# Patent

## Title
Diffractive optical element and optical device

## Abstract

In a diffractive optical element, first and second optical members are stacked, and a diffraction grating is formed at an interface between the first and second optical members. In the diffractive optical element, an absorption coefficient α (mm−1) of the first optical member and a grating height h (μm) of the diffraction grating satisfy expressions (1) and (2):

α≧0.04  (1)

h≦263.18×α−0.9454  (2).

## Background
CROSS-REFERENCE TO RELATED APPLICATION
This application claims priority to Japanese Patent Application No. 2009-298068 filed on Dec. 28, 2009, the disclosure of which including the specification, the drawings, and the claims is hereby incorporated by reference in its entirety.
BACKGROUND
The present disclosure relates to a diffractive optical element in which two optical members are stacked, and a diffraction grating is formed at an interface between the two optical members; and to an optical device including the diffractive optical element.
A diffractive optical element has been known, in which a plurality of optical members are stacked, and a relief pattern is formed at an interface between the optical members.
In a diffractive optical element described in, e.g., Japanese Patent Publication No. 09-127321, a relatively low-refractive high-dispersive optical material, and a relatively high-refractive low-dispersive optical material are stacked, and a diffraction grating having a saw-tooth cross-sectional shape is formed at an interface between the optical materials. More specifically, the diffractive optical element is configured so that a refractive index difference between the two optical materials is smaller for light having a shorter wavelength, and is larger for light having a longer wavelength. In a diffractive optical element described in Japanese Patent Publication No. 09-127321, a combination of such optical materials reduces wavelength dependency of diffraction efficiency.
Although a plurality of optical members are not stacked, a diffractive optical element described in Japanese Patent Publication No. 2009-134223 is a diffractive optical element including at least one element section in which a base section and a diffraction grating are formed on a substrate with a middle layer being interposed between the base section and diffraction grating. The base section and the diffraction grating are made of the same material, and extinction coefficients Ka and Kb for materials of the diffraction grating and the middle layer are properly set.
SUMMARY
In an optical device in which only light with a particular wavelength is diffracted, it is required that the wavelength dependency, i.e., wavelength selectivity of the diffraction efficiency is improved. For such a reason, a relatively high-refractive high-dispersive optical material and a relatively low-refractive low-dispersive optical material may be stacked contrary to the foregoing diffractive optical element. In such a manner, it is required to select the suitable optical materials in order to realize desired optical performance.
However, various properties such as formability, impact resistance, and transparency are required for the optical material other than the foregoing properties. Types of material satisfying the foregoing properties are not infinite. That is, more optical performance to be required results in a narrower range of optical material selection.
The present disclosure has been made in view of the foregoing, and it is an object of the present disclosure to reduce the wavelength dependency of the diffraction efficiency in the diffractive optical element in which the two optical materials are stacked, and the diffraction grating is formed at the interface between the two optical materials.
The present disclosure is intended for a diffractive optical element including first and second optical members which are stacked, and which have a diffraction grating formed at an interface between the first and second optical members. An absorption coefficient α (mm−1) of the first optical member and a grating height h (μm) of the diffraction grating satisfy expressions (1) and (2):

α≧0.04  (1)

h≦263.18×α−0.9454  (2)

According to the present disclosure, the diffraction efficiency can be maintained at high level, and the range of the optical material selection can be expanded.



BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a schematic view of a camera to which an interchangeable lens of an embodiment of the present disclosure is attached.
FIG. 2 is a schematic cross-sectional view of a diffractive optical element.
FIG. 3 is a model of a diffraction grating used for a simulation by a RCWA method.
FIG. 4 is a graph illustrating a relationship of diffraction efficiency with an absorption coefficient α and a grating height h.
FIG. 5 is a schematic diagram of a diffraction grating.
FIG. 6 is a graph illustrating a relationship of an average diffraction efficiency across visible wavelength with an inter-material gradient M and a blaze wavelength λb, and is a graph illustrating a preferable range of the inter-material gradient M.
FIG. 7 is a graph illustrating the relationship of the average diffraction efficiency across visible wavelength with the inter-material gradient M and the blaze wavelength λb, and is a graph illustrating preferable ranges of the inter-material gradient M and the blaze wavelength λb.
FIG. 8 is a graph illustrating a diffraction efficiency in a visible wavelength range, which corresponds to Table 1.
FIG. 9 is a graph illustrating the relationship of the average diffraction efficiency across visible wavelength with the inter-material gradient M and the blaze wavelength λb, and is a graph illustrating other preferable ranges of the inter-material gradient M and the blaze wavelength λb.
FIG. 10 is a graph illustrating the diffraction efficiency in the visible wavelength range, which corresponds to Table 2.
FIG. 11 is a graph illustrating a relationship between a principal dispersion and a reference refractive index of optical material, which corresponds to Table 3.
FIG. 12 is a schematic diagram for illustrating the grating height h for a non-uniform shape of the diffraction grating.



DETAILED DESCRIPTION
An embodiment of the present disclosure will be described in detail below with reference to the drawings.
<<Embodiment of the Disclosure>>
FIG. 1 is a schematic view of an interchangeable lens 200 with a diffractive optical element 1 illustrated as an example of the present embodiment, and a camera 100 to which the interchangeable lens 200 is attached. FIG. 2 is a schematic cross-sectional view of the diffractive optical element 1.
The interchangeable lens 200 is detachable from the camera 100. The interchangeable lens 200 is, e.g., a telephoto zoom lens. In the interchangeable lens 200, the diffractive optical element 1 serves as a lens element in addition to a refractive lens.
The diffractive optical element 1 is formed by stacking a first optical member 10 and a second optical member 11 which are transparent to light. In the present embodiment, the first optical member 10 is made of glass material, and the second optical member 11 is made of resin material. The first optical member 10 and the second optical member 11 are bonded together. A diffraction grating 13 having a saw-tooth cross-sectional shape is formed at an interface 12 defined by a bonding surface 10a of the first optical member 10 and a bonding surface 11a of the second optical member 11. Optical power of the diffraction grating 13 has wavelength dependency. Thus, the diffraction grating 13 provides the substantially same phase difference to light having different wavelengths, and diffracts the light having different wavelengths at diffraction angles which are different from each other.
Specifically, a recessed first diffraction grating 14 is formed in the bonding surface 10a of the first optical member 10, and a raised second diffraction grating 15 is formed in the bonding surface 11a of the second optical member 11. The first diffraction grating 14 includes a plurality of recessed sections which extend in a circumferential direction around an optical axis of the diffractive optical element 1, and which are concentrically and regularly arranged around the optical axis. Each of the recessed sections has a surface which is substantially parallel to the optical axis, and a surface inclined toward the optical axis; and has a substantially triangular cross section. In addition, the second diffraction grating 15 includes a plurality of raised sections which extend in the circumferential direction around the optical axis of the diffractive optical element 1, and which are concentrically and regularly arranged around the optical axis. Each of the raised sections has a surface which is substantially parallel to the optical axis, and a surface inclined toward the optical axis; and has a substantially triangular cross section. The first diffraction grating 14 and the second diffraction grating 15 have the same grating height and the same grating pitch. That is, the raised sections of the second diffraction grating 15 are fully engaged with the recessed sections of the first diffraction grating 14. As a result, the bonding surface 10a of the first optical member 10 contacts the bonding surface 11a of the second optical member 11 with no gap, thereby defining the single interface 12. Meanwhile, the first diffraction grating 14 and the second diffraction grating 15 together form the diffraction grating 13. Note, however, that a middle layer of, e.g., air, an anti-reflective film, and an adhesive, which has a refractive index different from those of the first diffraction grating 14 and the second diffraction grating 15 may be interposed between the bonding surface 10a and the bonding surface 11a as long as the bonding surface 10a and the bonding surface 11a are substantially parallel to each other.
Chamfering or R-chamfering may be applied to a valley of the recessed section of the first diffraction grating 14, and to a ridge of the raised section of the second diffraction grating 15 (i.e., a peak of the triangle as viewed in cross section). The inclined surface of the recessed section of the first diffraction grating 14, and the inclined surface of the raised section of the second diffraction grating 15 may be curved so as to define an aspherical or spherical surface.
A surface 10b of the first optical member 10 on a side opposite to the bonding surface 10a, and a surface 11b of the second optical member 11 on a side opposite to the bonding surface 11a are formed into flat surfaces parallel to each other. As illustrated in FIG. 1, e.g., light entering the diffractive optical element 1 from the first optical member 10 side is diffracted by the diffraction grating 13 to exit to the second optical member 11 side. Note that the surface 10b of the first optical member 10 and the surface 11b of the second optical member 11 may not be parallel to each other.
The diffractive optical element 1 configured as described above satisfies expressions (1) and (2):

α≧0.04  (1)

h≦263.18×α−0.9454  (2)

Within a range in which the expressions (1) and (2) are satisfied, even if material which is not optically transparent (i.e., material having an absorption coefficient α of greater than or equal to 0.04 mm−1) is used, the high diffraction efficiency can be realized. Thus, such material can be employed as the optical material of the first optical member 10. Specifically, the diffraction efficiency for the blaze wavelength λb can be greater than 85%.
Preferably, within a range satisfying an expression (3) in addition to the expressions (1) and (2), the diffraction efficiency can be greater than 90%:

h≧166.36×α−0.9444  (3)

More preferably, within a range satisfying an expression (4) in addition to the expressions (1) and (2), the diffraction efficiency can be greater than 95%:

h≦67.349×α−0.898  (4)

When using the diffractive optical element 1 for the interchangeable lens 200 as in the present embodiment, the diffractive optical element 1 is intended for white light. Thus, it is required that the wavelength dependency of the diffraction efficiency is low. For such a reason, the diffractive optical element 1 preferably satisfies an expression (5):

−6.30≦M≦−4.55  (5)

where M={n1(λ2)−n2(λ2)}/{n1(λ1)−n1(λ3)−n2(λ1)+n2(λ3)}; “n1(λ)” represents a refractive index of the first optical member for incident light having a wavelength λ; “n2(λ)” represents a refractive index of the second optical member for the incident light having the wavelength λ; “λ1” is 0.486133 μm; “λ2” is 0.587562 μm; and “λ3” is 0.656273 μm.
Specifically, in the expression (5), “λ1” is an F-line wavelength; “λ2” is a d-line wavelength; and “λ3” is a C-line wavelength. That is, a numerator of the fraction representing “M” is a difference between a reference refractive index (n1(λ2)) of the first optical member 10 and a reference refractive index (n2(λ2)) of the second optical member 11; and a denominator is a difference between a principal dispersion (n1(λ1)−n1(λ3)) of the first optical member 10 and a principal dispersion (n2(λ1)−n2(λ3)) of the second optical member 11. That is, “M” represents a ratio of an amount of change (difference) in the reference refractive indexes between the first optical member 10 and the second optical member 11, to an amount of change (difference) in the principal dispersions between the first optical member 10 and the second optical member 11. In the specification of the present disclosure, “M” is referred to as an “inter-material gradient.”
Wavelength dependency of diffraction efficiency of the diffractive optical element 1 is changed depending on the inter-material gradient M. The first and second optical members 10 and 11 are selected so that the expression (5) is satisfied, and then the first and second optical members 10 and 11 are used to produce the diffractive optical element 1. Thus, the diffraction efficiency of the diffractive optical element 1 can be uniformly enhanced across an entire visible wavelength range (range in which a wavelength is 0.400 μm-0.700 μm). That is, the wavelength dependency of the diffraction efficiency across the entire visible wavelength range can be reduced, and an average value of the diffraction efficiency across the entire visible wavelength range (hereinafter referred to as an “average diffraction efficiency across visible wavelength”) can be improved.
When using the diffractive optical element 1 for an optical device in which a wavelength of light to be used is limited, such as a pick-up device, it is preferred that only light having a particular wavelength is efficiently diffracted. In such a case, the first and second optical members 10 and 11 may be selected so that the wavelength dependency, i.e., the wavelength selectivity of the diffraction efficiency becomes higher. The optical materials of the first and second optical members 10 and 11 are selected within a range in which the inter-material gradient M is significantly out of the range specified by the expression (5).
In any cases, it is required that the first and second optical members are selected depending on the required optical performance, and there is a limitation to the optical material selection.
On the other hand, according to the present embodiment, the diffractive optical element 1 is configured so as to satisfy the expressions (1) and (2), thereby maintaining the high diffraction efficiency, and allowing light absorption. Consequently, the range of the optical material selection can be expanded. That is, an optical element is typically required, in which the absorption coefficient is as low as possible, i.e., the light is less absorbed. However, in view of the diffraction efficiency, the absorption is allowed within the range satisfying the expressions (1) and (2). Thus, even if the material having the absorption coefficient of greater than or equal to 0.04 mm−1, such as polycarbonate is used, such material can be employed as the optical material of the first optical member 10. Consequently, the diffraction efficiency can be maintained at high level, and the range of the optical material selection can be expanded.
EXAMPLES
Examples of the diffractive optical element will be described below. FIG. 3 is a schematic cross-sectional diagram of a diffraction grating used for a simulation.
It is assumed that the first optical member 10 is made of optical material having a complex refractive index, and the second optical member 11 is made of optical material having no absorption. As illustrated in FIG. 3, a grating pitch P of the diffraction grating 13 is 150 μm, and the blaze wavelength λb is at the d line (0.587562 μm). A simulation was performed by a rigorous coupled-wave analysis (RCWA) method while changing the grating height h within a range of 1-25 μm, and changing the complex refractive index. In this way, the diffraction efficiency of first-order diffracted light for the blaze wavelength λb was obtained. The diffraction efficiency for the grating height h (μm) and the absorption coefficient α (mm−1), which is obtained as described above is illustrated in FIG. 4.
As will be seen from FIG. 4, within a range satisfying expressions (1) and (2), the diffraction efficiency for the blaze wavelength λb can be greater than 85%:

α≧0.04  (1)

h≦263.18×α−0.9454  (2)

Thus, even if the absorption coefficient is greater than or equal to 0.04 mm−1, i.e., the optical material which is not optically transparent is used, the high diffraction efficiency can be realized as long as the expression (2) is satisfied. Thus, such material may be employed as the first optical member 10. Consequently, the range of the first optical member 10 to be selected can be expanded.
Preferably, within a range satisfying an expression (3) in addition to the expression (1), the diffraction efficiency can be greater than 90%:

h≦166.36×α−0.9444  (3)

More preferably, within a range satisfying an expression (4) in addition to the expression (1), the diffraction efficiency can be greater than 95%:

h≦67.349×α−0.898  (4)

As described above, the expression (3) or (4) is satisfied, and therefore the optical material which is not optically transparent is employed as the first optical member 10 while maintaining the high diffraction efficiency. That is, the range of the material selection can be expanded, and the diffraction efficiency can be further enhanced.
Next, a diffraction grating 13 illustrated in FIG. 5 is assumed. In this case, expressions (6) and (7) are satisfied:

φ(λ)=(h/λ)×{n1(λ)cos θm−n2(λ)cos θi}  (6)

n2(λ)sin θm=n1(λ)sin θi+mλ/P  (7)

where “φ(λ)” represents a phase difference; “h” represents a grating height (μm); “λ” represents a wavelength (μm); “m” represents a diffraction order; “n1(λ)” represents a refractive index of a first optical member for a wavelength λ; “n2(λ)” represents a refractive index of a second optical member for a wavelength λ; “θi” represents an angle of incidence (degrees); “θm” represents a m-order diffraction angle (degrees); and “P” represents a grating pitch (cycle) (μm).
The phase difference φ(λ) is used to obtain a diffraction efficiency ηm(λ) of m-order diffracted light for incident light having the wavelength λ based on an expression (8):

ηm(λ)=sinc2(φ(λ)−m)  (8)

In order to obtain a diffraction efficiency of first-order diffracted light for light incident in a direction parallel to an optical axis, θi=0 and m=1 are assumed. P>>λ is typically satisfied. Thus, the expression (7) provides θm=0. Consequently, each of the expressions (6) and (8) provides:

φ(λ)=(h/λ)×{n1(λ)−n2(λ)}  (9)

η1(λ)=sinc2(φ(λ)−1)  (10)

That is, the phase difference φ(λ) for each wavelength λ of the visible wavelength range can be obtained based on the expression (9) by changing the wavelength λ in a visible wavelength range. Further, by substituting the phase difference into the expression (10), a diffraction efficiency η1(λ) of first-order diffracted light for each wavelength λ of the visible wavelength range can be obtained. Then, the obtained diffraction efficiency η1(λ) is averaged across the visible wavelength range, and therefore an average diffraction efficiency η across visible wavelength can be obtained, which is an average value of the diffraction efficiency η1(λ) of first-order diffracted light in the visible wavelength range.
However, the expression (9) is a function not only for the wavelength λ, but also for the grating height h. The grating height h is determined depending on the blaze wavelength λb. That is, the blaze wavelength λb is equivalent to a diffraction efficiency ηm(λ) of 1 (i.e., 100%), thereby providing φ(λb)−m=0 based on the expression (8). This example is intended for the first-order diffracted light, and therefore φ(λb)=1 when m=1. When such a value is substituted into the expression (9), and the expression (9) is rearranged,

h=λb/{n1(λb)−n2(λb)}  (11)

As for material, a refractive index nd and an Abbe number vd of which at a d line are given, a refractive index n(λ) for each wavelength λ (μm) can be calculated based on the following Hertzberger's expressions (12)-(14):

A(λ)=0.088927×λ2−1.294878+0.37349/(λ2−0.035)+0.005799/(λ2−0.035)2  (12)

B(λ)=0.001255−0.007058×λ2+0.001071/(λ2−0.035)−0.000218/(λ2−0.035)2  (13)

n(λ)=1+(nd−1)×{1+B(λ)+(A(λ)/vd)}  (14)

Thus, the blaze wavelength λb and the materials of the first and second optical members 10 and 11 (i.e., a refractive index n1(λd) and an Abbe number vd1 at a d line of the first optical member 10, and a refractive index n2(λd) and an Abbe number vd2 at a d line of the second optical member 11) are first determined. Next, a refractive index n1(λb) of the first optical member 10 and a refractive index n2(λb) of the second optical member 11 for the blaze wavelength λb are obtained based on the expressions (12)-(14), and then such values are substituted into the expression (11) to obtain the grating height h. The obtained grating height h is substituted into the expression (9), and the wavelength λ is changed in the visible wavelength range. Then, the diffraction efficiency η1(λ) of first-order diffracted light for each wavelength λ is obtained based on the expression (10). At this point, the refractive index n1Q) of the first optical member 10 and the refractive index n2(λ) of the second optical member 11 for each wavelength λ are obtained based on the expressions (12)-(14). Finally, the diffraction efficiency η1(λ) of first-order diffracted light for each wavelength λ is averaged across the visible wavelength range to obtain the average diffraction efficiency η across visible wavelength.
Further, the inter-material gradient M is obtained based on an expression (15):

M={n1(λ2)−n2(λ2)}/{n1(λ1)−n1(λ3)−n2(λ1)+n2(λ3)}  (15)

where “n1(λ)” represents a refractive index of the first optical member for incident light having a wavelength λ; “n2(λ)” represents a refractive index of the second optical member for the incident light having the wavelength λ; “λ1” is 0.486133 μm; “λ2” is 0.587562 μm; and “λ3” is 0.656273 μm. As described above, the refractive index n1(λ) of the first optical member 10 and the refractive index n2(λ) of the second optical member 11 for each of the wavelengths λ1, λ2, and λ3 are obtained based on the expressions (12)-(14).
Thus, an average diffraction efficiency η1(λb, M) across visible wavelength for a certain inter-material gradient M and the blaze wavelength λb can be obtained.
The foregoing calculation is performed while changing the inter-material gradient M (i.e., at least one of the refractive index n1(λd) and the Abbe number vd1 at the d line of the first optical member 10; and the refractive index n2(λd) and the Abbe number vd2 at the d line of the second optical member 11) and the blaze wavelength λb. In such a manner, the average visible wavelength diffraction efficiencies η(λb, M) for various inter-material gradients M and blaze wavelengths λb can be obtained. Specifically, the blaze wavelength λb is changed by 0.001 μm within a range of 0.400 μm-0.700 μm. In addition, the refractive index n1(λd) at the d line of the first optical member 10 is fixed to 1.60000; the Abbe number vd1 of the first optical member 10 is fixed to 27.00; the refractive index n2(λd) at the d line of the second optical member 11 is fixed to 1.65000. The Abbe number vd2 of the second optical member 11 is changed to vary the inter-material gradient M. The results are illustrated in FIG. 6.
As will be seen from FIG. 6, the average diffraction efficiency η across visible wavelength can be improved within a range specified by an expression (5):

−6.30≦M≦−4.55  (5)

Specifically, selection of the suitable blaze wavelength λb allows the average diffraction efficiency η across visible wavelength to be greater than or equal to 98%, or further to be greater than or equal to 99% in some cases. The maximum value of the diffraction efficiency for the blaze wavelength λb is a constant value of 100%. Thus, the improvement of the average diffraction efficiency η across visible wavelength means reduction in deviation of the diffraction efficiency for each wavelength from 100%. That is, it means that the wavelength dependency of the diffraction efficiency across the entire visible wavelength range is reduced. The blaze wavelength λb is a design wavelength, and therefore can be relatively freely selected within, e.g., a range in which a desired optical performance can be realized in the diffractive optical element 1. In particular, as in the diffractive optical element 1, if the diffraction efficiency is uniformly high across the entire visible wavelength range, the high diffraction efficiency is realized for any wavelengths in the visible wavelength range. Thus, there is less limitation on the selection of the blaze wavelength λb. Consequently, as long as the first and second optical members 10 and 11 are selected so that the inter-material gradient M falls within the range specified by the expression (12), the blaze wavelength λb is adjusted as necessary to reduce the wavelength dependency of the diffraction efficiency in the visible wavelength range.
Within a range specified by expressions (16)-(18) or (19)-(21), the average diffraction efficiency η across visible wavelength can be further improved. The ranges corresponding to the expressions (16)-(18) and (19)-(21) are illustrated in FIG. 7. Data in some examples and comparative examples is illustrated in Table 1, and the diffraction efficiency in the visible wavelength range is illustrated in FIG. 8. A graph of the average diffraction efficiency η across visible wavelength based on the inter-material gradient M and the blaze wavelength λb in FIG. 7 is the same as that in FIG. 6.

0.400≦λb0.460  (16)

M≧1339242229.625×λb6−3467101052.6675×λb5+3739417158.03949×λb4−2150706261.50666×λb3+695699517.122797×λb2−120005677.292515×λb+8624042.63627238  (17)

M≦−1332094191.9375×λb6+3449257434.95906×λb5−3720886459.39374×λb4+2140458094.5947×λb3−692516647.829495×λb2+119479540.773725×λb−8587922.98149309  (18)

0.560≦λb≦0.650  (19)

M≧79855185.5390625×λb6291350087.799711×λb5+442815879.530274×λb4−358873164.839002×λb3+163567486.506001×λb2−39753252.4920047×λb+4024975.0978217  (20)

M≧−82526017.6289062×λb6+301239002.375121×λb5−458051447.988191×λb4+371372898.921825×λb3−169325896.092434×λb2+41165269.8970695×λb−4168933.51144255  (21)














TABLE 1












Average







Diffraction



First Optical Member
Second Optical Member

Efficiency




















Abbe


Abbe

Blaze
η across





Refractive
Number

Refractive
Number

Wavelength
Visible



Material
Index nd
νd
Material
Index nd
νd
Gradient M
λb (μm)
Wavelength





















Example 1-1
UV
1.60000
27.00
Hypothetical
1.65000
45.62
−6.27
0.409/0.587
99.0%
∘



Curable


Glass



Resin


Example 1-2
UV
1.60000
27.00
Hypothetical
1.65000
57.50
−4.58
0.447/0.632
99.0%
∘



Curable


Glass



Resin


Example 1-3
UV
1.60000
27.00
Hypothetical
1.65000
51.19
−5.25
0.432/0.607
99.3%
∘



Curable


Glass



Resin


Example 1-4
UV
1.60000
27.00
Hypothetical
1.65000
51.19
−5.25
0.449/0.569
99.0%
∘



Curable


Glass



Resin


Example 1-5
UV
1.60000
27.00
Hypothetical
1.65000
51.19
−5.25
0.420/0.641
99.0%
∘



Curable


Glass



Resin


Example 1-6
Acrylate
1.606
26.00
Phosphate
1.65650
48.7
−5.14
0.600
99.3%
∘



UV


Optical Glass



Curable



Resin


Example 1-7
Acrylate
1.606
26.00
K-VC78
1.66955
55.4
−5.66
0.588
99.2%
∘



UV


Manufactured



Curable


by Sumita



Resin


Optical Glass






Inc.


Example 1-8
SiO2TI2O
1.718
19.3
K-VC89
1.81000
41.0
−5.25
0.600
99.3%
∘



Sol-Gel


Manufactured



Glass


by Sumita






Optical Glass






Inc.


Comparative
UV
1.60000
27.00
Hypothetical
1.65000
51.19
−5.25
0.410/0.678
98.0%
x


Example 1-1
Curable


Glass



Resin


Comparative
UV
1.60000
27.00
Hypothetical
1.65000
51.19
−5.25
0.499
98.2%
x


Example 1-2
Curable


Glass



Resin


Comparative
UV
1.60000
27.00
Hypothetical
1.65000
63.17
−4.19
0.476/0.607
98.0%
x


Example 1-3
Curable


Glass



Resin


Comparative
UV
1.60000
27.00
Hypothetical
1.65000
41.53
−7.61
0.375/0.607
98.0%
x


Example 1-4
Curable


Glass



Resin









That is, a relationship with the blaze wavelength λb is considered in addition to the inter-material gradient M, thereby further improving the average diffraction efficiency η across visible wavelength. Specifically, as will be seen from FIG. 7, the average diffraction efficiency η across visible wavelength can be greater than or equal to 99%. In other words, the inter-material gradient M and the blaze wavelength are selected so that the expressions (17) and (18) are satisfied in a range in which the blaze wavelength 4 satisfies the expression (16). Alternatively, the inter-material gradient M and the blaze wavelength 4 are selected so that the expressions (20) and (21) are satisfied in a range in which the blaze wavelength λb satisfies the expression (19). In such a manner, the average diffraction efficiency η across visible wavelength can be further improved. As will be seen from FIG. 8, the deviation of the diffraction efficiency for each wavelength from 100% is reduced by improving the average diffraction efficiency across visible wavelength. Consequently, the wavelength dependency of the diffraction efficiency across the entire visible wavelength range can be further reduced. In addition, a less inter-material gradient M (i.e., a smaller absolute value of the inter-material gradient M) results in more degradation of the diffraction efficiency on a shorter wavelength side, whereas a greater inter-material gradient M (i.e., a larger absolute value of the inter-material gradient M) results in more degradation of the diffraction efficiency on a longer wavelength side.
Note that the expressions (16) and (19) provide a rough estimate of the blaze wavelength λb, and even the blaze wavelength λb falling within such an estimate may not satisfy the expressions (17) and (18), or (20) and (21). That is, it is required that the blaze wavelength λb satisfies the expression (16) or (19), as well as the expressions (17) and (18), or (20) and (21).
When satisfying expressions (22)-(26) within each of ranges of the blaze wavelength λb in (i)-(iii), the average diffraction efficiency η across visible wavelength can be improved. The ranges corresponding to the expressions (22)-(26) are illustrated in FIG. 9. Data in some examples and comparative examples is illustrated in Table 2, and the diffraction efficiency in the visible wavelength range is illustrated in FIG. 10. A graph of the average diffraction efficiency η across visible wavelength based on the inter-material gradient M and the blaze wavelength λb in FIG. 9 is the same as that in FIG. 6.
(i) When 0.402≦λb<0.423,

M≧−5.67  (22)

M≦−2059169.7421875×λb6+5816357.49453125×λb5−6788300.15627441×λb4+4193835.50001671×λb3−1448014.62341355×λb2+265253.074154754×λb−20174.8108751328  (23)

(ii) When 0.423×λb<0.664,

−5.67≦M≦−4.70  (24)

(iii) When 0.664≦λb≦0.695,

M≧−1737676.76663208×λb6+6606429.15555359λb5−10426872.1241855×λb4+8742622.74935995×λb3−4106195.43419261×λb2+1024012.6733048×λb−105911.832822947  (25)

M≦−4.70  (26)














TABLE 2












Average







Diffraction



First Optical Member
Second Optical Member

Efficiency




















Abbe


Abbe

Blaze
η across





Refractive
Number

Refractive
Number

Wavelength
Visible



Material
Index nd
νd
Material
Index nd
νd
Gradient M
λb (μm)
Wavelength





















Example 2-1
UV
1.60000
27.00
Hypothetical
1.65000
48.49
−5.67
0.488
98.0%
∘



Curable


Glass



Resin


Example 2-2
UV
1.60000
27.00
Hypothetical
1.65000
56.11
−4.70
0.514
98.0%
∘



Curable


Glass



Resin


Example 2-3
UV
1.60000
27.00
Hypothetical
1.65000
51.19
−5.25
0.410/0.678
98.0%
∘



Curable


Glass



Resin


Example 2-4
UV
1.60000
27.00
Hypothetical
1.65000
51.19
−5.25
0.499
98.2%
∘



Curable


Glass



Resin


Example 2-5
UV
1.60000
27.00
Hypothetical
1.65000
48.49
−5.67
0.402/0.664
98.0%
∘



Curable


Glass



Resin


Example 1-6
Acrylate
1.606
26.00
Phosphate
1.65650
48.7
−5.14
0.600
99.3%
∘



UV


Optical Glass



Curable



Resin


Example 1-7
Acrylate
1.606
26.00
K-VC78
1.66955
55.4
−5.66
0.588
99.2%
∘



UV


Manufactured



Curable


by Sumita



Resin


Optical Glass






Inc.


Example 1-8
SiO2TI2O
1.718
19.3
K-VC89
1.81000
41.0
−5.25
0.600
99.3%
∘



Sol-Gel


Manufactured



Glass


by Sumita






Optical Glass






Inc.


Comparative
UV
1.60000
27.00
Hypothetical
1.65000
48.49
−6.92
0.488
97.0%
x


Example 2-1
Curable


Glass



Resin


Comparative
UV
1.60000
27.00
Hypothetical
1.65000
48.49
−4.13
0.514
97.0%
x


Example 2-2
Curable


Glass



Resin


Comparative
UV
1.60000
27.00
Hypothetical
1.65000
51.19
−5.25
0.405/0.702
97.0%
x


Example 2-3
Curable


Glass



Resin









As will be seen from FIG. 9, within all of the ranges satisfying the expressions (22)-(26), the average diffraction efficiency η across visible wavelength is greater than or equal to 98%. Such ranges covers the substantially entire visible wavelength range. Thus, if the first and second optical members 10 and 11 are selected so that the expressions (22)-(26) are satisfied, the average diffraction efficiency η across visible wavelength can be greater than or equal to 98% for any blaze wavelengths λb in the visible wavelength range. That is, the blaze wavelength λb and the first and second optical members 10 and 11 can be more flexibly selected while the wavelength dependency of the diffraction efficiency across the entire visible wavelength range can be reduced.
Various combinations of the first and second optical members 10 and 11, which are selected so as to have the same inter-material gradient M are illustrated in Table 3 and FIG. 11. A vertical axis of a graph in FIG. 11 is a reference refractive index (n(λd)), and a horizontal axis is a principal dispersion (n(λF)−n(λC)).
















TABLE 3










Second



Refractive



First Optical
Refractive
Abbe
Optical
Refractive
Abbe

Index



Member
Index nd
Number νd
Member
Index nd
Number νd
Gradient M
Difference
























Example
SiO2/TI2O
1.503345
48.31435
BSL7
1.51633
64.1
−5.495
0.012985


3-1


Example
SiO2/TI2O
1.528818
38.87719
BAL5
1.547393
53.5507
−5.495
0.018575


3-2


Example
SiO2/TI2O
1.532572
37.84758
BAL50
1.559625
61.1727
−5.495
0.027053


3-3


Example
SiO2/TI2O
1.5375
36.59582
BAL22
1.568729
63.1624
−5.495
0.031229


3-4


Example
SiO2/TI2O
1.548684
34.1104
BAL42
1.58313
59.4
−5.495
0.034446


3-5


Example
SiO2/TI2O
1.564346
31.27741
BSM7
1.607291
59.3756
−5.495
0.042945


3-6


Example
SiO2/TI2O
1.585108
28.35037
BSM81
1.64
60.1
−5.495
0.054892


3-7


Example
SiO2/TI2O
1.598666
26.80608
LAL11
1.658293
57.3326
−5.495
0.059627


3-8


Example
SiO2/TI2O
1.612819
25.4257
LAL12
1.6779
55.3
−5.495
0.065081


3-9


Example
SiO2/TI2O
1.646697
22.82156
LAL18
1.72916
54.7
−5.495
0.082463


3-10


Example
SiO2/TI2O
1.665617
21.67982
YGH51
1.755
52.3
−5.495
0.089383


3-11


Example
SiO2/TI2O
1.699478
20.0224
LAH67
1.794997
45.294
−5.495
0.095519


3-12


Example
SiO2/TI2O
1.72959
18.85305
LAH55
1.83481
42.7
−5.495
0.10522


3-13


Example
SiO2/TI2O
1.769819
17.60496
LAH75
1.873996
35.286
−5.495
0.104177


3-14









The first optical member 10 is SiO2-Tl2O glass formed by mixing SiO2 and Tl2O together, and a mixing ratio of such components is changed to realize various refractive indexes n1(λd) and Abbe numbers vd1. The second optical member 11 is optical glass manufactured by Ohara Inc., and is illustrated with model numbers in Table 2. In any of the combinations of the first and second optical members 10 and 11, the inter-material gradient M is −5.495. That is, in FIG. 9, a line connecting between the first optical member 10 and the second optical member 11 in each of the combinations is parallel to other lines.
In each of the combinations of the first and second optical members 10 and 11, the blaze wavelength λb is set to 0.605 μm, and then the grating height h is obtained based on the expressions (11)-(14). The obtained grating height h is used to obtain the average diffraction efficiency η across visible wavelength as described above. That is, the grating height h is substituted into the expression (9), and the wavelength λ is changed in the visible wavelength range. Then, the diffraction efficiency η1(λ) of first-order diffracted light for each wavelength λ is obtained based on the expression (10). Finally, the diffraction efficiency η1(λ) of first-order diffracted light for each wavelength λ, is averaged across the visible wavelength range to obtain the average diffraction efficiency η across visible wavelength. Table 4 illustrates the average diffraction efficiency η across visible wavelength and diffraction efficiencies η1(λ) for some representative wavelengths in each of the combinations corresponding to Table 3.









TABLE 4









Diffraction Efficiency (%)




















Average












Diffraction





Efficiency



Blaze
Grating
η across



Wavelength
Height h
Visible



λb (μm)
(μm)
Wavelength
0.400 μm
0.450 μm
0.500 μm
0.550 μm
0.600 μm
0.650 μm
0.700 μm





















Example
0.605
45.9
99.3
97.5
99.4
98.8
99.4
100.0
99.4
97.1


3-1


Example
0.605
32.1
99.3
97.5
99.4
98.8
99.4
100.0
99.4
97.1


3-2


Example
0.605
22.0
99.3
97.5
99.4
98.8
99.4
100.0
99.4
97.1


3-3


Example
0.605
19.1
99.3
97.5
99.4
98.8
99.4
100.0
99.4
97.1


3-4


Example
0.605
17.3
99.3
97.5
99.4
98.8
99.4
100.0
99.4
97.1


3-5


Example
0.605
13.9
99.3
97.5
99.4
98.8
99.4
100.0
99.4
97.1


3-6


Example
0.605
10.9
99.3
97.5
99.4
98.8
99.4
100.0
99.4
97.1


3-7


Example
0.605
10.0
99.3
97.5
99.4
98.8
99.4
100.0
99.4
97.1


3-8


Example
0.605
9.2
99.3
97.5
99.4
98.8
99.4
100.0
99.4
97.1


3-9


Example
0.605
7.2
99.3
97.5
99.4
98.8
99.4
100.0
99.4
97.1


3-10


Example
0.605
6.7
99.3
97.5
99.4
98.8
99.4
100.0
99.4
97.1


3-11


Example
0.605
6.2
99.3
97.5
99.4
98.8
99.4
100.0
99.4
97.1


3-12


Example
0.605
5.7
99.3
97.5
99.4
98.8
99.4
100.0
99.4
97.1


3-13


Example
0.605
5.7
99.3
97.5
99.4
98.8
99.4
100.0
99.4
97.1


3-14









As will be seen from Table 4, an identical pair of the inter-material gradient M and the blaze wavelength produces constant diffraction efficiency λ1(λ) for each wavelength and constant average diffraction efficiency η across visible wavelength. The graphs of FIGS. 6, 7, and 9 illustrate the results when the inter-material gradient M is changed by changing the Abbe number vd2 of the second optical member 11 in the state in which the refractive index n1(λd) and the Abbe number vd1 at the d line of the first optical member 10, and the refractive index n2(λd) at the d line of the second optical member 11 are fixed to the predetermined values. However, an identical inter-material gradient M produces constant average diffraction efficiency η across visible wavelength for the certain blaze wavelength λb. Thus, even if the refractive index n1(λd) and the Abbe number vd1 at the d line of the first optical member 10, and the refractive index n2(λd) at the d line of the second optical member 11 are different, results similar to those in FIGS. 6, 7, and 9 may be obtained. Thus, the expressions (5) and (16)-(26) are satisfied regardless of the refractive index n1(λd) and the Abbe number vd1 at the d line of the first optical member 10, and the refractive index n2(λd) and the Abbe number vd2 at the d line of the second optical member 11.
As described above, the first and second optical members 10 and 11 are selected within the proper range, thereby reducing the wavelength dependency of the diffraction efficiency. In other words, in order to reduce the wavelength dependency of the diffraction efficiency, it is required that the first and second optical members 10 and 11 are selected within the proper range as described above. The foregoing results show that the wavelength dependency (i.e., wavelength selectivity) of the diffraction efficiency can be improved depending on the way to select the first and second optical members 10 and 11. That is, the inter-material gradient M is selected within the range in which the average diffraction efficiency across visible wavelength is low in the graph of FIG. 6, and then the first and second optical members 10 and 11 are selected so that such an inter-material gradient M can be realized. Thus, the wavelength dependency of the diffraction efficiency can be improved.
As described above, even if the wavelength dependency of the diffraction efficiency is reduced or improved, it is required that the proper inter-material gradient M is selected, and then the first and second optical members 10 and 11 are selected so that such an inter-material gradient M can be realized. In such a case, although the range of the optical material selection is narrowed, an optical member absorbing light can be also considered as an alternative of the first and second optical members 10 and 11 within the range satisfying the expression (1), and one of the expression (2), (3), or (4). Thus, the high diffraction efficiency can be maintained, and the range of the optical material selection can be expanded.
Other Embodiments
The present disclosure may have the following configurations in the foregoing embodiment.
That is, in the foregoing embodiment, the diffractive optical element 1 is employed in the interchangeable lens 200, but the present disclosure is not limited to such a configuration. The diffractive optical element 1 may be employed as a lens element inside the camera 100. In addition, the present disclosure is not limited to the diffractive optical element 1 serving as the lens, and the diffractive optical element 1 may be applied for purposes other than the foregoing purpose.
In the foregoing embodiment, the first optical member 10 is made of resin material, and the second optical member 11 is made of glass material. However, the present disclosure is not limited to such a configuration. The first optical member 10 may be made of glass material, and the second optical member 11 may be made of resin material. Alternatively, both of the first and second optical members 10 and 11 may be made of glass material or resin material. In addition, the first optical member 10 is made of the optical material having the absorption, and the second optical member 11 is made of the optical material having no absorption. However, the present disclosure is not limited to such a configuration. The first optical member 10 may be made of optical material having no absorption, and the second optical member 11 may be made of optical material having absorption. Alternatively, both of the first and second optical members 10 and 11 may be made of optical material having absorption.
The first and second optical members 10 and 11 may be made of material formed by mixing inorganic particulates (so-called “nanocomposites”) with resin. The inorganic particulates can adjust the refractive index and the Abbe number of the optical member.
The diffractive optical element 1 of the foregoing embodiment and examples is configured so that the conditions where the wavelength dependency of the diffraction efficiency is reduced are satisfied, but the present disclosure is not limited to such a configuration. The diffractive optical element 1 may not satisfy the conditions for the wavelength dependency of the diffraction efficiency. In particular, the diffractive optical element may be employed, in which the wavelength selectivity of the diffraction efficiency is improved.
If there are various grating heights as illustrated in FIG. 12, a distance between an intersection point of a line parallel to the optical axis, and one of the adjacent inclined surfaces; and an intersection point of the line and the other inclined surface is the grating height h.
The refractive index n(A) for each wavelength λ is calculated based on the Hertzberger's expressions, but the present disclosure is not limited to such a configuration. The refractive index n(λ) may be an actual measured value, or may be a value calculated by a publicly-known method.
The foregoing embodiments have been set forth merely for purposes of preferred examples in nature, and are not intended to limit the scope, applications, and use of the present disclosure.
As described above, the present disclosure is useful for the diffractive optical element in which the two optical members are stacked, and the diffraction grating is formed at the interface between the two optical members.

## Claims

1. A diffractive optical element, comprising:
first and second optical members which are stacked, and which have a diffraction grating formed at an interface between the first and second optical members,
wherein an absorption coefficient a (mm−1) of the first optical member and a grating height h (μm) of the diffraction grating in an entire wavelength range of 400-700 nm satisfy expressions (1) and (2):


α≧0.04  (1)



h≦263.18×α−0.9454  (2)

2. The diffractive optical element of claim 1, wherein
the absorption coefficient a (mm−1) of the first optical member and the grating height h (μm) of the diffraction grating further satisfy an expression (3):


h<166.36×α−0.9444  (3)

3. The diffractive optical element of claim 1, wherein
the absorption coefficient a (mm−1) of the first optical member and the grating height h (μm) of the diffraction grating further satisfy an expression (4):


h≦67.349×α−0.898  (4)

4. An optical device, comprising:
an optical imaging system for focusing light bundles on a predetermined surface,
wherein the optical imaging system has the diffractive optical element of claim 1.