JPH0428287B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION (Field of Industrial Application) The present invention relates to a stereoscopic display lens for displaying a two-dimensional image three-dimensionally. (Prior art) Conventionally, a method for stereoscopically viewing a planar image has been to obtain a three-dimensional effect by viewing two planar images with the same degree of visual difference as the left and right eyes of a person separately with both eyes. However, this method requires two different plane images,
It has been impossible to achieve stereoscopic viewing using a single flat image. Recently, there are some devices that enable stereoscopic display using a single planar image, such as the
Various methods using the lenticular method have been proposed, such as 59-2014. (Problems to be Solved by the Invention) However, since this type of stereoscopic image using the lenticular method uses a continuous array of fine lenticular shaped lenses, there may be two problems depending on the viewing position. Not only can it appear as a superimposed image, making it impossible to view stereoscopically, but since the structure uses fine lenses to create parallax on a pixel-by-pixel basis, it is difficult to obtain the parallax necessary for stereoscopic viewing of groups of pixels that are large enough to be visually discernible. Therefore, it was difficult to create a highly practical one for large screens. In addition, the mold used to manufacture this lens is extremely difficult to manufacture because it forms the minute lens part with a precise curvature. Not only was this limited to limited quantities, but it was also a factor in increasing costs. The present invention has been made with attention to these points, and it provides a large enough parallax to enable stereoscopic viewing of a group of pixels of a discernible size, and facilitates the production of a mold, thereby creating a large and highly practical mold. It is an object of the present invention to provide a stereoscopic prism plate that enables the realization of a screen and can be supplied at a relatively low cost. (Means for Solving the Problems) Therefore, in the present invention, a unit refracting surface group is formed by alternately arranging direction angle elements and flat parts of a size that allows the stereoscopic viewing prism plate to be identified, and this unit A group of refractive surfaces is repeatedly and continuously arranged on at least one surface of a see-through surface made of a transparent flat plate. (Function) By configuring as described above, the stereoscopic prism plate of the present invention displays a planar image with parallax through a transparent face piece in which direction anglers and planar portions of a discernible size are alternately arranged. This makes it possible to create a structure in which parallax is created using a pixel group, which is a collection of pixels, as a unit, and to obtain a sufficiently large parallax for stereoscopic viewing of a pixel group that is large enough to be visually discernible. Even if the position moves from perspective to near or to the left or to the right, each eye's line of sight focuses on the same pixel, so the same image can be viewed continuously over a wide area and viewed stereoscopically by many people. Furthermore, by forming a turning angle element by a combination of flat surfaces, curved surface machining is eliminated from the mold manufacturing process, and furthermore, this turning angle element is made relatively large so that it can be identified, making it easier to manufacture molds. This makes it extremely easy. (Example) FIGS. 1 to 7 are perspective views showing examples of implementations of stereoscopic prism plates according to the present invention. In each figure, reference numeral 1 denotes a see-through face piece, which is formed by a first face piece 2 and a second face piece 3, each of which is made of a transparent flat plate and arranged in parallel. On the upper surface of the first face piece 2, direction changers 5 and flat parts 6 are arranged alternately. 1 shown in Figure 1.
The turning elements 5a of the embodiment have a concave prism shape and are arranged in parallel in the vertical direction. The turning element 5b of the second embodiment shown in FIG. 2 has a convex prism shape and is formed in a mosaic shape, and the turning element 5c of the third embodiment shown in FIG.
is a compound direction turner shape in which the apex angle of a concave prism shape is formed into a small plane 6', and a concave prism-shaped direction turner 5'a is provided on the upper surface of the concave prism shape;
They are arranged in parallel in the vertical direction. Further, the direction changer 5d of the fourth embodiment shown in FIG. 4 is formed of a small circular hole with a bottom whose bottom part is a small plane 6' (a shape with a hole may also be used), and has a compound eye shape. is formed. Further, the direction changer 5e of the fifth embodiment shown in FIG.
is a shape in which the apex angle of a convex prism shape is formed by a small plane 6', and the turning element of the sixth embodiment shown in FIG. 6 uses the same turning element 5a as the first embodiment. Direction angle element 5 of the seventh embodiment shown in FIG.
f is a shape in which the apex angle of the concave prism shape is a small plane 6'. The direction changers of these fifth, sixth, and seventh embodiments are arranged in parallel in the vertical direction. The size of these direction anglers is not a minute shape, but is formed with a width that can be discerned by the human eye. Next, the flat portion 6 has a shape that is large enough to be discerned by the human eye, and in the first embodiment shown in FIG.
In the embodiments shown in FIGS. 2 and 4, they gradually become larger toward the right and forward, and in the third embodiment shown in FIG. As you move towards the right side, the width gradually changes such that it once widens and then narrows. In the fifth to seventh embodiments shown in Figs. It is something that continues to spread. Furthermore, the change in the size of the plane portion 6 shown in each figure other than the first embodiment shown in FIG. 2, this is arranged continuously over its entire upper surface. Also, the direction changer 8 is arranged alternately with the flat part 9 on the lower surface of the second face 3, and only the direction changer 8c of the third embodiment shown in FIG. 5c has a different shape, and the apex angle of the concave prism shape is a small plane 9', which is a continuous arrangement of direction turning elements 8c. The direction anglers 8a, 8b, 8d, 8e, and 8f of the other second face pieces 2 are the first
It is formed in the same shape as the direction angle element of the face piece 2, and the arrangement shape is also formed in the same manner. Only in the seventh embodiment shown in FIG. 7, the pitch is different from the arrangement pitch of the deflector of the first face 2, but in all other embodiments, the pitch of the deflector of the first face 2 and the deflector of the second face 3 are different. The arrangement pitch of the direction angle elements is the same. Next, stereoscopic viewing of one planar image using these stereoscopic viewing prism plates will be explained. below,
On the back image G, a pixel group in which multiple or more pixels are gathered is written as P , and a ray flux from the pixel group is written as a' ,
In addition, a beam of light is represented by a single line. A graphical representation of a pixel group is indicated by a - mark. FIG. 8 is an explanatory diagram showing the optical system of the first embodiment. A plane image G is placed a little apart from the surface of the transparent body 1 on the object plane side. In this case, the slightly spaced gap may be replaced with a transparent parallel plane plate, which is applicable to all implementations of the present invention. Now, when viewing the ray bundles a' ₁ to a _{' 6} from each pixel group P ₁ to P ₆ of the image G through the stereoscopic prism plate with the line of sight a ₁ to a ₆ of the eye A, the eyepiece surface of the first face piece 2 When the second face pieces 3 formed corresponding to 10 are superimposed and the ray bundles a' ₁ to a' ₆ are passed through, the ray bundles a' ₁ to a' ₂ become Y of the flat part 6 of the first face piece 2. _1point ,
It passes through the _Y2 point and the _Y'1 point and _Y'2 point of the plane part 9 of the second face 3, and is seen with lines of sight _a1 and _a2 . Then the ray bundle
Since a′ ₃ is refracted twice at the _Y4 point on the left side of the direction changer 5a of the first facet 2 and at the _Y3 point of the flat part 9 of the second facet 3, it exits in the direction _S1 in the figure. Although it cannot be seen from the line of sight _a3 , at this time, the diffused beam _a''1 from the pixel group _P1 is incident on the _Y3 point of the plane part 6 of the first surface body 2, and the normal line _N1 to _N'1 It moves away from , faces toward the lower left in the figure, approaches the normal line N ₂ to N' ₂ set at _{the 4} points Y' on the left side of the direction changer 8a of the second face 3, and from _{the 4} point Y' Since N ₂ to N' ₂ are moved away and refracted and bent to the lower left in the figure, the ray bundle a'' ₁ incident in the direction of points Y ₃ to E points is refracted twice and the direction angle is ∠
E, Q, O. In other words, the ray bundle a″ ₁ is the plane part 6
When it passes through the direction changer 8a, it advances in the direction of Q to O, so that the pixel group _P1 is seen from the aforementioned line of sight _a3 . Next, the ray group a _{' 4} of the pixel group P 4 is refracted toward the lower right side in the figure at point Y ₅ on the left side of the direction changer 5 a of the first surface 2 and proceeds to the flat part 9 of the second surface 3. It is further refracted at the Y′ ₆ point and exits in the direction of S ₂ , so it cannot be seen from the line of sight a ₄ . In addition, the ray bundles a' ₅ and a _' 6 of the pixel group P ₅ and the pixel group P ₆ are the Y ₇ point and Y ₈ point plane portion 9 of each plane portion 6 of the first and second face pieces 2 and 3, respectively. Y′ ₇ points, Y′ ₈
The pixel groups P ₅ and P ₆ are seen through the line of sight a ₅ and a ₆ . At this time, the diffused ray bundle a″ ₆ radiating from the pixel group _P6 mentioned above is located between the point _Y6 of the plane part 6 of the first surface body 2 and the second
It is refracted at ₅ points on the right side Y of the direction angle element 8a of the facepiece 3 and is deflected to the lower right side in the figure, so that the pixel group P ₆ is viewed from the line of sight a ₄ by this ray bundle a″ ₆ . Become.
As a result, the original image G becomes the image group P ₁ , P ₂ , P ₃ ,
If it is formed in the order of arrangement of pixel groups P ₄ , P ₅ , P ₆ , then in eye A, it is formed in the order of arrangement of pixel groups P ₁ , P ₂ , P ₁ , P ₆ , P ₅ , P ₆ We will see another image G'. In this way, since the arrangement order differs not in units of pixels but in units of pixel groups, the difference in shape from the original image G is large. Next, FIG. 9 shows the optical system of the second embodiment. When the pixel groups P ₁ to _{P 4} of the planar image G are viewed from the line of sight a ₁ to a ₄ of the eye A through this stereoscopic prism plate,
Of the ray bundles a' ₁ to a' ₄ from each pixel group, a' ₂ and a' ₃ pass through the deflector 5b of the first facet 2 and the deflector 8b of the second facet 3, and are refracted twice. Since the positions of both pixel groups are swapped, the arrangement order of each pixel group is P ₁ , P ₃ , P ₂ ,
P ₄ , and the original image G appears to eye A as a different image G'. Moreover, FIG. 10 shows the optical system of the third embodiment, in which the pixel group of the planar image G is transmitted through such a stereoscopic prism plate.
When viewing P ₁ to P ₆ from the line of sight a ₁ to _{a 6} of eye A, each ray bundle a' ₁ to a' ₆ from each pixel group is
Due to the refractive action of the direction angle elements 5a' and 5c of the facepiece 2 and the planes 9 and 9' of the second facepiece 3, the arrangement order of the pixel groups of the original image G changes to the eye A, and the pixel groups P ₁ , P ₁ ,
Another image formed by the array P ₂ , P ₅ , P ₆ , P ₆
We will see G′. Next, FIGS. 11 a to 11 c show the optical system of the fourth embodiment.
When viewed at position a with the lines of sight a ₁ to _{a 4} of eye A passing through the face piece 3, the ray bundle a′ ₂ of the pixel group P ₂ alone enters the plane 6 of the first face piece 2 and travels to the second face piece. Since the light is incident at a large angle on the left inner surface _Y1 of the direction changer 8d of the facepiece 3, it is totally reflected and exits in the direction of S1 shown in the figure at the plane part ₉ . In addition, the diffused ray bundle a'' ₃ of the pixel group P ₃ is the direction angler 8 of the second surface 3 described above.
Since it is incident at a large angle on the left outer surface Y′ ₁ of d, it is totally reflected and directed toward the line of sight a ₂ . On the other hand, pixel group P ₁ ,
The ray bundles a′ ₁ , a′ ₃ , and a′ ₄ from P _{3 and} P 4 are the line of sight, respectively.
The image G' seen by the eye A is formed by the pixel groups P ₁ , P ₃ , P _{3 ,} and P ₄ as the image moves to a 1 , a ₃ , and a ₄ .
Next, when the eye A is moved to the position b and the image G is viewed in the same manner as described above, the ray bundle a′ ₁ from the pixel group P ₁ and P ₄ is
Since a′ ₄ exits in the directions of S ₁ and S ₂ in the figure, the image G′ seen by eye A is formed by pixel groups P ₂ , P ₂ , P ₃ , and P ₃ . Furthermore, when eye A is moved to position c and image G is viewed in the same way as described above, the ray flux of pixel group P ₃ is
Since a′ ₃ exits in the direction of S ₂ in the figure, the image G′ seen by eye A is formed by pixel groups P ₂ , P ₂ , P ₄ , and P ₅ . The parallax phenomenon in which each pixel that forms an image is rearranged in pixel group units to create a separate image is further explained by the optical system operation in the case of a unit refractive surface group 7 in which the size of the plane part changes sequentially. This will be explained with reference to FIG. FIG. 12 shows the optical system of the sixth embodiment. Using such a stereoscopic prism plate, a plane image G is displayed on the first facet 2 as shown in the figure.
When viewed from each line of sight a ₁ to _{a 14} of the eye A through the second faceted body 3, the ray bundles a' ₁ to a' of the pixel groups P ₁ to _{P 14} are Of ₁₄ , the ray flux
a′ ₂ , a′ ₄ , a′ ₇ , a′ ₁₂ go out in the directions of S ₁ to S ₄ in the figure, respectively, and the ray bundles a′ ₄ , a′ ₅ , a′ ₈ , a′ ₁₃
appear in the directions S' ₁ to S' ₄ in the figure, respectively, so the image G' seen by eye A consists of pixel groups P ₁ , P ₃ , P ₃ , P ₃ ,
P ₆ , P ₆ , P ₆ , P ₉ , P ₁₀ , P ₉ , P ₁₀ , P ₁₁ , P ₁₁ , P ₁₄
The way to rearrange this arrangement order is to change the direction angle element 5.
It appears more conspicuously in areas where the arrangement of a is finer and more numerous. In this way, by further expanding the parallax that has been achieved by rearranging the arrangement order in units of pixel groups and obtaining the parallax in which the arrangement order is rearranged in units of unit refractive surface groups, the image G′ seen by eye A becomes the original image. This makes it possible to increase the difference in shape from image G. Such visual phenomena occur when the transparent face piece 1 has a mosaic shape, a compound eye shape, two vertically parallel shapes perpendicular to each other, or an orthogonal shape where the front and back surfaces are perpendicular to two vertically parallel shapes, etc. This creates a visual effect that clearly distinguishes the foreground and background of the image. In this way, due to differences in viewing angles even for the same image, the arrangement order of pixel groups is rearranged for each pixel group and for each unit refracting surface, and the direction angle is large enough to distinguish the effects of the optical system that appear as separate images. A feature of the present invention is that parallax can be created by alternately arranging plane parts. A case in which such a parallax phenomenon is viewed with both eyes will be described next. FIG. 13 shows the optical system of the fifth embodiment. If a planar image G is placed a little apart from the object plane side of the perspective facet 1, and this image G is formed by pixel groups _P1 to _P5 , then when viewing the image G with both eyes A and B, If the visual lines a ₁ to _{a 3} and b ₁ to b ₃ of both eyes are focused on the pixel groups P ₁ , P ₃ , and P ₅ , respectively, the image focusing position will be different for the visual line of the right eye A. three imaging points
Since we will see ap′ ₂ , ap′ ₃ , and ap′ ₅ , the arrangement order of the pixel groups will be changed from the original image G, and we will see another image G′ with the left side intersected. . left eye B
There are three image forming points with different image forming positions in the line of sight.
You will see bp′ ₁ , bp′ ₃ , bp′ ₄ , and you will see another image G′ in which the right side is sandwiched and the arrangement of the pixel groups has been rearranged. As a result, the right eye and left eye see completely separate images with different shapes on both sides. In this way, the phenomenon of horizontal parallax when viewing a single plane image with both eyes using unit refracting surface groups for each pixel group can be explained using the
The operation of the optical system of the seventh embodiment shown in the figure will be explained. Assuming that the plane image 12 shown in FIG. 15 is now displayed on the surface of the plane image G, the plane image G
Through the perspective facet 1, each line of sight of both eyes a ₁ to _{a 7} and b ₁
Binocular visual points are located at the points g, h, i, j, k, l, and m of the pixel group constituting the plane image 12 with ~b ₇
When looking at lines x ₁ to _{x 7} with different inclination angles, each line of sight at the points of view x ₁ to _{x 7} of right eye A
a ₁ to _{a 7} will look at h, i, i, j, k, l, m among the points g to m of each pixel group of the plane image 12,
In addition, each line of sight b ₁ to _{b 7} at the focal points x ₁ to x ₇ of the left eye B
out of the points g to m of the pixel group of the plane image 12, g,
You will see h, i, j, k, k, l. Also, when you move both eyes A and B to the points of interest x ₁ to x ₇ , the line of sight changes.
The parts a ₂ h, b ₁ g seen through a 1 and b ₁ continuously move to the right, reaching parts a ₃ i _, b ₂ h, and similarly a ₇
m, b The pixel group seen by both eyes up to ₇ m moves to different parts. As a result, the continuous image seen by the right eye A consists of points h, i, i, j, k,
1 and m, the plane image 12 appears narrower on the left side, as shown in FIG. 16a. Also, the continuous images seen in the left eye B are the points g, h,
It is formed by i, j, k, k, l, so Figure 16b
As shown in , the plane image 12 appears narrower on the right side. In these two consecutive images, the pixel groups are rearranged for each pixel group, and the binocular disparity occurs for each unit refractive surface group, and the images with greatly different shapes are disparaged for the left and right eyes separately, resulting in a stereoscopic effect. This gives a great three-dimensional effect. Next, when the prism plate for stereoscopic vision of the present invention has the shape shown in FIGS. 3 to 7, in which the direction angle element forms a small plane, each of the prism plates is small due to the difference in thickness between the small plane and the plane part. This provides a parallax effect.
That is, as shown in FIG. 17, instead of the prism plate, a transparent plane plate 1' is placed facing the plane image G so that both eyes A,
When viewing pixels P ₁ and P ₂ of image G at B, both lines of sight a ₁ ,
Since a ₂ , b ₁ , and b ₂ are all viewed through a plane of the same thickness, pixels P ₁ and P ₂ are viewed as being raised to points P' ₁ and P' ₂ in space by the light angle θ. At this time, the transparent flat plate 1'
Another transparent flat plate 1'' with the thickness shown by the phantom line is provided on a part of the upper surface, so that only the line of sight _A1 is separate from the line of sight _B1 .
If it passes through this plane 1'', the position of the refraction point of the line of sight _a1 changes, the light angle changes to θ', the line of sight becomes _a'1 , and the image P'' of the pixel P appears on the extension line. Become. This image P'' stands out a little more than the pixel P'. This means that when the line of sight of both eyes is viewed through a stereoscopic prism plate, the line of sight of the eyes is always equidistant from both eyes (in the figure). a ₂ , b ₂ ) is seen connecting the writing point x, but other lines of sight a′ ₁ , b ₁
When looking through a plane and a small plane with different thicknesses, the line of sight a′ ₁ moves in the direction shown by the dashed line, so
Strictly speaking, both lines of sight a′ ₁ and b ₁ are each the image point x
are shifted and become P′, P″, resulting in a double image.
The fusion adjustment action of the binoculars that brings these discrepancies together works autonomously, allowing the viewing point to be shifted, which has the effect of further enhancing the three-dimensional effect. In this way, the present invention provides a unit refractor in which the flat parts are formed to have the same size or the size of the flat parts gradually changes in a relationship in which direction anglers formed with discernible sizes and flat parts are arranged alternately. Since they are formed into a group of planes and arranged continuously, the difference in visual perception between the left and right eyes when viewing a single plane image creates a difference in the images reflected on the retinas of the left and right eyes, resulting in a three-dimensional effect. Although the present invention has been described above in detail according to the illustrated embodiments, the present invention should not be limited to these only. That is, in each of the embodiments described above, the first facet and the second facet are separate bodies, but they may be formed integrally, and the optical system functions substantially the same as in the third embodiment described above. Therefore, stereoscopic prism plates as shown in FIGS. 18 and 19, which have the effect of rearranging the arrangement of pixel groups, can also be used to implement the present invention. In addition, the present invention provides a first facet or a first facet in which unit refractive surfaces formed by sequentially arranging flat parts and refracting elements of equal size, or by sequentially changing the arrangement of refractive angle elements alternately with flat surfaces, or Even if it is a dihedron with only a flat back surface, it can be used in the practice of the present invention without changing the optical system function of the present invention. It can be formed by Further, the viewing facets having a vertically parallel shape, a mosaic shape, and a compound eye shape can be used to implement the present invention without changing the function of the optical system of the present invention even if they are replaced or combined with each other regardless of the shape of the respective direction angle elements. . For example, it is conceivable to form one surface into a vertically parallel shape and the other surface into a mosaic shape. Furthermore, the present invention can be practiced with an optical system similar to a mosaic shape in which the front and back surfaces of the vertically parallel shape are orthogonal to each other. Furthermore, either of the first and second facets described above can be used as the object surface or the eyepiece surface. In the stereoscopic prism plate of the present invention, the direction changer formed on the surface of the first facet or the second facet needs to have a width formed by each direction changer or a difference in thickness from the flat part, etc., alternately or sequentially. Even if they are formed with slight differences to the extent that they are, they can be used to implement the present invention. (Effects of the Invention) The stereoscopic prism plate according to the present invention has at least one surface of a transparent face piece made of a transparent flat plate.
A group of unit refractive surfaces formed by alternately arranging diversion angle elements and flat parts of discernible size are arranged repeatedly, and the diversion angle elements form an apex angle of a concave prism shape as a small plane, Since the planar image is parallaxed by providing a concave prism-shaped turning element on the small plane to form a compound turning element, the parallax is sufficient to stereoscopically view a group of pixels of a size that can be visually distinguished. It becomes possible to obtain. In other words,
Parallax is generated in units of pixel groups, and the arrangement order of pixel groups whose direction is turned by a direction angle plane is rearranged in units of pixel groups, and the difference can be seen as a large parallax with both eyes. In addition, even if the viewing position moves, both eyes are focused on the same pixel, making it possible for many people to see the same image repeatedly over a wide area. . Furthermore, the compound direction turner has the effect of making the user perceive a sense of depth by utilizing the difference in the thickness of the small plane and the plane part to create a visual sense of depth due to the difference in relative imaging points. Further, since the compound direction rotator is composed of a combination of relatively large planes, curve machining is not necessary in the manufacturing process of the manufacturing mold, and manufacturing of the mold becomes easy. Therefore, it is possible to realize a large screen and is effective in reducing costs. Further, when the stereoscopic prism plate of the present invention is applied to a moving image of a flat image, hidden parts appear due to the movement of the image, and the three-dimensional effect can be further increased.

[Brief explanation of drawings]

FIGS. 1 to 7 are perspective views showing an example of implementation of a prism plate for stereoscopic vision according to the present invention, and FIGS.
FIG. 14 is an explanatory diagram showing the optical system of each of these embodiments, FIG. 15 is a plan view showing an example of a planar image drawn on a planar image, and FIG. 16 is an image seen by the left and right eyes, respectively. FIG. 17 is an explanatory diagram showing an optical system when a transparent flat plate is used instead of a prism, and FIGS. 18 and 19 are perspective views of stereoscopic prism plates of other embodiments. It is an explanatory diagram showing an optical system. 1... Perspective face piece, 2... First face piece, 3... Second face piece
Face piece, 5a to 5f, 8a to 8f...direction angle element,
6, 9...Plane portion, 7...Single refractive surface group, G...
Planar image.

Claims (1)

[Scope of Claims] 1. On at least one surface of a see-through face piece made of a transparent flat plate, a group of unit refractive surfaces formed by alternately arranging diversion angle elements and flat parts of discernible size are repeatedly arranged. , a prism plate for stereoscopic vision, characterized in that the direction turning element has a concave prism shape whose apex angle is a small plane, and a concave prism-shaped direction turning element is provided on the small plane to form a compound direction turning element. . 2. The prism plate for stereoscopic vision according to claim 1, characterized in that the size of the plane portion of the unit refracting surface group is formed so as to gradually change. 3 The transparent face piece is made of a first face piece made of a transparent flat plate and a second face piece made of a transparent flat plate.
Claims 1 or 2 are characterized in that the unit refractive surface group is continuously arranged on one surface of the first facet and is formed by arranging the facets substantially parallel to each other.
A prism plate for stereoscopic vision as described in Section 1. 4. A patent claim characterized in that on one surface of the dihedron, a group of unit refractive surfaces formed by alternately arranging diversion angle elements and flat parts of discernible size are repeatedly arranged. A prism plate for stereoscopic viewing according to scope 3. 5. The prism plate for stereoscopic vision according to claim 4, wherein the planar portion of the unit refractive surface group formed on one surface of the dihedron is formed such that the size thereof gradually changes. . 6. A prism plate for stereoscopic viewing according to claim 4, characterized in that the arrangement pitch of the direction angle elements is made to correspond between the unit refractive surface group of the first facet and the unit refractive facet group of the second facet. .