Optical lighting system

Abstract

Optical illumination system comprising a light source (200) and a single convex lens (100) provided with a diffraction structure on one surface thereof, wherein the phase function of the diffraction structure is represented by ϕ ( r ) = ∑ i = 1 N β 2 ir 2 i , where r represents a distance from the central axis of the lens (100), β represents coefficients, and N and i represent natural numbers, and the relationship | β 2 | ⋅ ( 0.3 R ) 2 < | β 4 | ⋅ ( 0.3 R ) 4 is satisfied, where R represents an effective radius of the lens (100), and where the second derivative with respect to r of the phase function has at least one extremal value and at least one inflection point in the region of r in which r is greater than 30% of the effective radius of the lens (100), a difference of a spherical aberration between the maximum value and the minimum value for each r in 0 ≤ r ≤ R is equal to or less than the longitudinal chromatic aberration for each value of a wavelength of visible light, and the diffraction pattern is provided at least partially in the region of r where r is greater than 30% of the effective radius of the lens (100), and wherein the light source (200) has a surface having a luminance in a specified region and the area of ​​the surface of the light source (200) is equal to or greater than 3% of the area of ​​the entrance pupil when the light source side of the lens (100) is defined as the image side.

Description

Technical field

[0001] The present invention relates to an optical lighting system used for headlights of vehicles or the like. Background technology

[0002] In an optical lighting system used for vehicle headlights or similar applications, chromatic aberrations of lenses problematically cause color gradients at the periphery of an area to be illuminated and around the boundary between an illuminated and an unilluminated area. To reduce such color gradients, the chromatic aberrations of the lenses must be corrected. Under the situation described above, an optical lighting system has been developed which includes a lens with a surface provided with a diffraction structure for correcting chromatic aberrations (for example, patent document 1).

[0003] However, an optical lighting system that incorporates a lens with a diffraction structure exhibits the following problems. First, so-called glare is generated by diffraction light from undesired diffraction orders. The reason for this is that diffraction efficiency varies depending on the position on the lens surface and the angle of incidence of a ray onto the lens, thereby transferring energy from the diffracted light to undesired diffraction orders. Second, a diffraction structure impairs transmission.

[0004] Therefore, an optical illumination system has not yet been developed which has a lens provided with a diffraction structure for correcting chromatic aberrations, wherein the optical illumination system is able to sufficiently suppress the generation of glare and impairment of transmission. State of the art document / Patent document

[0005] Patent document 1: JP 2014 - 26 741 A US 6 870 805 B1 discloses an exemplary optical recording device for reproducing information from an optical information storage medium or for storing information on an optical information storage medium. Overview of the invention; Problem to be solved by the invention

[0006] In the situation described above, there is a need for an optical illumination system comprising a lens equipped with a diffraction pattern for correcting chromatic aberrations, wherein the optical illumination system is capable of sufficiently suppressing glare and transmission impairment. The object of the present invention is to provide an optical illumination system comprising a lens equipped with a diffraction pattern for correcting chromatic aberrations, wherein the optical illumination system is capable of sufficiently suppressing glare and transmission impairment. Means of solving the task

[0007] An optical illumination system according to the present invention comprises a light source and a single convex lens, the latter having a diffraction structure on one surface thereof. The phase function of the diffraction structure is represented by: ϕ(r)=∑i=1Nβ2ir2i, where r represents a distance from the central axis of the lens, β represents coefficients, and N and i represent natural numbers, and where the relationship |β2|⋅(0.3R)2<|β4|⋅(0.3R)4 is satisfied, where R represents an effective radius of the lens. The second derivative with respect to r of the phase function has at least one extremum and at least one inflection point in the range of r where r is greater than 30% of the effective radius of the lens, where the difference in spherical aberration between the maximum and minimum values ​​for each r in 0≤r≤R The diffraction pattern is equal to or less than the longitudinal chromatic aberration for each value of the wavelength of visible light, and the diffraction pattern is at least partially provided in the region of r where r is greater than 30% of the effective radius of the lens. The light source has a surface exhibiting a luminance in a predetermined region, and the area of ​​the surface of the light source is equal to or greater than 3% of the area of ​​the entrance pupil, where the light source side of the lens is defined as the image side.

[0008] In the lens of the optical illumination system according to the present invention, glare due to diffracted light that differs from the diffracted light of the desired order can be reduced by making the coefficient β2 of the second-order term of r of the phase function relatively small and by making the component of a curvature of a spherical surface corresponding to the second-order term relatively small. Furthermore, the lens of the optical illumination system according to the present invention is configured such that the diffraction pattern is at least partially provided on the surface in the region of r where r is greater than 30%, and the second derivative with respect to r of the phase function has at least one extremum and at least one inflection point in the region described above.Accordingly, when the lens is used in combination with the light source described above, chromatic aberrations in the area described above can be reduced, while a decrease in the transmission of light through the lens is suppressed.

[0009] In the optical illumination system according to a first embodiment of the present invention, the surface of the light source is arranged such that the distance between the surface of the light source and a curved surface, which represents a field curvature of the lens when the light source side of the lens is defined as the image side, is equal to or less than 3% of the focal length of the lens.

[0010] According to the present embodiment, by using the light source provided with the surface, which is provided along a curved surface that represents field curvature, field curvature can be corrected to a very satisfactory extent.

[0011] In the optical illumination system according to a second embodiment of the present invention, the second derivative with respect to r of the phase function has at least one extremal value and at least one inflection point in the region of r in which r is greater than 50% of the effective radius of the lens, and the diffraction structure is at least partially provided in the region of r in which r is greater than 50% of the effective radius of the lens.

[0012] In the optical illumination system according to a third embodiment of the present invention, the relationship 0<β62β4β8<5 fulfilled.

[0013] In the lens of the optical illumination system according to a fourth embodiment of the present invention, β4 and β8 are negative and β6 is positive.

[0014] In the lens of the optical illumination system according to a fifth embodiment of the present invention, the depth of the diffraction structure is corrected as a function of r.

[0015] In the lens of the optical illumination system according to a sixth embodiment of the present invention, the two side surfaces of the lens are convex.

[0016] In the optical illumination system according to a seventh embodiment of the present invention, the surface of the light source is arranged such that the distance between the surface of the light source and a curved surface, which represents a field curvature of the lens when the light source side of the lens is defined as the image side, is equal to or less than 1% of the focal length of the lens. Brief description of the drawings Fig. Figure 1 illustrates a lens according to the present invention; Fig. Figure 2 illustrates a tangent angle of a lens surface; Fig. Figure 3 is a conceptual representation to illustrate a depth in the direction of the optical axis D(r) of the diffraction structure; Fig. Figure 4 shows a relationship between r and a tangent angle θ at the surface S1, which is provided by the diffraction pattern of the lens from Example 1; Fig. Figure 5 shows a relationship between r and an angle of incidence Π(r) of a light ray on the surface S1, which is provided by the diffraction structure of the lens from Example 1; Fig. Figure 6 shows a relationship between a groove number and a grating depth corresponding to each groove (depth of a groove) in the diffraction structure of the lens of Example 1; Fig.Figure 7 shows spherical aberrations of the lens from Example 1; Fig. Figure 8 shows a second derivative with respect to r of the phase function from Example 1; Fig. Figure 9 shows a third derivative with respect to r of the phase function from Example 1; Fig. Figure 10 shows a fourth derivative of r of the phase function from Example 1; Fig. Figure 11 shows a relationship between r and a tangent angle θ at the surface S2, which is provided by the diffraction structure of the lens from Example 2; Fig. Figure 12 shows a relationship between r and an angle of incidence Π(r) of a light ray on the surface S2, which is provided by the diffraction structure of the lens from Example 2; Fig. Figure 13 shows a relationship between a groove number and a grating depth that corresponds to each groove in the diffraction pattern of the lens of Example 2; Fig.Figure 14 shows spherical aberrations of the lens from Example 2; Fig. Figure 15 shows a second derivative with respect to r of the phase function of Example 2; Fig. Figure 16 shows a third derivative with respect to r of the phase function of Example 2; Fig. Figure 17 shows a fourth derivative with respect to r of the phase function of Example 2; Fig. Figure 18 shows a relationship between r and a tangent angle θ at the surface S1, which is provided by the diffraction structure of the lens from Example 3; Fig. Figure 19 shows a relationship between r and an angle of incidence Π(r) of a light ray on the surface S1, which is provided by the diffraction structure of the lens from Example 3; Fig. Figure 20 shows a relationship between a groove number and a grating depth that corresponds to each groove in the diffraction structure of the lens of Example 3; Fig.Figure 21 shows spherical aberrations of the lens from Example 3; Fig. Figure 22 shows a second derivative with respect to r of the phase function from Example 3; Fig. Figure 23 shows a third derivative with respect to r of the phase function of Example 3; Fig. Figure 24 shows a fourth derivative of r of the phase function from Example 3; Fig. Figure 25 shows an image field curvature of the lens of Example 1 when the light source side of the lens is defined as the image side; Fig. Figure 26 shows field curvature when the surface of the light source is oriented along the in Fig. The image field curvature shown in 25 is formed; Fig. Figure 27 shows an image field curvature of the lens of Example 2 when the light source side of the lens is defined as the image side; Fig. 28 shows field curvature when the surface of the light source is oriented along the in Fig. The image field curvature shown in 27 is formed; Fig. Figure 29 shows an image field curvature of the lens from Example 3 when the light source side of the lens is defined as the image side; and Fig. Figure 30 shows field curvature when the surface of the light source is oriented along the in Fig. The image field curvature shown in 29 is formed. Description of embodiments

[0017] Fig. Figure 1 illustrates an optical illumination system according to the present invention. Light rays propagating from a light source 200 are projected through the lens 100. The surface on the light source side of the lens is represented by S2, and the surface on the side of the lens opposite the light source is represented by S1. The surfaces S1 and S2 are represented by the following even function for an aspherical surface. S(r)=cr21+1−(1+k)c2r2+∑i=1Nα2ir2i

[0018] S(r) represents a coordinate in the direction of the central axis of a lens, with the origin defined at the vertex of a lens surface; r represents a distance from the central axis; c represents a curvature at the center of the surface; k represents a conic constant; α represents coefficients; and N and i represent natural numbers. The central axis of the lens is defined as the optical axis. Fig. 1 is defined as a coordinate represented by S(r) if the coordinate is on the right side of the vertex of the lens surface. As in Fig. As shown in Figure 1, the optical axis passes through the center O of the light source 200. Surfaces S1 and S2 are axially symmetrical with respect to the optical axis. The lens 100 of the optical illumination system is described below.

[0019] Fig.Figure 2 illustrates a tangent angle of a lens surface. The tangent angle θ is an angle formed by a tangent line at a lens surface and the direction orthogonal to the optical axis in a cross-section containing the optical axis of lens 100, and is represented by the following expression θ(r)=tan−1dSdr

[0020] Lenses according to the present invention are provided with a diffraction structure on surface S1 or surface S2.

[0021] In general, the following relationship applies between a grid spacing P of a diffraction pattern of a transmission type, an angle of incidence θ. in , a diffraction angle θ out , a diffraction order m, a wavelength λ of a light ray, a refractive index n in a medium on the entry side and a refractive index n out of a medium on the exit side. P⋅(nin⋅sin θin−nout⋅sin θout)=mλ

[0022] The diffraction angle θ out The diffraction of m-th order light can be changed by changing the grid size P.

[0023] The phase function of the diffracted light of the first order of the diffraction structure can be represented by a polynomial of r of even order, as shown below. ϕ(r)=∑i=1Nβ2ir2i Φ (r) represents the phase function, r represents a distance from the central axis, β represents coefficients, and N and i represent natural numbers.

[0024] The following relationship applies with regard to the phase function. dϕ(r)dr=sin θin−sin θout

[0025] Accordingly, a derivative with respect to r of the phase function is proportional to a diffraction angle.

[0026] The shape of the diffraction pattern is described below. It is assumed that a light ray propagating along the optical axis passes through the diffraction pattern. The depth d(r) of the diffraction pattern along the optical axis is represented by the following expression. d(r)=Δ{ϕ(r)−η(r)}2π Δ in expression (4) is represented by the following expression. Δ=λ(n−1) λ represents the wavelength of a light ray at which diffraction efficiency is maximized, and n represents a refractive index of d at the wavelength. n(r) in expression (4) can be represented using a rounding function by the following expression. η(r)=⌊ϕ2π⌋×2π

[0027] The diffraction pattern is provided on a lens surface, and d(r) is corrected according to a position on the lens surface and the angle of incidence of a light ray onto the diffraction pattern. A correction factor for a position on the lens surface can be represented by the following expression, which uses the tangent angle θ. T(r)=1cos θ(r)

[0028] The previously described angle of incidence of a light ray means an angle of incidence of a ray that propagates from the center O of the light source to the surface provided with the diffraction structure. Fig. Figure 1 shows the angle of incidence Π(r) of a light ray on the surface S1, which is provided with the diffraction pattern. The angle of incidence Π(r) of a light ray is represented as a function of r by the following expression. Π(r)=γ1r+∑i=1Nγ2ir2i In expression (7) γ represents coefficients and N and i represent natural numbers.

[0029] A correction factor I(r) for an angle of incidence Π(r) of a light ray is represented by the following expression. I(r)=cosninnoutΠ(r)

[0030] In expression (8) n represents in represents a refractive index of a medium on the entry side and n out represents the refractive index of a medium at the exit side. The term ninnout∏(r) corresponds to the diffraction angle.

[0031] A depth in the direction of the optical axis D(r) of the diffraction structure is represented by the following expression which uses expressions (4), (6) and (8). D(r)=T(r)×l(r)×d(r)

[0032] Fig. Figure 3 is a conceptual representation to illustrate depth in the direction of the optical axis D(r) of the diffraction structure.

[0033] The absolute value of a deflection |Sag (r)| of the bottom of a groove of the diffraction structure is represented by the following expression which uses expressions (1) and (9). |Sag(r)|=|S(r)|−D(r)

[0034] The achromatic feature of the diffraction pattern is described below. The Abbe number of the diffraction pattern is -3.453.

[0035] In a single lens without a diffraction pattern, spherical aberrations are determined by the component of curvature of the lens's spherical surface. In an aberration diagram, the shapes of the curves representing the relationships between spherical aberrations for specific wavelengths and image height are similar. Abbe numbers represent chromatic aberrations that correspond to differences in spherical aberrations for specific wavelengths. Abbe number values ​​for lenses are positive.

[0036] Accordingly, by appropriately combining a lens that has a positive Abbe number and a diffraction structure that has a negative Abbe number, the lens can be achromatized, i.e., differences in spherical aberrations for respective wavelength values ​​can be reduced.

[0037] As previously described, spherical aberrations are determined by the component of curvature of a lens's spherical surface, and in an aberration diagram, the shapes of the curves representing relationships between spherical aberrations for specific wavelengths and image height are similar. Accordingly, to achromatize a lens with a diffraction pattern, the second-order term r of the phase function is typically used, where the term corresponds to the component of curvature of a spherical surface. For example, longitudinal chromatic aberrations can be reduced using the second-order term r.

[0038] However, if the component of a spherical surface curvature corresponding to the second-order term r of the phase function is large, then differences in focal length between diffracted first-order light and absorbed lights of different orders are large, and magnifications of the absorbed lights of different orders change considerably. Typically, in a diffraction structure, the ratio of absorbed lights of different orders to the amount of light of the planned order is several percent, and when magnifications of the absorbed lights differ from those of the planned order, glare and color separation due to the absorbed lights of different orders appear to a degree that is clearly perceptible.

[0039] In the present invention, the second-order coefficient β2 of r of the phase function is made relatively small. More precisely, β2 and β4 are determined such that the following relationship is satisfied, where R represents an effective radius of the lens. |β2|⋅(0.3R)2<|β4|⋅(0.3R)4

[0040] The signs of β4, β6, and β8 preferably include at least one positive sign and at least one negative sign. Furthermore, it is preferred that the sign of β4 is identical to that of β8 and different from that of β6.

[0041] Furthermore, the following relationship should preferably be fulfilled. 0<β62β4β8<5

[0042] In a projection lens for spotlights, for example, correcting chromatic aberrations at a height close to that of the main beam is not as important, while correcting chromatic aberrations against color separation generated at the boundary between an illuminated and an unilluminated area—that is, correcting chromatic aberrations at a position away from the main beam—is more important. Accordingly, even if the second-order term r of the phase function, the term corresponding to the component of curvature of a spherical surface, is made relatively small, a sufficient degree of correction for chromatic aberrations against color separation generated at the boundary between an illuminated and an unilluminated area can be achieved.

[0043] As described above, the first derivative of the phase function dϕ(r)dr proportional to a diffraction angle. Accordingly, the second derivative of the phase function corresponds d2ϕ(r)dr2 to a change in the diffraction angle.

[0044] At an extremum or inflection point of the second derivative of the phase function, the diffraction angle changes drastically. In fact, values ​​of r corresponding to positions of different points on a curve representing a spherical aberration in an aberration diagram essentially coincide with values ​​of r at extrema or inflection points of the second derivative of the phase function. More precisely, near r corresponding to an extremum of the second derivative of the phase function, extrema of spherical aberrations appear for the respective wavelengths, and near r corresponding to an inflection point of the second derivative of the phase function, the absolute values ​​of spherical aberrations for the respective wavelengths are relatively small.

[0045] Accordingly, in order to effectively correct chromatic aberrations at a position away from the main ray, the phase function should preferably be determined such that the second derivative of r of the phase function has at least one extremal value and at least one inflection point in the region where r is greater than 30% or 50% of the effective radius R.

[0046] Furthermore, the phase function should preferably be determined such that in an aberration diagram there is a difference in the spherical aberration between the maximum and minimum values ​​for each value of r. 0≤r≤R equal to or less than the longitudinal chromatic aberration, i.e., the difference in spherical aberration between the maximum and minimum values ​​at r = 0 for each wavelength value of visible light.

[0047] Furthermore, a lens without a diffraction structure should be designed such that the longitudinal chromatic aberration is preferably 2 mm or less and preferably 1.2 mm or less.

[0048] The examples of the present invention are described below. The lenses of the examples are biconvex lenses. The lens thickness along the central axis is 33.0 mm, the lens diameter is 64 mm (the effective radius is 32 mm), and the refractive index of the lenses is 1.4973. Example 1

[0049] The lens of Example 1 is provided with a diffraction structure on the surface S1.

[0050] The surfaces S1 and S2 are represented by the following even function for an aspherical surface. S(r)=cr21+1−(1+k)c2r2+∑i=1Nα2ir2i

[0051] Table 1 shows values ​​of constants and coefficients of expression (1). Table 1 S1 (with diffraction pattern) S2 c 2,60330E-02 -4,84012E-03 k -1,00000E+00 0,00000E+00 α2 0,00000E+00 0,00000E+00 α4 -2,05183E-06 9,75242E-07 α6 3,38505E-09 0,00000E+00 α8 -9,42564E-13 0,00000E+00 α 10 0,00000E+00 0,00000E+00

[0052] The phase function of the diffraction pattern at surface S1 is represented by the following polynomial of even order r. ϕ(r)=∑i=1Nβ2ir2i

[0053] Table 2 shows values ​​of coefficients of expression (3) and values ​​of expression (5). Table 2 Table 2λ 492.3 nm n 1,4973 Δ 989.92 nm β2 0,00000E+00 β4 -1,80613E-02 β6 2,01057E-05 β8 -7,26942E-09 β 10 0,00000E+00

[0054] According to Table 2, β2 equals 0 and the following relationship is satisfied. |β2|⋅(0.3R)2<|β4|⋅(0.3R)4

[0055] Furthermore, the following value can be calculated from Table 2. β62β4β8=3.07886

[0056] Accordingly, the following relationship is fulfilled. 0<β62β4β8<5

[0057] The angle of incidence Π(r) of a light ray on the surface S1 is represented as a function of r by the following expression. ∏(r)=γ1r+∑i=1Nγ2ir2i

[0058] Table 3 shows values ​​of coefficients of expression (7). Table 3 γ1 1,15528434 γ2 -0,015836148 γ4 7,57675E-06 γ6 1,38968E-08 γ8 -1,32952E-11

[0059] Fig. Figure 4 shows a relationship between r and a tangent angle θ at the surface S1, which is provided by the diffraction pattern of the lens from Example 1. The horizontal axis of Fig. 4 indicates a distance r from the optical axis, and the unit is millimeters. The vertical axis of Fig. 4 gives a tangent angle θ, which is represented by expression (2), and the unit is degrees.

[0060] Fig. Figure 5 shows a relationship between r and an angle of incidence Π(r) of a light ray on the surface S1, which is provided by the diffraction pattern of the lens from Example 1. The horizontal axis of Fig. 5 indicates a distance r from the optical axis, and the unit is millimeters. The vertical axis of Fig.5 gives an angle of incidence Π(r) of a light ray, which is represented by expression (7), and the unit is degrees.

[0061] Fig. Figure 6 shows a relationship between a groove number and a grating depth of each groove (depth of a groove) in the diffraction pattern of the lens from Example 1. The groove numbers are assigned sequentially from the optical axis to the periphery of the lens. The horizontal axis of Fig. 6 indicates a groove number. The vertical axis of Fig. 6 indicates the grid depth of each groove, and the unit is micrometers.

[0062] Fig. Figure 7 shows spherical aberrations of the lens, which is provided with the diffraction pattern from Example 1. The horizontal axis of Fig. 7 indicates the position of a focal point along the optical axis, and the unit is millimeters. The vertical axis of Fig.7 indicates an image height, i.e., the height of incident rays parallel to the optical axis with respect to the optical axis, and the unit is millimeters. According to Fig. At 7, the longitudinal chromatic aberration is 1.7 millimeters. Across the entire image height, the difference in spherical aberration between the maximum and minimum values ​​for each wavelength is equal to or less than the value of the longitudinal chromatic aberration. The effective radius R is 32 mm, and in this range rR≥0.3 On the vertical axis, the difference in spherical aberration between the maximum and minimum values ​​for each wavelength is equal to or less than 30% of the value of the longitudinal chromatic aberration.

[0063] Fig. Figure 8 shows a second derivative with respect to r of the phase function from Example 1. The horizontal axis of Fig.8 indicates r and the unit is millimeters. The vertical axis of Fig. 8 gives the second derivative.

[0064] Fig. Figure 9 shows a third derivative with respect to r of the phase function from Example 1. The horizontal axis of Fig. 9 indicates r and the unit is millimeters. The vertical axis of Fig. 9 gives the third derivative.

[0065] Fig. Figure 10 shows a fourth derivative with respect to r of the phase function from Example 1. The horizontal axis of Fig. 10 indicates r and the unit is millimeters. The vertical axis of Fig. 10 gives the fourth derivative.

[0066] According to the Fig. The second derivative of the phase function with respect to r in the range 8-10 exhibits extrema at r = 15 and r = 27 and inflection points at r = 8 and r = 22. The effective radius R is 32 mm, and the second derivative of the phase function with respect to r shows two extrema and one inflection point in this range. rR≥0.3 and exhibits an extremum and an inflection point in the range rR≥0.5 on. Example 2

[0067] The lens of Example 2 is provided with a diffraction structure on surface S2.

[0068] The surfaces S1 and S2 are represented by the following even function for an aspherical surface. S(r)=cr21+1−(1+k)c2r2+∑i=1Nα2ir2i

[0069] Table 4 shows values ​​of constants and coefficients of expression (1). Table 4 S1 S2 (with diffraction pattern) c 3,08729E-02 -5,51711 E-03 k -1,05001 E+00 1,03188E+00 α2 0,00000E+00 0,00000E+00 α4 2,41612E-06 3,20000E-06 α6 4,05612E-11 -1,66000E-09 α8 0,00000E+00 0,00000E+00 α 10 0,00000E+00 0,00000E+00

[0070] The phase function of the diffraction pattern at surface S2 is represented by the following even-order polynomial of r. ϕ(r)=∑i=1Nβ2ir2i

[0071] Table 5 shows values ​​of coefficients of expression (3) and values ​​of expression (5). Table 5 λ 492.3 nm n 1,4973 Δ 989.92 nm β2 0,00000E+00 β4 -2,44001 E-02 β6 5,03007E-05 β8 -5,17006E-08 β 10 2,13000E-11

[0072] According to Table 5, β2 equals 0 and the following relationship is satisfied. |β2|⋅(0.3R)2<|β4|⋅(0.3R)4

[0073] Furthermore, the following value can be calculated from Table 5. β62β4β8=2.00568

[0074] Accordingly, the following relationship is fulfilled. 0<β62β4β8<5

[0075] The angle of incidence Π(r) of a light ray on the surface S2 is represented as a function of r by the following expression. π(r)=γ1r+∑i=1Nγ2ir2i

[0076] Table 6 shows values ​​of coefficients of expression (7). Table 6 γ1 1,208888165 γ2 0,002086964 γ4 -8,94647E-06 γ6 -3,83905E-09 γ8 1,02306E-11

[0077] Fig. Figure 11 shows a relationship between r and a tangent angle θ at the surface S2, which is provided by the diffraction pattern of the lens from Example 2. The horizontal axis of Fig.11 specifies a distance r from the optical axis, and the unit is millimeters. The vertical axis of Fig. 11 gives a tangent angle θ, which is represented by expression (2), and the unit is degrees.

[0078] Fig. Figure 12 shows a relationship between r and an angle of incidence Π(r) of a light ray on the surface S2, which is provided by the diffraction pattern of the lens from Example 2. The horizontal axis of Fig. 12 indicates a distance r from the optical axis, and the unit is millimeters. The vertical axis of Fig. 12 gives an angle of incidence Π(r) of a light ray, which is represented by expression (7), and the unit is degrees.

[0079] Fig.Figure 13 shows a relationship between a groove number and a grating depth of each groove (depth of a groove) in the diffraction pattern of the lens from Example 2. The groove numbers are assigned sequentially from the optical axis to the periphery of the lens. The horizontal axis of Fig. 13 indicates a groove number. The vertical axis of Fig. 13 indicates the grid depth of each groove, and the unit is micrometers.

[0080] Fig. Figure 14 shows spherical aberrations of the lens, which is provided with the diffraction pattern from Example 2. The horizontal axis of Fig. 14 indicates the position of a focal point along the optical axis, and the unit is millimeters. The vertical axis of Fig. 14 specifies an image height, i.e., a height of incident rays parallel to the optical axis with respect to the optical axis, and the unit is millimeters. According to Fig.The longitudinal chromatic aberration is 0.9 mm. Across the entire image height, the difference in spherical aberration between the maximum and minimum values ​​for each wavelength is equal to or less than the value of the longitudinal chromatic aberration. The effective radius R is 32 mm, and in this range rR≥0.3 On the vertical axis, the difference in spherical aberration between the maximum and minimum values ​​for each wavelength is equal to or less than 70% of the value of the longitudinal chromatic aberration.

[0081] Fig. Figure 15 shows a second derivative with respect to r of the phase function from Example 2. The horizontal axis of Fig. 15 indicates r and the unit is millimeters. The vertical axis of Fig. 15 gives the second derivative.

[0082] Fig.Figure 16 shows a third derivative with respect to r of the phase function from Example 2. The horizontal axis of Fig. 16 indicates r and the unit is millimeters. The vertical axis of Fig. 16 gives the third derivative.

[0083] Fig. Figure 17 shows a fourth derivative with respect to r of the phase function from Example 2. The horizontal axis of Fig. 17 indicates r and the unit is millimeters. The vertical axis of Fig. 17 gives the fourth derivative.

[0084] According to the Fig. In the range 15-17, the second derivative with respect to r of the phase function has an extremum at r = 27 and inflection points at r = 11 and r = 23. The effective radius R is 32 mm, and the second derivative with respect to r of the phase function has an extremum and two inflection points in this range. rR≥0.3 and exhibits an extremum and an inflection point in the range rR≥0.5 on. Example 3

[0085] The lens of Example 3 is provided with a diffraction structure on surface S1.

[0086] The surfaces S1 and S2 are represented by the following even function for an aspherical surface. S(r)=cr21+1−(1+k)c2r2+∑i=1Nα2ir2i

[0087] Table 7 shows values ​​of constants and coefficients of expression (1). Table 7 S1 (with diffraction pattern) S2 c 3,31362E-02 -2,27662E-03 k -1,00000E+00 0,00000E+00 α2 0,00000E+00 0,00000E+00 α4 -2,76448E-06 0,00000E+00 α6 9,54570E-09 0,00000E+00 α8 -9,19235E-12 0,00000E+00 α 10 3,26366E-15 0,00000E+00

[0088] The phase function of the diffraction pattern at surface S1 is represented by the following polynomial of even order r. ϕ(r)=∑i=1Nβ2ir2i

[0089] Table 8 shows values ​​of coefficients of expression (3) and values ​​of expression (5). Table 8 λ 492.3 nm n 1,4973 Δ 989.92 nm β2 0,00000E+00 β4 -2,36108E-02 β6 4,45979E-05 β8 -4,13122E-08 β 10 1,41398E-11

[0090] According to Table 8, β2 equals 0 and the following relationship is satisfied. |β2|⋅(0.3R)2<|β4|⋅(0.3R)4

[0091] Furthermore, the following value can be calculated from Table 8. β62β4β8=2.03911

[0092] Accordingly, the following relationship is fulfilled. 0<β62β4β8<5

[0093] The angle of incidence Π(r) of a light ray on the surface S1 is represented as a function of r by the following expression. ∏(r)=γ1r+∑i=1Nγ2ir2i

[0094] Table 9 shows values ​​of coefficients of expression (7). Table 9 γ1 1,34210E+00 γ2 -1,93586E-02 γ4 2,62334E-05 γ6 -3,49328E-08 γ8 1,55802E-11

[0095] Fig. Figure 18 shows a relationship between r and a tangent angle θ at the surface S1, which is provided by the diffraction pattern of the lens from Example 3. The horizontal axis of Fig. 18 indicates a distance r from the optical axis, and the unit is millimeters. The vertical axis of Fig.18 gives a tangent angle θ, which is represented by expression (2), and the unit is degrees.

[0096] Fig. Figure 19 shows a relationship between r and an angle of incidence Π(r) of a light ray on the surface S1, which is provided by the diffraction pattern of the lens from Example 3. The horizontal axis of Fig. 19 indicates a distance r from the optical axis, and the unit is millimeters. The vertical axis of Fig. 19 gives an angle of incidence Π(r) of a light ray, which is represented by expression (7), and the unit is degrees.

[0097] Fig. Figure 20 shows a relationship between a groove number and a grating depth of each groove (depth of a groove) in the diffraction pattern of the lens from Example 3. The groove numbers are assigned sequentially from the optical axis to the periphery of the lens. The horizontal axis of Fig. 20 indicates the groove number. The vertical axis of Fig. 20 indicates the grid depth of each groove, and the unit is micrometers.

[0098] Fig. Figure 21 shows spherical aberrations of the lens, which is provided with the diffraction pattern from Example 3. The horizontal axis of Fig. 21 indicates the position of a focal point along the optical axis, and the unit is millimeters. The vertical axis of Fig. 21 specifies an image height, i.e., a height of incident rays parallel to the optical axis with respect to the optical axis, and the unit is millimeters. According to Fig. At 21, the longitudinal chromatic aberration is 1.3 mm. Across the entire image height, the difference in spherical aberration between the maximum and minimum values ​​for each wavelength is equal to or less than the value of the longitudinal chromatic aberration. The effective radius R is 32 mm, and in this range rR≥0.3 On the vertical axis, the difference in spherical aberration between the maximum and minimum values ​​for each wavelength is equal to or less than 30% of the value of the longitudinal chromatic aberration.

[0099] Fig. Figure 22 shows a second derivative with respect to r of the phase function from Example 3. The horizontal axis of Fig. 22 indicates r and the unit is millimeters. The vertical axis of Fig. 22 gives the second derivative.

[0100] Fig. Figure 23 shows a third derivative with respect to r of the phase function from Example 3. The horizontal axis of Fig. 23 indicates r and the unit is millimeters. The vertical axis of Fig. 23 gives the third derivative.

[0101] Fig. Figure 24 shows a fourth derivative with respect to r of the phase function from Example 3. The horizontal axis of Fig. 24 indicates r and the unit is millimeters. The vertical axis of Fig.24 gives the fourth derivative.

[0102] According to Fig. The second derivative of the phase function with respect to r in the range 22-24 exhibits extrema at r = 14, r = 20, and r = 28, and inflection points at r = 7, r = 18, and r = 25. The effective radius R is 32 mm, and the second derivative of the phase function with respect to r has three extrema and two inflection points in this range. rR≥0.3 and exhibits two extreme values ​​and two inflection points in the range rR≥0.5 on.

[0103] Table 10 shows focal length values ​​for the lenses of examples 1-3. Table 10 Focal length [mm] Example 1 67,5563 Example 2 58,1286 Example 3 58,5073

[0104] Table 11 shows values ​​of an entrance pupil diameter and an exit pupil diameter for the lenses of Examples 1-3, when the light source side of the lens is defined as the image side. Table 11 Entrance pupil diameter Exit pupil diameter Example 1 70.00 mm 72.68 mm Example 2 64.00 mm 67.06 mm Example 3 64.00 mm 65.63 mm

[0105] The light source 200 of the optical illumination system is described below. The light source 200 of the optical illumination system has a surface exhibiting a luminance within a specified range, and the area of ​​the surface should preferably be equal to or greater than 3% of the area of ​​the entrance pupil described above. The surface may be a single gently curved surface. Alternatively, the surface may be a combination of several curved surfaces, a combination of several flat surfaces, or a combination of a single curved surface or several curved surfaces and a single flat surface or several flat surfaces.The surface is arranged such that the distance between the surface and the curved surface, which represents a field curvature when the light source side of the lens is defined as the image side, is equal to or less than 3%, preferably equal to or less than 1%, of the focal length of the lens 100.

[0106] For example, the surface of the light source 200 can be the curved surface representing the field curvature. The intersection point between the curved surface representing the field curvature and the optical axis is the focal point of the lens 100.

[0107] Fig. Figure 25 shows an image field curvature of lens 100 from Example 1, when the light source side of the lens is defined as the image side. The horizontal axis of Fig. 25 specifies a coordinate along the optical axis and the vertical axis of Fig. 25 indicates a distance r from the optical axis. Fig.Figure 25 shows that the thick line represents the image surface formed by sagittal rays of the d-line (wavelength of 587.6 nm), and the thin line represents the image surface formed by tangential rays of the d-line (wavelength of 587.6 nm). The surface containing the midpoints between the two previously described image surfaces is the surface representing the field curvature.

[0108] Fig. Figure 26 shows field curvature when the surface of the light source is oriented along the in Fig. The image field curvature shown in 25 is formed. The horizontal axis of Fig. 26 gives a coordinate along the optical axis and the vertical axis of Fig. 26 indicates a distance r from the optical axis. Fig.Figure 26 shows that the thick line represents the image surface formed by sagittal rays of the d-line (wavelength of 587.6 nm), and the thin line represents the image surface formed by tangential rays of the d-line (wavelength of 587.6 nm). The surface containing the midpoints between the two previously described image surfaces is the surface representing the field curvature.

[0109] Fig. Figure 27 shows an image field curvature of lens 100 from Example 2 when the light source side of the lens is defined as the image side. The horizontal axis of Fig. 27 gives a coordinate along the optical axis and the vertical axis of Fig. 27 indicates a distance r from the optical axis. Fig.Figure 27 shows that the thick line represents the image surface formed by sagittal rays of the d-line (wavelength of 587.6 nm), and the thin line represents the image surface formed by tangential rays of the d-line (wavelength of 587.6 nm). The surface containing the midpoints between the two image surfaces described above is the surface representing the field curvature.

[0110] Fig. 28 shows field curvature when the surface of the light source is oriented along the in Fig. The image field curvature shown in 27 is formed. The horizontal axis of Fig. 28 gives a coordinate along the optical axis and the vertical axis of Fig. 28 indicates a distance r from the optical axis. Fig.Figure 28 shows that the thick line represents the image surface formed by sagittal rays of the d-line (wavelength of 587.6 nm), and the thin line represents the image surface formed by tangential rays of the d-line (wavelength of 587.6 nm). The surface containing the midpoints between the two previously described image surfaces is the surface representing the field curvature.

[0111] Fig. Figure 29 shows an image field curvature of lens 100 from Example 3 when the light source side of the lens is defined as the image side. The horizontal axis of Fig. 29 specifies a coordinate along the optical axis and the vertical axis of Fig. 29 indicates a distance r from the optical axis. Fig.Figure 29 shows the thick line representing the image surface formed by sagittal rays of the d-line (wavelength of 587.6 nm), and the thin line representing the image surface formed by tangential rays of the d-line (wavelength of 587.6 nm). The surface containing the midpoints between the two previously described image surfaces is the surface representing the field curvature.

[0112] Fig. Figure 30 shows field curvature when the surface of the light source is oriented along the in Fig. The image field curvature shown in 29 is formed. The horizontal axis of Fig. 30 specifies a coordinate along the optical axis and the vertical axis of Fig. 30 indicates a distance r from the optical axis. Fig.Figure 30 shows the thick line representing the image surface formed by sagittal rays of the d-line (wavelength of 587.6 nm), and the thin line representing the image surface formed by tangential rays of the d-line (wavelength of 587.6 nm). The surface containing the midpoints between the two previously described image surfaces is the surface representing the field curvature.

[0113] In general, field curvature can hardly be corrected in a single lens. However, by using a light source with a surface that is curved along a surface exhibiting field curvature, the field curvature can be corrected to a very satisfactory degree, as shown in the Fig. 26, Fig. 28 and Fig. 30 shown, will be corrected.

[0114] The luminance of the surface of the light source can be uneven. The luminance of the surface of the light source can be changed depending on the area being illuminated.

[0115] Embodiments of a surface exhibiting luminance within a predetermined range are described below. The surface (curved surface) exhibiting luminance within a predetermined range can be realized using LEDs arranged along a curved surface and covered with a light-diffusing material, such as frosted glass or a flexible illumination panel, as disclosed in JP 2005103768 A, JP 2006114873 A, or the like. The surface (curved surface) exhibiting luminance within a predetermined range can also be realized by an imaging intermediate surface formed by another light source, or by the end surfaces of multiple optical fibers arranged along a curved surface.

[0116] By combining one of the lenses described above and one of the light sources described above, an illumination system can be realized that is provided with a single lens capable of projecting a bright image with corrected chromatic aberrations, reduced glare and high resolution.

Claims

[1] An illumination optical system comprising a light source (200) and a single convex lens (100) provided with a diffraction structure on a surface thereof, the phase function of the diffraction structure being represented by ϕ(r)=∑i=1Nβ2ir2i, where r represents a distance from the central axis of the lens (100), β represents coefficients and N and i represent natural numbers and the relationship |β2|⋅(0.3R)2<|β4|⋅(0.3R)4 is satisfied, where R represents an effective radius of the lens (100), and where the second derivative with respect to r of the phase function has at least one extremal value and at least one inflection point in the range of r in which r is greater than 30% of the effective radius of the lens (100), a difference of a spherical aberration between the maximum value and the minimum value for each r in 0≤r≤R is equal to or less than the longitudinal chromatic aberration for each value of a wavelength of visible light, and the diffraction structure is provided at least partially in the range of r in which r is greater than 30% of the effective radius of the lens (100), and wherein the light source (200) has a surface having a luminance in a predetermined range and the area of the surface of the light source (200) is equal to or greater than 3% of the area of the entrance pupil when the light source side of the lens (100) is defined as the image side. [2] The illumination optical system according to claim 1, wherein the surface of the light source (200) is arranged such that a distance between the surface of the light source (200) and a curved surface representing a field curvature of the lens (100) when the light source side of the lens (100) is defined as the image side is equal to or less than 3% of the focal length of the lens (100). [3] An optical illumination system according to claim 1 or 2, wherein the second derivative with respect to r of the phase function has at least one extremum value and at least one inflection point in the range of r in which r is greater than 50% of the effective radius of the lens (100), and the diffraction structure is at least partially provided on the surface in the range of r in which r is greater than 50% of the effective radius of the lens (100). [4] Optical illumination system according to one of claims 1 to 3, wherein the relationship 0<β62β4β8<5 is fulfilled. [5] An optical illumination system according to any one of claims 1 to 4, wherein β4 and β8 are negative and β6 is positive. [6] An optical illumination system according to any one of claims 1 to 5, wherein a depth of the diffraction structure is corrected as a function of r. [7] An illumination optical system according to any one of claims 1 to 6, wherein the two side surfaces of the lens (100) are convex. [8] An optical illumination system according to any one of claims 1 to 7, wherein the surface of the light source (200) is arranged such that a distance between the surface of the light source (200) and a curved surface representing a field curvature of the lens (100) is equal to or less than 1% of the focal length of the lens (100).

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