1. Field of the Invention
The present invention relates to a diffractive optical element, an optical system, and an optical apparatus.
2. Description of the Related Art
A diffractive optical element of a blazed structure is configured to highly efficiently diffract light of one specific order (or designed order) and a specific wavelength. For sufficiently high diffractive efficiency of the specific order in an overall visible wavelength range, Japanese Patent No. 3,717,555 discloses two diffractive gratings adhered to each other. Each diffractive grating is made of a low refractive index high dispersion material and a high refractive index low dispersion material. A height of the diffractive grating is properly set. The diffractive optical element of this type will be referred to as an “adhesion two-layer DOE” hereinafter. For high diffractive efficiency equal to or higher than 99% in the overall visible wavelength range, Japanese Patent Laid-Open No. 2008-241734 uses a material which has a partial dispersion ratio θgF smaller than that of a usual material (or a linear abnormal dispersion).
However, due to the behavior of the wall surface section that provides no diffractive action, the wavelength characteristic of the diffractive efficiency of the diffracted light of the designed order reduces on the long wavelength side, and the diffractive efficiency of the red wavelength range becomes lower than that of the blue wavelength range. Unnecessarily diffracted light other than the designed order is likely to stand out on the red wavelength range. If the red wavelength range is relatively intensified by using an antireflective film, image processing, etc. for color balancing of the diffracted light of the designed order, unnecessary light in the red wavelength is also intensified and highlighted.
The present invention provides a diffractive optical element, optical system, and optical apparatus, which can reduce wavelength characteristic scattering of diffractive efficiency in diffracted light of a designed order.
A diffractive optical element according to the present invention is made by adhering a first diffractive grating and a second diffractive grating to each other. Each of the first diffractive grating and the second diffractive grating includes a blazed structure in which a plurality of gratings each having a sawtooth shape are arranged in a grating period direction. At least one of the first diffractive grating and the second diffractive grating is made of a material having a refractive index distribution in a plane normal direction perpendicular to the grating period direction. The following expressions are satisfied for an arbitrary wavelength λ in a visible wavelength range:
ΔΦ1(λ)=1−{n22(λ)−n11(λ)}d/mλ
ΔΦ2(λ)=1−{n21(λ)−n12(λ)}d/mλ
ΔΦ1(λ)×ΔΦ2(λ)<0.
Herein, n11(λ) and n12(λ) are refractive indices for light having the wavelength λ of a base section of the sawtooth shape of the first diffractive grating and an apex section of the sawtooth shape of the first diffractive grating, respectively, n21(λ) and n22(λ) are refractive indices for the light having the wavelength λ of a base section of the sawtooth shape of the second diffractive grating and an apex section of the sawtooth shape of the second diffractive grating, respectively, d is an absolute value of a grating height of the first or second diffractive grating, and m is a designed order.
Further features of the present invention will become apparent from the following description of exemplary embodiments with reference to the attached drawings.
The DOE 10 is provided on a cementing surface of the front lens in
The optical apparatus for the optical system is not limited to the image pickup lens for the digital still camera, and may be applied to an image pickup lens for a video camera, a reader lens for a scanner or a digital copier in a business machine, and an optical system for an optical apparatus for a wide wavelength range.
A detailed description will now be given of a variety of embodiments of the DOE 10 with reference to the accompanying drawings.
The DOE 10 is an adhesion DOE in which a first diffractive grating 1 and a second diffractive grating 2 are adhered to each other (or laminated). Each of the first and second diffractive gratings 1 and 2 has a concentric grating shape of a blazed structure, and exhibits a lens operation (convergence effect or divergence effect) by gradually changing the grating pitch from the center (optical axis) to the periphery. Each of the diffractive gratings 1 and 2 serves as one DOE 10 through all layers. The blazed structure enables the incident light upon the DOE 10 to diffract in a specific diffracted order direction (which is the +1st order direction in
Since the operating wavelength range of the DOE 10 is a visible range, the materials and the grating height for the first diffractive grating 1 and the second diffractive grating 2 are selected so that the diffractive efficiency of the diffracted light of the designed order can increase in the overall visible range. In other words, the material and the grating height of each diffractive grating are determined so that a maximum optical path length difference of light that passes a plurality of diffractive gratings, such as the first and second diffractive gratings 1 and 2, (which is a maximum value of the optical path length difference between the thread and root in the diffractive portion) can be equal to or close to an integral multiple of the wavelength in the operating wavelength range. High diffractive efficiency is obtained in the overall operating wavelength range by properly setting the material and the shape of each diffractive grating. In general, the grating height of the diffractive grating is defined as a distance between the grating groove and the grating tip in a plane normal direction perpendicular to the grating period direction.
A description will now be given of the diffractive efficiency that uses the conventional scalar diffraction theory, with reference to
An abscissa axis in a lower left graph in
Since the DOE 50 is made by adhering two grating surfaces of the two diffractive gratings to each other, a conditional expression that maximizes the diffractive efficiency of the diffracted light of the diffracted order m for a wavelength λ under the vertical incidence upon the base surface of the diffractive grating becomes as follows:
(n2−n1)d=mλ (1)
In Expression (1), n1 denotes a refractive index of the material of the first diffractive grating 51 for the wavelength λ, n2 denotes a refractive index of the material of the second diffractive grating 52 for the wavelength λ, d denotes the grating height of each of the first and second diffractive grating 51 and 52, and m denotes the diffracted order. When it is assumed that a ray that downwardly diffracts from the 0-th light in
In the configuration of
η(λ)=sin c2[π{m−(n2−n1)d/λ}] (2)
The adhesion two-layer DOE can provide high diffractive efficiency in a wide wavelength range when a low refractive index high dispersion material is used for the first diffractive grating 51 and a high refractive index low dispersion material is used for the second diffractive grating 52. It is known that use of a low refractive index high dispersion material that has a linear dispersion characteristic or a partial dispersion ratio θgF smaller than that of a usual material is effective for diffractive efficiency of 99% or higher in the overall visible range. One known method of obtaining this linear dispersion characteristic is to disperse Indium Tin Oxide (ITO hereinafter) nanoparticles in the base resin material.
The diffractive efficiency of each of the DOEs disclosed in Japanese Patent No. 3,717,555 and Japanese Laid-Open No. 2008-241734 is calculated by using the scalar diffraction theory for the design evaluation. It is known that the calculation based upon the scalar diffraction theory can be precise as long as the pitch of the diffractive grating is sufficiently larger than the wavelength, but the behavior of the wall surface section 54 of the diffractive grating is not considered at all.
A description will now be given of the diffractive efficiency using the rigorous electromagnetic field calculation. The rigorous electromagnetic field calculation is a calculating method that considers the wall surface section of the DOE. In this embodiment, the diffractive efficiency of the DOE is evaluated with Rigorous Coupled Wave Analysis (“RCWA” hereinafter) as one of the rigorous electromagnetic field calculations.
In the DOE of this embodiment, a material of the diffractive grating has a refractive index distribution in the plane normal direction from the base surface whereas the conventional diffractive grating is made of a uniform material pursuant to the scalar diffraction theory. In this embodiment, the first diffractive grating 1 is made of a material that has a refractive index distribution in the plane normal direction, as illustrated in
The abscissa axis of a lower left graph in
The first diffractive grating 1 is made of ultraviolet (“UV”) curing resin in which ITO nanoparticles are mixed with acrylic fluorine UV curing resin, and has a refractive index distribution. The refractive index n11 of the base section 11 corresponds to the refractive index in which the ITO nanoparticles are mixed by 13.95%, and the refractive index n12 of the apex section 12 corresponds to the refractive index in which the ITO nanoparticles are mixed by 16.05%. The refractive index distribution linearly (or monotonously) increases from the base section 11 to the apex section 12. The dispersion ratio of the ITO nanoparticle is 13.95% different from 16.05% in the plane normal direction.
The second diffractive grating 2 is made of UV curing resin in which ZrO2 nanoparticles are uniformly mixed by 6% with acrylic UV curing resin.
Table 1 illustrates numerical values of the refractive indices of the base sections and the apex sections of the first and second diffractive gratings 1 and 2 and refractive indices of the apex section. The grating height d is 11.02 μm, the designed order is +1st order, and the grating pitch is 100 μm.
A refractive index relationship of the adhesion two-layer DOE having a refractive index distribution is defined with ΔΦ1 and ΔΦ2 in the following expressions:
ΔΦ1(λ)=1−{n22(λ)−n11(λ)}d/mλ
ΔΦ2(λ)=1−{n21(λ)−n12(λ)}d/mλ (3)
As illustrated in
When the material of the diffractive grating has a refractive index distribution, ΔΦ1 and ΔΦ2 are different from each other, a phase difference occurs, and the diffractive efficiency deteriorates. Nevertheless, when the phase changes of ΔΦ1 and ΔΦ2 are cancelled out (for example, by making ΔΦ1 positive and ΔΦ2 negative), the diffractive efficiency of the diffracted light of the designed order can be improved in the adhesion two-layer DOE that has a refractive index distribution.
From
The low order diffracted light on the short wavelength side is less conspicuous and thus less influential. The low order diffracted light on the short wavelength side tends to be less influential because the absorption on the short wavelength side tends to increase due to the increased number of lenses in the image pickup optical system required for high image quality in the digitalization and large printing of the recent optical apparatus.
Table 2 illustrates numerical values of ΔΦ1 ΔΦ2, ΔΦ1×ΔΦ2, and ΔΦ1+ΔΦ2 expressed in Expression (3), and Φav expressed in the following expression according to the first embodiment:
Φav(λ)={n1av(λ)−n2av(λ)}d/mλ (4)
Herein, n1av(λ) and n2av(λ) are average refractive indices for the wavelength λ of the base sections and the apex sections of the materials of the first and second diffractive gratings 1 and 2 as follows:
n1av(λ)={n11(λ)+n12(λ)}/2 (5)
n2av(λ)={n21(λ)+n22(λ)}/2 (6)
This inventor has discovered that the wavelength characteristic of the diffractive efficiency becomes almost uniform when at least one diffractive grating is made of a material having a refractive index distribution in the plane normal direction and the refractive index satisfies the following expression for an arbitrary wavelength λ in the visible wavelength range:
ΔΦ1(λ)×ΔΦ2(λ)<0 (7)
When Expression (7) is satisfied, the phase change between the base section of the first diffractive grating and the apex section of the second diffractive grating and the phase change between the apex section of the first diffractive grating and the base section of the second diffractive grating can be cancelled out. Unless Expression (7) is satisfied, these phase changes cannot be cancelled out and the diffractive efficiency is deteriorated.
As the product ΔΦ1×ΔΦ2 between ΔΦ1 and ΔΦ2 in Expression (3) is made smaller for a shorter wavelength, the wavelength characteristic of the diffractive efficiency can be almost uniform. When this relationship is satisfied, the unnecessary light of the high order light and the unnecessary light of the low order light can be well balanced on the short wavelength side.
When the visible wavelength range contains a wavelength that enables the product ΔΦ1×ΔΦ2 between ΔΦ1 and ΔΦ2 in Expression (3) to be 0, the wavelength characteristic of the diffractive efficiency can be almost uniform. When this relationship is satisfied, the wavelength characteristic of the diffractive efficiency can be almost uniform in the overall visible wavelength range.
When ΔΦ1+ΔΦ2 satisfies the following expression for the arbitrary wavelength λ in the visible wavelength range, the uniform wavelength characteristic and high diffractive efficiency can be obtained:
|ΔΦ1(λ)+ΔΦ2(λ)|<0.03 (8)
When this relationship is satisfied, the phase change between the base section of the first diffractive grating and the apex section of the second diffractive grating and the phase change between the apex section of the first diffractive grating and the base section of the second diffractive grating can be cancelled out and high diffractive efficiency can be obtained.
The uniformity of the wavelength characteristic can be improved when ΔΦ1+ΔΦ2 continuously increases or continuously decreases with a shorter wavelength in one half or more of the visible wavelength range. When ΔΦ1+ΔΦ2 is 0, the refractive index distribution can be cancelled out and the diffractive grating equivalent to the scalar diffraction theory can be obtained.
When ΔΦ1+ΔΦ2 continuously increases or continuously decreases with a shorter wavelength, the low order unnecessary light increases on the short wavelength side. The unnecessary light of the high order diffracted light reduces with a shorter wavelength due to the diffraction phenomenon by the wall surface section. As a result, the unnecessary light of the higher order light and the unnecessary light of the low order light can be well balanced, and the uniformity of the wavelength characteristic of the diffractive efficiency of the designed order can be improved. Although it continuously decreases in this embodiment, a similar effect can be obtained even when it continuously increases.
High diffractive efficiency can be obtained when the refractive index in the refractive index distribution of the DOE satisfies the following expression for the arbitrary wavelength λ in the visible wavelength range:
0.98<{n1av(λ)−n2av(λ)}d/mλ<1.02 (9)
Herein, n1av(λ) and n2av(λ) are average refractive indices for the wavelength λ of the base sections and the apex sections of the materials of the first and second diffractive gratings 1 and 2. Unless Expression (9) is satisfied, it parts from the scalar diffraction theory and it is difficult to obtain high diffractive efficiency even when the refractive index distribution is cancelled.
Unless the maximum refractive index difference for the d-line in the refractive index distribution of the DOE is 0.015 or less, the refractive index distribution has an excessively large amount and it is difficult to obtain the uniform wavelength characteristic and high diffractive efficiency. Unless the maximum refractive index difference for the d-line in the refractive index distribution of the DOE is 0.002 or higher, the scalar diffraction theory becomes dominant and the effect of this embodiment is hard to obtain.
While this embodiment uses the material in which nanoparticles are mixed with the base resin material, the refractive index can be adjusted by changing a nanoparticle mixture ratio. Moreover, the refractive index of each diffractive grating may be adjusted by changing the UV curing manufacturing process.
In particular, the refractive index distribution can be controlled by optimizing the UV irradiation process. When the irradiance condition is adjusted, the nanoparticles gather in the counter direction to the UV irradiation direction because the UV curing resin components cure. As a result, the nanoparticle mixture ratio changes in the UV irradiating direction and the refractive index distribution occurs. More specifically, a refractive index distribution can be wider by lowering the UV irradiation intensity and by extending the irradiation time period even if the UV irradiation energy is the same because it takes a longer time for the UV curing resin components to cure.
In order for the DOE of this embodiment to obtain high diffractive efficiency of 99% or higher in the overall visible wavelength range, use of a material that has a partial dispersion ratio egF smaller than that of a usual material (linear abnormal dispersion characteristic) is effective and use of the resin in which ITO nanoparticles are dispersed is also effective.
Unless a volume ratio of the refractive index difference is 0.5% or higher in the resin that has dispersed nanoparticles and a refractive index distribution, the effect of this embodiment is hard to obtain. Unless it is 5% or less, the refractive index distribution has an excessively large amount and it becomes difficult to obtain the uniformity of the wavelength characteristic and high diffractive efficiency.
While this embodiment utilizes a material in which the base resin material is mixed with nanoparticles, the material of the diffractive grating is not limited to this material as long as there is a refractive index distribution.
The manufacturing process of the diffractive grating may be arbitrarily changed. The absolute value of the diffractive efficiency becomes larger when the refractive index distribution of the apex section is wider than that of the base section in the plane normal direction in the diffractive grating.
In one of the first diffractive grating 1 and the second diffractive grating 2, a refractive index distribution of the base section 11 is wider than that of the apex section 12. The other of the first diffractive grating 1 and the second diffractive grating 2 has a constant refractive index or a refractive index distribution of the apex section 12 is narrower than that of the base section 11. At this time, an absolute value of a maximum refractive index difference in the refractive index distribution of one of the first diffractive grating 1 and the second diffractive grating 2 may be larger than that of the other of the first diffractive grating 1 and the second diffractive grating 2. This is because the absolute value of the diffractive efficiency can be improved by increasing the influence of the diffractive grating in which the refractive index distribution of the apex section is wider than that of the base section.
The absolute value of the diffractive efficiency improves when the refractive index distribution of the apex section is wider than that of the base section in each of the first and second diffractive gratings in the plane normal direction. Since the diffractive efficiency of the oblique incidence upon the DOE decreases, the +1st order or −1st order is suitable for the designed order. Since the diffraction phenomenon by the grating wall surface in the DOE becomes more influential and the diffractive efficiency of the designed order decreases, a grating pitch of 80 μm or wider is suitable. In general, the grating pitch for the DOE 10 is 10 mm or less for use with the image pickup lens.
Comparative example 1 is illustrated so as to further clarify the effects of this embodiment. Comparative example 1 is designed on the basis of the scalar diffraction theory. The first diffractive grating is made of UV curing resin in which ITO nanoparticles are uniformly mixed by 15% with acrylic fluorine UV curing resin, and the second diffractive grating is made of UV curing resin in which ZrO2 nanoparticles are uniformly mixed by 6% with acrylic fluorine UV curing resin. Table 3 illustrates numerical values of refractive indices of the first and second diffractive gratings. The grating height d is 11.02 μm, the designed order is +1st order, and the grating pitch is 100 μm.
Hence, it is understood that the DOE based upon the conventional scalar diffraction theory is undesirable when the grating wall surface is considered.
A second embodiment is different from the first embodiment in refractive index distribution and grating pitch of the first diffractive grating. The first diffractive grating 1 is made of UV curing resin in which ITO nanoparticles are mixed with acrylic fluorine UV curing resin, and has a refractive index distribution. The refractive index n11 of the base section 11 corresponds to the refractive index in which the ITO nanoparticles are mixed by 14.25%, and the refractive index n12 of the apex section 12 corresponds to the refractive index in which the ITO nanoparticles are mixed by 15.75%. The refractive index distribution linearly increases from the base section 11 to the apex section 12. The second diffractive grating 2 is made of UV curing resin in which ZrO2 nanoparticles are uniformly mixed by 6% with the acrylic UV curing resin.
Table 4 illustrates numerical values of the refractive indices of the base sections and the apex sections of the first and second diffractive gratings 1 and 2. The grating height d is 11.02 μm, the designed order is +1st order, and the grating pitch is 200 μm.
From
Hence, even when the grating pitch is different, the effects of the present invention are obtained. Table 5 illustrates numerical values of ΔΦ1 ΔΦ2, ΔΦ1×ΔΦ2, ΔΦ1+ΔΦ2, and Φav according to the second embodiment:
The second embodiment also satisfies the relationship illustrated in the first embodiment.
Comparative example 2 is illustrated so as to further clarify the effect of this embodiment. Comparative example 2 has the same grating pitch as that of the second embodiment and is designed on the basis of the scalar diffraction theory. The scalar diffraction theory does not depend upon the grating pitch. The refractive index of the comparative example is the same as that illustrated in Table 3 of Comparative example 1. The grating height d is 11.02 μm, the designed order is +1st order, and the grating pitch is 200 μm.
Hence, even when the grating pitch is different, it is understood that the DOE based on a conventional scalar diffraction theory is undesirable when the grating wall surface is considered.
A third embodiment is different from the first and second embodiments in slope direction of a refractive index distribution of the first diffractive grating.
As illustrated in
Table 6 illustrates numerical values of the refractive indices of the base sections and the apex sections of the first and second diffractive gratings 1 and 2. The grating height d is 11.02 μm, the designed order is +1st order, and the grating pitch is 100 μm.
Table 7 illustrates numerical values of ΔΦ1 ΔΦ2, ΔΦ1×ΔΦ2, ΔΦ1+ΔΦ2, and Φav according to the third embodiment:
The third embodiment also satisfies the relationship illustrated in the first embodiment.
A fourth embodiment is different from the first and second embodiments in that the refractive index distribution of the first diffractive grating is nonlinear.
As illustrated in
Table 8 illustrates numerical values of the refractive indices of the base sections and the apex sections of the first and second diffractive gratings 1 and 2. The grating height d is 11.02 μm, the designed order is +1st order, and the grating pitch is 100 μm.
Table 9 illustrates numerical values of ΔΦ1 ΔΦ2, ΔΦ1×ΔΦ2, ΔΦ1+ΔΦ2, and Φav according to the fourth embodiment:
The fourth embodiment also satisfies the relationship illustrated in the first embodiment.
According to a fifth embodiment, both the first and second diffractive gratings have refractive index distributions.
As illustrated in
The second diffractive grating 2 of this embodiment is made of UV curing resin in which ZrO2 nanoparticles are mixed with the acrylic UV curing resin. The refractive index n22 of the apex section 22 corresponds to the refractive index in which the ZrO2 nanoparticles are mixed by 6.3%, and the refractive index n21 of the base section 21 corresponds to the refractive index in which the ZrO2 nanoparticles are mixed by 5.7%. The refractive index distribution linearly decreases from the apex section 22 to the base section 21.
Table 10 illustrates numerical values of the refractive indices of the base sections and the apex sections of the first and second diffractive gratings 1 and 2. The grating height d is 11.02 μm, the designed order is +1st order, and the grating pitch is 100 μm.
Table 11 illustrates numerical values of ΔΦ1 ΔΦ2, ΔΦ1×ΔΦ2, ΔΦ1+ΔΦ2, and Φav according to the fifth embodiment.
The fifth embodiment also satisfies the relationship illustrated in the first embodiment.
The sixth embodiment is different from the fifth embodiment in slope direction of the refractive index distribution of the first diffractive grating.
A seventh embodiment is different from the fifth and sixth embodiments in slope direction of the refractive index distribution of the first diffractive grating.
An eighth embodiment is different from the fifth to seventh embodiments in slope direction of the refractive index distribution of the first diffractive grating.
Thus, the effect of the present invention can be obtained in any combinations of the directions of the refractive index distributions of the first and second diffractive gratings.
While the present invention has been described with reference to exemplary embodiments, it is to be understood that the invention is not limited to the disclosed exemplary embodiments. The scope of the following claims is to be accorded the broadest interpretation so as to encompass all such modifications and equivalent structures and functions.
This application claims the benefit of Japanese Patent Application No. 2011-275790, filed Dec. 16, 2011, which is hereby incorporated by reference herein in its entirety.
Number | Date | Country | Kind |
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2011-275790 | Dec 2011 | JP | national |
Number | Name | Date | Kind |
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8270080 | Nakabayashi | Sep 2012 | B2 |
20120120494 | Takayama | May 2012 | A1 |
20120320461 | Nakabayashi | Dec 2012 | A1 |
Number | Date | Country |
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09-127321 | May 1997 | JP |
2008-241734 | Oct 2008 | JP |
2008242390 | Oct 2008 | JP |
2010160474 | Jul 2010 | JP |
2011099550 | Aug 2011 | WO |
Entry |
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Japanese Office Action issued in counterpart application No. JP2011-275790, dated Sep. 29, 2015. |
Number | Date | Country | |
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20130155514 A1 | Jun 2013 | US |