JP2006330141A - Optical element, and optical system and electronic apparatus using same - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide an optical element that can effectively prevent degradation in an image by diffracted light, and to provide an optical system and an electronic apparatus using the element. <P>SOLUTION: The optical elements 10, 20 have at least one plane of reflecting planes 12, 22, 23 and a plurality of grooves adjoining to each other at an equal interval on the surface of the reflecting plane, wherein the cross section of the groove or the cross section of a projection between adjacent grooves is an arc and satisfies condition formula (1):0.03≤(n<SB>0</SB>×P<SP>2</SP>)/(R×λ<SB>0</SB>)≤0.17. In the formula, λ<SB>0</SB>represents a reference wavelength in the wavelength region for use; n<SB>0</SB>represents the refractive index of a material constituting the optical element at the reference wavelength; R represents a radius of curvature in the cross section of the groove or the arc cross section of the projection between adjacent grooves; and P represents an interval between adjacent grooves. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to an optical element, an optical system using the optical element, and an electronic apparatus. Here, examples of the optical element include a lens, a prism, and a mirror. And this optical element has optical surfaces, such as a spherical surface, an aspherical surface, or a free-form surface, for example. The optical surface is manufactured by, for example, cutting or using a die processed by cutting. The optical system includes the above-described optical element. This optical element or optical system is built in or externally attached to the electronic apparatus. Examples of the electronic device include a digital camera, a video camera, a digital video unit, a personal computer, a mobile computer, a mobile phone, and an information portable terminal.

  In recent years, portable information terminals and mobile phones called PDAs have become explosive. And among these electronic devices, those incorporating compact digital cameras and digital video units are increasing. In digital cameras and digital video units, CCD (Charge Coupled Device) and CMOS (Complementary Metal Oxide Semiconductor) sensors are used as imaging devices. In such a digital camera or the like, it is necessary to achieve both miniaturization and cost reduction while maintaining high performance of the optical system. As one means for miniaturization, there is a method of using an image sensor having a relatively small effective area of the light receiving surface. Another means for reducing the size is to reduce the size of the optical system.

  As one of small and low cost optical systems, there is an optical system including an optical element using an aspherical surface or a free-form surface. An example of such an optical system is disclosed in Patent Document 1. In general, when mass-producing optical elements including such aspherical surfaces or free-form surfaces, molding is used. In this case, the mold is often manufactured by cutting.

Here, the aspherical surface has an axisymmetric surface shape, and the free-form surface has a surface shape that is not axially symmetric. Therefore, when an aspherical surface is formed by cutting, the workpiece W is rotated and cut with the cutting tool B as schematically shown in FIG. When a free curved surface is formed by cutting, the workpiece W is moved in the same direction as the rotation direction while rotating the cutting tool B as schematically shown in FIG. Alternatively, as shown in FIG. 2B, there is a method of moving the workpiece W in a direction perpendicular to the rotation direction while rotating the tool B. In any case, the shape of the cutting edge T of the cutting tool B is circular.
JP 2002-318366 A Toru Kusagawa and one other translation "Principle of optics II" (Tokai University Press, luminescence, August 20, 1995, 9th printing) 608-622

  However, when cutting is performed as described above, a grind G is formed on the surface of the workpiece W. The grind G is a groove having a circular cross section. The radius of this arc is equal to the radius of curvature of the cutting edge T of the processing machine in the case of FIGS. 1 and 2A. On the other hand, in the case of FIG. 2B, the radius of the arc is equal to the turning radius of the cutting edge T. At this time, the cross-sectional shape of the entire surface of the workpiece W is a shape in which the grooves 51 are regularly (periodically) aligned as shown in FIG. Here, in FIG. 3, R is the radius of curvature of the cutting edge T or the turning radius of the cutting edge T.

  When the workpiece W is an optical element, the optical element W is directly shaved with the cutting tool B. Then, such grooves 51 are periodically formed on the surface of the optical element. When the workpiece W is a mold, grooves 51 are periodically formed on the surface of the mold as shown in FIG. Therefore, when the optical element 60 is molded using the mold, the shape of FIG. 3A is transferred to the surface of the optical element 60. As a result, a groove in which the shape of FIG. 3A is inverted upside down is formed on the surface of the optical element 60 as shown in FIG. That is, the surface shape of the optical element 60 is a shape in which the protrusions are regularly arranged. In addition, in the shape shown in FIG.3 (b), the center part of a projection part is the highest, and a peripheral part is the lowest. Therefore, when a boundary between one protrusion and the protrusion adjacent to the protrusion is considered as a groove, a plurality of grooves are formed also in FIG. And as shown in FIG.3 (b), the space | interval P of an adjacent groove | channel becomes the period of the cross-sectional shape shown in FIG.3 (b).

  When light enters such a surface, diffraction occurs during refraction or reflection. As a result, diffracted light (± first order light) is generated. The traveling direction of the diffracted light is different from the traveling direction of the light beam at the time of design. Therefore, for example, in the imaging optical system, the diffracted light becomes unnecessary light (ghost light or flare light) and enters the image sensor together with normal light (light forming an object image). As a result, the image quality is degraded. In particular, when diffraction occurs on the reflecting surface, even if the grooves 51 and 52 are shallow, the diffraction efficiency tends to be high, which is likely to be a problem.

  The present invention has been made in view of such problems, and an object thereof is to provide an optical element that can effectively prevent image degradation due to diffracted light, an optical system using the optical element, and an electronic apparatus. is there.

  The optical element of the present invention that achieves the above object is an optical element including at least one reflecting surface, and the reflecting surface has a plurality of grooves formed in a predetermined period on the surface, The cross section in each of the grooves is substantially arc-shaped, and satisfies the following conditional expression.

0.03 ≦ (n ₀ × P ² ) / (R × λ ₀ ) ≦ 0.17 (1)
Where λ ₀ is a reference wavelength within a wavelength range in which the optical element is used,
n ₀ : refractive index at the reference wavelength of the material constituting the optical element,
R: radius of curvature of the arc,
P: the predetermined period;
It is.

  The optical element of the present invention is characterized in that the optical element is a prism having at least one optical surface made of a free-form surface.

  The optical system of the present invention is characterized by having the optical element described above.

  In addition, an electronic apparatus according to the present invention includes the above-described optical element or the above-described optical system.

  According to the present invention as described above, even if grooves having substantially equal intervals exist on the reflection surface of the optical element, the intensity of the diffracted light generated by these grooves can be made weaker than the zero-order light. Therefore, it is possible to realize an optical element, an optical system, and an electronic device that can effectively prevent image deterioration due to diffracted light.

    An embodiment of the present invention will be described. The optical element of this embodiment is an optical element including at least one reflecting surface. This reflecting surface has a plurality of grooves formed on the surface thereof at a predetermined cycle. Further, the cross section in each of the plurality of grooves is substantially arcuate. And the following conditional expressions are satisfied.

0.03 ≦ (n ₀ × P ² ) / (R × λ ₀ ) ≦ 0.17 (1)
Where λ ₀ is a reference wavelength within a wavelength range in which the optical element is used,
n ₀ : refractive index at the reference wavelength of the material constituting the optical element,
R: radius of curvature of the arc,
P: the predetermined period;
It is.

    The reason why the above configuration is adopted in the optical element of this embodiment will be described below.

It is assumed that an arcuate groove 51 as shown in FIG. 3A is formed on the reflecting surface. In this case, the depth of the groove 51 is about P ² / 8R. It is assumed that a plurality of such grooves 51 are periodically formed. Then, as shown in FIG. 4, most of the light L _i incident from the medium side of the optical element W is specularly reflected as _0th-order diffracted light L ₀ . However, diffracted light L ₊₁ , L _{−1 and the} like are generated other than the 0th order. The diffracted light L ₊₁ , L _−1, etc. travels in a different direction from the _0th-order diffracted light L ₀ . When the 0th-order light is designed light, diffracted light L _{+ 1} , L- _{1 and the} like travel in a different direction from the designed light. The diffraction efficiency is determined by the relationship between the depth of the groove 51, the wavelength of light, and the refractive index of the medium at that wavelength. In the case where the groove 51 is a cut line by cutting, the depth of the groove 51 becomes very shallow. Therefore, except for the 0th-order diffracted light L ₀ , the diffraction efficiency of the 1st-order diffracted light L ₊₁ (+ 1st order) and L ₋₁ (−1st order) is the highest among the diffracted lights. The first-order diffracted lights L ₊₁ and L ₋₁ are originally unnecessary light. Therefore, the presence of the first-order diffracted lights L _{+ 1} and L- ₁ becomes a problem. For example, assume that an image of an object is formed using such a reflective surface. In this case, in addition to the original image (image formed by the _0th-order diffracted light L ₀ ), an image of unnecessary light (image formed by the 1st-order diffracted light L ₊₁ and L ₋₁ ) is formed. The image due to unnecessary light is called a ghost image or flare image, and degrades the image (image quality when captured).

Therefore, it is desirable that the reflecting surface be a surface having a high diffraction efficiency of the _0th- order diffracted light _L0 and a low diffraction efficiency of the 1st-order diffracted light L _{+ 1} , L- ₁ . The diffraction efficiencies of the first-order diffracted lights L ₊₁ and L ₋₁ are that the 0th-order diffracted light L decreases as the depth of the groove 51 decreases, the wavelength of incident light increases, and the refractive index of the optical element W decreases. Relative to ₀ diffraction efficiency. That is, as the value of (n ₀ × P ² ) / (R × λ ₀ ) decreases, the diffraction efficiency of the first-order diffracted light decreases. In this way, the influence of the first-order diffracted beams L _{+ 1} and L- ₁ on the image quality is reduced.

Further, it is assumed that the groove 52 having a shape as shown in FIG. 3B is formed on the reflection surface. In this case, the depth of the groove is about P ² / 8R. The relationship between the diffraction efficiency, the groove depth, the wavelength of light, and the refractive index of the medium at that wavelength is the same as in the case of FIG. That is, the smaller the value of (n ₀ × P ² ) / (R × λ ₀ ), the lower the diffraction efficiency of the first-order diffracted lights L ₊₁ and L ₋₁ .

Hereinafter, the fact that the intensity of the first-order diffracted light is proportional to (n ₀ × P ² ) / (R × λ ₀ ) will be described with reference to the description of Non-Patent Document 1.

  Consider a one-dimensional diffraction grating having N grooves of arbitrary shape. In this one-dimensional diffraction grating, the intensity I (x) of the diffracted light is as follows when Equation (5) on page 611 of Non-Patent Document 1 is applied.

I (x) = {(1-cosNkP′x) / (1-cosP′x)} × I ⁽⁰⁾ (x) (2)
Here, P ′: period in the ξ direction of the lattice (d in Non-Patent Document 1),
x: x coordinate of point P in the diffraction image (p in Non-Patent Document 1),
I ⁽⁰⁾ (x): intensity of diffracted light by a grating of one period,
It is.

Function of formula (6) on page 611 of Non-Patent Document 1:
H (N, x) = (sinNx / sinx) ² (3)
When equation (2) is introduced,
I (x) = {sinN (kP′x / 2) / sin (kP′x / 2)} ²
× I ⁽⁰⁾ (x)
= H (N, kP′x / 2) I ⁽⁰⁾ (x) (4)
It becomes. Here, the function H (N, kP′x / 2) is
kP′x / 2 = mπ (m: integer) (5)
Is a function that has a maximum value N ² .

  FIG. 5 shows a function H (N, mπ) where N is 10.

  That is, the intensity I (m) of the m-th order diffracted light depends on kP′x / 2, and becomes stronger as kP′x / 2 approaches m.

Here, consider the lattice of FIG. The groove depth d is
d = R−√ {R ² − (P / 2) ² } = R−R {1−P ² / (4R ² )} ^1/2
It is. Since P ² / (4R ² ) << 1, the groove depth d is as follows.

d≈R−R {1−P ² / (8R ² )} = P ² / 8R (6)
This result is the same for the lattice of FIG.

The condition that the intensity of the m-th order reflected diffracted light becomes maximum is the wavelength λ ₀ and the refractive index of the grating is n ₀ .
2dn ₀ / λ ₀ = m (7)
It is. Therefore, substituting equation (6), m is
m = n ₀ P ² / 4Rλ ₀ (8)
It can be expressed.

Therefore, in the structure of FIG. 3, H (N, kPx / 2) can be expressed as H (N, n ₀ P ² π / 4Rλ ₀ ). The intensity of the m-th order diffracted light depends on the value of n ₀ P ² / Rλ ₀ ,
n ₀ P ² / Rλ ₀ = 4 m
It becomes maximum at the time. P ′ is replaced with P.

Here, the specularly reflected light is zero-order diffracted light. Therefore, the intensity of the specularly reflected light is increased when m approaches 0 (FIG. 5), that is, when (n ₀ × P ² ) / (R × λ ₀ ) approaches 0. At this time, the intensity of the first-order diffracted light is reduced and the diffraction efficiency is also lowered.

As described above, it has been clarified that the intensities of the first-order diffracted beams L ₊₁ and L ₋₁ are proportional to (n ₀ × P ² ) / (R × λ ₀ ).

Here, when the incident light has a width in the wavelength range such as white light, the wavelength λ ₀ may be considered as a certain reference wavelength. For example, the following can be considered as the reference wavelength.

  1) The wavelength at which the light intensity becomes maximum in the emission spectrum characteristics of the light source used.

  2) The wavelength at which the transmittance (reflectance) is maximum in the spectral transmittance characteristic or spectral reflectance characteristic of the optical system.

  3) The wavelength at which the transmittance (reflectance) is maximum in the spectral transmittance characteristic or spectral reflectance characteristic of the wavelength filter.

  4) The wavelength at which the sensitivity becomes maximum in the photoelectric converter (sensor) spectral sensitivity characteristic.

  5) The wavelength at which the relative visibility is highest in the human eye.

  6) The central wavelength in the wavelength range involved in imaging.

  7) Among the characteristics obtained from at least two of the above characteristics 1) to 4) (emission spectrum characteristics, spectral transmittance characteristics, spectral reflectance characteristics, spectral sensitivity characteristics), wavelength.

  8) The wavelength at which the transmittance or reflectance is maximized in the spectral transmittance characteristic or spectral reflectance characteristic of the RGB filter.

  The selection criteria for the reference wavelength are not limited to the above 1) to 8). That is, an optimum reference wavelength may be selected according to the purpose of using the optical system, the usage environment, the sensitivity of the sensor, and the like. Therefore, any wavelength may be used.

  When the conditional expression (1) is satisfied, the diffraction efficiency of ± 1st order diffracted light is about 0.3% or less, and the intensity of ± 1st order diffracted light becomes very weak. Therefore, image quality deterioration due to unnecessary diffracted light can be prevented. When the upper limit of 0.17 in conditional expression (1) is exceeded, the diffraction efficiency of ± 1st order diffracted light becomes higher than that of regular reflection 0th order diffracted light. As a result, image quality degradation due to ± first-order diffracted light occurs. On the other hand, if the lower limit of 0.03 is not reached, the refractive index becomes too small. Therefore, there is no material that can be used for the optical element W. Or the space | interval of a groove | channel becomes too narrow and processing is substantially difficult. In addition, the fact that the gap between the grooves is narrow means that the pitch of the tool movement during processing is narrow. Therefore, it takes a very long time to process a large area.

  Moreover, when the following conditional expression (1-2) is satisfied, the intensity of ± first-order diffracted light becomes weaker, which is more preferable.

0.05 ≦ (n ₀ × P ² ) / (R × λ ₀ ) ≦ 0.14 (1-1)
Moreover, when the following conditional expression (1-3) is satisfied, the intensity of the ± first-order diffracted light is further decreased, which is more preferable.

0.07 ≦ (n ₀ × P ² ) / (R × λ ₀ ) ≦ 0.099 (1-2)
As an optical element of this embodiment, for example, there is a prism having at least one optical surface composed of a free-form surface.

  Here, the free-form surface is defined by the following equation (a). Note that the Z axis of this defining formula is the axis of the free-form surface.

₆₆
Z = cr ² / [1 + √ {1− (1 + k) c ² r ² }] + ΣC _j X ^m Y ^{n
j = 2}
... (a)
Here, the first term of the equation (a) is a spherical term, and the second term is a free-form surface term.

In the spherical term,
c: curvature of vertex k: conic constant (conical constant)
r = √ (X ² + Y ² )
It is.

  The free-form surface term can be expanded as shown in the following equation (b).

∞
ΣC _j X ^m Y ^{n
j = 2}
= C ₂ X + C ₃ Y
+ C ₄ X ² + C ₅ XY + C ₆ Y ²
+ C ₇ X ³ + C ₈ X ² Y + C ₉ XY ² + C ₁₀ Y ³
+ C ₁₁ X ⁴ + C ₁₂ X ³ Y + C ₁₃ X ² Y ² + C ₁₄ XY ³ + C ₁₅ Y ⁴
+ C ₁₆ X ⁵ + C ₁₇ X ⁴ Y + C ₁₈ X ³ Y ² + C ₁₉ X ² Y ³ + C ₂₀ XY ⁴
+ C ₂₁ Y ⁵
+ C ₂₂ X ⁶ + C ₂₃ X ⁵ Y + C ₂₄ X ⁴ Y ² + C ₂₅ X ³ Y ³ + C ₂₆ X ² Y ⁴
+ C ₂₇ XY ⁵ + C ₂₈ Y ⁶
+ C ₂₉ X ⁷ + C ₃₀ X ⁶ Y + C ₃₁ X ⁵ Y ² + C ₃₂ X ⁴ Y ³ + C ₃₃ X ³ Y ⁴
+ C ₃₄ X ² Y ⁵ + C ₃₅ XY ⁶ + C ₃₆ Y ⁷
・ ・ ・ ・ ・ ・
... (b)
However, C _j (j is an integer of 2 or more) is a coefficient.

The free-form surface generally does not have a symmetric surface in both the XZ plane and the YZ plane, but the coefficients of odd-order terms of X, that is, C ₂ , C ₅ , C ₇ , C ₉ , By setting all of C ₁₂ , C ₁₄ , C ₁₆ , C ₁₈ , C ₂₀ , C ₂₃ , C ₂₅ , C ₂₇ , C ₂₉ , C ₃₁ , C ₃₃ , C _35. Is a free-form surface having only one plane of symmetry parallel to the. Further, coefficients of odd-order terms of Y, that is, C ₃ , C ₅ , C ₈ , C ₁₀ , C ₁₂ , C ₁₄ , C ₁₇ , C ₁₉ , C ₂₁ , C ₂₃ , C ₂₅ , C ₂₇ , C ₃₀ , By setting all of C ₃₂ , C ₃₄ , C ₃₆ ... To 0, a free-form surface having only one symmetry plane parallel to the XZ plane is obtained.

  A prism having such a free-form surface as an optical surface (reflecting surface, refracting surface) (hereinafter referred to as a free-form surface prism) has a higher degree of design freedom than an optical system having only an axisymmetric surface. A performance optical system can be constructed. In addition, the optical path can be bent by reflecting in the prism, which is advantageous in terms of miniaturization.

  Further, the optical system can be configured to have the optical elements as described above.

  That is, since the optical system includes an optical element that satisfies the conditional expression (1), the light intensity of unnecessary diffracted light can be suppressed to a low level even if diffraction occurs on the reflection surface of the optical element. Therefore, image deterioration can be effectively prevented, and a high-quality image can be obtained by such an optical system.

  The optical system may include at least one optical element using an organic-inorganic composite material as an optical material.

  When an organic-inorganic composite material is used as the optical material of the optical element, various optical properties (refractive index, wavelength dispersion) are exhibited depending on the type and abundance ratio of the organic component and the inorganic component (obtained). ). Thus, an optical material having desired optical characteristics or high optical characteristics can be realized by blending an organic component and an inorganic component in an arbitrary ratio. Thereby, since an optical element with high performance can be obtained, various aberrations can be corrected with a smaller number of sheets. Therefore, the optical system can be reduced in cost and size.

  Examples of organic / inorganic composites include zirconia nanoparticles, zirconia and alumina nanoparticles, niobium oxide nanoparticles, zirconium alkoxide hydrolysates and alumina nanoparticles, etc. There is.

  The nanoparticles of these materials are examples of inorganic components. Then, by dispersing such nanoparticles in an organic component plastic at a predetermined abundance ratio, various optical characteristics (refractive index, wavelength dispersibility) can be expressed.

  Further, the electronic device may be configured so that the optical element or the optical system as described above is included.

  Subsequently, Numerical Example 1 of an imaging optical system including the optical element (an imaging device is configured by arranging an imaging element on an image plane) will be described. Based on the optical system of Numerical Example 1, means for reducing diffracted light will be described in order.

  FIG. 6 shows an optical path diagram in the meridional section for this example. Here, the imaging optical system of the present invention includes a front group, a stop, and a rear group in the order in which light passes from the object side. A cover glass 30 and a first prism 10 are arranged in the front group before the stop 2. A second prism 20 and a cover glass 40 are disposed in the rear group after the stop 2. Here, the cover glass 30 consists of a plane in which the front surface 31 and the rear surface 32 are parallel. Moreover, the cover glass 40 consists of a plane in which the front surface 41 and the rear surface 42 are parallel. And immediately after the cover glass 40, the image pick-up element (image surface) 3 is located. In this embodiment, the axial principal ray 1 incident on the image sensor 3 and the axial principal ray 1 in the object space are parallel and in the same direction.

  The first prism 10 includes a first surface 11 to a third surface 13. The first surface 11 is an incident surface, the second surface 12 is a reflecting surface, and the third surface 13 is an exit surface. Light rays from the object pass through the incident surface 11, are internally reflected by the reflecting surface 12, and pass through the exit surface 13. Further, the second prism 20 is composed of a first surface 21 to a fourth surface 24. The first surface 21 is an incident surface, the second surface 22 is a first reflecting surface, the third surface 23 is a second reflecting surface, and the fourth surface 24 is an emitting surface. The light beam that has passed through the diaphragm 2 from the first prism 10 is transmitted through the incident surface 21, is internally reflected by the first reflecting surface 22, is internally reflected by the second reflecting surface 23, and is transmitted through the exit surface 24. The transmitted light forms an image on the imaging surface of the image sensor 3.

  In this imaging optical system, the diaphragm 2 functions as an aperture diaphragm. The imaging optical system is an optical system that does not form an intermediate image. Further, the first surface 21 and the second surface 22 of the second prism 20 are disposed to face each other with the prism medium interposed therebetween, and the third surface 23 and the fourth surface 24 are disposed to face each other with the prism medium interposed therebetween. Therefore, in the second prism 20, the optical path connecting the first surface 21 and the second surface 22 intersects the optical path connecting the third surface 23 and the fourth surface 24 in the prism. Note that the first surface 11 to the third surface 13 of the first prism 10 and the first surface 21 to the fourth surface 24 of the second prism 20 all have the plane (YZ plane) in FIG. It consists of a free-form surface. Therefore, the entire optical system is also an optical system that is plane-symmetric with respect to the meridional section in FIG.

  The configuration parameters of the above embodiment are shown below. The surface number is the surface number of the forward ray tracing from the object through the front group of the optical system, through the diaphragm 2, and through the rear group to the imaging surface of the image sensor 3. It is shown as Regarding how to take the coordinates, as shown in FIG. 6, the axial principal ray 1 is defined as a ray from the center of the stop 2 to the center of the image sensor 3. The axial principal ray 1 on the object side of the first surface 31 of the cover glass 30 is defined as the Z axis, the direction orthogonal to the Z axis and the direction in the meridional section is defined as the Y axis direction, and the Z axis A direction perpendicular to the direction of the Y axis and perpendicular to the direction of the Y axis is defined as the direction of the X axis. The intersection of the surface 31 of the cover glass 30 and the Z axis is the origin of this coordinate system. The direction from the cover glass 30 toward the first prism 10 is the positive direction of the Z axis, the direction of the Y axis toward the image sensor 3 is the positive direction of the Y axis, and the Y axis, the Z axis, and the X axis constituting the right-handed system Are defined as the positive direction of the X axis. This coordinate system is called a global coordinate system.

  Apart from this, a coordinate system (local coordinate system) that defines a surface shape for each surface is considered. Place the origin at the top of each surface and set the YZ plane in the meridional section.

  The free-form surface used in this embodiment is defined by the above equation (a) with respect to the local coordinate system. Note that the Z axis of the defining formula is the axis of the free-form surface.

  For the eccentric surface, from the origin of the corresponding global coordinate system, the amount of eccentricity of the surface top position of the surface (X-axis direction, Y-axis direction, Z-axis direction respectively X, Y, Z) and its surface And the inclination angles (α, β, γ (°), respectively) about the X axis, the Y axis, and the Z axis of the equation (a) for the free-form surface are given. ing. In this case, positive α and β mean counterclockwise rotation with respect to the positive direction of each axis, and positive γ means clockwise rotation with respect to the positive direction of the Z axis. Note that the α, β, and γ rotations of the central axis of the surface are performed by first rotating the central axis of the surface and its XYZ orthogonal coordinate system by α counterclockwise around the X axis, and then rotating the rotation. The center axis of the surface is rotated β counterclockwise around the Y axis of the new coordinate system, and the coordinate system rotated once is also rotated β counterclockwise around the Y axis and then rotated twice. The center axis of the surface is rotated γ clockwise around the Z axis of the new coordinate system.

  In addition, when a specific surface and subsequent surfaces of the optical working surface constituting the optical system constitute a coaxial optical system, a surface interval is given, and in addition, the refractive index of the medium and the Abbe number are It is given according to common usage.

  In addition, there is a Zernike polynomial as another defining formula of the free-form surface. The shape of this surface is defined by the following equation (c). The Z axis of the defining formula (c) is the axis of the Zernike polynomial. The definition of the rotationally asymmetric surface is defined by polar coordinates of the height of the Z axis relative to the XY plane, R is the distance from the Z axis in the XY plane, A is the azimuth around the Z axis, and the X axis It is expressed by the rotation angle measured from.

x = R × cos (A)
y = R × sin (A)
Z = D ₂
+ D ₃ Rcos (A) + D ₄ Rsin (A)
+ D ₅ R ² cos (2A) + D ₆ (R ² −1) + D ₇ R ² sin (2A)
+ D ₈ R ³ cos (3A) + D ₉ (3R ³ −2R) cos (A)
+ D ₁₀ (3R ³ -2R) sin (A) + D ₁₁ R ³ sin (3A)
+ D ₁₂ Recos (4A) + D ₁₃ (4R ⁴ -3R ² ) cos (2A)
+ D ₁₄ (6R ⁴ -6R ² +1) + D ₁₅ (4R ⁴ -3R ² ) sin (2A)
+ D ₁₆ R ⁴ sin (4A)
+ D ₁₇ R ⁵ cos (5A) + D ₁₈ (5R ⁵ -4R ³ ) cos (3A)
+ D ₁₉ (10R ⁵ -12R ³ + 3R) cos (A)
+ D ₂₀ (10R ⁵ -12R ³ + 3R) sin (A)
^{_{+ D 21 (5R 5 -4R 3}} ) sin (3A) + D 22 R 5 sin (5A)
+ D ₂₃ Rocos (6A) + D ₂₄ (6R ⁶ -5R ⁴ ) cos (4A)
+ D ₂₅ (15R ⁶ -20R ⁴ + 6R ² ) cos (2A)
+ D ₂₆ (20R ⁶ -30R ⁴ + 12R ² -1)
+ D ₂₇ (15R ⁶ -20R ⁴ + 6R ² ) sin (2A)
+ D ₂₈ (6R ⁶ -5R ⁴ ) sin (4A) + D ₂₉ Rosin (6A)
... (c)
However, _Dm (m is an integer greater than or equal to 2) is a coefficient.

  The numerical data of Numerical Example 1 is shown below. In these tables, “FFS” indicates a free-form surface, and “RE” indicates a reflective surface.

Numerical example 1
Size of entrance pupil system Φ1.3mm
Image size Width 3.6mm Height 2.7mm
Half angle of view X direction 26.06 ° Y direction 20.15 °
Focal length 3.68mm F-number 2.8
Surface number Curvature radius Surface spacing Eccentricity Refractive index Abbe number Object surface ∞ ∞
1 ∞ Eccentricity (1) 1.4950 65.0
2 ∞ Eccentricity (2)
3 FFS [1] Eccentricity (3) 1.6069 27.0
4 FFS [2] (RE) Eccentricity (4) 1.6069 27.0
5 FFS [3] Eccentricity (5)
6 ∞ (diaphragm surface) Eccentricity (6)
7 FFS [4] Eccentricity (7) 1.5256 56.4
8 FFS [5] (RE) Eccentricity (8) 1.5256 56.4
9 FFS [6] (RE) Eccentricity (9) 1.5256 56.4
10 FFS [7] Eccentricity (10)
11 ∞ Eccentricity (11) 1.5163 64.1
12 ∞ Eccentricity (12)
Image plane ∞ Eccentricity (13)
FFS [1]
C ₄ 4.1709 × 10 ^-2 C ₆ 6.5908 × 10 ^-2 C ₈ -1.0688 × 10 ^-4
C ₁₀ -1.1246 × 10 ^-3 C ₁₁ 6.6599 × 10 ^-4 C ₁₃ 1.6298 × 10 ^-3
C ₁₅ 7.4708 × 10 ^-4 C ₁₇ -2.9507 × 10 ^-5 C ₁₉ 9.7169 × 10 ^-5
C ₂₁ -1.7566 × 10 ^-4 C ₂₂ -2.5840 × 10 ^-6 C ₂₄ 5.7315 × 10 ^-5
C ₂₆ -3.4271 × 10 ^-5 C ₂₈ 3.0860 × 10 ^-5
FFS [2]
C ₄ -3.9587 × 10 ^-3 C ₆ 2.7654 × 10 ^-2 C ₈ -1.0723 × 10 ^-3
C ₁₀ 1.9555 × 10 ^-3 C ₁₁ 7.7516 × 10 ^-5 C ₁₃ -1.7029 × 10 ^-4
C ₁₅ 3.4007 × 10 ^-4 C ₁₇ -3.4680 × 10 ^-5 C ₁₉ 1.0476 × 10 ^-4
C ₂₁ 4.8180 × 10 ^-6 C ₂₂ -6.2801 × 10 ^-6 C ₂₄ -4.7571 × 10 ^-7
C ₂₆ 1.6082 × 10 ^-5 C ₂₈ -8.1118 × 10 ^-6
FFS [3]
C ₃ -3.3425 × 10 ^-2 C ₄ -7.8403 × 10 ^-2 C ₆ -4.0695 × 10 ^-2
C ₈ -8.8984 × 10 ^-3 C ₁₀ 6.2496 × 10 ^-3 C ₁₁ -1.5720 × 10 ^-3
C ₁₃ -2.7166 × 10 ^-2 C ₁₅ 1.4357 × 10 ^-3 C ₁₇ -6.5515 × 10 ^-4
C ₁₉ 3.6911 × 10 ^-4 C ₂₁ -2.1928 × 10 ^-4 C ₂₂ 1.8341 × 10 ^-3
C ₂₄ -3.0393 × 10 ^-3 C ₂₆ 2.0951 × 10 ^-3 C ₂₈ -6.7649 × 10 ^-4
FFS [4]
C ₃ -2.8391 × 10 ^-2 C ₄ 1.2123 × 10 ^-1 C ₆ -8.3113 × 10 ^-2
C ₈ 7.8309 × 10 ^-3 C ₁₀ 2.1910 × 10 ^-3 C ₁₁ 6.5 905 × 10 ^-3
C ₁₃ -1.7892 × 10 ^-2 C ₁₅ 1.5127 × 10 ^-3 C ₁₇ -6.7547 × 10 ^-4
C ₁₉ 4.3224 × 10 ^-4 C ₂₁ -8.3463 × 10 ^-5 C ₂₂ -2.3991 × 10 ^-4
C ₂₄ -8.1334 × 10 ^-3 C ₂₆ 7.9144 × 10 ^-4 C ₂₈ -4.9662 × 10 ^-4
FFS [5]
C ₄ 3.8550 × 10 ^-2 C ₆ 4.1924 × 10 ^-2 C ₈ 1.7538 × 10 ^-3
C ₁₀ -3.9045 × 10 ^-4 C ₁₁ 8.7475 × 10 ^-5 C ₁₃ 6.4778 × 10 ^-4
C ₁₅ 1.7386 × 10 ^-4 C ₁₇ -1.0376 × 10 ^-5 C ₁₉ -1.6202 × 10 ^-6
C ₂₁ -1.7314 × 10 ^-5 C ₂₂ -2.3351 × 10 ^-7 C ₂₄ 1.1257 × 10 ^-5
C ₂₆ -9.6773 × 10 ^-6 C ₂₈ -9.8518 × 10 ^-6
FFS [6]
C ₄ -2.4098 × 10 ^-2 C ₆ 1.1095 × 10 ^-2 C ₈ 2.5243 × 10 ^-4
C ₁₀ 8.0683 × 10 ^-5 C ₁₁ -1.0086 × 10 ^-4 C ₁₃ 8.3763 × 10 ^-4
C ₁₅ 3.5919 × 10 ^-4 C ₁₇ -6.6515 × 10 ^-5 C ₁₉ 5.2149 × 10 ^-5
C ₂₁ 6.6212 × 10 ^-5 C ₂₂ 4.1040 × 10 ^-7 C ₂₄ 4.0895 × 10 ^-6
C ₂₆ -6.4842 × 10 ^-6 C ₂₈ -9.8152 × 10 ^-6
FFS [7]
C ₃ 4.8640 × 10 ^-2 C ₄ 3.7051 × 10 ^-2 C ₆ 6.3083 × 10 ^-2
C ₈ 1.4429 × 10 ^-3 C ₁₀ 2.1610 × 10 ^-4 C ₁₁ -8.4235 × 10 ^-3
C ₁₃ -8.8574 × 10 ^-3 C ₁₅ -4.6112 × 10 ^-3 C ₁₇ -4.4861 × 10 ^-4
C ₁₉ 5.3081 × 10 ^-4 C ₂₁ 1.1103 × 10 ^-3 C ₂₂ 4.3529 × 10 ^-4
C ₂₄ 5.0879 × 10 ^-4 C ₂₆ 1.0880 × 10 ^-3 C ₂₈ -1.2467 × 10 ^-4
Eccentricity (1)
X 0.00 Y 0.00 Z 0.00
α 0.00 β 0.00 γ 0.00
Eccentricity (2)
X 0.00 Y 0.00 Z 0.50
α 0.00 β 0.00 γ 0.00
Eccentricity (3)
X 0.00 Y -0.00 Z 0.64
α -0.95 β 0.00 γ 0.00
Eccentricity (4)
X 0.00 Y -0.02 Z 3.34
α -41.75 β 0.00 γ 0.00
Eccentricity (5)
X 0.00 Y 2.63 Z 3.02
α -83.86 β 0.00 γ 0.00
Eccentricity (6)
X 0.00 Y 3.21 Z 2.96
α -83.86 β 0.00 γ 0.00
Eccentricity (7)
X 0.00 Y 3.39 Z 2.94
α -83.86 β 0.00 γ 0.00
Eccentricity (8)
X 0.00 Y 7.89 Z 2.41
α -101.29 β 0.00 γ 0.00
Eccentric (9)
X 0.00 Y 5.44 Z 1.03
α -150.09 β 0.00 γ 0.00
Eccentric (10)
X 0.00 Y 5.38 Z 4.48
α -180.00 β 0.00 γ 0.00
Eccentric (11)
X 0.00 Y 5.38 Z 4.79
α 0.00 β 0.00 γ 0.00
Eccentric (12)
X 0.00 Y 5.38 Z 5.09
α 0.00 β 0.00 γ 0.00
Eccentric (13)
X 0.00 Y 5.38 Z 5.72
α 0.00 β 0.00 γ 0.00.

[Example 1]
Surface numbers 7 to 10 of the numerical example 1 represent the prism of the first example. This prism is a prism having four free-form surfaces. An example in which this prism is incorporated in an optical system is shown in FIG. FIG. 6 is an example of an imaging apparatus, and includes two prisms. In FIG. 6, the second prism 20 is the prism of the first embodiment. In the second prism 20, light enters from the 21st surface. The incident light reaches the second surface 22. An aluminum coat is applied to the second surface 22 and the third surface 23. Therefore, the second surface 22 reflects the light incident from the first surface 21. The light reflected by the second surface 22 enters the third surface 23 and is reflected here. The light reflected by the third surface is emitted from the fourth surface 24. The material of the prism 20 is ZEONEX480R (manufactured by Nippon Zeon Co., Ltd.).

  The second prism 20 is manufactured by directly cutting an optical material with a cutting machine. Therefore, a plurality of grooves are periodically formed on any of the four surfaces as shown in FIG. Here, the second surface 22 and the third surface 23 are reflecting surfaces. Therefore, the generation of diffracted light on these two surfaces becomes a problem.

At this time, the cross-sectional shape of the groove is substantially arcuate (convex toward the optical element W), and the radius of curvature R of the arc is 3.5 mm. The interval (period) P between adjacent grooves is 0.01 mm. This second prism 20 is used in an optical system as shown in FIG. This optical system is assumed to be used in a wavelength range of 400 to 700 nm. Further, it is assumed that a CCD is used as the image sensor 3. Here, the RGB color filter is provided in the CCD. Therefore, for example, spectral sensitivity characteristics as shown in FIG. 7 are obtained from the spectral transmittance distribution of the RGB color filter and the spectral sensitivity of the CCD. In the case of FIG. 7, the transmittance is highest in the graph indicated by G. Therefore, from FIG. 7, the reference wavelength λ ₀ is 530 nm. The refractive index n _{0 at} the reference wavelength λ ₀ = 530 nm is 1.52881. The spectral transmittance of the first prism 10 and the second prism 20 is substantially constant in the wavelength range of 400 to 700 nm.

At this time, the value of (n ₀ × P ² ) / (R × λ ₀ ) is 0.082. Further, the regular reflection light on the second surface 22 and the third surface 23, that is, the diffraction efficiency of _0th -order diffracted light is 99.85%, and the diffraction efficiency of ± 1st-order diffracted light is 0.07% (λ ₀ = 530 nm). . Thus, the intensity of ± 1st order diffracted light that causes image quality degradation is sufficiently weaker than 0th order diffracted light. Therefore, even if an optical system is configured using the second prism 20 and a subject is imaged using the optical system, an image without image quality deterioration due to diffraction can be obtained. The diffraction efficiency of ± 1st order diffracted light in this example is shown in FIG. Here, the wavelength range is 400 to 700 nm.

[Example 2]
Surface numbers 3 to 5 of the numerical example 1 represent the prisms of the example 2. This prism is a prism having three free-form surfaces. An example in which this prism is incorporated in an optical system is shown in FIG. In FIG. 6, the first prism 10 is the prism of the second embodiment. In the first prism 10, light enters from the first surface 11. The incident light reaches the second surface 12. The second surface 12 is provided with an aluminum coat. Therefore, the second surface 12 reflects the light incident from the first surface 11. The light reflected by the second surface 12 exits from the third surface 13. The material of the first prism 10 is PC (polycarbonate).

  The first prism 10 is a molded product by injection molding. Therefore, as shown in FIG. 3B, a plurality of protrusions are periodically formed on each of the three surfaces (transferred by a mold). Here, the second surface 12 is a reflecting surface. Therefore, generation of diffracted light on this surface becomes a problem.

At this time, the shape of the protrusion is substantially arcuate (concave toward the optical element 60 side), and the radius of curvature R of the arc is 2.0 mm. The interval P (cycle) between adjacent grooves is 0.008 mm. The first prism 10 is used by being incorporated in the optical system shown in FIG. However, in the second embodiment, it is assumed that the user observes an image of an object through this optical system instead of using a CCD. At this time, the wavelength range is a visible range of 400 nm to 700 nm. Therefore, if the center wavelength of the used wavelength band is the reference wavelength, the reference wavelength λ ₀ is 550 nm. Further, the refractive index n _{0 at} the reference wavelength λ ₀ = 550 nm is 1.58710. The spectral transmittance of the first prism 10 and the second prism 20 is substantially constant in the wavelength range of 400 to 700 nm.

At this time, the value of (n ₀ × P ² ) / (R × λ ₀ ) is 0.092. Further, the diffraction efficiency of specularly reflected light on the second surface 12, that is, the 0th-order diffracted light is 99.81%, and the diffraction efficiency of ± 1st-order diffracted light is 0.09%. Thus, the intensity of ± 1st order diffracted light that causes image quality degradation is sufficiently weaker than 0th order diffracted light. Therefore, even when an optical system is configured using the first prism 10 and observation is performed using the optical system, an image without deterioration due to diffraction can be observed.

Note that the combination of the radius of curvature R, the groove interval P, the wavelength λ _0, and the refractive index n ₀ at that wavelength in the cross section of the groove or protrusion is not limited to the combination of the above embodiments. The table below shows combinations of other examples (Examples 3, 4, and 5) in addition to the above Examples 1 and 2. In addition, any prism manufacturing method may be direct processing or molding by a mold. Since all of Examples 1 to 5 satisfy the conditional expression (1), the intensity of ± 1st order diffracted light is sufficiently weaker than 0th order diffracted light. Therefore, even if the optical system is configured using the optical elements of Examples 1 to 5, it is possible to obtain an image or image that is not deteriorated by diffraction.

〔table〕
Example 1 Example 2 Example 3 Example 4 Example 5
Material ZEONEX480R PC OKP4 ZEONEX330R ZEONEX330R
R (mm) 3.5 2.0 0.5 0.2 1.0
P (μm) 10 8 5 3 5
λ ₀ (μm) 0.53 0.55 0.6328 0.58756 0.54
n ₀ 1.52881 1.58710 1.60235 1.50913 1.52818
(N ₀ × P ² )
/ (R × λ ₀ ) 0.082 0.092 0.127 0.116 0.071
Zero-order diffraction efficiency
(%) 99.85 99.81 99.65 99.71 99.89
± 1st order diffraction efficiency
(%) 0.07 0.09 0.16 0.14 0.05
.

In the third to fifth embodiments, the reference wavelength λ ₀ is as follows.

  In Example 3, the wavelength at which the light intensity becomes maximum in the emission spectrum characteristics of the light source.

  In Example 4, the wavelength at which the value of the characteristic is maximized in the characteristic obtained from the emission spectral characteristic of the light source and the spectral transmittance characteristic of the wavelength filter.

  In Example 5, the wavelength at which the sensitivity is maximum in the spectral sensitivity characteristics of the photoelectric converter (Si photodiode (S7123-01: manufactured by Hamamatsu Photonics)).

  Then, for example, an optical system as shown in FIG. 6 can be configured by combining two prisms whose reflecting surfaces satisfy the conditional expression (1), for example, the prisms of the first to fifth embodiments. By doing in this way, an optical system can be made compact and an image and an image which do not deteriorate by diffraction can be obtained.

  In the above embodiments, glass or resin material is used for the optical element, but an organic-inorganic composite material may be used instead. The organic-inorganic composite usable in the present invention will be described.

  The organic-inorganic composite is a composite in which an organic component and an inorganic component are mixed and combined at a molecular level or nanoscale. Its form is (1) a structure in which a polymer matrix composed of an organic skeleton and a matrix composed of an inorganic skeleton are intertwined with each other and penetrated into each other's matrix. There are those in which inorganic fine particles (so-called nanoparticles) sufficiently smaller than the light wavelength of the scale are uniformly dispersed, and (3) those having a composite structure of these. Some interaction acts between the organic component and the inorganic component, such as intermolecular forces such as hydrogen bonds, dispersion forces, and Coulomb forces, and attractive forces due to covalent bonds, ionic bonds, and π electron cloud interactions. In the organic-inorganic composite, as described above, the organic component and the inorganic component are mixed at a molecular level or a scale region smaller than the wavelength of light. For this reason, there is almost no influence on light scattering, and a transparent body can be obtained. Further, as derived from the Maxwell equation, the material reflects the optical characteristics of the organic component and the inorganic component. Therefore, various optical characteristics (refractive index, wavelength dispersion) are developed according to the types and abundance ratios of the organic component and the inorganic component. Therefore, various optical characteristics can be obtained by blending organic and inorganic components in any ratio.

Table 1 below shows a composition example of an organic-inorganic composite of acrylate resin (ultraviolet curable) and zirconia (ZrO ₂ ) nanoparticles. Table 2 shows a composition example of an organic-inorganic composite of an acrylate resin and zirconia (ZrO ₂ ) / alumina (Al ₂ O ₃ ) nanoparticles. Table 3 shows a composition example of an organic-inorganic composite of acrylate resin and niobium oxide (Nb ₂ O ₅ ) nanoparticles. Table 4 shows a composition example of an organic-inorganic composite of acrylate resin, zirconium alkoxide, and alumina (Al ₂ O ₃ ) nanoparticles.

Table 1
┌────┬────┬────┬┬────┬────┬────┬─────┐
│ zirconia _{│n d │ν d │n C │n F} │n g │ Notes │
│A content│ │ │ │ │ │ │
├────┼────┼────┼┼────┼────┼────┼─────┤
│ 0 │1.49236 │57.85664 │1.48981 │1.49832 │1.50309 │Acrylic │
│ │ │ │ │ │ │ 100% │
├────┼────┼────┼┼────┼────┼────┼─────┤
│ 0.1 │1.579526 │54.85037 │1.57579 │1.586355 │1.59311 │ │
├────┼────┼────┼┼────┼────┼────┼─────┤
│ 0.2 │1.662128 │53.223 │1.657315 │1.669756 │1.678308│ │
├────┼────┼────┼┼────┼────┼────┼─────┤
│ 0.3 │1.740814│52.27971│1.735014│1.749184│1.759385│ │
├────┼────┼────┼┼────┼────┼────┼─────┤
│ 0.4 │1.816094│51.71726│1.809379│1.825159│1.836887│ │
├────┼────┼────┼┼────┼────┼────┼─────┤
│ 0.5 │1.888376 │51.3837 │1.880807 │1.898096 │1.911249│ │
└────┴────┴────┴┴────┴────┴────┴─────┘
.

Table 2
┌───┬───┬────┬────┬────┬────┬┬────┬────┐
_{│AlsO 3 │ZrOs │n d │ν d │n} C │n F │n g │ Notes │
│ presence rate │ presence rate │ │ │ │ │ │
├───┼───┼────┼────┼────┼────┼┼────┼────┤
│0.1 │0.4 │1.831515│53.56672│1.824851│1.840374│1.851956│Acryl│
│ │ │ │ │ │ │ │50% │
├───┼───┼────┼────┼────┼────┼┼────┼────┤
│0.2 │0.3 │1.772832│56.58516│1.767125│1.780783│1.790701│ │
├───┼───┼────┼────┼────┼────┼┼────┼────┤
│0.3 │0.2 │1.712138│60.97687│1.707449│1.719127│1.727275│ │
├───┼───┼────┼────┼────┼────┼┼────┼────┤
│0.4 │0.1 │1.649213│67.85669│1.645609│1.655177│1.661429│ │
├───┼───┼────┼────┼────┼────┼┼────┼────┤
│0.2 │0.2 │1.695632│58.32581│1.690903│1.702829│1.774891│ │
└───┴───┴────┴────┴────┴────┴┴────┴────┘
.

Table 3
┌───┬───┬────┬────┬────┬┬────┬────┐
_{│NbsO 5 │AlsO 3 │n d │ν d} │n C │n F │n g │
│Content│Content│ │ │ │ │ │
├───┼───┼────┼────┼────┼┼────┼────┤
│0.1 │ 0 │1.589861│29.55772│1.584508│1.604464│1.617565│
├───┼───┼────┼────┼────┼┼────┼────┤
│0.2 │ 0 │1.681719 │22.6091 │1.673857 │1.70401 │1.724457│
├───┼───┼────┼────┼────┼┼────┼────┤
│0.3 │ 0 │1.768813 │19.52321 │1.758673 │1.798053 │1.8251 │
├───┼───┼────┼────┼────┼┼────┼────┤
│0.4 │ 0 │1.851815 │17.80818 │1.839583 │1.887415 │1.920475│
├───┼───┼────┼────┼────┼┼────┼────┤
│0.5 │ 0 │1.931253 │16.73291 │1.91708 │1.972734 │2.011334│
└───┴───┴────┴────┴────┴┴────┴────┘
.

Table 4
┌─────┬──────┬────┬────┬┬────┬────┐
￨AlsOc (film) │ zirconia A _{│n d │ν d │n C │n F} │
│Content │Lucoxide │ │ │ │ │
├─────┼──────┼────┼────┼┼────┼────┤
│ 0 │ 0.3 │1.533113│58.39837│1.530205│1.539334│
├─────┼──────┼────┼────┼┼────┼────┤
│ 0.1 │ 0.27 │1.54737 │62.10192│1.544525│1.553339│
├─────┼──────┼────┼────┼┼────┼────┤
│ 0.2 │ 0.24 │1.561498│66.01481│1.558713│1.567219│
├─────┼──────┼────┼────┼┼────┼────┤
│ 0.3 │ 0.21 │1.575498│70.15415│1.572774│1.580977│
├─────┼──────┼────┼────┼┼────┼────┤
│ 0.4 │ 0.18 │1.589376│74.53905│1.586709│1.594616│
└─────┴──────┴────┴────┴┴────┴────┘
.

  Now, an optical system that combines the optical elements of the present invention as described above can be used in, for example, the imaging apparatus shown in FIG. In the imaging apparatus of FIG. 6, an object image is formed through two prisms. Then, the formed image is received by an image sensor such as a CCD or a silver salt film and photographed. Examples of such a photographing apparatus include a silver salt film camera and an electronic camera (digital camera). It can also be used as an observation optical device for observing an object image through an eyepiece, for example, an objective optical system of a camera finder.

  9 to 11 are conceptual diagrams of the objective optical system of the finder of the electronic camera. Here, the imaging optical system of FIG. 6 is incorporated in the objective optical system. 9 is a front perspective view showing the appearance of the electronic camera 140, FIG. 10 is a rear perspective view thereof, and FIG. 11 is a cross-sectional view showing the configuration of the electronic camera 140.

  In this example, the electronic camera 140 includes a photographing optical system 141 having a photographing optical path 142, a finder optical system 143 having a finder optical path 144, a shutter 145, a flash 146, a liquid crystal display monitor 147, and the like. In such a configuration, when the user presses the shutter 145 disposed on the upper part of the camera 140, photographing is performed through the photographing objective optical system 148 in conjunction therewith.

  An object image formed by the photographing objective optical system 148 is formed on the imaging surface 150 of the CCD 149 through a filter 151 such as a low-pass filter or an infrared cut filter. The object image received by the CCD 149 is displayed as an electronic image on a liquid crystal display monitor 147 provided on the back of the camera via the processing means 152. In addition, the processing means 152 is provided with a memory or the like, and a photographed electronic image can be recorded. This memory may be provided separately from the processing means 152, or may be configured to perform recording and writing electronically using a floppy (registered trademark) disk or the like. Further, instead of the CCD 149, a silver salt camera in which a silver salt film is arranged may be configured.

  Further, a finder objective optical system 153 is disposed on the finder optical path 144. The finder objective optical system 153 includes a cover lens 154, a first prism 10, an aperture stop 2, a second prism 20, and a focusing lens 166. Here, the optical system according to the present invention is used for the cover lens 154 or the optical system from the first prism 10 to the second prism 20.

  Further, the cover lens 154 used as a cover member is a lens having negative power, and has an enlarged view angle. Further, a focusing lens 166 is disposed behind the rear group prism 20. The focus lens 166 can be adjusted in position in the front-rear direction of the optical axis, and is used for adjusting the focus of the finder objective optical system 153. The object image formed on the imaging plane 167 by the finder objective optical system 153 is formed on the field frame 157 of the Porro prism 155 that is an image erecting member. The field frame 157 separates the first reflecting surface 156 and the second reflecting surface 158 of the Porro prism 155 and is disposed therebetween. Behind this polyprism 155, an eyepiece optical system 159 for guiding an erect image to the observer eyeball E is disposed.

  The camera 140 configured as described above can configure the finder objective optical system 153 that changes magnification in conjunction with the photographing objective optical system 148 with a small number of optical members. Further, high performance and low cost can be realized, and the optical path of the objective optical system 153 can be bent. This increases the degree of freedom of arrangement inside the camera, which is advantageous in design.

  In the configuration of FIG. 11, the configuration of the photographing objective optical system 148 is not mentioned, but a refractive coaxial optical system can be used as the photographing objective optical system 148. Alternatively, it is naturally possible to use any type of imaging optical system including two or more prisms 10 and 20 according to the present invention.

  Next, FIG. 12 shows a conceptual diagram of a configuration in which the imaging optical system as shown in FIG. 6 according to the present invention is incorporated in the objective optical system 148 of the photographing unit of the electronic camera 140. In this case, an imaging optical system according to the present invention including the first prism 10, the aperture stop 2, and the second prism 20 is used for the imaging objective optical system 148 disposed on the imaging optical path 142.

  An object image formed by the photographing objective optical system 148 is formed on the imaging surface 150 of the CCD 149 through a filter 151 such as a low-pass filter or an infrared cut filter. The object image received by the CCD 149 is displayed as an electronic image on the liquid crystal display element (LCD) 160 via the processing means 152. The processing unit 152 also controls the recording unit 161. The recording unit 161 is for recording an object image photographed by the CCD 149 as electronic information. The image displayed on the LCD 160 is guided to the observer eyeball E via the eyepiece optical system 159.

  The eyepiece optical system 159 includes a decentered prism. In this example, the eyepiece optical system 159 includes three surfaces, that is, an incident surface 162, a reflective surface 163, and a combined reflective / refracted surface 164. In addition, at least one of the two reflecting surfaces 63 and 64, preferably both surfaces, provides power to the light beam and has a single symmetry plane that corrects decentration aberrations. It consists of a curved surface. The only symmetry plane is formed on substantially the same plane as the only symmetry plane of the plane-symmetric free-form surface of the prisms 10 and 20 of the objective optical system 148 for photographing. The photographing objective optical system 148 may include other lenses (positive lens, negative lens) as components of the prisms 10 and 20 on the object side, between the prisms, or on the image side.

  In the camera 140 configured in this way, the photographing objective optical system 148 can be configured with a small number of optical members, high performance and low cost can be realized, and the entire optical system can be arranged on the same plane. Therefore, it is possible to realize a book shape having a thickness in a direction perpendicular to the arrangement plane.

  In this example, a plane parallel plate is disposed as the cover member 165 of the photographing objective optical system 148, but a lens having power may be used as in the previous example.

  Here, without providing the cover member, the surface disposed closest to the object side in the optical system of the present invention can also be used as the cover member.

  Next, FIG. 13 to FIG. 15 are conceptual diagrams showing a configuration in which the imaging optical system as shown in FIG. 6 according to the present invention is built in a personal computer which is an example of an information processing apparatus.

  13 is a front perspective view with the cover of the personal computer 300 opened, FIG. 14 is a sectional view of the photographing optical system 303 of the personal computer 300, and FIG. 15 is a side view of the state of FIG. As shown in FIGS. 13 to 15, the personal computer 300 includes a keyboard 301, information processing means and recording means, a monitor 302, and a photographing optical system 303.

  Here, the keyboard 301 is used for a writer to input information from the outside. Further, the information processing means and recording means are not shown. The monitor 302 is for displaying information to the operator. The monitor 302 may be a transmissive liquid crystal display element that is illuminated from the back by a backlight (not shown), a reflective liquid crystal display element that reflects and displays light from the front, a CRT display, or the like. The photographing optical system 303 is for photographing an image of the operator himself or a surrounding area. Note that the photographic optical system 303 is built in the upper right of the monitor 302 in the figure, but is not limited to that location. The photographing optical system 303 may be anywhere around the monitor 302 or the keyboard 301, for example.

  The photographic optical system 303 includes an objective optical system 200 including an imaging optical system according to the present invention and an imaging element chip 262 that receives an image on a photographic optical path 304. These are built in the personal computer 300.

  Here, an lR cut filter 280 is additionally attached on the image sensor chip 262. That is, the imaging element chip 262 and the lR cut filter 280 are integrally formed as the imaging unit 260. The imaging unit 260 can be attached to the rear end of the lens frame 201 of the objective optical system 200 by one-touch fitting. Therefore, centering of the objective optical system 200 and the image sensor chip 262 and adjustment of the surface interval are unnecessary, and assembly is simple. A cover glass 202 for protecting the objective optical system 200 is disposed at the tip of the lens frame 201.

  The object image received by the image sensor chip 262 is input to the processing means of the personal computer 300 through the terminal 266 and displayed on the monitor 302 as an electronic image. FIG. A rendered image 305 is shown. Further, this image 305 can be transmitted to the outside through the processing means. Therefore, it can be transmitted to a communication partner at a remote place via the Internet or a telephone. As a result, the image 305 can be displayed on the personal computer of the communication partner.

  Next, as another example of the information processing apparatus, FIG. 16 shows an example in which an imaging optical system as shown in FIG. 6 according to the present invention is built in a telephone, in particular, a portable telephone that is easy to carry.

  16A is a front view of the mobile phone 400, FIG. 16B is a side view, and FIG. 16C is a cross-sectional view of the photographing optical system 405. As shown in FIGS. 16A to 16C, the mobile phone 400 includes a microphone unit 401, a speaker unit 402, an input dial 403, a monitor 404, a photographing optical system 405, an antenna 406, and processing. Means (not shown).

  Here, the microphone unit 401 is for inputting an operator's voice as information. The speaker unit 402 is for outputting the voice of the other party. An input dial 403 is used by an operator to input information. The monitor 404 is for displaying information such as a photographed image of the operator himself or the other party, a telephone number, and the like. The monitor 404 is a liquid crystal display element. The antenna 406 is for transmitting and receiving communication radio waves. The processing means is for processing image information, communication information, input signals, and the like. In the drawing, the arrangement positions of the respective components are not particularly limited to these.

  The photographing optical system 405 includes an objective optical system 200 including an imaging optical system according to the present invention, and an imaging element chip 262 that receives an image. Here, the objective optical system 200 uses the optical system of the present invention and is disposed on the photographing optical path 407. These are built in the mobile phone 400.

  Here, an lR cut filter 280 is additionally attached on the image sensor chip 262. That is, the imaging element chip 262 and the lR cut filter 280 are integrally formed as the imaging unit 260. The imaging unit 260 can be attached to the rear end of the lens frame 201 of the objective optical system 200 by one-touch fitting. Therefore, centering of the objective optical system 200 and the image sensor chip 262 and adjustment of the surface interval are unnecessary, and assembly is simple. A cover glass 202 for protecting the objective optical system 200 is disposed at the tip of the lens frame 201.

  The object image received by the imaging element chip 262 is input to a processing unit (not shown) via a terminal 266 and displayed as an electronic image on the monitor 404, the communication partner monitor, or both. . In addition, when transmitting an image to a communication partner, the processing means includes a signal processing function for converting information of an object image received by the image sensor chip 262 into a signal that can be transmitted.

  As in the above embodiment, by mounting an optical system such as that shown in FIG. 6 in which the optical element of the present invention is combined with a digital camera, a mobile phone, a notebook personal computer, etc., it is compact and image quality degradation due to diffraction is reduced. It is possible to obtain an electronic apparatus having a high-performance optical system that is not required.

  The above optical element of the present invention, an optical system using the same, and an electronic apparatus can be configured as follows, for example.

[1] An optical element including at least one reflecting surface,
The reflective surface has a plurality of grooves formed on the surface thereof with a predetermined period,
The cross section of each of the plurality of grooves is substantially arc-shaped,
An optical element satisfying the following conditional expression:

0.03 ≦ (n ₀ × P ² ) / (R × λ ₀ ) ≦ 0.17 (1)
Where λ ₀ is a reference wavelength within a wavelength range in which the optical element is used,
n ₀ : refractive index at the reference wavelength of the material constituting the optical element,
R: radius of curvature of the arc,
P: the predetermined period;
It is.

    [2] The optical element as described in [1] above, wherein the reference wavelength is a wavelength of maximum intensity in a spectrum of a light source.

    [3] The optical element according to [1], wherein the reference wavelength is a wavelength of maximum transmittance in the transmittance distribution of the optical system.

    [4] The optical element as described in 1 above, wherein the reference wavelength is a wavelength of maximum transmittance of the wavelength filter.

    [5] The optical element as described in 1 above, wherein the reference wavelength is a wavelength of maximum sensitivity of the photoelectric converter.

    [6] The optical element as described in [1] above, wherein the reference wavelength is a wavelength having the highest specific visual sensitivity of human eyes.

    [7] The optical element as described in [1], wherein the reference wavelength is a wavelength at the center of a wavelength region used for imaging.

    [8] The reference wavelength is the maximum sensitivity in the sensitivity distribution obtained by multiplying at least two of the spectrum of the light source, the transmittance distribution of the optical system, the transmittance distribution of the wavelength filter, and the sensitivity distribution of the photoelectric converter. 2. The optical element as described in 1 above, which has a wavelength.

    [9] The optical element according to [1], wherein the reference wavelength is a wavelength having the highest transmittance in the G filter portion of the RGB filter.

    [10] The optical element as described in any one of 1 to 9 above, wherein the optical element is a prism having at least one optical surface composed of a free-form surface.

    [11] An optical system comprising the optical element described in any one of 1 to 10 above.

    [12] The optical system as described in 11 above, comprising at least one optical element using an organic-inorganic composite material as the optical material.

    [13] The optical system as set forth in [12], wherein the organic-inorganic composite includes zirconia nanoparticles.

    [14] The optical system as set forth in [12], wherein the organic-inorganic composite includes nanoparticles of zirconia and alumina.

    [15] The optical system as set forth in [12], wherein the organic-inorganic composite includes niobium oxide nanoparticles.

    [16] The optical system as described in 12 above, wherein the organic-inorganic composite includes a hydrolyzate of zirconium alkoxide and alumina nanoparticles.

    [17] An electronic apparatus comprising the optical element according to any one of 1 to 10 or the optical system according to any one of 11 to 16.

It is a figure which shows typically the cutting of an axisymmetric surface. It is a figure which shows typically the cutting of the surface which is not axisymmetric, (a) moves a workpiece | work to the same direction as a rotation direction, rotating a cutting tool with a circular cutting edge, (b) is a cutting tool with a circular cutting edge. This is a case where the workpiece is moved in a direction perpendicular to the rotation direction while rotating. It is a figure which shows the cross-sectional shape of the surface of the optical element obtained under the cutting process of FIG. 2, (a) is the cross-sectional shape of the surface of a workpiece | work, (b) is the optical element shape | molded from the metal mold | die of (a). The cross-sectional shape of the surface. It is a figure which shows the light which injects into the surface of a shape like Fig.3 (a), and the light diffracted. It is a figure which shows the function H (N, m (pi)) when N is set to 10. 3 is a diagram showing an optical path diagram in a meridional section of the optical system of Numerical Example 1. FIG. It is a figure which shows the spectral sensitivity characteristic which considered the transmittance | permeability distribution of the RGB color filter of Example 1, and the sensitivity of CCD. It is a figure which shows the diffraction efficiency of the +/- 1st order diffracted light in the wavelength range of 400-700 nm in Example 1. FIG. It is a front perspective view which shows the external appearance of the electronic camera to which the imaging optical system like FIG. 6 by this invention is applied. FIG. 10 is a rear perspective view of the electronic camera of FIG. 9. It is sectional drawing which shows the structure of the electronic camera of FIG. It is a conceptual diagram of another electronic camera to which the imaging optical system as shown in FIG. 6 according to the present invention is applied. It is the front perspective view which opened the cover of the personal computer in which the imaging optical system like FIG. 6 by this invention was integrated as an objective optical system. It is sectional drawing of the imaging optical system of a personal computer. It is a side view of the state of FIG. FIG. 7 is a front view (a), a side view (b), and a sectional view (c) of the photographing optical system of a mobile phone in which the imaging optical system as shown in FIG. 6 according to the present invention is incorporated as an objective optical system.

Explanation of symbols

1 ... On-axis chief ray (optical axis)
2 ... Aperture 3 ... Image sensor (image plane)
DESCRIPTION OF SYMBOLS 10 ... 1st prism 11 ... 1st surface 12 of 1st prism ... 2nd surface 13 of 1st prism ... 3rd surface 20 of 1st prism ... 2nd prism 21 ... 1st surface 22 of 2nd prism ... 2nd The second surface 23 of the prism ... The third surface 24 of the second prism ... The fourth surface 30 of the second prism ... The cover glass 31 ... The front surface 32 of the cover glass ... The rear surface 40 of the cover glass 41 ... The front surface 42 of the cover glass ... rear surfaces 51 and 52 of cover glass ... groove 60 ... optical element 140 ... electronic camera 141 ... photographing optical system 142 ... photographing optical path 143 ... finder optical system 144 ... finder optical path 145 ... shutter 146 ... flash 147 ... liquid crystal display monitor 148 ... Objective optical system 149 ... CCD
150 ... Imaging surface 151 ... Filter 152 ... Processing means 153 ... Finder objective optical system 154 ... Cover lens 155 ... Porro prism 156 ... First reflecting surface 157 ... Field frame 158 ... Second reflecting surface 159 ... Eyepiece optical system 160 ... Liquid crystal Display element (LCD)
161: Recording means 162 ... Incident surface 163 ... Reflecting surface 164 ... Reflective and refracting surface 165 ... Cover member 166 ... Focusing lens 167 ... Imaging surface 200 ... Objective optical system 201 ... Lens frame 202 ... Cover glass 260 ... Imaging Unit 262 ... Image sensor chip 266 ... Terminal 280 ... lR cut filter 300 ... PC 301 ... Keyboard 302 ... Monitor 303 ... Shooting optical system 304 ... Shooting optical path 305 ... Image 400 ... Mobile phone 401 ... Microphone part 402 ... Speaker part 403 ... Input dial 404 ... monitor 405 ... imaging optical system 406 ... antenna 407 ... photographing optical path W ... workpiece B ... byte T ... cutting edge G ... kerf L _i ... incident light L _+1, L _-1 ... 1-order diffracted light E ... observer's eyeball

Claims (4)

An optical element including at least one reflecting surface,
The reflective surface has a plurality of grooves formed on the surface thereof with a predetermined period,
The cross section of each of the plurality of grooves is substantially arc-shaped,
An optical element satisfying the following conditional expression:
0.03 ≦ (n ₀ × P ² ) / (R × λ ₀ ) ≦ 0.17 (1)
Where λ ₀ is a reference wavelength within a wavelength range in which the optical element is used,
n ₀ : refractive index at the reference wavelength of the material constituting the optical element,
R: radius of curvature of the arc,
P: the predetermined period;
It is. 2. The optical element according to claim 1, wherein the optical element is a prism having at least one optical surface composed of a free-form surface. An optical system comprising the optical element according to claim 1. An electronic device comprising the optical element according to claim 1 or 2, or the optical system according to claim 3.

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