JP2013186445A - Optical apparatus - Google Patents

Abstract

An optical system capable of adjusting an average power and astigmatism with only two lenses, and particularly capable of adjusting astigmatism without separately rotating the two lenses when adjusting astigmatism. An optical device is provided.
For a base shape having a reference surface for synthesizing an additional sag amount on the front and back surfaces, a curved surface represented by the following formula is synthesized as an additional sag amount on one of the surfaces. And the second lens element is obtained, and the first and second lens elements are arranged in parallel so as to coincide with each other in the X-axis and Y-axis directions to constitute an optical system. The amount of astigmatism is controlled by causing the lens element to move two-dimensionally.

[Selection figure] None

Description

  The present invention relates to an optical apparatus including an optical system using lenses such as glasses, an optometry apparatus, and a laser beam pickup.

In general optical products, second-order aberrations among high-order aberrations are expressed as “average power, astigmatism magnitude, and astigmatism direction”. The power of the spectacle lens generally represents second-order aberration by “S power / C power / axis”. The S frequency is a plus or minus frequency (which is optional), and the axis indicates the direction. In the frequency with astigmatism, the C frequency is a value obtained by subtracting the S frequency from the frequency on the side different from the S frequency. In the frequency without astigmatism, the C frequency is 0D.
Conventionally, a technique for setting a user's arbitrary average power or astigmatic power (C power) by combining a plurality of lenses has been proposed. For example, Patent Document 1 discloses an optometry system that sets an average power by moving two aspherical lenses up and down in the vertical direction and further sets the astigmatism power by rotating two cylinder lenses. Yes. If this idea is applied, it is possible to provide an optical device capable of adjusting the average power and the astigmatism power (or astigmatism) with one optical system.

JP 2004-657 A

However, adjusting the average power and astigmatism with as many as four lenses as in Patent Document 1 is very complicated, and transmitted light is attenuated by passing through as many as four lenses, and a ghost is generated due to reflection. This is not preferable because it includes an aberration component inherent in each lens. Further, since the thickness and weight increase as the number of lenses increases, it is extremely unsuitable as a lens for eyeglasses. Furthermore, in the optical system of Patent Document 1, a cylinder lens is used to adjust the astigmatism power (astigmatism), and the two cylinder lenses are operated so as to be rotated separately, respectively. (Aberration) is adjusted, but it must be adjusted in cooperation with a lens for adjusting the average power, and the operation is complicated. Therefore, an optical system provided with an optical system that can adjust the average power and astigmatism with only two lenses, or that does not operate to rotate the two lenses separately to adjust astigmatism. A device was sought.
The present invention has been made paying attention to such problems existing in the prior art. An object of the present invention is to adjust the average power and astigmatism with only two lenses, and in particular to adjust astigmatism without rotating the two lenses separately when adjusting astigmatism. An object of the present invention is to provide an optical device including an optical system that can be used.

  In order to solve the above-mentioned problem, in the invention of claim 1, the X-axis direction and the Y-axis direction orthogonal to each other on a two-dimensional plane perpendicular to the optical axis are set, and are represented by the X-axis and the Y-axis. A plurality of new axial directions existing on the two-dimensional plane are set based on the coordinates, and the refractive power of the cross section determined by the refractive index of the medium before and after the surface along the same axial direction and the curvature of the cross section in that direction. Design a curved surface that has a curved shape that changes linearly and continuously along each axial direction, and either one of the base shapes on which the reference surface for synthesizing the additional sag amount is formed on the front and back The first and second lens elements are obtained by synthesizing the curved surface with the surface, and the first and second lens elements have the X-axis and Y-axis directions and the new plurality of axial directions. Place them in parallel to match each other And the optical system, and its gist in that so as to control the astigmatism amount by which the two-dimensional movement to said first and second lens elements.

Further, in the invention of claim 2, in addition to the configuration of the invention of claim 1, the curved surface of the first lens element is defined by the following equation 1, and the curved surface of the second lens element is A medium having a refractive index n ₁₁ , the curved surface of the first lens element, a medium having a refractive index n _12, a medium having a refractive index n ₂₂ , the curved surface and the refraction of the second lens element. that the expression of the following expression 3 holds as its gist if it is arranged in the order of medium rate n _21.

Further, in the invention of claim 3, in addition to the configuration of the invention of claim 1 or 2, the two-dimensional movement is a movement direction of the two lens elements relatively in the two-dimensional plane. The gist is that it enables linear movement in a plurality of directions that are not parallel to each other.
Further, in the invention of claim 4, in addition to the configuration of the invention of claim 1 or 2, the two-dimensional movement means that the two lens elements are rotated in the same direction around the optical axis. The gist is that the two lenses can be linearly moved in a plurality of directions in which the flow line directions are not relatively parallel to each other in the two-dimensional plane at a predetermined rotational displacement position. And

According to a fifth aspect of the invention, in addition to the configuration of the first or second aspect of the invention, the two lens elements are relatively moved along a certain first direction, whereby the first The cross-sectional refractive power in the direction is increased / decreased, and the direction perpendicular to the first direction is not increased / decreased, and the relative power is moved along the second direction that is not parallel to the first direction. The gist of the invention is that the cross-sectional refractive power in the second direction is increased or decreased and the cross-sectional refractive power is not increased or decreased in the direction orthogonal to the second direction.
Further, in the invention of claim 6, in addition to the configuration of the invention of claim 3 or 4, the two lens elements are moved relative to each other along a specific first direction, whereby cross-sectional refraction in all directions is achieved. By increasing or decreasing the force evenly and relatively moving along a second direction that is not parallel to the first direction, the cross-sectional refractive index in the second direction is increased or decreased and orthogonal to the second direction. The gist is not to increase or decrease the cross-sectional refractive power.

Further, in the invention of claim 7, in addition to the structure of the invention of claim 5, astigmatism in a certain direction can be obtained by relatively moving the two lens elements along a certain first direction. Astigmatism in a direction different from the above is increased or decreased by relatively moving along a second direction that is not parallel to the first direction. The gist is that the average frequency does not change due to movement of.
According to an eighth aspect of the present invention, the curved surface of the first lens element defined by the formula 1 is defined as the curved surface of the lens element according to the fifth or sixth aspect, and the mathematical formula 2 is defined. The curved surface of the second lens element has a relationship of A ₁ = A ₂ and B ₁ = B ₂ , and the medium having the refractive index n ₁₁ , the medium having the refractive index n ₁₂ , and the medium having the refractive index n ₂₂ When the medium having the refractive index n ₂₁ has a relationship of n ₁₁ = n ₂₁ and n ₁₂ = n ₂₂ , the gist of the curved surfaces of the both lens elements is defined by the following equation (4): And

According to a ninth aspect of the present invention, the curved surface of the first lens element defined by the formula (1) as the curved surface of the lens element according to the seventh aspect and the first defined by the formula (2). The curved surface of the lens element _{2 has} a relationship of A ₁ = A ₂ and B ₁ = B ₂ , and the medium having the refractive index n ₁₁ , the medium having the refractive index n ₁₂ , the medium having the refractive index n ₂₂ , When the medium having a refractive index n ₂₁ has a relationship of n ₁₁ = n ₂₁ and n ₁₂ = n ₂₂ , the curved surface of the lens element is defined by the following equation (5), and A, B, C in the equation: , P, q are summarized in the relationship of the following formula (6).

  The gist of the invention of claim 10 is that the curved surfaces of the two lens elements of claim 9 are defined by the following formula.

The gist of the invention of claim 11 is that the reference surface for synthesizing the additional sag amount on the front and back surfaces is any one of a spherical surface, a flat surface, and an astigmatic surface.
Further, in the invention of claim 12, in addition to the structure of the invention of any one of claims 1 to 11, the two lens elements are simultaneously moved in opposite directions when moved linearly. The gist.
The gist of the invention of claim 13 is that, in addition to the configuration of the invention of claim 12, the two lens elements are simultaneously moved in the opposite directions by the same distance.
Further, the invention of claim 14 is characterized in that, in addition to the configuration of the invention of any one of claims 1 to 13, the two lens elements are arranged in surface contact with each other.
Further, the gist of the invention of claim 15 is that, in addition to the configuration of the invention of any one of claims 1 to 14, an optical functional film is interposed between the two lens elements.
The gist of the invention of claim 16 is that the optical device of claims 1 to 15 is glasses.

In the configuration as described above, first, a plurality of new axial directions existing on a two-dimensional plane perpendicular to the optical axis are set, the refractive index of the medium before and after the surface along each axial direction, and the A curved surface having a curved shape in which the cross-sectional refractive power determined by the curvature of the cross-section in a direction changes linearly and continuously along each axial direction is synthesized with either one of the front and back surfaces of the base shape. 2 lens elements are obtained. The curved surface characteristics synthesized in both lens elements are not necessarily the same. Here, as a method of synthesizing a curved surface with a reference surface for synthesizing the additional sag amount of the base shape, it is preferable to provide a curved surface as the additional sag amount because it is easy to calculate.
The first and second lens elements that combine the curved surfaces as described above are arranged in parallel so that the optical axes coincide with each other and the X-axis and Y-axis directions and the plurality of axial directions all coincide with each other to constitute an optical system. If such axis coincidence is obtained, the direction of the surface is basically not limited regardless of whether the front and back surfaces of the lens element are the object side or the eyeball side. By moving the first and second lens elements two-dimensionally, the amount of astigmatism of the optical system can be controlled.
With such a configuration, it is possible to easily control the amount of astigmatism by only two-dimensionally moving a two-dimensional plane perpendicular to the optical axis using only two lens elements. it can.

Here, “two-dimensional movement” means that a plurality of displacements (coordinate movements) are performed independently from one position to another position. For example, a straight line movement in a plurality of directions is representatively given. The movement amount is defined by two coordinates in the X-axis direction and the Y-axis direction, but the movement in the X-axis direction and the Y-axis direction may be performed separately or simultaneously. The simple rotation in the circumferential direction is not considered as a two-dimensional movement in the present invention.
Moreover, it does not matter that a plurality of new axial directions coincide with the X-axis and Y-axis directions.
In the present application, there are a plurality of new axial directions existing on the two-dimensional plane, that is, the first and second curved surfaces having curved shapes that change linearly and continuously along the axial directions with respect to two or more axes. The lens element is supposed to have. A lens pair that combines a lens element that has only one axis and has a curved surface that has a curved shape that changes linearly and continuously along the axial direction can be moved in any way. The cross-sectional refractive power in the direction orthogonal to the axis is not increased or decreased. Such optical products are eliminated. Further, an optical product having a structure in which the optical axis direction of an optical system composed of two lens elements is made to coincide with each other and rotated relatively, such as a cross cylinder lens, is excluded. Further, the surface of the cross-cylinder lens is excluded in that sense because the curve along the axis does not increase or decrease regardless of the direction in which the axis is taken.
When the first and second lens elements are each a single lens composed of two surfaces, and the surfaces are used by joining the surfaces, the material refractive indexes of the first and second lens elements are the same. It is desirable that This is because if there is a difference in refractive index between the two lenses, reflection occurs on the cemented surface. If the refractive index difference is small, the reflection is small, but a gap is generated on the joint surface, and if the gap is not constant depending on the location, interference fringes are generated. However, there is no problem when using a light control film / polarizing film between the bonding surfaces. When making a difference between the refractive indexes of the two lenses, the additional sag amount is proportionally distributed according to the value of 1 / (each refractive index-1).

As specific two-dimensional movement of the first and second lens elements, the first and second lens elements are linearly moved in a plurality of directions in which the flow line directions are relatively not parallel to each other in the two-dimensional plane. It is conceivable to move it. This movement pattern is reflected in Examples 1 and 2 in the present application.
Similarly, as the two-dimensional movement, the first and second lens elements are rotated in the same direction around the optical axis and the two lenses are moved two-dimensionally at a predetermined rotational displacement position. It is conceivable to move linearly in a plurality of directions in which the flow line directions are not relatively parallel to each other in the plane. By rotating the first and second lens elements in the same direction around the optical axis, the axial direction of astigmatism can be freely changed, and astigmatism with reference to the predetermined axial direction of astigmatism. The amount can be controlled. For example, this corresponds to rotating the first and second lens elements in the first and second embodiments.

  In addition, as a case where predetermined optical characteristics are given to the optical system by two-dimensional movement, the first and second lens elements are relatively moved along a certain first direction, so that the first The cross-sectional refractive power in the direction is increased or decreased, and the cross-sectional refractive power is not increased or decreased in the direction orthogonal to the first direction, but is relatively moved along the second direction that is not parallel to the first direction. It is conceivable to increase or decrease the cross-sectional refractive power in the second direction and not increase or decrease the cross-sectional refractive power in the direction orthogonal to the second direction. This movement pattern is reflected in Examples 1 and 2 in the present application.

Further, as a case where predetermined optical characteristics are given to the optical system by two-dimensional movement, the sectional refractive powers in all directions can be obtained by relatively moving two lens elements along a certain first direction. For the direction orthogonal to the second direction, the cross-sectional refractive index in the second direction is increased or decreased by relatively moving along the second direction that is not parallel to the first direction. It is conceivable that the cross-sectional refractive power is not increased or decreased. This movement pattern is reflected in Examples 1 and 2 in the present application.
In addition, astigmatism in a certain direction is increased or decreased by relatively moving the two lens elements along a certain first direction, and in a second direction that is not parallel to the first direction. It can be considered that the astigmatism in the direction different from the above is increased or decreased by relatively moving along the direction, and the average power is not changed by the movement in the first and second directions. This movement pattern is reflected in Example 3 in the present application.

Here, the relationship between the surface shape and the refractive power will be outlined.
An equation of a circle having a radius R and a center (0, R) is represented by x ² + (y−R) ² = R ² .
This equation is transformed as y = R−√ (R ² −x ² ). However, when obtaining the square root, since it is a compound minus of √, it represents a region close to the X axis of the circle. This equation is approximated as follows near the origin where the value of x is sufficiently small with respect to R.
y = R−R (1−x ² / R ² ) ^1/2 ≈R−R + R · (x ² / R ² ) · (1/2) = (1/2) x ² / R
When second order differentiation is performed with y = (1/2) x ² / Rx, ∂ ² f (x) / ∂x ² = 1 / R is obtained. From this, the second derivative at a certain point on the curve is the reciprocal of the radius of curvature, that is, the curvature.
When the upper side of the circle is vacuum or air having a refractive index of 1, the material refractive index of the lower side of the circle is n, and the curvature is multiplied by 1000 (n-1), surface power is obtained. The reason why 1000 is multiplied is because R is expressed in mm. When R is expressed in m, (n-1) is multiplied to obtain surface refractive power.
From the above, the cross-sectional refractive power in the X-axis direction can be obtained from ∂ ² f (x) / ∂x ² · 1000 (n-1).
The above description relates to a circular cross section, but for a lens having a three-dimensional solid shape, the difference between the second-order partial differential values at two corresponding points on the outer surface and inner surface of the lens is multiplied by 1000 (n-1). Refractive power (called power in eyeglass lenses) is obtained. Here, various cross-sectional directions including a direction along the X-axis and a direction along the Y-axis are assumed, and cross-sectional refractive power is obtained by performing second-order partial differentiation with respect to that direction. Of the cross-sectional refractive powers in all directions, the difference between the maximum value and the minimum value is called astigmatism, and half thereof is called astigmatism. The average value of the cross-sectional refractive powers in all directions is called the average refractive power.

The curved surface synthesized with the first and second lens elements can be defined by the above formulas 1 and 2 generalized as more specific curved surfaces.
Equations 1 and 2 are defined for each of the first and second lens elements. When these are generalized,

It becomes. The general formula of Equation 5 is a cubic function of x and y. In order to construct a curved surface having a curved shape that changes linearly and continuously as described above, the mathematical expression must be a cubic equation. In this expression, only the first-order terms of x and y remain by second-order partial differentiation with x or second-order partial differentiation with y. Since the value at a point of a function obtained by second-order partial differentiation of a function means that the value is proportional to the cross-sectional curve in the direction of partial differentiation at that point, this equation is a shape in which the curve changes linearly and continuously. Represents. In the present application, a curved surface having a curved shape that changes linearly and continuously along one axial direction is referred to as a partial tertiary structure. A structure that has only two axes and includes not only the case where they are orthogonal but also the case where they are not orthogonal is referred to as a bi-cubic structure.
The general formula of Formula 5 is a general form that can include all of the following examples. Depending on the shape of the object to be considered, the coordinates are rotated and the X coordinate is used as a reference, so A ≠ 0.
C (x + qy) No matter what value q is in the term ³ , the curve in the Y-axis direction cannot be expressed. Therefore, in order to be able to represent a curve in the Y-axis direction when p = 0 in the term B (px + y) ³ , B ≠ 0.
Term Ax ³ represents polarized tertiary structure of the X-axis direction. Here, this direction is also referred to as the A-axis direction.
The term B (px + y) ³ represents a partial tertiary structure in a direction different from the X-axis direction, that is, the A-axis direction (not parallel nor reversing). This direction will be referred to as the B-axis direction. In the first embodiment, B = A, and in the second embodiment, B = 2A. However, both C = 0 and p = 0, and the B-axis direction matches the Y-axis direction.
C (x + qy) ³ represents a partial tertiary structure in a direction different from both the A axis and the B axis. This direction will be referred to as the C-axis direction. In Example 3, B = A, C = −A / 2, p = 0, q = 1, and represents a partial tertiary structure in the linear direction represented by y = x. In this state, the B-axis direction coincides with the Y-axis direction, and the C-axis forms 135 degrees with the A-axis and the B-axis.
As described above, the B-axis and the C-axis can coincide with the Y-axis direction, but it does not necessarily have to coincide. It is also possible to add fourth and subsequent eccentric tertiary structures in the direction different from all of the A axis, B axis, and C axis. In that case, a term of the form “D (rx + sy) ³ ” is further added to Equation 5. However, it is assumed that D ≠ 0 and the ratio of r: s does not coincide with p: 1 or 1: q. What added such a new axis is also included in the present invention.

Further, the general formula of Formula 5 does not necessarily mean that the curved surfaces of the first and second lens elements must be the same. If the curved surfaces of the first and second lens elements are defined as shown in Equations 1 and 2, it is sufficient if the conditions as shown in Equation 3 can be obtained, and therefore there may be different curved surfaces. Furthermore, the reference surface for synthesizing the additional sag amounts of the base shapes of the first and second lens elements need not be the same.
In the equation (3), the relationship between the “medium with a refractive index n ₁₂ ” and the “medium with a refractive index n ₂₂ ” may be any of the following (1), (2), and (3).
(1) The refractive indexes of the two media may be the same or different.
(2) The two media may be the same liquid. In that case, the two media may or may not be separated on some surface.
(3) There may be other media (including air and vacuum) or another lens system between the two media.

This general formula (5) can be applied to a functional expression representing a curved surface structure that can be applied to some more specific inventions of the present application.
For example, in the case of C = 0 and p = 0, the formula represents a bicubic structure in which two axes are orthogonal. Specifically, it is a bi-cubic structure expressed by a functional expression of Formula 4. The formula (4) is used for the curved surface of the bicubic structure of the first and second lens elements of Examples 1 and 2.
This formula 4 is equivalent to the general formula of the Alvarez structure represented by the following formula 8 when B = A. Here, the Alvarez structure means a lens having a lens surface as shown by the equation (8). It can be proved as follows.
The Alvarez structure is rotated 45 degrees to the center of the origin (execution of coordinate matrix conversion). That is, the direction of the axis is set to a straight line direction of y = x and y = −x. Furthermore, when the image is enlarged or reduced to a similar shape in the xy plane, it can be expressed in the following format.
(A / 6) (x + y) ³ + (A / 2) (x + y) (xy) ²
This equation is modified as follows.
(A / 6) (x ³ + 3x ² y + 3xy ² + y ³ ) + (A / 2) (x ³ −x ² y−xy ² + y ³ ) = (2A / 3) x ³ + (2A / 3) y ³
This can be said to be the same as when B = A, C = 0, and p = 0, where A is an arbitrary value other than 0 in the general formula (5).

Further, in order to control the direction of astigmatism without rotating the lens element, it is more preferable that each coefficient satisfies the formula of formula 6 in the formula of formula 5. The reason will be described below. First, an expression of Formula 5 representing a general shape of a curved surface to be combined with a lens element is developed.
f (x, y) = Ax ³ + B (px + y) ³ + C (x + qy) ³
= Ax ³ + B (p ³ x ³ + 3p ² x ² y + 3pxy ² + y ³ ) + C (x ³ + 3qx ² y + 3q ² xy ² + q ³ y ³ )
This is second-order partial differentiated by x and y, respectively.
∂ ² f / ∂ x ² = (6A + 6Bp ³ + 6C) x + (6Bp ² + 6Cq) y
∂ ² f / ∂ y ² = (6B + 6Cq ³ ) y + (6p + 6q ² C) x
Multiplying these two formulas by 1000 (material refractive index-1) gives the cross-sectional refractive power in the X-axis direction and the Y-axis direction. In order for the sum of them to be constant, the value of ∂ ² f / ∂x ² + ∂ ² f / ∂y ² needs to be constant regardless of x and y. It must be established.
(6A + 6Bp ³ + 6C) + (6p + 6q ² C) = 0
(6Bp ² + 6Cq) + (6B + 6Cq ³ ) = 0
If this is rearranged, the formula 6 is obtained. When the coefficients of A, B, C, p, and q satisfy the formula (6), the average value of the refractive powers in all cross-sectional directions is 0D everywhere on the curved surface combined with the lens element. Further, by appropriately setting the values of the coefficients, ∂ ² f / ∂x ² and ∂ ² f / ∂y ² are non-zero everywhere except the origin of x = y = 0, that is, the surface Astigmatism can exist. The power obtained by combining such surfaces is a cross-cylinder power that has astigmatism except when the average power is always 0D and the positional relationship of the lens elements is the reference position. Furthermore, the direction and magnitude of astigmatism can be adjusted by the positional relationship of the lens elements, and the principle will be described in Example 3.
What limited this condition more is the equation (7). Expression 7 is a general expression of the cross cylinder structure, and this expression is a modification of Expression 5 and is also equivalent to Expression 5. The curved surfaces of the first and second lens elements of the third embodiment use the formula (7). Here, the cross-cylinder structure means a lens having a lens surface represented by the formula (7).
When the cross-cylinder structure is rotated right by 45 degrees about the origin (execution of coordinate matrix conversion), and further enlarged or reduced to a similar shape in the xy plane, it can be expressed in the following form.
(A / 6) (x + y) ³ − (A / 2) (x + y) (xy) ²
This equation is modified as follows.
(A / 6) (x ³ + 3x ² y + 3xy ² + y ³ ) − (A / 2) (x ³ −x ² y−xy ² + y ³ )
= − (A / 3) x ³ + Ax ² y + Axy ² − (A / 3) y ³
= − (2A / 3) x ³ − (2A / 3) y ³ + (A / 3) (x + y) ³
Therefore, it can be said that the cross cylinder structure is the same as the case where B = A, C = −A / 2, p = 0, q = 1 in the general formula of Formula 5 where A is an arbitrary value other than 0. This satisfies the condition of equation (6). In addition to this, when B = 2A, C = −A / 5, p = 0, q = 2, etc., the condition of the equation (6) is satisfied, and astigmatism can be reduced without rotating the lens element. The direction can be controlled.

In the present invention, when the first and second lens elements are linearly moved, it is preferable that they are simultaneously moved in the opposite directions.
This is because by moving both lens elements at the same time, it is possible to apply a portion with as little aberration as possible in the center of the lens to the visible region, and to suppress prism generation at least near the center of the lens.
In addition, when the material refractive indexes of the two lens elements are the same, it is necessary to move the two lenses at the same distance in the opposite direction at the same time in order to cancel the prism generation when moving in the opposite directions at the same time. is there.
In addition, it is preferable from the viewpoint of thickness reduction that the first and second lens elements are arranged in surface contact with each other. Examples of shapes that can be contact surfaces of the first and second lens elements include a cylinder surface having one principal curvature of 0 as a special case of a flat surface, a spherical surface, or a trick surface. On the other hand, the curved surface of the base shape is not particularly limited as long as the first and second lens elements do not contact each other. Therefore, when the first and second lens elements do not contact, the curved surface to be synthesized is set for both the front and back surfaces of the first and second lens elements (that is, practically, an additional sag amount is given to both surfaces). You may do it.

In addition, a suitable curved surface may be set for each spectacle lens manufactured as a base shape in which a reference surface for synthesizing the additional sag amount is formed on the front and back surfaces.
If the base shape of either of the two lens elements produces a refracting power with respect to light rays that pass through it, this is referred to as the base refracting power. When the base refractive power is not constant depending on the location on the lens surface, the distribution of the base refractive power changes as the lens element moves. When the refractive power for each cross-sectional direction changes at each point on the lens surface, the direction and magnitude of astigmatism at that point changes. The purpose of the present invention is to adjust astigmatism. Therefore, it is not preferable that the distribution of the base refractive power changes greatly as the lens element moves. From the above, it is preferable that the base refractive power is as constant as possible in each cross-sectional direction. However, it does not matter that the refractive powers are different for different cross-sectional directions. For example, an astigmatic lens having both sides as a trick surface, or a single-sided spherical surface and a one-sided trick surface can have such a base shape. In the 8th to 14th sets of the second embodiment, the base shape of the first and second lens elements is a double-sided trick surface.

As shown in FIG. 5, for example, a base shape in which a first lens element is arranged on the outside and a second lens element is arranged on the inside, and a spherical surface with the same curve or an aspheric surface with the same reference spherical curve is set on the front and back surfaces. (Indicated by the dashed line in the figure). The opposing surfaces of both lens elements are flat. Then, an additional sag amount is given to the object side surface of the first lens element and the eyeball side surface of the second lens element, respectively. This is a basic structure for providing an additional sag amount when both lens elements are brought into contact with each other.
Next, considering a meniscus-shaped lens, as shown in FIG. 6, for example, the first lens element is arranged on the outer side, the second lens element is arranged on the inner side, and the spherical surface or reference spherical surface of the same curve is arranged on the front and back surfaces. Assume a base shape with an aspheric surface with the same curve (shown in broken lines in the figure). If the opposing surfaces of both lens elements are contact surfaces, an additional sag amount is given to the object-side surface of the first lens element and the eyeball-side surface of the second lens element, respectively.
Furthermore, since the error for approximation increases when the amount of additional sag for creating surface refractive power is large, it is better to divide the power range into multiple parts and generate the central refractive power of each range by the base shape. . That is, it is desirable to generate a large refractive power by making a difference between the curvatures of the outer surface and the joint surface, and further by making a difference between the curvatures of the joint surface and the inner surface, and adjusting this by the bi-cubic structure surface. For example, as shown in FIG. 7, an additional sag amount may be given to the object side surface of the first lens element and the eyeball side surface of the second lens element starting from a plus lens as the base shape. Further, as shown in FIG. 8, an additional sag amount may be given to the object side surface of the first lens element and the eyeball side surface of the second lens element starting from a minus lens as the base shape. 5 to 8 are in contact with each other on the assumption that the eyeball side surface of the first lens element and the object side surface (opposing surface) of the second lens element have the same curved surface. Although illustrated and described, both lens elements may be spaced apart.

  Further, when the additional sag amount is given, it is not necessary to give the same amount of additional sag amount to the first and second lens elements. In particular, when considering use as a spectacle lens, most of the plus or minus power may be distributed to either the outer lens (first lens element) or the inner lens (second lens element). . If it does so, the lens for one side can be shared in a different production power range, and the number of items can be reduced. In this case, the amount of movement of the two lenses may be reduced by reducing the lens on the side that shares a large frequency. The reason for this is that the amount of prism changes greatly when a lens with a high frequency is moved. FIG. 9 shows a structure in which the minus frequency is largely shared on the inner surface side as an example in which the additional sag amount is different. The reference curve of the outer surface of the outer lens is the same as the curve of the cemented surface. In this case, since the moving ratio of the inner lens is small, the inner lens may have a smaller diameter than the outer lens. The inner lens has a small diameter corresponding to the amount of movement.

  In the inventions of the above claims, the average power and astigmatism can be adjusted with only two lenses, and there is no need to perform an operation for rotating the two lenses separately, particularly when adjusting astigmatism. It is possible to provide an optical device including an optical system.

The top view of the lens used for the present Example which put the dimension. FIG. 2 is an explanatory diagram in which a displacement state when the lens of FIG. The top view of the spectacles lens used for the present Example which put the dimension. FIG. 4 is an explanatory diagram in which a displacement state when the spectacle lens of FIG. A state in which the first and second lens elements are arranged in contact, and an additional sag amount is applied to the object side surface of the first lens element and the eyeball side surface of the second lens element with respect to the base shape. FIG. A state in which the first and second lens elements are arranged in contact, and an additional sag amount is applied to the object side surface of the first lens element and the eyeball side surface of the second lens element with respect to the base shape. FIG. The first and second lens elements are arranged in contact, and an additional sag amount is provided on the object side surface of the first lens element and the eyeball side surface of the second lens element with respect to the base shape for the plus lens. Explanatory drawing explaining the state which gave. The first and second lens elements are arranged in contact, and an additional sag amount is provided on the object side surface of the first lens element and the eyeball side surface of the second lens element with respect to the base shape for the minus lens. Explanatory drawing explaining the state which gave. The first and second lens elements are arranged in contact with each other, and different additional sag amounts are applied to the object-side surface of the first lens element and the eyeball-side surface of the second lens element with respect to different base shapes. Explanatory drawing explaining the given state.

Example 1
In the first embodiment, the structure and principle are first described, and a specific optical system based on the principle is described.
1. Structure In Example 1, as an optical device, two lenses were brought into surface contact, and a lens for an optometry apparatus having a flat contact surface was used. Therefore, a lens with specific numerical values as shown in FIG. 1 was designed. Two identical lenses are used by attaching them to a lens frame (not shown). Both lenses are supported so as to be movable in all directions relatively from the completely overlapped state (reference position). As a means for moving, for example, the first lens is supported by a first axis so as to be movable in the left-right direction, and the second lens is supported by a second axis so as to be movable in a vertical direction perpendicular thereto. It is conceivable to control the two-dimensional movement by providing a planar motor for each lens so that the members supporting the first and second shafts can move two-dimensionally.

2. Principle (1) Design Method A predetermined additional sag amount is synthesized with a predetermined base shape for each lens to design the object side surface of the outer lens and the eyeball side surface of the inner lens. As the additional sag amount, a bi-cubic structure of the formula (4) is given.
(2) Refractive power control mechanism Base shape When b (x, y) = CT,
External surface shape of outer lens f ₁ (x, y) = CT + (A / 6) x ³ + (B / 6) y ³
Inner lens inner surface shape f ₂ (x, y) = − CT + (A / 6) x ³ + (B / 6) y ³
When the bi-ternary lens pair is at the reference position, that is, when the design origin of the outer lens and the design origin of the inner lens are both at x = y = 0, the outer surface and the inner surface are parallel, so any position ( The thickness of x, y) is a constant value 2CT regardless of xy.

First, the outer lens is moved in the X-axis direction by Δx from the reference position, and the inner lens is moved in the X-axis direction by −Δx. That is, the two lenses are moved by an equal amount symmetrically with respect to the XY origin. At this time, the thickness at an arbitrary position (x, y) is expressed by the following equation.
t (x, y)
= 2CT + {(A / 6) (x−Δx) ³ + (B / 6) y ³ } − {(A / 6) (x + Δx) ³ + (B / 6) y ³ }
= 2CT−Ax ² Δx− (A / 3) Δx ³
The out 2CT- (A / ³⁾ Δx 3 is the thickness of the XY origin, does not depend on xy values. The remaining −Ax ² Δx is a quadratic expression of x. This indicates that the thickness of the lens increases in proportion to the square of the distance in the X-axis direction from the origin (or decreases if the value of A is negative). Therefore, it can be seen that the lens effect of the bi-cubic lens pair is approximately equivalent to the cylinder lens. The refractive power of the lens pair is generated in the X-axis direction, and the refractive power in the Y-axis direction remains zero everywhere. That is, the sectional refractive power is changed by moving the lens in the X-axis direction, and the power of the optical system is changed.
Next, the outer lens is moved in the Y axis direction by Δy from the reference position, and the inner lens is moved in the Y axis direction by −Δy. At this time, it can be seen from the same calculation that the lens effect of the bicubic lens pair is approximately equivalent to that of the cylinder lens. The refractive power of this lens occurs only in the Y-axis direction, and the refractive power in the X-axis direction remains zero everywhere. That is, the lens refractive power in the Y-axis direction is changed in the same manner, and the power of the optical system changes.

Here, the outer lens is moved from the reference position by Δx in the X-axis direction and by Δy in the Y-axis direction. The inner lens is moved in the X axis direction by −Δx and in the Y axis direction by −Δy. That is, the two lenses are moved symmetrically with respect to the XY origin. At this time, the thickness at an arbitrary position (x, y) is expressed by the following equation.
t (x, y)
= 2CT + {(A / 6) (x−Δx) ³ + (B / 6) (y−Δy) ³ }
− {(A / 6) (x + Δx) ³ + (B / 6) (y + Δy) ³ }
= 2CT−Ax ² Δx− (A / 3) Δx ³ −By ² Δy− (B / 3) Δy ³
Among these, the term 2CT− (A / 3) Δx ³ − (B / 3) Δy ³ is the thickness of the XY origin, and this does not depend on the value of xy. The remaining terms -Ax ² Δx-By ² Δy are quadratic expressions of x and y. Here, when A = B and Δx = Δy, this expression is expressed as −AΔx (x ² + y ² ). x ² + y ² is the square of the distance from the XY origin. Therefore, this expression indicates that the thickness of the lens increases in proportion to the square of the distance from the origin (or decreases if the value of A is negative). From this, it can be seen that the lens effect (refractive power) of the bi-ternary structure lens pair is approximately equivalent to that of the spherical lens. If A = B, Δx and Δy are synchronized, and if A = B, if the movement amounts Δx and Δy of the lens pair are controlled so as to maintain the relationship Δy = Δx (A / B), an approximation can be obtained. In addition, a refractive power equivalent to that of a spherical lens can be obtained.

(3) Prism control mechanism For the above equation -Ax ² Δx-By ² Δy,
Partial differentiation with x ∂t / ∂x = -2AxΔx
Partial differentiation by y ∂t / ∂y = -2ByΔy
Therefore, if the movement amounts of the outer lens and the inner lens are equal in the X-axis direction and the Y-axis direction, respectively, ｘt / ∂x = ∂t / ∂y = 0 at x = y = 0. This means that the thickness change along the X-axis direction and the Y-axis direction is zero, that is, the prism effect in the horizontal direction and the vertical direction is zero. Furthermore, not only the X axis direction and the Y axis direction, but also the amount of increase (decrease) in thickness along the two opposite directions from the origin is the same. Thus, the thickness gradient at the origin is zero for all cross-sectional directions, indicating that no prism effect occurs at the origin, ie, the origin is the optical center.
On the other hand, when the movement amount of the outer lens and the inner lens is unequal, for example, if the movement amount of the outer lens and the inner lens is unequal in the X-axis direction, the thickness of the lens pair is
t (x, y)
= 2CT + {(A / 6) (x−Δx ₁ ) ³ + (B / 6) y ³ } − {(A / 6) (x + Δx ₂ ) ³ + (B / 6) y ³ }
= 2CT− (A / 2) x ² (Δx ₁ + Δx ₂ ) − (A / 2) x (Δx ₁ ² −Δx ₂ ² ) − (A / 6) (Δx ₁ ³ + Δx ₂ ³ )
Partial differential with x ∂t / ∂x = −Ax (Δx ₁ + Δx ₂ ) − (A / 2) (Δx ₁ ² −Δx ₂ ² )
In this case, ∂t / ∂x does not become 0 even when x = 0. Therefore, a horizontal prism is generated at x = y = 0. Similarly, it can be seen that a vertical prism is generated if the amount is unequal in the Y-axis direction. That is, the bi-cubic lens pair according to the present invention can control the amount of prisms in the horizontal and vertical directions to an arbitrary value in addition to the refractive power in the horizontal and vertical directions. This corresponds to the degree of freedom of moving two lenses being 4 (the degree of freedom of moving one lens is horizontal and vertical).

3. Specific Lens Configuration For the lens in FIG. 1, the effective diameter was 30 mm, and the thickness of one lens was 1 mm. A lens material having a refractive index n of 1.5 was used. One lens is used by moving it 10 mm upward, downward, leftward and rightward, and obliquely at 45 degrees. With a 10 mm movement along either the A-axis or the B-axis, the change in the cross-sectional refractive power in the axial direction of one lens is 0.5D. Since the two lenses move relative to each other, the cross-sectional refractive power in the axial direction can be changed by ± 1.0 D if both are moved by 10 mm along either the A axis or the B axis.
Based on these assumptions, the cross-sectional refractive power in the X-axis direction is 1000 (n−1) AΔx (D). Δx = 10 and the cross-sectional refractive power is 0.5D. Since the refractive index n of the lens material is 1.5, 1000 (1.5-1) A · 10 = 0.5, and therefore the coefficient A = 0.0001 (in the first embodiment, A = B). ). FIG. 2 shows an arrangement state in which two such lenses are moved in each slide movable direction and lens characteristics at that time. In FIG. 2, as an example of movement, a movement pattern in a total of 8 directions from the reference position up and down, left and right and 45 degrees up and down is illustrated, but the movement pattern can be moved to any position, and numerical values such as S frequency and C frequency at the movement position. Can be calculated from the horizontal distance and the vertical distance.
When the lens pair is relatively moved in the X-axis direction, only the refractive power of the X-axis direction cross section changes, and when the lens pair is relatively moved in the Y-axis direction, only the refractive power of the Y-axis direction cross section changes. When the X-axis direction and the Y-axis direction are moved by an equal amount, the total power (the S power of the spectacle lens) changes depending on the direction of the movement, or a mix expressed as S + 1.00D, C-2.00D Get a power lens.
According to FIG. 2, the sectional refractive power in the horizontal direction and the vertical direction can be increased or decreased by moving the lens pair in the horizontal direction and the vertical direction relatively from the reference position. At that time, the average frequency can be increased or decreased. On the other hand, when the lens pair is relatively moved in the upper left and lower right diagonal directions, the average power does not change. Conversely, when the lens pair is relatively moved in the upper right and lower left diagonal directions, only the average power can be increased or decreased without generating astigmatism power.
Astigmatism axes are set in two directions of 90 degrees and 180 degrees. The conventional cross cylinder lens needs to rotate the two lenses individually by at least 90 degrees, but in this embodiment, all axial directions can be realized by synchronous rotation up to 45 degrees.

(Example 2)
The structure and principle of the second embodiment will be described first, and then a specific optical system based on the principle will be described.
1. Structure Example 2 is an example applied to a spectacle lens (that is, spectacles as an optical device). A spectacle lens with specific numerical values as shown in FIG. 3 was designed. The spectacle lens has a meniscus lens shape, and both lenses arranged outside and inside are in surface contact with a predetermined base curve surface. The binocular lenses can be moved in all directions relatively from the completely overlapped state (reference position). For example, an ophthalmologist determines the most suitable lens power for the wearer by optometry, and the spectacle store cuts unnecessary parts with the positional relationship between the two lenses determined based on the prescription power, and inserts the frame. The eyeglasses are produced as described above.

2. Principle (1) Design method The same additional sag amount is synthesized with a predetermined base shape for each lens to design the object side surface of the outer lens and the eyeball side surface of the inner lens. As the additional sag amount, the bi-cubic structure of the above formula 4 is given. The base shape in this case is
b (x, y) = CT + Cx + Dy
And
(2) Mechanism of refractive power control Although this point is the same as that of Example 1, in Example 2, since the formula of a bi-cubic structure differs from Example 1, it demonstrates anew.
First, the outer lens is moved in the X-axis direction by Δx from the reference position, and the inner lens is moved in the X-axis direction by −Δx. That is, the two lenses are moved by an equal amount symmetrically with respect to the XY origin. At this time, the thickness at an arbitrary position (x, y) is expressed by the following equation.
When base shape b (x, y) = CT + Cx + Dy,
Outer lens outer surface shape f ₁ (x, y) = CT + Cx + Dy + (A / 6) x ³ + (B / 6) y ³
The inner surface shape of the inner lens f ₂ (x, y) = − CT + Cx + Dy + (A / 6) x ³ + (B / 6) y ³
t (x, y)
= 2CT + {(A / 6) (x−Δx) ³ + C (x−Δx)}
− {(A / 6) (x + Δx) ³ + C (x + Δx)}
= 2CT−Ax ² Δx− (A / 3) Δx ³ −2CΔx
Here, 2CT− (A / 3) Δx ³ −2CΔx is the thickness of the XY origin, and does not depend on the value of xy. The term −Ax ² Δx represents that the thickness of the lens changes in proportion to the square of the distance in the X-axis direction from the origin, that is, the refractive power in the X-axis direction. Therefore, it can be seen that this lens pair is approximately equivalent to a cylinder lens. The refractive power of this lens pair occurs only in the X-axis direction, and the refractive power in the Y-axis direction remains zero everywhere. That is, the sectional refractive power is changed by moving the lens in the X-axis direction, and the power of the optical system is changed.

Next, the outer lens is moved in the Y axis direction by Δy from the reference position, and the inner lens is moved in the Y axis direction by −Δy.
t (x, y)
= 2CT + {(B / 6) (y−Δy) ³ + D (y−Δy)}
− {(B / 6) (y + Δy) ³ + D (y + Δy)}
= 2CT−By ² Δy− (B / 3) Δy ³ −2DΔy
Here, 2CT− (B / 3) Δy ³ −2DΔy is the thickness of the XY origin and does not depend on the value of xy. The term −By ² Δy represents the refractive power in the Y-axis direction, and indicates that this lens pair is approximately equivalent to a cylinder lens. That is, the sectional refractive power is changed by moving the lens in the Y-axis direction, and the power of the optical system is changed.
From the above description, it is possible to independently control the refractive power in the X-axis direction and the refractive power in the Y-axis direction by appropriately combining the horizontal relative movement and the vertical relative movement of the lens pair. I know that there is.

(3) Thickness adjustment In order to move the two lenses relatively by 10 mm in the X-axis direction and change the cross-sectional refractive power in the X-axis direction within a range of ± 1D, the same theory as in Example 1 is used. Therefore, A = 0.0001.
However, since the lens in Example 2 is large, the additional sag in the lens horizontal direction of the end position (x = 40, y = 0 ) , with respect to the term (A / 6) ^{x 3,} by substituting x = 40 Thus, (0.0001 / 6) · 40 ³ = 1.067. Since this is 1.067 mm, if CT = 1 mm, the thickness will be negative depending on the location. Therefore, an x1 order term that cancels out this additional sag amount by half is provided in the base shape to balance the overall thickness.
(0.0001 / 6) · 40 ³ = 1.067
From C · 40 = −1.067 / 2, the coefficient C = −0.0133.
Further, the two lenses are moved by 20 mm relative to each other in the Y-axis direction to change the cross-sectional refractive power in the Y-axis direction within a range of 0 to −4D.
The amount of change in the cross-sectional refractive power in the Y-axis direction is 1000 (n−1) BΔY.
When ΔY = 20, the amount of change in cross-sectional refractive power is 2.0. The refractive index n of the lens material is 1.5 (1000 (1.5-1) B · 20 = 2.0). Accordingly, the coefficient B = 0.0002.
Further, a position (x = 0, y = −35) at which the lens is thinnest at the end in the lens vertical direction is set. The amount of additional sag in this case is (0.006 / 6) · (−35) ³ = −1.429, substituting y = −35 for the term (B / 6) y ^3. Become. Since this is -1.429 mm, in order to cancel out the additional sag amount by half, a y1 order term Dy is provided in the base shape to balance the entire thickness.
From D · (−35) = 1.429 / 2, the coefficient D = −0.0204.

(4) Prism control mechanism From the reference position, the outer lens is moved by Δx in the X-axis direction, by Δy by Y-axis, and the inner lens is moved by −Δx by X-axis, and by −Δy by Y-axis. . That is, the two lenses are moved by an equal amount symmetrically with respect to the XY origin. At this time, the thickness at an arbitrary position (x, y) is expressed by the following equation.
t (x, y) = 2CT−Ax ² Δx− (A / 3) Δx ³ −2CΔx
-By ² Δy- (B / 3) Δy ³ -2DΔy
Since ∂t / ∂x = 2AxΔx, there is no thickness change in the X-axis direction at the origin, and the horizontal prism is zero.
Since ∂t / ∂y = 2AyΔy, there is no thickness change in the Y-axis direction at the origin, and the vertical prism is zero.
It is the portion of -Ax ² Δx−By ² Δy that changes in value according to xy. In two coordinates that are symmetric with respect to the origin, this value is equal. Therefore, when x = y = 0, the thickness change rate is 0 in any direction, and the prism effect does not occur in all directions, not only in the horizontal and vertical directions. Therefore, the origin can be maintained as the optical center.

(5) About the base curve of the lens It is impossible to make it compatible with lenses of all S and C degrees with only one base curve, so apply the base curve to each area in several areas. And In the second embodiment, the production power ranges are S-8.00D to + 6.00D and C-0.00D to -4.00D. As shown in Table 1 below, the area is divided so as to cover 14 sets.
In Table 1, the outer base curve of the outer lens, the inner base curve of the inner lens, and the curve of the cemented surface are represented by a 1.5 conversion curve of the material refractive index. The curve value is obtained by dividing (1.5-1) by the value of the radius of curvature in m units. For example, if the radius of curvature is 500 mm, it is 1 curve, 100 mm is 5 curves, and 200 mm is 2.5 curves. In this embodiment, the power is evenly distributed between the outer lens and the inner lens.

3. 3. Specific Lens Configuration The range in which a circular shape having a diameter of 60 mm moves 20 mm vertically and horizontally for the spectacle lens of FIG. 3 is the shape of one lens. In FIG. 3, as an example of movement, a movement pattern in a total of 8 directions when moving from the reference position up and down, left and right and 27 degrees (26.6 degrees) diagonally up and down (a total of 8 directions) is illustrated. It is possible to move, and all numerical values such as S frequency and C frequency at the moving position can be calculated from the horizontal distance and the vertical distance. A trajectory drawn by a circle with a diameter of 60 mm was defined as a horizontal movement of 20 mm + a vertical movement of 10 mm and a vertical movement of 10 mm. FIG. 4 shows an arrangement state in which two such spectacle lenses are moved in respective sliding movable directions and lens characteristics at that time. In FIG. 4, the lens is moved from the beginning based on a state in which the lens is inclined by 27 degrees (26.6 degrees) with respect to the horizontal plane. This is because the coefficients A and B are A ≠ B unlike the first embodiment. Therefore, the amount of movement in the x-axis direction and the y-axis direction is not the same, and thus the ease of calculation is taken into consideration. In addition, in order to secure the widest possible use area (that is, to set the reference size to 60 mm), the two spectacle lenses are shifted from the design origin by 10 mm in the vertical direction and the astigmatism is C-0.00D (in another set group). The width was set to 80 mm in a state of being overlapped at the reference position C-2.00D). Then, both lenses are moved left and right (X-axis direction) by 20 mm and up and down (Y-axis direction) by 10 mm, and the S frequency is changed within a range of ± 1.00 D. Both lenses are moved vertically by 10 mm in the vertical direction (Y-axis direction) to obtain the maximum astigmatism C-2.00D (C-4.00D in another set group). Then, both lenses are moved left and right (X-axis direction) by 20 mm and up and down (Y-axis direction) by 10 mm, and the S frequency is changed within a range of ± 1.00 D.

Example 3
1. Structure A slightly smaller lens for a laser beam pickup lens is assumed. In Example 3, astigmatism in an arbitrary direction (called astigmatism in Example 1 of the optometry apparatus and Example 2 of the spectacle lens) is obtained by combining the horizontal movement amount and the vertical movement amount without rotating the lens. produce. The third embodiment is intended to quickly achieve a small change in refractive power with a smaller movement than the above embodiment.
The refractive index of the two lenses was assumed to be 1.5, and the single lens was assumed to be a square having a thickness of 1 mm and a side of 12 mm. The effective diameter was 10 mm, and the maximum movement amount of each lens was 1 mm in the vertical and horizontal directions.

2. Principle (1) Design Method A predetermined additional sag amount is synthesized with a predetermined base shape for each lens to design the object side surface of the outer lens and the eyeball side surface of the inner pickup lens. As the additional sag amount, the surface structure of the equation (7) is given. The design center of each lens was made to coincide with the geometric center. The value of the coefficient A was 0.0001.

(2) Mechanism of Astigmatism Generation The geometric center of each lens is placed at the origin, and the state where the two lenses are completely overlapped is set as the reference position. When the lens pair is in the reference position, the thickness of the entire lens pair is constant 2CT everywhere. As in the embodiments described so far, when the two lenses are moved, the thickness varies depending on the location. As a result, the lens pair obtains the prism effect and the refractive power in the specific cross-sectional direction.
The outer lens is moved from the reference position by Δx in the X-axis direction and by Δy in the Y-axis direction. The inner lens is moved in the X axis direction by −Δx and in the Y axis direction by −Δy. That is, the two lenses are moved symmetrically with respect to the XY origin. At this time, the thickness at an arbitrary position (x, y) is expressed by the following equation.

t (x, y)
= 2CT + {(A / 6) (x−Δx) ³ − (A / 2) (x−Δx) (y−Δy) ² } − {(A / 6) (x + Δx) ³ − (A / 2) ( x + Δx) (y + Δy) ² }
= 2CT−Ax ² Δx− (A / 3) Δx ³
− (A / 2) (x−Δx) (y ² −2yΔy + Δy ² ) + (A / 2) (x + Δx) (y ² + 2yΔy + Δy ² )
= 2CT−Ax ² Δx− (A / 3) Δx ³
− (A / 2) (xy ² −2xyΔy + xΔy ² −y ² Δx + 2yΔxΔy−ΔxΔy ² )
+ (A / 2) (xy ² + 2xyΔy + xΔy ² + y2Δx + 2yΔxΔy + ΔxΔy ² )
= 2CT−Ax ² Δx− (A / 3) Δx ³ + 2AxyΔy + Ay ² Δx + AΔxΔy ²
Of these, the portion 2CT− (A / 3) Δx ³ + AΔxΔy ² is a constant value regardless of xy, and the center thickness is a value changed from 2CT. The remaining terms affect the refractive power, which will be explained in two parts.
AΔx (−x ² + y ² ) (A)
2AxyΔy (B)
Here, when Δx = 1 and Δy = 0, the equation (A) is a cross cylinder lens of S + 0.10D, C−0.20D, and AX180 (a lens having an astigmatic power and an average power of 0D). Is approximately equivalent to Actually, since the value of Δx moves within a range of ± 1, the power of the lens pair changes continuously as the astigmatic axis moves as shown in Table 2, while the average power does not change (in this table, the average power does not change). The frequency is 0D at any position).

Next, Δx = 0 and Δy = 1.
There are two points on the straight line y = x and the distance from the origin is 1. At these two points, x = y = 1 / √2 or x = y = −1 / √2 It is. At any point, the value of equation (B) is A. Therefore, in the cross section along the straight line y = x, the equation (B) is approximately equal to a circle having a refractive power of −0.1D.
There are two points on the straight line y = −x and the distance from the origin is 1. At these two points, x = 1 / √2, y = −1 / √2, or x− 1 / √2, y = 1 / √2. At any point, the value of equation (B) is -A. Therefore, in the cross section along the line y = −x, the equation (B) is approximately equal to a circle having a refractive power of 0.1D.
From the above, if Δx = 0 and Δy = 1, the component represented by the formula (B) produces a refractive power approximately equivalent to the cross cylinder lens of S + 0.10D, C−0.20D, and AX135. Actually, since the value of Δy moves within the range of ± 1, the power of the lens pair changes continuously as the astigmatism axis moves as shown in Table 3, while the average power does not change (in this table, the average power does not change). The frequency is 0D at any position).
Note that the average frequency does not change depending on the movement in any direction, except when the movement amount is in the range of Δx = ± 1, Δy = 0, and Δx = 0, Δy = ± 1. .

(3) Creation of Arbitrary Astigmatism Power It is known that astigmatism of an arbitrary size and an arbitrary direction can be generated by combining two cross cylinder lenses having different axes of 45 degrees or 135 degrees. By applying this and combining (A) and (B) that produce an effect equivalent to that of a cross-cylinder lens, a pickup lens that controls the magnitude and direction of astigmatism can be configured without a rotating structure.
The calculation which synthesize | combines S + 0.05D and C-0.10D AX180 in the said Table 2 and S + 0.05D and C-0.10D AX45 in Table 3 is illustrated. At this time, the respective lens center coordinates are the outer lens (+0.05, −0.05) and the inner lens (−0.05, +0.05).
First, when S + 0.05D, C-0.10D AX180 is converted to JCC (Jackson Kuroshi cylinder),
M 0.00D, J00 0.05D, J45 0.00D.
Next, when S + 0.05D, C-0.10D AX45 is converted to JCC,
M 0.00D, J00 0.00D, J45 0.05D.
When these two results are added together, M 0.00D, J00 0.05D, and J45 0.05D are obtained.
When this is converted back to the SCA system, S + 0.07D, C-0.14D, and AX22.5 are obtained.
In this way, a method for controlling the magnitude and direction of astigmatism without a rotating structure can be provided. This is suitable for devices that require high-speed response, such as a laser beam pickup lens.

(4) From the prism control mechanism reference position, the outer lens is moved by Δx in the X-axis direction, by Δy by Y-axis, and the inner lens is moved by −Δx by X-axis, and by −Δy by Y-axis. . That is, the two lenses are moved by an equal amount symmetrically with respect to the XY origin. At this time, the thickness at an arbitrary position (x, y) is expressed by the following equation.
t (x, y)
= 2CT−Ax ² Δx− (A / 3) Δx ³ + 2AxyΔy + Ay ² Δx + AΔxΔy ²
Of these, the 2CT− (A / 3) Δx ³ + AΔxΔy ² portion is a constant value regardless of xy, and thus does not affect not only the refractive power but also the prism. The remaining term AΔx (−x ² + y ² ) + 2AxyΔy affects the prism. However, this term does not change when the value of x is -x and the value of y is -y. Therefore, since the thicknesses of two points that are symmetric with respect to the origin are equal, the prism effect does not occur in all directions including horizontal and vertical at the origin. Therefore, the origin can be maintained as the optical center.

It should be noted that the present invention can be modified and embodied as follows.
In order to optimize the aberration distribution in each lens arrangement, a term having a higher order than the third-order additional sag amount as described above may be used. Specifically, the terms x ^α y ^β (α ≧ 0, β ≧ 0, α + β ≧ 4) are set, and the coefficient is adjusted. Reasons for using a fourth-order or higher term to optimize the aberration distribution include the following.
(1) For example, in the case of a spectacle lens, a light beam that passes through the lens and passes through the pupil is used to see the object. Then, in the peripheral region of the lens, the light beam is inclined with respect to the optical axis. Then, the difference in the XY coordinates of the light beam passage positions on the outer surface and the inner surface becomes large. In the present invention, since the relationship between the curve shapes at the corresponding light ray passing points on the outer surface and the inner surface is used, adjustment is necessary when the difference in the XY coordinates of the corresponding points is large.
(2) Even when the light beam transmitted through the lens is substantially parallel to the optical axis, the surface is inclined with respect to the optical axis at most positions on the outer surface or inner surface of the lens. Therefore, since there is a prism effect in which the angle of the light ray changes, the XY coordinates of the corresponding light ray passing points on the outer surface and the inner surface are different, although not as in (1) above.
(3) To control higher-order aberrations of the third order or higher. (The present invention controls secondary aberrations among higher order aberrations).
In the above embodiment, the movement direction of the lens is specified in a total of eight directions, but it may be movable in all other directions.
For example, in the first embodiment, nine types of frequencies are shown in the figure. They are any of A to C below.
A) A so-called spherical power with three astigmatic powers (3 types in the first embodiment)
B) A so-called monochromatic astigmatism power in which one of the frequencies in the two main meridian directions is 0D (four types in the first embodiment)
C) Frequency with astigmatic power and average power of 0D. Frequency at which a cross cylinder lens is generated (two types in the first embodiment)
Here, as another variation of the power change mode, there is D) astigmatism power, the average power is not 0D, and both powers in the two main meridian directions are not 0D, for example, S-0.50D, C In order to obtain −0.50D and AX90, Δx = −10 and Δy = −5 in the first embodiment may be used.

In the above, the “lens element” itself is a single lens body. However, an optical system in which a plurality of lens bodies are combined or different media (air, gas, liquid, etc.) are interposed therebetween. It is good also as a structure which comprises a system | strain.
-You may make it apply this invention as the spectacles which can adjust an astigmatism power, especially for emergency. As a means for moving the lens, it is usually fixed by sandwiching from the front and back so that both lenses do not move in the spectacle frame, and once moved, loosened and moved to a predetermined moving position and fixed again. Means are envisioned.
-In this invention, both lenses rotate integrally, and both lenses do not rotate respectively. In order to prevent such rotation of one lens relative to the other lens, a joint surface where both lenses are in surface contact may be used as a cylinder surface to prevent relative rotation.
A polarizing film may be sandwiched between both lenses. Moreover, you may dye | stain a joint surface. There is little demand for dimming lenses, polarized lenses, and dyed lenses, so it is difficult to keep stock lenses in eyeglass stores. Especially for polarized lenses, the direction of polarized light that passes through the lens must be constant, so it is not possible to rotate the lens into a frame for prescriptions with different astigmatic axes. Almost impossible to do. Therefore, in general, a semi-finish having a polarizing film is manufactured, and the semi-finish is manufactured by a method in which this is set in a predetermined direction and cut according to the prescription astigmatic axis. A method of manufacturing a finish lens by injecting and polymerizing a monomer with a polarizing film sandwiched between two glass molds may be considered, but it takes time to manufacture a lens after receiving an order. There is a practical problem that it is difficult to fix the orientation of the polarizing film sandwiched between the two. However, according to the present invention, both lenses can be cemented and fixed with the astigmatism axis set as prescribed and the polarizing film set in a predetermined direction. Then, by inserting the frame after fixing (or fixing by inserting the frame), it is possible to easily produce spectacles in which the astigmatic axis direction and the direction of the polarizing film are accurate.
-Hard multi secondary processing may be performed in advance on the non-joint side of both lenses. When the plastic lens is subjected to secondary processing after cutting, the lens is slightly deformed or altered in the process and the power changes, so it is very difficult to finish the lens power accurately. If both lenses subjected to the next processing are joined by determining the joining position while measuring the power, an accurate power can be easily obtained.

Claims (16)

An X-axis direction and a Y-axis direction orthogonal to each other on a two-dimensional plane perpendicular to the optical axis are set, and a new one existing on the two-dimensional plane based on coordinates represented by the X axis and the Y axis. Multiple axial directions are set, and the refractive power of the cross section determined by the refractive index of the medium before and after the surface along the same axial direction and the curvature of the cross section in that direction changes linearly and continuously along each axial direction. The first and second curved surfaces are designed by combining the curved surface with one of the surfaces of the base shape on which the reference surface for synthesizing the additional sag amount is formed on the front and back surfaces. And the first and second lens elements are arranged in parallel so that the X-axis and Y-axis directions and the new plurality of axial directions coincide with each other. The first and second lens elements. Optical apparatus is characterized in that so as to control the astigmatism amount by which the two-dimensional movement on. The curved surface of the first lens element is defined by the following equation number 1, the curved surface of the second lens element is defined by the following equation number 2, the medium of refractive index n _11, the first lens the curved surface of the element, the medium of refractive index n _12, a medium of refractive index n _22, wherein the curved surface and wherein the following equation 3 when it is arranged in the order of a medium refractive index n ₂₁ of the second lens element is The optical device according to claim 1, wherein:
  The two-dimensional movement means that the two lens elements can be linearly moved in a plurality of directions whose flow line directions are not parallel to each other in the two-dimensional plane. The optical device according to 1 or 2.   The two-dimensional movement refers to rotating the two lens elements in the same direction around the optical axis, and moving the two lenses in the two-dimensional plane at a predetermined rotational displacement position. The optical device according to claim 1, wherein the optical device is capable of linear movement in a plurality of directions in which the flow line directions are not relatively parallel to each other.   By relatively moving the two lens elements along a specific first direction, the cross-sectional refractive power in the first direction is increased or decreased, and the cross section in the direction orthogonal to the first direction is used. The refractive power is not increased or decreased, and the sectional refractive power in the second direction is increased or decreased by relatively moving along a predetermined second direction that is not parallel to the first direction. The optical apparatus according to claim 1, wherein the cross-sectional refractive power is not increased or decreased in a direction perpendicular to the optical axis.   By relatively moving the two lens elements along a specific first direction, the cross-sectional refractive power in all directions is increased or decreased uniformly, and a predetermined second that is not parallel to the first direction. 4. The cross-sectional refractive index in the second direction is increased or decreased by relatively moving along the direction, and the cross-sectional refractive power is not increased or decreased in the direction orthogonal to the second direction. Or the optical apparatus of 4.   By relatively moving the two lens elements along a certain first direction, astigmatism in a certain direction is increased or decreased, and in a second direction not parallel to the first direction. The astigmatism in a direction different from the above is increased or decreased by relatively moving along the direction, and the average power does not change by the movement in the first and second directions. Optical device. The curved surface of the first lens element defined by the formula (1) and the curved surface of the second lens element defined by the formula (2) are A ₁ = A ₂ and B ₁ = B _2. And the medium having the refractive index n ₁₁ , the medium having the refractive index n ₁₂ , the medium having the refractive index n ₂₂ , and the medium having the refractive index n ₂₁ satisfy n ₁₁ = n ₂₁ and n ₁₂ = n ₂₂ . The optical apparatus according to claim 5 or 6, wherein the curved surfaces of the two lens elements are defined by the following formula (4) when the relationship is satisfied.
The curved surface of the first lens element defined by the formula ( _{1) and the} curved surface A ₁ = A ₂ and B ₁ = B ₂ of the second lens element defined by the formula ( ₂ ). The lens element when the medium having the refractive index n11, the medium having the refractive index n12, the medium having the refractive index n22, and the medium having the refractive index n21 are in the relationship of n11 = n21 and n12 = n22 8. The optical apparatus according to claim 7, wherein the curved surface is defined by the following equation (5), and A, B, C, p, and q in the equation satisfy the relationship of the following equation (6).
The optical apparatus according to claim 9, wherein the curved surfaces of the two lens elements are defined by the following formula.
The optical device according to claim 1, wherein a surface serving as a reference for synthesizing the additional sag amount on the front and back surfaces is any one of a spherical surface, a flat surface, and an astigmatic surface.   The optical apparatus according to claim 1, wherein when moving linearly, the two lens elements are simultaneously moved in opposite directions.   The optical apparatus according to claim 12, wherein the two lens elements are simultaneously moved in the opposite directions by an equal distance.   The optical device according to claim 1, wherein the two lens elements are arranged in surface contact with each other.   The optical device according to claim 1, wherein an optical functional film is interposed between the two lens elements.   The optical device according to claim 1, wherein the optical device is eyeglasses.