JPH0391702A - Fresnel lens and its applied optical system, and manufacture of fresnel lens - Google Patents

Abstract

PURPOSE:To reduce the formation of moire fringes when the Fresnel lens is used in combination with a lenticular lens by combining polygonally and dividing a lens surface, and providing a prescribed slant to each polygon to form many prisms. CONSTITUTION:One kind or plural kinds of polygons 13a, 13b... are combined and divided, and the prisms are formed on the respective polygons slantingly as specified. When this Fresnel lens and the lenticular lens formed with specific pitch (r) in a specific direction (x direction) are put on over the other, a combination of the polygons is selected so that the Fourier transformation image by the combination of the polygons of the Fresnel lens is not present on the straight line passing an origin and the Foruier transformation image of the lenticular lens. Consequently, the generation of moire fringes which can be observed is reduced.

Description

[Detailed description of the invention]

(Industrial Application Field) The present invention relates to a Fresnel lens that is highly effective when used, for example, in a projection television screen, an applied optical system thereof, and a method for manufacturing the Fresnel lens. [Summary of the Invention] Conventionally, there are many Fresnel lenses. It was constructed by combining annular prisms and had spatial frequency components in all directions.The present invention constructs a Fresnel lens by combining one or more types of polygonal prisms, and has spatial frequency components in a predetermined manner. This makes it possible to suppress the occurrence of moire fringes, for example, when combined with a lenticular lens. (Conventional technology 1) Although there is a demand for larger TV screens, Because it is difficult to increase the size of a cathode ray tube, so-called projection televisions were developed in which the cathode ray tube screen is enlarged using an optical system and projected onto a screen. Figure 8 shows a projection type television using a conventional transmissive screen. 8 shows a television, 1 is a cathode ray tube, 2 is a projection optical system, and 3 is a transmission type screen. This screen 3 has a Fresnel lens 4 made of resin and a lenticular lens 5 with a pitch r overlapped. At the same time, it is constructed by forming a diffusion layer 6 on the plane of the viewing sky r1 side of this lenticular lens 5.The reason why the Fresnel lens 4 is used is to converge the diffused light so that the peripheral part of the screen becomes dark. The lenticular lens 5 is used to adjust the diffusion angle of light in the horizontal direction (θ, direction), and the diffusion layer 6 is used to adjust the diffusion angle of light in the vertical direction (θ2 direction). The Fresnel lens 4 in Fig. 8 has coaxial annular zones 4a, 4b, 4c1, . . . with a pitch of U, as shown in Fig. 9<A).
These ring zones 4a, 4b, 4C,...
forms a prism with a steep slope. Therefore, when a parallel ray is incident on the Fresnel lens 4, the ray L1 incident on the annular zone 4C and the ray L2 incident on the annular zone 4e are at approximately the same point on the optical axis, as shown in FIG. Because of the convergence, the Fresnel lens 4 acts as a convex lens. Advantages of Fresnel lenses over regular lenses include: ■
Large lenses can be mass-produced at low cost using horse chestnut resin, ■lenses can be made thinner, and ■lightweight.

[Problem to be solved by the invention]

However, the Fresnel lens 4 and the
When the lenticular lens 5 of pitch r in FIG. 9(B) is overlapped with the lenticular lens 5, moire fringes 7 as shown in FIG. 9(C) occur. Moiré fringes generally refer to fringes with a large pitch, that is, with a small spatial frequency, which are observed when two optical gratings with the same pitch are stacked so that the gratings are substantially parallel. To consider in detail the mechanism by which moiré fringes occur on a two-dimensional plane, let the pitches of the two optical gratings in the X direction be tix and t2x, respectively, and the pitch in the y direction be t1V, respectively.
, t2V. In this case, the vectors Vv and Vz on the spatial frequency plane are respectively ■+= (1/C1x, 1/j
1y), Vz=(1/12x, 1/12y) ・=
(1), the transmittances Φ1 and Φ2 of these two optical gratings are respectively expressed as follows. Φ+ = (sin 27rv+ -X) +1 -
(2) 02= (sin 2πVz−x>+i
++ (3) However, X, = (x, V) T
ct5,■?・x and Vz・X each mean the inner product of vectors. At this time, the relative intensity ■ of the light passing through those two optical gratings is ■=Φ1Φz=1+sin (27rVt ・X)
+sin (27rVz @X)+1/2-c
os(2π (VI Vz) ・X) 1/
2・cos(27r (V+ +V2) ・X)
−(4). In equation (4), the third term is a moiré fringe component, and the fourth term is a noise component that has a high spatial frequency and is generally indiscernible to the naked eye. When each component of equation (4) is expressed on the Fourier transform plane, that is, the spatial frequency space (fx, fy) in FIG.
, Vz, V+-Vz, and V1+V2 are points P1, P2, Ps, and Ps-, respectively. Although spectra also exist at points symmetrical to the origin with respect to the points P1 to P3', illustration thereof is omitted. Furthermore, in FIG. 11, if the area of spatial frequency that can be identified with the naked eye is the diagonally shaded area surrounded by circle 8, then if point P3 (■+V'z in vector) falls inside this circle 8, then This component will be observed as moire fringes. For more rigorous consideration, assume a window function Ω having a predetermined distribution within the circle 8, and calculate the moiré intensity function ψ using the following equation. ψ=ffF (φ1φ2)Ω+Hxdry −<
5) In equation (5), E(φ1φ2) is the Fourier transform of φ1φ2. In addition, in order to simply evaluate the presence or absence of moire fringes,
Assuming the radius of circle 8 in Figure 1 as Fo, V+ V21≦F
o...If (6) holds, it can be evaluated that moire fringes are observed, and if VI V21>FO=(7) holds, it can be evaluated that moire fringes are not observed. Then, the spectrum on the Fourier transform plane of those two optical gratings is, for example, point P4 (f 4
, O) and Ps (f s, O), when they are on the same straight line passing through the origin, PG (f 4 - f s, 0), which indicates the spectrum of moire fringes, is always the point P4 and Ps
Moiré fringes are likely to occur because the lens is located closer to the origin than the Fresnel lens 4 in FIG. 9(A) and the Fresnel lens 4 in FIG. 9(B)
Considering the intensity distribution when the lenticular lens 5 is superimposed with the lenticular lens 5, the pitch of the lenticular lens 5 in the X direction is r, and the spatial frequency of the fundamental wave is 1/r, but generally the spatial frequency of the harmonic wave is Component 2/r, 3
/r,... are included. Therefore, as shown in FIG. 12, the Fourier transform image of the lenticular lens 5 exists at points P7, Pa s P s . . . and symmetrical points P7Pg, P9 . . . with respect to the origin. On the other hand, since the Fresnel lens 4 is axially symmetrical with a pitch U, the Fourier transform image of its fundamental wave has a radius of 1/2 as shown in FIG.
Exists on circle 9 of U. Therefore, the point Po (1/u −1/r, 0)(l
= 1.2.3, mountain) is or Pa-(1/11+m/r
) always exists between point P7 and the origin, and those points Po
and Po− are likely to fall within the circle 8, which is the moiré fringe observation area. In this case, in order to make the moire fringes less noticeable by moving the points Pa and Pa- away from the origin and raising the spatial frequency of the moire fringes, the circle 9 in FIG.
It should be between P 9 , . . . . This condition uses an integer m of 1 or more, l/r +0.25/r
<1/u <m /r +0.75/r That is, ... (8) It is expressed as follows. Also, considering the harmonic components of the Fresnel lens 5, in conditional expression (8>), r/U is changed to u/r
The conditional expression replaced with is also a moiré reduction condition. In this application, the conditional expression (8) and its replacement conditional expression are referred to as "one-dimensional moiré reduction conditions." Conditional expression <8> is also disclosed in, for example, Japanese Patent Laid-Open No. 60-263932. However, as mentioned above, as long as the Fresnel lens is axially symmetrical and has spatial frequency components in all directions, a spectrum of moiré fringes will occur between the Fourier transform image of the lenticular lens and the origin, so in principle it can be observed with the naked eye. This creates an environment in which unsightly moire fringes are extremely likely to occur. In view of this, the present invention provides a Fresnel lens with low moiré interference that can reduce the occurrence of observable moiré fringes more than before when used in combination with an optical element having a spatial frequency component in a predetermined direction, such as a lenticular lens. The purpose is to propose lenses. Another object of the present invention is to propose an arrangement direction that can reduce the occurrence of observable moiré fringes when such a Fresnel lens is combined with an optical element having directionality, and a method for manufacturing such a Fresnel lens. shall be. (Means for Solving the Problem) The Fresnel lens according to claim 1 has one or more types of polygons 13a, i3b, .
... are combined and divided, and a predetermined inclination is provided for each of these polygons to form a prism. The applied optical system of the Fresnel lens according to claim 2 is an optical system in which the Fresnel lens according to claim 1 and lenticular lenses formed at a predetermined pitch r in a predetermined direction (x direction) are overlapped, as shown in FIG. 5, for example. system, and the Fourier transform image of the combination of polygons of the Fresnel lens (Figure 5 (C
The combination of these polygons is selected so that the points Q1, Q, Qz, Qz) of ) are not on a straight line passing through the origin and the Fourier transformed image (points R, R-) of the lenticular lens. An applied optical system for a Fresnel lens according to a third aspect of the present invention is, for example, as shown in FIG. y
This uses regular hexagons 17 arranged perpendicular to the direction. The Fresnel lens applied optical system according to claim 4 is, for example, as shown in FIG. This uses diamonds 16 arranged perpendicular to the y-direction. The Fresnel lens applied optical system according to claim 5 is, for example, as shown in FIG. The ratio between q2 and the pitch of the lenticular lens is set in the range of n + 0.25 to n + 0.75 (n is an integer). As shown in the figure, the Fresnel lens according to claim 1 and 2
It is an optical system in which lens arrays formed at a predetermined pitch r1 are superimposed in the x direction and the y direction, respectively, and a Fourier transform image (the seventh
Points Q+, Q1-1Q2, Q2-) in Figure 7(C) are on a straight line passing through the origin and the Fourier transformed image of the lens array (points R1, R1-1R2, R2- in Figure 7(C)). The combination of polygons was selected to ensure that there are no such combinations. The method for manufacturing a Fresnel lens according to claim 7 includes, for example, as shown in FIG. Later, a matrix (FIG. 1C) is formed by bringing a plane into contact with this lens surface go 2 and shifting each of the polygonal columns 10 in the longitudinal direction so that each of the polygonal columns 10 comes into contact with the plane. The Fresnel lens according to claim 1 is manufactured using this matrix (for example, by press molding or the like). An applied optical system for a Fresnel lens according to claim 8 is an optical system in which the Fresnel lens according to claim 1 and a lenticular lens formed at a predetermined pitch in a predetermined direction x direction are stacked, One side of the polygon is arranged parallel to its predetermined direction (x direction), and the pitch of the polygon in the predetermined direction is the pitch r of the lenticular lens.
is set to the same value as . (Function) The Fresnel lens according to claim 1 has the same characteristics as a conventional axially symmetric Fresnel lens, but the spatial frequency components exist only in the directions determined by these polygons. The occurrence of moire fringes can be suppressed by rotating the lens by a predetermined angle when superimposed on the lens. does not exist on the line segment connecting the Fourier transformed image of the lenticular lens and the origin, it is possible to reduce the occurrence of observable moiré fringes. Since conditional expression (8), which is a moire reduction condition, is satisfied, it is possible to more effectively reduce the occurrence of moire fringes. Since it does not exist on the line segment connecting the origin and the point of origin, it is possible to reduce the occurrence of observable moiré fringes.According to the invention set forth in claim 7, the Fresnel lens set forth in claim 1 can be mass-produced. According to the invention as set forth in claim 8, the spatial frequency of the observable moiré fringes is O (DC component), but in this case, the brightness of the entire screen changes only slightly, so it does not become an eyesore. The occurrence of observable moiré fringes is substantially reduced.

【Example】

Hereinafter, one embodiment of the present invention will be described with reference to FIGS. 1 to 7. Since the shape of the Fresnel lens of this example is complex and difficult to understand as it is, in order to facilitate understanding, the method of manufacturing the Fresnel lens of this example will first be explained with reference to FIG. 1. In Fig. 1 (A), the cross section is 0, 5311111X 0,
The figure shows a state in which 53 mm aluminum prisms 10 are bundled with their end faces aligned without any gaps, and 11 is the central axis of the whole. After firmly fixing the bundle of prisms 10 shown in FIG.
8>, the lens surface 12 is formed. This lens surface 12 may be spherical or aspherical. Then, by sliding the prisms 10 in two longitudinal directions with a plane (not shown) horizontally (perpendicular to the central axis 11) in contact with the apex of the lens surface 12, the prisms 10 are One end of each should be in contact with the plane. The state shown in FIG. 1C is obtained by removing the plane from this state, and this becomes the matrix of the Fresnel lens of this example. The Fresnel lens 13 of this example as shown in FIG. 2 is obtained by transferring the mother mold shown in FIG. can get. The lens surface of this Fresnel lens 13 is divided into squares 13a, 13b, 13C1..., and a kind of prism is formed with a predetermined inclination for each of the squares 13a, 13b, 13c,... ing. According to the Fresnel lens 13 of this example, the characteristics as a lens are substantially the same as those of the lens surface 12 shown in FIG. 1 (8), and spatial frequency components exist only in two directions. Furthermore, by bundling triangular prisms, rhombic prisms, hexagonal prisms, etc. instead of the prism 10 in FIG. 1A, the lens surface of the Fresnel lens 13 can be divided into desired polygons. Since the Fresnel lens 13 shown in FIG. 2 is likely to generate moiré fringes when superimposed on a lenticular lens, the Fresnel lens 13 is cut along the quadrilateral 14 as shown in FIGS. 3 and 4. Like Fresnel lens 1
5 Manufacture. This Fresnel lens 15 is overlapped with a lenticular lens L having a pitch r in the X direction in the positional relationship shown in FIGS. 5(A) and 5(B). Also, let the length of one side of one square 16 of the Fresnel lens 15 in FIG. 5(A) be ql, and make one diagonal 16a of the square 16 perpendicular to the pattern (y direction) of the lenticular lens L. . In this case, the pitch q2 of the Fresnel lens 15 in the X direction is J2Q1. The Fourier transform image of the fundamental wave of the lenticular lens L with pitch r in the X direction is the point R (1/r, o) R-(-1/r, o) in Fig. 5 (C) when the DC component is viewed as S. , the Fourier transform image of the fundamental wave of the Fresnel lens 15 in FIG. 5(A) has a radius of 1 centered at the origin O in FIG. 5(C).
Points Q1, Q + −, Q 2 , Q on the circumference of /q1
It becomes 2-. If we assume that the spatial frequency region that can be observed with the naked eye is inside the circle 8 inside the points R, R'', then Fig. 5 (
C) As is clearer, the vector RQ1 etc. which are the components of the moire fringe in this example are not on the line segment connecting the origin 0 and the point R and are difficult to fit inside the circle 8. Therefore, this example has the advantage that observable moiré fringes are less likely to occur. Furthermore, even if a general rhombus is used instead of the square 16 in FIG. 5A, observable moiré fringes are similarly unlikely to occur. From FIG. 5(C), vector RQ+ is minimum when point Q1 is at point T, that is, when point Q1 is at point T,
It can be seen that this is the case when the spatial frequency 1/Q2 of the direction matches 1/r or its harmonics. Therefore, the diamond 1
The spatial frequencies of 6 in the X direction are m/r and (m+1>/r
(m = 1.2.3, ...), the generation of harmful moire fringes is suppressed. This also applies to the "one-dimensional moiré reduction" shown earlier in this example. If conditional expression (8) is satisfied, it means that the occurrence of moire fringes is further suppressed. In this example, the variable U in conditional expression (8>) is replaced with pitch q2. Next, , the regular hexagon 17 shown in FIG. 6 (A>) can also be used as a polygon that divides the lens surface of the Fresnel lens.
The lenticular lens L is arranged perpendicularly to the pattern (y direction) of the lenticular lens L shown in FIG. Assuming that the height of the regular hexagon 17 is q3, the Fourier transform image of the reference wave of the Fresnel lens pattern in which regular hexagons are arranged without gaps is the 6th
As shown in Figure (C), the points Qs, Q3+, Qa, Q4Qs, Qs on the circumference with radius 1/q3 centering on the origin are the points Qs, Q3+, Qa, Q4Qs, Qs''. Therefore, the generation of harmful moiré fringes is also suppressed in this example. In addition, since a regular hexagon can be constructed by combining regular triangles, it is possible to suppress the generation of harmful moiré fringes even when using a Fresnel lens whose lens surface is divided into regular triangles. Square 1 as an example of a diamond shown
6, a Fresnel lens whose lens surface is divided by squares 16 shown in FIG. 7A, and a lens array AL divided by squares 18 shown in FIG. 7(B). Optical systems stacked in the axial direction are also conceivable. The lens array is a microlens 1 shown in FIG.
It has a structure in which 9 are lined up without any gaps. In this case, the Fresnel lens is positioned so that one diagonal line 16a of the square 16 of the Fresnel lens is parallel to the direction of one pattern of the lens array (the X direction in the example). q the length of
l, and the length of one side of the square 18 is rl, then the Fourier transform image of the fundamental wave of the Fresnel lens is at point Q in <C> in Figure 7.
+ , Q 1, Q2N Qz-1, whereas the Fourier transform images of the lens array AL become points R1, Rt-1R2, R2- in FIG. 7(C), and both Fourier transform images point to the origin. It cannot be located on a straight line. Therefore, there is an advantage that generation of harmful moiré fringes, in which frequency components are concentrated inside the circle 8, can be prevented. Furthermore, in the example of FIG. 7, if the -dimensional moire reduction condition (conditional expression (8)) j is satisfied not only in the X direction but also in the y direction, the occurrence of moire fringes can be more effectively suppressed. In addition, in the above-mentioned embodiment, the Fresnel lens and the lenticular lens were crossed diagonally to prevent the generation of harmful moiré fringes, but the Fresnel lens and the lenticular lens were deliberately arranged in parallel (for example, as shown in Fig. 5). A) square 16
The diagonal line 16a may be arranged to intersect the x-axis at an angle of 45°. However, in this case, it is necessary to match the pitch of the Fresnel lens in the X direction with the pitch of the lenticular lens in the X direction. In principle, if the pitches of the two match, moire fringes with a spatial frequency of 0 will occur, but moiré fringes with a spatial frequency of O are direct current components and become mere background, so this is an advantage that cannot be observed with the naked eye. . It should be noted that the present invention is not limited to the above-described embodiments, and it goes without saying that various other configurations may be adopted without departing from the gist of the present invention. (Effects of the Invention) According to the invention described in claim 1, in addition to maintaining the characteristics as a lens comparable to that of an axially symmetric Fresnel lens, it has only spatial frequency components in a predetermined direction, so it can be superimposed with a lenticular lens or a lens array. There is an effect that the generation of harmful moire fringes can be prevented even when used in the same manner.According to the inventions described in claims 2.3.4.5 and 6, there is an effect that the generation of harmful moire fringes can be prevented.Claim According to the invention set forth in claim 7, there is an effect that the Fresnel lens set forth in claim 1 can be easily mass-produced.According to the invention set forth in claim 8, only moiré fringes with a spatial frequency component of O are generated, and substantially no This has the effect of preventing the occurrence of harmful moire fringes.

[Brief explanation of drawings]

FIG. 1 is a perspective view showing the manufacturing process of the Fresnel lens matrix of the example. FIG. 2 is a perspective view showing an example of the Fresnel lens of the example. FIG. 4 is a cross-sectional view taken along the line IV-IV of FIG. FIG. 7 is a diagram for explaining an applied optical system formed by superimposing a Fresnel lens and a lens array according to the embodiment. FIG. 8 is a perspective view of a conventional projection television. , FIG. 9 is a diagram for explaining the conventional generation process of moire fringes, FIG. 10 is a cross-sectional view taken along the line X-X in FIG. 9, and FIGS. FIG. 3 is a diagram showing a Fourier transform surface that provides an explanation of the mechanism of occurrence. 10...Prismatic prism, 12...Lens surface, 13.1
5... Fresnel lens, 16... Square as an example of a rhombus, 17... Regular hexagon, L... Lenticular lens, LA... Lens array.

Claims (8)

[Claims] (1) A Fresnel lens in which a lens surface is divided into one type or a combination of polygons, and each of the polygons is provided with a predetermined inclination to form a prism. (2) An optical system in which the Fresnel lens according to claim 1 and a lenticular lens formed at a predetermined pitch in a predetermined direction are overlapped, wherein a Fourier transform image of a combination of polygons of the Fresnel lens is the origin and the lenticular lens. An applied optical system of a Fresnel lens in which the combination of the polygons is selected so as not to be on a straight line passing through the Fourier transform image of (3) The Fresnel lens applied optical system according to claim 2, wherein the polygon of the Fresnel lens is a regular hexagon arranged so that one side is perpendicular to the pattern of the lenticular lens. system. (4) The Fresnel lens applied optical system according to claim 2, wherein the Fresnel lens applied optical system uses a diamond shape arranged perpendicularly to the pattern of the Fresnel lens. (5) In the Fresnel lens applied optical system according to claim 4, the ratio of the pitch of the rhombic lenticular lens in a predetermined direction to the pitch of the lenticular lens is n+0.
An applied optical system using a Fresnel lens set in the range of 25 to n+0.75 (n is an integer). (6) An optical system in which the Fresnel lens according to claim 1 and a lens array formed at a predetermined pitch in two directions are superimposed, wherein a Fourier transformed image of a combination of polygons of the Fresnel lens is the origin and the lens An applied optical system of a Fresnel lens in which the combination of polygons is selected so as not to be on a straight line passing through the Fourier transformed image of the array. (7) After bundling one or more types of polygonal prisms and forming a predetermined lens surface at one end of the bundled polygonal prisms, a plane is brought into contact with the lens surface so that each of the polygonal prisms is brought into contact with the plane. A method for manufacturing a Fresnel lens, comprising: forming a matrix by shifting each of the polygonal prisms in the longitudinal direction so as to contact each other, and manufacturing the Fresnel lens according to claim 1 using the matrix. (8) An optical system in which the Fresnel lens according to claim 1 and lenticular lenses formed at a predetermined pitch in a predetermined direction are stacked, wherein one side of the polygon of the Fresnel lens is arranged parallel to the predetermined direction. . A Fresnel lens applied optical system, wherein the pitch of the polygon in the predetermined direction is set to the same value as the pitch of the lenticular lens.