simultaneously displayed so as to overlap in the longitudinal direction of the cylindrical lens .
(108) The unit pixel group that radiates or reflects the light passing through one filter is arranged so that the cylindrical lens provided with the filter is located at the approximate center of the unit pixel group. The image display device according to claim 1, wherein M = N. The image display device according to claim 1, wherein the filter includes a filter that selectively transmits light of M different wavelengths. The image display device according to claim 1, wherein the filter includes a linear polarization filter that selectively transmits two types of polarized light different from 90 °. The image display device according to any one of claims 1 to 4, further satisfying the following requirements (501) and (502).
(501) The unit pixel emits or reflects one kind of light.
(502) N unit pixel groups adjacent to each other are arranged so as not to overlap in the arrangement direction of the cylindrical lenses. The image display device according to any one of claims 1 to 4, further satisfying the following requirements (601) and (602).
(601) The rear image display body simultaneously radiates or reflects N types of light passing through N types of filters at one unit pixel position, thereby forming N types of unit pixel groups at one unit pixel position. Unit pixels can be displayed in an overlapping manner.
(602) N unit pixel groups adjacent to each other are arranged so as to overlap in the arrangement direction of the cylindrical lenses.

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