JP2006285069A - Equi-magnification imaging optical system - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide an equi-magnification imaging optical system designed such that a depth range that allows an object to be imaged at an equal magnification is wide and its configuration is simple. <P>SOLUTION: The equi-magnification imaging optical system has a plurality of imaging elements and images an object at an equal magnification. The plurality of imaging elements have an equal focal distance. The plurality of imaging elements are disposed at regular intervals so that light made incident on the optical system is passed through the imaging elements n times (n is an integer of 2 or more) before emitted from the optical system. Where the focal distance of the imaging elements is f and the magnification of an image formed with the light emitted from the optical system is M<SB>n</SB>, the interval d between the imaging elements has a value that satisfies M<SB>n</SB>= 1 or -1 and does not depend on L<SB>0</SB>. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to an equal-magnification imaging optical system, and more particularly to a technique effective when applied to an optical system for imaging a three-dimensional object at an equal magnification.

  2. Description of the Related Art Conventionally, there is a so-called symmetric telecentric optical system as an equal-magnification lens for imaging an object at an equal magnification (see, for example, Patent Document 1).

The symmetric telecentric optical system described in Patent Document 1 is an optical system having good imaging performance while maintaining both-side telecentricity, and includes a front group GF and a rear group GR arranged symmetrically with respect to the aperture stop. The front group GF, in order from the object side, is a positive lens L1 having a surface with a smaller radius of curvature toward the aperture stop side and a surface with a larger radius of curvature toward the aperture stop side. A rear lens GR, in order from the aperture stop side, a negative lens L4 with a concave surface facing the aperture stop side, and an aperture A positive lens L5 facing the surface with the larger absolute value of the curvature radius on the aperture side, and a positive lens L6 facing the surface with the smaller absolute value of the curvature radius on the aperture stop side, and the front group GF The focal length is F, the object side surface of the positive lens Ll of the front group GF and the aperture stop A distance along the optical axis between the positive lens Ll and the positive lens L2, and an axial air space between the positive lens L2 and d2, and an axial air between the positive lens L2 and the negative lens L3. The optical system satisfies the conditions 1 <D / F and d4 <d7 <d2, where the distance is d4 and the axial air distance between the negative lens L3 and the aperture stop is d7.
JP 09-080306 A

  However, it is not limited to the symmetrical telecentric optical system described in Patent Document 1, and in the case of an equal magnification lens composed of an optical system in which a plurality of lenses are stacked, in general, only in a certain narrow depth range, excellent with very little aberration Image characteristics. Therefore, for example, there is a problem that it is difficult to form an image of a three-dimensional object having a large change in the depth direction.

  Further, in the same magnification lens as the symmetric telecentric optical system described in Patent Document 1, a plurality of lenses having different shapes must be arranged so as to satisfy the above conditions, and the configuration becomes complicated. The inventors of the present invention consider that there is a problem that it is difficult to obtain an arrangement position that satisfies a condition.

  Further, in the case of a 1 × magnification lens such as the symmetric telecentric optical system described in Patent Document 1, for example, each lens to be laminated is different in shape and material, and a lens such as an aspherical surface that is difficult to process is frequently used. There is a problem that the manufacturing cost increases because it is sensitive to the arrangement of the lenses and requires high assembly accuracy.

  An object of the present invention is to provide an equal-magnification imaging optical system having a wide depth range in which an object can be imaged at equal magnification and a simple configuration.

  The above and other objects and novel features of the present invention will be apparent from the description of this specification and the accompanying drawings.

  The outline of the invention disclosed in the present application will be described as follows.

(1) An equal-magnification imaging optical system that includes a plurality of imaging elements and forms an object at an equal magnification. The plurality of imaging elements all have the same focal length, and the plurality of imaging elements. The imaging elements are arranged at equal intervals, and are arranged so that light incident on the optical system passes through the imaging element n times (n is an integer of 2 or more) before exiting from the optical system. The distance d between the imaging elements is expressed by the following formulas (1) to (1), where f is the focal length of the imaging elements, and M _k is the magnification of the imaging of the light that has passed through the k imaging elements. This is an equal-magnification imaging optical system that satisfies M _{k = n} = 1 or −1 in the recurrence formula represented by Expression (4) and that does not depend on L ₀ .

(2) An equal-magnification imaging optical system that includes a plurality of imaging elements, a plane mirror, and an optical component that switches the light emission direction in accordance with the light incident direction, and forms an object at an equal magnification. The plurality of imaging elements have the same focal length, the plurality of imaging elements, the plane mirror, and the optical component have the imaging elements at equal intervals, and the optical element. It is arranged so that the light incident on the system passes through the imaging element n times (n is an integer of 2 or more) before exiting from the optical system, and the interval d between the imaging elements is the imaging element in the focal length of the f, the magnification of the imaging of the light passing through the k-number of the imaging element when the M _k equation (1) to a recurrence formula represented by equation (4), M _{k This} is an equal-magnification imaging optical system that satisfies _{= n} = 1 or −1 and that does not depend on L ₀ .

(3) An equal-magnification imaging optical system that includes a plurality of imaging elements and forms an image of an object at an equal magnification, wherein the plurality of imaging elements are n + 1 (n is an integer of 1 or more). The lens has a focal length f ₁ and n focal length f ₂ lenses. The focal length f ₁ lens and the focal length f ₂ lens are alternately arranged, and the focal length The lenses with the distance f ₁ are arranged at equal intervals, and the distance d between the lenses with the focal length f ₁ is as follows when the magnification of imaging of the light that has passed through the k imaging elements is M _k. This is an equal-magnification imaging optical system satisfying M _{k = 2n + 1} = 1 or −1 and satisfying L ₀ in the recurrence formulas represented by Expressions (5) to (8). .

  The equal-magnification imaging optical system of the present invention has a very simple configuration in which a plurality of imaging elements having the same focal length are arranged at equal intervals, for example, as in the means (1). At this time, the imaging elements need only be arranged at an interval d that satisfies the conditions described in the means (1). For this reason, it is possible to easily realize an equal-magnification lens having a simple configuration as compared with a conventional equal-magnification lens.

L ₀ in the means (1) corresponds to the distance between the object and the imaging element through which light incident from the object side first passes. Therefore, by setting the value independent of L ₀ , an object existing at any depth position can be imaged at equal magnification. In addition, when an image of a three-dimensional object is formed, the entire area of the object can be formed at an equal magnification. For example, it can be combined with a three-dimensional display device (three-dimensional display device) for various uses. It will be possible to apply.

  In the means (1), the plurality of imaging elements may be, for example, n lenses or n curved mirrors.

  Further, in the means (1), the plurality of imaging elements only have to have the same focal length, so that the lens and the curved mirror may be combined without being limited to only the lens or the curved mirror. . At this time, if the total number of the lenses and curved mirrors is n, the same effect as the case of only the lenses or the curved mirrors can be obtained.

  Further, when the light incident on the optical system is allowed to pass through the imaging element n times before exiting from the optical system, if the plane mirror and the optical component are used as in the means (2), There can be less than n imaging elements. Even if the number of imaging elements is less than n, for example, the light that has passed through a certain imaging element is reflected by the plane mirror and passed again through the certain imaging element, thereby passing the imaging element n times. be able to. Therefore, the optical system of the means (2) can be downsized as compared with the optical system of the means (1).

  Further, when the equal-magnification imaging optical system is configured as in the means (2), for example, the plurality of imaging elements may be less than n lenses and the optical component may be a half mirror. Good.

  Further, when the equal-magnification imaging optical system is configured as in the means (2), the optical component is not limited to the half mirror, for example, a combination of a polarizing beam splitter and a quarter wavelength plate, Alternatively, it may be a component composed of a combination of the polarizing beam splitter, the quarter wavelength plate, and the polarizing plate.

In the means (1) or means (2), the plurality of imaging elements have the same focal length, in other words, one type of focal length. However, the present invention is not limited to this. As in 3), the optical system may be a combination of two types of lenses, a lens having a focal length of f _{1 and} a lens having a focal length of f ₂ . In the configuration of said means (3), for example, distance of the lens at which to the focal length f ₁ of the lens is m stacked, the focal length is m laminating the lens f ₁ in the configuration of the means (1) It can be made narrower than the interval at the time of making it.

Further, in the case of the configuration like the means (3), by changing the focal length f ₁ and the focal length f ₂ , it is possible to change the imaging position of the image with the same magnification as the object. Therefore, if a variable focus lens is used as the lens, a wide depth range can be expressed even when the depth display range that can be displayed by the three-dimensional display device is narrow.

Hereinafter, the present invention will be described in detail together with embodiments (examples) with reference to the drawings.
In all the drawings for explaining the embodiments, parts having the same function are given the same reference numerals and their repeated explanation is omitted.

  In the equal-magnification imaging optical system of the present invention, two or more imaging elements having the same focal length are arranged at equal intervals so as to satisfy a predetermined condition, thereby imaging an object at equal magnification. The depth range that can be imaged at the same magnification is widened. At this time, by combining less than n imaging elements and optical components such as a plane mirror and a half mirror, the light incident on the optical system passes through the imaging element n times before being emitted from the optical system. Thus, the optical system is made compact.

In addition, by alternately stacking n + 1 lenses having a focal length of f ₁ and n lenses having a focal length of f ₂ , an interval when the m lenses having the focal length f ₁ are stacked is defined as the focal point. The optical system is miniaturized by making it narrower than the interval when only m lenses having a distance of f ₁ are stacked. At this time, by changing the focal length f ₁ and the focal length f ₂ , the imaging position of the image with the same magnification as the object is changed.

FIGS. 1 and 2 are schematic diagrams showing a schematic configuration of the equal-magnification imaging optical system of Example 1 according to the present invention, and FIG. 1 is a diagram showing a configuration example when an erect image of equal magnification is formed, FIG. 2 is a diagram showing a configuration example in the case of forming an erect image of equal magnification.
In FIG. 1, 1A is an object, 1B is an erect image having the same magnification as the object, 1C is an inverted image having the same magnification as the object, 2 is an equal magnification imaging optical system, 201 _h (h = 1, 2,..., N) Is a lens with a focal length f.

The equal-magnification imaging optical system according to the first embodiment is, for example, an equal-magnification lens that forms an erect image 1B having an equal magnification of an object 1A as shown in FIG. ) Is an optical system in which lenses 201 _h (h = 1, 2,..., N) having the same focal length are arranged at equal intervals at a distance d1. At this time, the distance d1 between the lenses 201 _h (h = 1, 2,..., N) is obtained from a recurrence formula as described below.

When the object 1A is imaged at the same magnification, not only the erect image 1B as shown in FIG. 1, that is, the object 1A and the image 1B are aligned in the same direction, but also the image shown in FIG. As shown, an inverted image 1C with the same magnification of the object 1A, that is, an image can be formed so that the direction of the object 1A is opposite to the direction of the imaging 1C. In this case, the distance d2 between the n lenses 201 _h (h = 1, 2,..., N) having the same focal length is different from the distance d1 when the erect image 1B is formed. It can be obtained from the same recurrence formula as the recurrence formula for obtaining the interval d1 when forming the standing image 1B.

When the lenses 201 _h (h = 1, 2,..., N) having the same focal length are arranged at equal intervals as in the equal magnification imaging optical system of the first embodiment, the focal length of the lens is Where f is the distance between the lenses, and d is the distance between the lenses, the imaging magnification M _k of the light that has passed through the k lenses is expressed by a recurrence formula as shown in the following formulas (1) to (4).

In the mathematical formula (1), when an erect image 1B having the same magnification is formed, M _{k = n} = 1. Therefore, the distance d1 between the lenses 201 _h (h = 1, 2,..., N) is obtained by obtaining d satisfying M _n = 1 using the equations (1) to (4). When an inverted image 1C having the same magnification is formed, M _{k = n} = −1. Therefore, the distance d2 between the lenses 201 _k (h = 1, 2,..., N) is obtained by obtaining d satisfying M _n = −1 using the equations (1) to (4).

Here, as an example of how to obtain the distances d1, d2 between the lenses 201 _h (h = 1, 2,..., N), a case of an optical system in which two lenses having a focal length f are stacked is given as an example. A simple explanation of how to solve the equation.

  FIG. 3 is a schematic diagram for explaining how to obtain the lens interval in the equal magnification imaging optical system according to the first embodiment.

First, it is assumed that _two lenses 201 ₁ and 201 ₂ having a focal length f are arranged at a distance d _{1 as} shown in FIG. At this time, the distance from the _first lens 201 ₁ to the object is −L ₀ , and the distance from the first lens 2011 ₁ to the imaging 1D with the magnification M ₁ at the _first lens 2011 ₁ is L _1. Let L ₂ be the distance from the _second lens 201 ₂ to the image of the magnification M ₂ (upright image 1B). At this time, the L ₂ is represented by the following formula (9) from the formulas (3) and (4), and the M ₂ is represented by the following formula (10) from the formulas (1) and (9). The

In the mathematical formula (9) and the mathematical formula (10), the L ₁ is represented by the following mathematical formula (11) from the mathematical formula (3) and the mathematical formula (4), and the M ₁ is represented by the mathematical formula (1) and the mathematical formula ( 11) to the following formula (12).

When L ₁ represented by the mathematical formula (11) and M ₁ represented by the mathematical formula (12) are substituted into the mathematical formula (10), M ₂ is represented by the following mathematical formula (13).

When the equation (13) obtained in this way is solved for d with M ₂ = 1, d becomes the following equation (14).

However, in this case, as shown in the equation (14), the value of d depends on the distance L ₀ from the _first lens 201 ₁ to the object 1A. Therefore, for example, if the object 1A is planar and the distance L _{0 at} each point of the object is substantially constant, lenses are stacked at an interval d based on the distance L ₀ , so that an erect image of the object 1A is obtained. Can be imaged. However, the object 1A is, for example, the case of three-dimensional objects, the distance L ₀ at each point of the object is different, it is impossible to determine the distance d1 = d of the lens on the basis of the equation (14). Therefore, d obtained by the mathematical formula (14) is not suitable as a solution.

On the other hand, when Equation (14) is solved for d with M ₂ = −1, d becomes Equation (15) below.

In this case, since the value of d does not depend on the distance L ₀ from the _first lens 2011 ₁ to the object 1A, if the distance between the two lenses is d2 = 2f, the distance from the _first lens 2011 ₁ An object at an arbitrary distance L ₀ can be formed as an inverted image with the same magnification. Further, even if the object is three-dimensional, the entire area of the object can be imaged at an equal magnification.

When n = 3 or more, that is, when three or more lenses are laminated, the recurrence formula is solved in the same procedure to obtain d that does not depend on the distance L ₀ from the _first lens 201 ₁ to the object. In other words, the upright image 1B or the inverted image 1C having the same magnification can be formed by arranging the lenses at intervals of the values. At this time, although a detailed calculation procedure is omitted, in the case of n = 2 to 8 using the above recurrence formula, the lens interval d1 and the inverted magnification of the equal magnification when the erect image 1B having the same magnification is formed are formed. When the value of the lens interval d2 in the case of forming the image 1C is obtained, it is as shown in Table 1 below.

  FIG. 4 is a diagram illustrating an application example of the equal-magnification imaging optical system according to the first embodiment. FIG. 4 is a diagram illustrating an example in which an inverted image with equal magnification is formed by stacking four lenses.

  The equal-magnification imaging optical system of the first embodiment, for example, in a touch panel display device, displays images displayed on the DFD display screens 301A and 302A around the touch panel 4 as shown in FIG. Can be applied to.

At this time, the equal-magnification imaging optical system 2 may be an optical system that forms an erect image 1B as shown in FIG. 1, or an inverted image 1C as shown in FIG. Although an optical system may be used, as shown in Table 1, when the same number of lenses are stacked, forming an inverted image can narrow the distance between the lenses and reduce the thickness of the optical system. Therefore, for example, as shown in FIG. 4, when four lenses are stacked and inverted images 301C and 302C having the same magnification are formed in the vicinity of the touch panel 4, each lens is obtained from Table 1. The interval d2 of 201 _h (h = 1, 2, 3, 4) may be 0.6f. At this time, assuming that the focal length f of each lens 201 _h (h = 1,2,3,4) is 77 mm, the distance between the lenses 201 _h (h = 1,2,3,4) is shown in FIG. As shown, it is about 46 mm.

Further, as the display device, for example, as shown in FIG. 4, when a DFD in which two display screens 301A and 302A are stacked at intervals of 5 mm is used, four lenses 201 _h (having a focal length of 77 mm) When the equal-magnification imaging optical system 2 in which h = 1, 2, 3, 4 is arranged at an interval of 46 mm is arranged so as to be almost in close contact with the front display screen 301A, the lens farthest from the DFD (at the right end of the paper) lens) 201 from ₄ of the front surface of the display screen 301A at a position of about 20mm inverted image 301C is imaged, that inverted image 302C of the display screen 302A of the rear surface at a position of about 15mm is imaged, the inventors of the present invention Confirmed by experiments. Therefore, by providing the touch panel 4 in the vicinity of the position where the inverted images 301C and 302C on the front and rear display screens are formed, the image formed in the vicinity of the touch panel 4 (the inverted images 301C and 302C) is viewed. The touch panel 4 can be operated.

  In the example shown in FIG. 4, an example is shown in which a DFD that displays an object three-dimensionally using two display screens 301A and 302A is used. However, a three-dimensional display device such as the DFD is used. Not limited to this, a two-dimensional display device or a three-dimensional display device may be used.

  Further, the number of lenses to be laminated is not limited to four as shown in FIG. 4, and may be two or more as shown in Table 1, for example. However, when the number of lenses is small, the viewing angle becomes narrow. In addition, when the number of lenses is large, the viewing angle is widened, but the image is deteriorated due to absorption loss or scattering of the lens. For these reasons, it is preferable that the number of laminated lenses is about 4 to 8.

  In addition, various lenses such as a variable focus lens such as a bulk lens, a Fresnel lens, and a liquid crystal lens can be used as the lens, but it is preferable to use a Fresnel lens from the viewpoint of reducing the thickness.

  In addition, various optical materials such as acrylic, polycarbonate, and glass can be used as the material of the lens, but it is preferable to use acrylic from the viewpoints of ease of processing and high transparency.

As described above, according to the equal-magnification imaging optical system according to the first embodiment, n lenses having the same focal length are represented by the recurrence formulas expressed by the formulas (1) to (4). , M _{k = n} = 1 or −1, and stacking at an interval d that does not depend on L ₀ , it is possible to form an equal-size erect image or inverted image with a simple configuration.

L ₀ corresponds to the distance between the object and the lens through which the light incident from the object side first passes. Therefore, by setting the value independent of L ₀ , an object existing at any depth position can be imaged at equal magnification. In addition, when an image of a three-dimensional object is formed, the entire area of the object can be formed at an equal magnification. For example, it can be combined with a three-dimensional display device (three-dimensional display device) for various uses. It will be possible to apply.

  FIGS. 5 to 8 are schematic diagrams for explaining an application example of the first embodiment. FIG. 5 is a diagram showing the principle of the first embodiment. FIG. 6 is an optical system and an optical system shown in FIG. FIG. 7 is a diagram showing a second configuration example of an optical system optically equivalent to the optical system shown in FIG. 5, and FIG. 8 is a diagram showing FIG. It is a figure which shows the 3rd structural example of the optical system optically equivalent to the optical system.

For example, as shown in FIG. 5, the equal-magnification imaging optical system of Example 1 includes four lenses 201 _h (h = 1, 2, 3, 4) having the same focal length (f) at a distance d2. Are stacked at equal intervals. At this time, if the distance d2 between the lenses 201 _h (h = 1, 2, 3, 4) is set to 0.6 f as shown in Table 1, as shown in FIG. An inverted image 1C having a magnification can be formed. In other words, even if the configuration and arrangement shown in FIG. 5 are not used, the light (incident on the optical system from the object 1A side) is arranged with a distance (d2 = 0.6f). This means that an inverted image 1C having the same magnification as that of the object 1A can be formed by exiting from the optical system after passing through the imaging element 4 times. Therefore, a configuration example of an optical system that is optically equivalent to the optical system shown in FIG. 5 and can form an inverted image 1C having the same magnification as the object 1A will be described below.

As an optical system optically equivalent to the optical system shown in FIG. 5, for example, as shown in FIG. 6, three lenses 201 _h (h = 1, 2, 4) having the same focal length, and a plane mirror are used. An optical system composed of 202 and the half mirror 203 is conceivable. In this case, the light incident from the object 1A side initially passes first sheet of lens 201 ₁ and the second sheet of lenses 201 ₂ passing a second time to place at intervals d2 (= 0.6f). The half mirror 203 is disposed between the _first lens 201 ₁ and the second lens 201 ₂ . At this time, for example, the half mirror 203 causes the light traveling from the _first lens 201 ₁ to the second lens 201 ₂ to go straight, and from the _second lens 201 ₂ to the first lens 201. _The light traveling toward ₁ is arranged so that its path changes in the orthogonal direction. Then, placing the third sheet of lens 201 ₄ in the traveling direction of the light path is changed by the half mirror 203. In this case, said second sheet of lenses 201 ₂ and 3rd lens 201 _4, the spacing on the optical axis shown in 1 chain line in FIG. 6 are arranged such that d2.

Also, the plane mirror 202, the light having passed through the second sheet of lenses 201 ₂ is arranged to pass through the second sheet of lenses 201 ₂ again. At this time, the plane mirror 202 is disposed at a distance d2 / 2 from the _second lens 201 ₂ .

In the case of the optical system having such a configuration, the light incident from the object 1A side passes through the _first lens 201 ₁ , the half mirror 203, and the second lens 201 ₂ , and then the plane mirror 202. And pass through the _second lens 2012 again. Then, light passing through the second sheet of lenses 201 ₂ again, the route is changed by the half mirror 203, passes through the lens 201 ₄ of the third image, emitted from the optical system.

At this time, the light incident from the object 1A side passes through a lens having a focal length f four times in total before being emitted. Therefore, when the interval between the lenses 201 _h (h = 1,2,4) distance and said second sheet of lenses 201 ₂ and the plane mirror 202 as described above, the optical system and the optical shown in FIG. 5 The inverted image 1C having the same magnification as the object 1A can be formed.

In the optical system shown in FIG. 6, the light path is changed using the half mirror 203. However, the present invention is not limited to this. For example, a polarizing beam splitter 204, a quarter wavelength plate 205, and a polarizing plate 206 are combined. You can also change the course of light. In this case, for example, as shown in FIG. 7, instead of the half mirror 203, the polarizing beam splitter 204 is disposed between the first lens 201 ₁ and the second lens 201 ₂ so that the two eye lenses 201 ₂ and disposing the quarter-wave plate 205 between the plane mirror 202. Further, as shown in FIG. 7, for example, the polarizing plate 206 is configured such that light incident from the object 1A side becomes p-polarized light at a position optically in front of the _first lens 20111. To place. At this time, the distance between the lenses 201 _h (h = 1, 2, 4) and the distance between the second lens 201 ₂ and the plane mirror 202 are the same as those in the optical system shown in FIG. .

For an optical system having such a configuration, the light incident from the object 1A side, the state of the p-polarized first sheet of lens 201 _1, passes through the polarization beam splitter 204, the second sheet of lenses 201 ₂ After that, when the light passes through the quarter wavelength plate 205, the plane mirror 202, and the quarter wavelength plate 205 in this order, the light passes through the _second lens 2012 again and becomes s-polarized light. Therefore, light passing through the second sheet of lenses 201 ₂ again, the polarization beam splitter 204 path is changed, passes through the lens 201 ₄ of the third image, emitted from the optical system.

Also in this case, the light incident from the object 1A side passes through a lens having a focal length f four times in total before being emitted. Therefore, when the interval between the lenses 201 _h (h = 1,2,4) distance and said second sheet of lenses 201 ₂ and the plane mirror 202 as described above, the optical system and the optical shown in FIG. 5 The inverted image 1C having the same magnification as the object 1A can be formed.

  In the example shown in FIG. 7, the polarizing plate 206 is provided in the optical system. For example, the object 1A is an object displayed on a liquid crystal display or the like. The polarizing plate 206 is not necessary when it is in the p-polarized state.

As described above, when the plane mirror 202 and the optical components such as the half mirror 203 and the polarization beam splitter 204 are used, the optical system shown in FIG. 5 with three lenses 201 _h (h = 1, 2, 4) An optically equivalent equal-magnification imaging optical system can be configured. Therefore, it can be made more compact than the optical system described in the first embodiment.

Further, the optical system shown in FIG. 5 has four lenses 201 _h (h = 1, 2, 3, 4) laminated, but instead of the lens, an imaging effect equivalent to that of the lens is obtained. The resulting imaging element, for example, a curved mirror with a focal length f can also be used.

As an optical system using the curved mirror, for example, as shown in FIG. 8, an optical system in which a curved mirror 207 having a focal length f instead of the _third lens 2013 is arranged. In this case, the distance between the _first lens 201 ₁ and the second lens 201 ₂ , the distance between the second lens 201 ₂ and the curved mirror 207 on the optical axis indicated by the one-dot chain line in FIG. be placed so that the distance of the curved surface mirror 207 and 4th lens 201 ₄ respectively become d2 = 0.6f, optical system and becomes optically equivalent shown in FIG. 5, the object 1A and equivalent magnification The inverted image 1C can be formed.

Although FIG. 8 shows an example in which the curved mirror 207 is used instead of the _third lens 2013, the present invention is not limited to this, and the curved mirror may be used instead of other lenses. The curved mirror may be used in place of a single lens, a plurality of lenses, or all lenses.

  The optical system shown in FIGS. 6 to 8 is an example of an optical system that is optically equivalent to the optical system shown in FIG. 5. The optical system shown in FIG. Other configurations and arrangements may be used as long as they are optically equivalent. 6 to 8, the case where there are four lenses has been described. However, in the case where the number of lenses is not four, any configuration and arrangement may be used as long as they are optically equivalent.

FIG. 9 is a schematic diagram showing a schematic configuration of the equal-magnification imaging optical system of Example 2 according to the present invention.
In FIG. 9, 201 _h (h = 1, 2,..., N + 1) is a lens with a focal length f ₁ , and 208 _j (j = 1, 2,..., N) is a lens with a focal length f ₂ . is there.

For example, as shown in FIG. 9, the equal-magnification imaging optical system according to the second embodiment includes n + 1 lenses 201 _h (h = 1, 2,..., N + 1) having a focal length f ₁ , n The lenses 208 _j (j = 1, 2,..., N) having a focal length of f ₂ are alternately stacked, and the lenses 201 _h (h = 1, 2,..., N) having the focal length of f ₁ are stacked. +1) is an optical system arranged at equal intervals with an interval d3. At this time, the distance d3 between the lenses 201 _h (h = 1, 2,..., N + 1) having the focal length f ₁ is obtained from a recurrence formula as described below.

As the magnification imaging optical system of this embodiment 2, n + 1 sheets of focal length f ₁ of the lens _{201 h (h = 1,2, ...} , n + 1) and the focal length of the m sheets f ₂ When the lenses 208 _j (j = 1, 2,..., N) are alternately stacked, the distance between the lenses 201 _h (h = 1, 2,..., N + 1) having the focal length f ₁ is d. Then, the magnification M _k of the image formation of the light that has passed through the k lenses is expressed by a recurrence formula such as the following formulas (5) to (8).

In the equation (5), M _{k = 2n + 1} = 1 when an erect image of equal magnification is formed. Therefore, the lens 201 _h (h = 1, 2,..., N +) having the focal length f ₁ is obtained by obtaining d satisfying M _{2n + 1} = 1 using the equations (5) to (8). The interval d3 of 1) is obtained. Further, when forming an inverted image of equal magnification, M _{k = 2n + 1} = −1. Therefore, the lens 201 _h (h = 1, 2,...) Having the focal length f ₁ is obtained by obtaining d satisfying M _{k = 2n + 1} = −1 using the equations (5) to (8). , n + 1) is obtained. The procedure for obtaining d satisfying M _{2n + 1} = 1 or −1 using the formulas (5) to (8) is the same as the procedure described in the first embodiment, and therefore will not be described in detail. Is omitted.

Further, in the equal-magnification imaging optical system according to the second embodiment, up to n = 1, that is, a lens having a focal length f ₁ is 2 using the recurrence formulas expressed by the equations (5) to (8). In the case of a sheet, for example, if f ₂ = −2f _{1 and} the lens interval d3 when forming an inverted image of the same magnification is obtained, d3 = 1.6f. When there are two lenses having the focal length f _{1 in} the configuration as in the first embodiment, the lens interval d2 is 2f as shown in Table 1 above. In other words, while the focal length of the two lenses of f _1, that the focal length sandwich the lens f _2, can be the focal length to reduce the distance of the lens f _1. Although explanation is omitted, in the case of other numbers, the interval between the lenses having the focal length f ₁ can be reduced by sandwiching the lenses having the focal length f ₂ .

In other words, in the same magnification imaging optical system as in the second embodiment, the distance d3 when the m lenses having the focal distance f ₁ are stacked is the same as the first embodiment in which the focal distance is f ₁ . It is possible to make it narrower than when only m sheets are stacked. Therefore, the equal magnification imaging optical system can be thinned.

Further, in the equal-magnification imaging optical system according to the second embodiment, since the focal length f ₁ and the focal length f ₂ are independent variables, the condition that satisfies M _{2n + 1} = 1 or −1 in the equation (5) is satisfied. By changing the focal length f ₁ and the focal length f ₂ , the imaging position L _{2n + 1} can be freely changed. As a most typical example of this point, consider a case where n = 2, that is, the total number of lenses is five. At this time, for example, when M ₅ = −1 is solved in the equation (5), the following equation (16) is obtained as one of the solutions.

At this time, by changing f ₁ and f ₂ so as to satisfy the formula (16), the imaging position L ₅ can be controlled while maintaining the same magnification relationship.

In the case of an equal magnification imaging optical system configured as in the second embodiment, it is preferable to use a variable focus lens, that is, a lens whose focal length can be changed, as the lenses 201 _h and 208 _j . An example of the variable focus lens is a liquid crystal lens.

When a variable focus lens is used as the lenses 201 _h and 208 _j , for example, the focal length f ₁ is satisfied under the condition that M _{2n + 1} = 1 or −1 in the formula (5) in one set of optical systems. And the focal length f ₂ can be changed. In other words, for example, when the total number of the lenses is 5, when the lenses 201 _h (h = 1, 2, 3) having the focal length f ₁ are arranged at a certain distance d3, the lenses 201 _h , focal length f _1, f ₂ of 208 _j, the if they meet the equation (16) may be any combination. When the combination of the focal lengths f ₁ and f ₂ of the lenses 201 _h and 208 _j is changed, the imaging position L _{5 of the} object is changed from the equation (7). Therefore, for example, even when the depth display range that can be displayed by the three-dimensional display device is narrow, a wide depth range can be expressed by changing the focal lengths f ₁ and f ₂ of the lenses 201 _h and 208 _j. it can.

As described above, according to the equal-magnification imaging optical system of the second embodiment, n + 1 focal length f ₁ lenses and n focal length f ₂ lenses are alternately stacked, and the focal point In the recurrence formula expressed by the formulas (5) to (8), the distance between the lenses having the distance f ₁ satisfies M _{k = 2n + 1} = 1 or −1 and does not depend on L _0. By laminating at intervals d, it is possible to form an equal-magnification erect image or an inverted image with a simple configuration.

Further, since the focal length focal length between the lens f ₁ places the lens f _2, the interval d3 of lens when the focal length formed by laminating m sheets of lens f _1, the Example 1 Thus, it is possible to make it narrower than when only m lenses having a focal length of f ₁ are stacked. Therefore, the equal magnification imaging optical system can be thinned.

Further, in the equal-magnification imaging optical system according to the second embodiment, since the focal length f ₁ and the focal length f ₂ are independent variables, the condition that satisfies M _{2n + 1} = 1 or −1 in the equation (5) is satisfied. By changing the focal length f ₁ and the focal length f ₂ , the imaging position L _{2n + 1} can be freely changed. At this time, if a variable focus lens is used as the lens, a wide depth range can be expressed even when the depth display range that can be displayed by the three-dimensional display device is narrow.

In the case of the equal-magnification imaging optical system according to the second embodiment, the number of lenses having the focal length f ₁ to be stacked may be any number as long as the above condition is satisfied. However, when the number of lenses having the focal length f ₁ is small, the viewing angle becomes narrow. If the number of lenses having the focal length f ₁ is large, the viewing angle is widened, but the image is deteriorated due to absorption loss or scattering of the lenses. For these reasons, the number of lenses having the focal length f ₁ is preferably about 4 to 8.

The lens having the focal length f _{1 and} the lens having the focal length f ₂ may be various lenses such as a bulk lens, a Fresnel lens, and a variable focus lens such as a liquid crystal lens. At this time, in order to make the optical system thin, it is preferable to use a Fresnel lens.

The material of the lens having the focal length f _{1 and} the lens having the focal length f ₂ is preferably acrylic, for example, because of ease of processing of the lens and high transparency, but is not limited to the acrylic. Various optical materials such as polycarbonate and glass can be used.

In the equal-magnification imaging optical system according to the second embodiment, a concave lens is used as the lens having the focal length f _2. However, the present invention is not limited to this, and a convex lens may be used.

  Although not described in detail, the same magnification imaging optical system as in the second embodiment is not limited to the configuration and arrangement as shown in FIG. 9, but as shown in FIG. As long as it is optically equivalent to the optical system, the optical system may have any configuration and arrangement.

  The present invention has been specifically described above based on the above-described embodiments. However, the present invention is not limited to the above-described embodiments, and various modifications can be made without departing from the scope of the present invention. is there.

  The equal-magnification imaging optical system can image an object at equal magnification by stacking a plurality of lenses having the same focal length. Therefore, in addition to the touch panel display device described in the first embodiment, for example, display of interiors (objects) such as bronze statues, vases, sculptures, and advertisements displayed on display devices installed outdoors or in public facilities. The present invention can also be applied to a display system that displays in a floating state.

FIG. 3 is a schematic diagram illustrating a schematic configuration of the equal magnification imaging optical system according to the first exemplary embodiment of the present invention, and illustrates a configuration example when an erect image of equal magnification is formed. FIG. 2 is a schematic diagram illustrating a schematic configuration of an equal magnification imaging optical system according to a first embodiment of the present invention, and is a diagram illustrating a configuration example in the case of forming an inverted image of equal magnification. FIG. 6 is a schematic diagram for explaining how to obtain the lens interval in the equal magnification imaging optical system according to the first embodiment. It is a figure which shows the example of application of the equal magnification imaging optical system of the present Example 1, and is a figure which shows the example in the case of laminating | stacking four lenses and forming an inverted image of equal magnification. FIG. 5 is a schematic diagram for explaining an application example of the first embodiment, and illustrates the principle of the first embodiment. FIG. 6 is a schematic diagram for explaining an application example of the first embodiment, and is a diagram illustrating a first configuration example of an optical system that is optically equivalent to the optical system illustrated in FIG. 5. FIG. 6 is a schematic diagram for explaining an application example of the first embodiment, and is a diagram illustrating a second configuration example of an optical system optically equivalent to the optical system illustrated in FIG. 5. FIG. 6 is a schematic diagram for explaining an application example of the first embodiment, and is a diagram illustrating a third configuration example of an optical system that is optically equivalent to the optical system illustrated in FIG. 5. It is a schematic diagram which shows schematic structure of the equal magnification imaging optical system of Example 2 by this invention.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1A ... Object 1B ... Erect image with equal magnification 1C ... Inverted image with equal magnification 201 ₁ , 201 ₂ , 201 ₃ , 201 _n , 201 _{n + 1} ... Lens with focal length f (f ₁ ) 202 ... Plane mirror 203 ... Half Mirror 204 ... Polarizing beam splitter 205 ... 1/4 wavelength plate 206 ... Polarizing plate 207 ... Curved mirror 208 ₁ , 208 ₂ , 208 ₃ , 208 _n ... Lens with focal length f ₂ 301A ... Display screen 302A on the front surface of DFD ... Display screen on the rear surface of the DFD 301C: Inverted image of the display screen on the front surface of the DFD 302C: Inverted image of the display screen on the rear surface of the DFD 4 ... Touch panel

Claims (8)

An equal-magnification imaging optical system comprising a plurality of imaging elements and imaging an object at an equal magnification,
The plurality of imaging elements have the same focal length,
The plurality of imaging elements are equally spaced so that light incident on the optical system passes through the imaging elements n times (n is an integer of 2 or more) before exiting the optical system. Has been placed,
The distance d between the imaging elements is expressed by the following formulas (1) to (1), where f is the focal length of the imaging elements and M _k is the imaging magnification of the light that has passed through the k imaging elements. 4. An equal-magnification imaging optical system characterized by satisfying M _{k = n} = 1 or −1 in the recurrence formula represented by 4) and having a value independent of L ₀ .

  2. The equal-magnification imaging optical system according to claim 1, wherein the plurality of imaging elements include n lenses or n curved mirrors.   2. The equal-magnification imaging optical system according to claim 1, wherein the plurality of imaging elements include lenses and curved mirrors, and the total number of the lenses and curved mirrors is n. An equal-magnification imaging optical system comprising a plurality of imaging elements, a plane mirror, and an optical component that switches the light emission direction in accordance with the light incident direction, and forms an object at an equal magnification,
The plurality of imaging elements have the same focal length,
The plurality of imaging elements, the plane mirror, and the optical component are arranged in such a manner that the imaging elements are arranged at equal intervals, and the imaging elements are n before the light incident on the optical system exits from the optical system. Are arranged to pass through (n is an integer of 2 or more),
The distance d between the imaging elements is expressed by the following formulas (1) to (1), where f is the focal length of the imaging elements and M _k is the imaging magnification of the light that has passed through the k imaging elements. 4. An equal-magnification imaging optical system characterized by satisfying M _{k = n} = 1 or −1 in the recurrence formula represented by 4) and having a value independent of L ₀ .

The plurality of imaging elements are composed of less than n lenses,
The equal-magnification imaging optical system according to claim 4, wherein the optical component is a half mirror. The plurality of imaging elements are composed of less than n lenses,
5. The equal-magnification imaging according to claim 4, wherein the optical component is a combination of a polarizing beam splitter and a quarter-wave plate, or a combination of the polarizing beam splitter, a quarter-wave plate and a polarizing plate. Optical system. An equal-magnification imaging optical system comprising a plurality of imaging elements and imaging an object at an equal magnification,
The plurality of imaging elements are composed of n + 1 (n is an integer of 1 or more) lenses having a focal length of f ₁ and n lenses having a focal length of f ₂ .
The lens having the focal length f _{1 and} the lens having the focal length f ₂ are alternately arranged, and the lenses having the focal length f ₁ are arranged at equal intervals.
The distance d between the lenses having the focal length f1 is a recurrence expressed by the following formulas (5) to (8), where M _k is the imaging magnification of the light that has passed through the k imaging elements. An equal-magnification imaging optical system characterized by satisfying M _{k = 2n + 1} = 1 or −1 in the expression and not depending on L ₀ .

8. The equal-magnification imaging optical system according to claim 7, wherein one or both of the lens having the focal length f _{1 and} the lens having the focal length f ₂ or both are variable focal length lenses.

Images