JP5515848B2 - Optical element and manufacturing method thereof - Google Patents

Description

  The present invention relates to an optical element and a method for manufacturing the same, and more particularly to an optical element capable of recording and reproducing a three-dimensional image as a hologram and a method for manufacturing the same.

  Holographic technology has long been known as a method for recording and reproducing stereoscopic images on a medium. Holograms created by this method are used in various fields such as ornamental art and anti-counterfeiting seals. It's being used. As a method of optically creating a hologram, a method of recording interference fringes between object light emitted from an object and reference light on a photosensitive medium is generally used. As a light source for object light and reference light, laser light having excellent coherence is usually used. In general, the behavior of electromagnetic waves such as light can be considered as propagation of wavefronts having amplitude and phase, and a hologram can be said to be an optical element having a function of reproducing such wavefronts. Therefore, it is necessary to record information for accurately reproducing the phase and amplitude of the object light at each position in the space on the hologram recording medium. If interference fringes generated by object light and reference light are recorded on a photosensitive medium, information including both the phase and amplitude of the object light can be recorded, and illumination equivalent to the reference light can be recorded on this medium. By irradiating the reproduction light, a part of the illumination reproduction light can be observed as light having a wavefront equivalent to the object light.

  Thus, when creating a hologram by an optical method using laser light or the like, the phase and amplitude of the object light can be recorded only as interference fringes with the reference light. This is because the photosensitive medium on which the hologram is recorded has the property of being exposed according to the light intensity. On the other hand, recently, a method of creating a hologram by computation using a computer has been put into practical use. This method is called Computer Generated Hologram (CGH), which calculates the wavefront of object light using a computer and records its phase and amplitude on a physical medium in some way. Thus, a hologram is created. Of course, if this computer generated hologram method is used, it is possible to record an image as an interference fringe between the object beam and the reference beam, but without using the reference beam, information on the phase and amplitude of the object beam can be directly obtained. It is also possible to record on the recording surface. For example, Patent Document 1 below discloses a recording method in which the amplitude is represented by the size of the opening formed on the recording medium and the phase is represented by the position of the opening. Patent Document 2 below proposes a recording method in which a medium is composed of two recording layers, the amplitude is recorded on one recording layer, and the phase is recorded on the other recording layer. .

JP-A-5-46062 U.S. Pat. No. 3,957,353

  The method of recording an image as interference fringes, which is widely used as an optical hologram creation method, generally provides a high-resolution reproduced image and can be executed by an optical method, so that productivity is high. Although there is a merit that it is high, there is a problem that the image becomes dark due to poor diffraction efficiency due to interference fringes during reproduction. In contrast, the method of directly recording the phase and amplitude of the object light on the medium, which has been proposed as a method of a computer generated hologram, has the advantage that high diffraction efficiency can be obtained. Recording on a medium is technically difficult, and there is a problem that productivity is lowered in practice.

  Therefore, an object of the present invention is to provide an optical element that can obtain high diffraction efficiency during reproduction and that is excellent in productivity.

(1) A first aspect of the present invention is an optical element comprising a set of a plurality of three-dimensional cells.
Each cell has a specific amplitude and a specific phase defined, and the specific amplitude is expressed by any one of four or more ranges obtained by dividing a range of 0 to 100%. The specific phase is represented by any one of four or more ranges obtained by dividing a range of 0 to 2π.
Each cell has an amplitude modulator with transmittance or reflectance according to the specific amplitude defined in the cell, and phase modulation with a refractive index or optical path length according to the specific phase defined in the cell. And
The amplitude modulation part of each cell has a transmittance corresponding to each specific amplitude by changing the content of the colorant, or according to each specific amplitude by changing the surface roughness of the reflecting surface. Has reflectivity,
The phase modulation unit of each cell has a refractive index corresponding to each specific phase by changing the refractive index of the constituent material, or changes the traveling distance of light in the material having a predetermined refractive index. Has an optical path length corresponding to each specific phase,
When given incident light is given to an individual cell, each individual cell is specified so that emission light with the amplitude and phase of the incident light changed according to the specific amplitude and phase defined for the cell can be obtained. The optical characteristics are as follows.

(2) According to a second aspect of the present invention, in the optical element according to the first aspect described above,
Individual cells are arranged one-dimensionally or two-dimensionally.

(3) According to a third aspect of the present invention, in the optical element according to the second aspect described above,
The individual cells are arranged so that the vertical pitch and the horizontal pitch of the cells are equal to each other.

(4) According to a fourth aspect of the present invention, in the optical element according to the first to third aspects described above,
The complex amplitude distribution of the object light from the object image is recorded so that the object image can be reproduced when observed from a predetermined viewpoint position, and can be used as a hologram.

(5) According to a fifth aspect of the present invention, in the method of manufacturing an optical element in which a predetermined object image is recorded,
A cell definition stage for defining a set of a plurality of three-dimensional virtual cells;
A representative point definition stage for defining a representative point for each virtual cell;
An object image definition stage for defining an object image to be recorded;
One of four or more ranges obtained by dividing a range of 0 to 100% into individual virtual cells by calculating a complex amplitude at each representative point position of the object light emitted from the object image. An amplitude phase defining step that defines a specific amplitude expressed by one and a specific phase expressed by any one of four or more ranges obtained by dividing a range of 0 to 2π;
A physical cell forming stage in which each virtual cell is replaced with a physical cell, and an optical element composed of a set of three-dimensional physical cells is formed;
And
In the physical cell formation stage, when predetermined incident light is given to each physical cell, the emission and amplitude of the incident light are changed according to the specific amplitude and specific phase defined in the virtual cell corresponding to the physical cell. In order to obtain light, an amplitude modulator having a transmittance or reflectance corresponding to a specific amplitude defined in the virtual cell and a refractive index or optical path length corresponding to a specific phase defined in the virtual cell A phase modulation unit, each of which is replaced by a physical cell having specific optical characteristics ,
The amplitude modulation unit of each physical cell has a transmittance corresponding to each specific amplitude by changing the content of the colorant, or according to each specific amplitude by changing the surface roughness of the reflecting surface. Has a high reflectivity,
The phase modulation unit of each physical cell has a refractive index corresponding to each specific phase by changing the refractive index of the constituent material, or changes the traveling distance of light in the material having a predetermined refractive index. Thus, the optical path length corresponding to each specific phase is provided.

(6) According to a sixth aspect of the present invention, in the method for manufacturing an optical element according to the fifth aspect,
In the cell definition stage, block-like virtual cells are arranged one-dimensionally or two-dimensionally to define a cell set.

(7) According to a seventh aspect of the present invention, in the method for manufacturing an optical element according to the fifth or sixth aspect described above,
In the amplitude phase definition stage, a plurality of point light sources are defined on the object image, and object light composed of spherical waves having a predetermined amplitude and a predetermined phase is emitted from each point light source. The total complex amplitude of the object light from each point light source at the point position is calculated.

(8) According to an eighth aspect of the present invention, in the method for manufacturing an optical element according to the seventh aspect,
Define K point light sources that emit object light of wavelength λ on the object image, the amplitude of the object light emitted from the k-th (k = 1 to K) point light source O (k) is Ak, and the phase is θk. And the total complex amplitude of the object light from the K point light sources at the predetermined representative point P is Σ, where rk is the distance between the predetermined representative point P and the kth point light source O (k). _{(K = 1 to K)} (Ak / rk · cos (θk ± 2πrk / λ) + iAk / rk · sin (θk ± 2πrk / λ))

(9) According to a ninth aspect of the present invention, in the method for manufacturing an optical element according to the fifth to eighth aspects described above,
In consideration of the direction of illumination light irradiated at the time of reproduction or the viewpoint position at the time of reproduction, a phase correction step of correcting the specific phase defined for each virtual cell is further performed.

(10) According to a tenth aspect of the present invention, in the method for manufacturing an optical element according to the fifth to ninth aspects described above,
In the cell definition stage, by arranging virtual cells in the horizontal and vertical directions, a cell set consisting of virtual cells arranged on a two-dimensional matrix is defined,
In the amplitude phase definition stage, a plurality of M point light source columns that extend in the horizontal direction and are arranged in the vertical direction are defined on the object image, and belong to a plurality of adjacent rows in the vertical direction in the two-dimensional matrix. A total of M groups are defined by setting the virtual cell group to be one group, and the M point light source columns and the M groups are associated with each other according to the arrangement order in the vertical direction, and the mth (m = 1) (M), the object light emitted from the point light sources in the point light source array reaches only the virtual cell belonging to the mth group, and the total complex amplitude is calculated at each representative point position. It is a thing.

  (11) In an eleventh aspect of the present invention, an optical element is manufactured using the method for manufacturing an optical element according to the fifth to tenth aspects described above.

  According to the present invention, since the object image is recorded not as interference fringes but as a complex amplitude distribution of object light, high diffraction efficiency can be obtained during reproduction. In addition, since the complex amplitude distribution is recorded using the optical characteristics of the three-dimensional cell, an optical element with excellent productivity can be provided.

It is a perspective view which shows the general holographic method of recording an object image optically as an interference fringe using reference light. FIG. 4 is a perspective view showing the amplitude and phase of object light that has reached a representative point P (x, y) on the recording surface 20 when a point light source O and a recording surface 20 are defined. Complex amplitude of object light at the position of the representative point P (x, y) when the object light emitted from each point light source on the object image 10 reaches the representative point P (x, y) on the recording surface 20 FIG. It is a figure which shows that amplitude A (x, y) and phase (theta) (x, y) are calculated | required based on the complex amplitude shown by the coordinate point Q on a complex coordinate plane. 3 is a perspective view showing an example of a three-dimensional virtual cell set 30 defined for recording an object image 10. FIG. It is a figure which shows the function of the amplitude modulation and phase modulation of the three-dimensional cell C (x, y) used for this invention. It is a figure which shows an example of 16 types of physical cells from which the transmittance | permeability and refractive index which should become a component of the optical element which concerns on this invention differ. It is a perspective view which shows an example of the structure of the physical cell C (x, y) considered to be most suitable for utilizing for this invention. When the physical cell C (x, y) shown in FIG. 8 is used as a transmissive cell, the amplitude information is recorded as the width G1 of the groove G (x, y), and the phase information is the groove G (x, y). It is a front view explaining the reason recorded as the depth G2. When the physical cell C (x, y) shown in FIG. 8 is used as a reflection type cell, the amplitude information is recorded as the width G1 of the groove G (x, y), and the phase information is the groove G (x, y). It is a front view explaining the reason recorded as the depth G2. FIG. 9 is a perspective view showing an example in which seven types of groove widths and four types of depths are defined and a total of 28 types of physical cells are prepared in the structure of the physical cell C (x, y) shown in FIG. 8. It is a figure which shows the relationship between the refractive index of each part, and the depth of a groove | channel about transmissive cell C (x, y). It is a figure which shows the relationship between the refractive index of each part, and the depth of a groove | channel about reflection type cell C (x, y). It is a side view which shows the basic form which irradiates the illumination light for reproduction | regeneration from the normal line direction with respect to the optical element which concerns on this invention, and observes the object image currently recorded as a hologram from a normal line direction. It is a side view which shows the form which irradiates the illumination light for reproduction | regeneration with respect to the optical element which concerns on this invention from the diagonal direction, and observes the object image currently recorded as a hologram from a normal line direction. It is a side view which shows the form which irradiates the illumination light for reproduction | regeneration from the normal line direction with respect to the optical element which concerns on this invention, and observes the object image currently recorded as a hologram from the diagonal direction. FIG. 16 is a side view showing the principle of performing a specific phase correction process in order to create an optical element corresponding to the reproduction environment shown in FIG. 15. FIG. 17 is a side view showing the principle of performing a specific phase correction process in order to create an optical element corresponding to the reproduction environment shown in FIG. 16. It is a perspective view which shows the method for producing the optical element corresponding to the reproduction environment using the illumination light for white reproduction | regeneration. 3 is a perspective view illustrating an example in which a three-dimensional virtual cell set 30 is configured by arranging three-dimensional cells in a one-dimensional matrix. FIG.

  Hereinafter, the present invention will be described based on the illustrated embodiments.

<<< §1. Basic principle of the present invention >>
FIG. 1 is a perspective view showing a general holographic technique for optically recording an object image as an interference fringe using reference light. When a stereoscopic image of the object 10 is recorded on the recording medium 20, the object 10 is illuminated with light having the same wavelength as the reference light R (usually laser light), and the recording medium is irradiated with the object light from the object 10 and the reference light R. Interference fringes formed on 20 are recorded. Here, when an XY coordinate system is defined on the recording medium 20 and attention is paid to an arbitrary point P (x, y) located at the coordinates (x, y), the object 10 is placed at the point P (x, y). The amplitude intensity of the combined wave due to the interference between the object light from each of the above points O (1), O (2),..., O (k),. become. Similarly, the amplitude intensity of the combined wave due to the interference between the object light from each point and the reference light R is recorded at another point P (x ′, y ′) on the recording medium 20. Since the distances are different, the amplitude intensity recorded at the point P (x, y) is different from the amplitude intensity recorded at the point P (x ′, y ′). In this way, the amplitude intensity distribution is recorded on the recording medium 20, and the amplitude and phase of the object light are expressed by this amplitude intensity distribution. At the time of reproduction, a three-dimensional reproduction image of the object 10 is obtained by irradiating reproduction illumination light having the same wavelength as the reference light R from the same direction as the reference light R (or a direction that is plane-symmetric with respect to the recording medium 20).

  In order to record interference fringes on the recording medium 20 by an optical method, a photosensitive material is used as the recording medium 20, and the interference fringes are recorded as a shading pattern on the recording medium 20. On the other hand, when using the computer generated hologram method, the phenomenon that occurs in the optical system shown in FIG. 1 may be simulated on a computer. Specifically, instead of the real object 10 and the recording medium 20, the object image 10 and the recording surface 20 are defined in a virtual three-dimensional space on the computer, and a large number of point light sources O (1 ), O (2),..., O (k),. For each point light source, object light (spherical wave) having a predetermined wavelength, amplitude, and phase is defined, and further, reference light having the same wavelength as the object light is defined. On the other hand, a large number of representative points P (x, y) are defined on the recording surface 20, and the amplitude intensity of the combined wave of the object light and the reference light reaching the position of each representative point is obtained by calculation. Thus, the amplitude intensity distribution (interference fringes) is obtained on the recording surface 20 by calculation. Therefore, if this amplitude intensity distribution is recorded on a physical recording medium as a light / dark distribution or an uneven distribution, A holographic recording medium can be produced.

  However, if the computer generated hologram method is used, it is not always necessary to record as interference fringes using the reference light R, and the object light itself from the object image 10 can be directly recorded on the recording surface 20. That is, in the case of optically creating a hologram, an interference wave must be generated on the recording medium 20 made of a photosensitive material for a certain period of time required for exposure and recorded as interference fringes. For this reason, it is necessary to generate an interference wave that becomes a standing wave by using the reference light. However, if the computer generated hologram method is used, the state of the wave at a certain moment existing on the recording surface 20 can be observed as if the time is stationary, and this can be recorded. In other words, the amplitude and phase of the object light at each representative point position on the recording surface 20 at a predetermined reference time can be obtained by calculation. In the present invention, taking advantage of such a computer generated hologram, a method of directly recording the amplitude and phase of the object light is employed without using a method of recording the object light as interference fringes with the reference light.

Now, for example, as shown in the perspective view of FIG. 2, when the point light source O and the recording surface 20 are defined, the amplitude of the object light reaching the representative point P (x, y) on the recording surface 20 Let's consider how the phase is calculated. In general, the wave considering the amplitude and phase is
Acosθ + i Asinθ
(I is an imaginary unit). Here, A is a parameter indicating the amplitude, and θ is a parameter indicating the phase. Therefore, if the object light emitted from the point light source O is defined by the complex function, the object light at the position of the representative point P (x, y) is
A / r · cos (θ + 2πr / λ)
+ I A / r · sin (θ + 2πr / λ)
It is expressed by a complex function. Here, r is the distance between the point light source O and the representative point P (x, y), and λ is the wavelength of the object light. The amplitude of the object light attenuates as the distance r increases, and the phase is determined by the relationship between the distance r and the wavelength λ. This complex function does not include a variable indicating time because, as described above, it is an expression indicating the instantaneous state of a wave observed when the time is stopped at a predetermined reference time.

Eventually, in order to record the information of the object image 10 on the recording surface 20, as shown in the perspective view of FIG. 3, a number of point light sources O (1), O (2), .., O (k),..., O (K) are defined, and at each representative point position on the recording surface 20, the amplitude and phase of the combined wave of the object light emitted from each point light source are obtained by calculation. What is necessary is just to record by some method. Now, a total of K point light sources are defined on the object image 10, and the object light emitted from the kth point light source O (k) is as shown in FIG.
Ak cos θk + i Ak sin θk
Suppose that it is expressed by a complex function. If the object image 10 is composed of a set of pixels each having a predetermined gradation value (density value), the parameter Ak indicating the amplitude is a value of the pixel existing at the position of the point light source O (k). It is determined corresponding to the gradation value. In general, the phase θk may be set such that θk = 0, but it is also possible to perform setting so that object light having a different phase is emitted from each part of the object image 10 as necessary. . If the object light expressed by the complex function can be defined for all K point light sources, the combined wave of all K object lights at the position of an arbitrary representative point P (x, y) on the recording surface 20. As shown in FIG.
Σ _{k = 1 to K} (Ak / rk cos (θk + 2πrk / λ))
+ I Ak / rk sin (θk + 2πrk / λ))
It is expressed by a complex function. Here, rk is the distance between the kth point light source O (k) and the representative point P (x, y). The above formula corresponds to a formula for reproducing the object image 10 in the back of the recording medium. When reproducing the object image 10 so as to be raised toward the front side of the recording medium,
Σ _{k = 1 to K} (Ak / rk cos (θk−2πrk / λ))
+ I Ak / rk sin (θk−2πrk / λ))
The complex function may be calculated by the following formula (the sign of the phase term is negative). Therefore, the complex function considering both cases is
Σ _{k = 1 to K} (Ak / rk cos (θk ± 2πrk / λ))
+ I Ak / rk sin (θk ± 2πrk / λ))
It becomes. If the real part of this function is Rxy and the imaginary part is Ixy, and Rxy + iIxy is formed, the complex amplitude (amplitude in consideration of the phase) at the position of the representative point P (x, y) of this composite wave is shown in FIG. As shown, this is indicated by a coordinate point Q on the complex coordinate plane. Eventually, the amplitude of the object light synthesized wave at the representative point P (x, y) is given by the distance A (x, y) between the origin O and the coordinate point Q in the coordinate plane shown in FIG. 4, and the phase is a vector OQ and a real number. It is given by an angle θ (x, y) formed with the axis.

  Thus, the amplitude A (x, y) and the phase θ (x, y) of the object light synthesized wave at the position of an arbitrary representative point P (x, y) defined on the recording surface 20 are obtained by calculation. Become. Therefore, a complex amplitude distribution of object light emitted from the object image 10 (amplitude and phase distribution of the object light synthesized wave) is obtained on the recording surface 20. If the complex amplitude distribution thus obtained is recorded on a physical recording medium in some form and the wavefront of the object light is reproduced when given reproduction illumination light is given, the object image 10 is It can be recorded as a hologram.

  The inventor of the present application has conceived a method using a three-dimensional cell in order to record the complex amplitude distribution of the object light emitted from the object image 10 on the recording surface 20. In order to record a complex amplitude distribution using a three-dimensional cell and record the object image 10 as a hologram, the following procedure may be performed. First, for example, as shown in FIG. 5, a three-dimensional virtual cell set 30 is defined at the position of the recording surface 20. The three-dimensional virtual cell set 30 is a two-dimensional array of cells by arranging block-shaped virtual cells having predetermined dimensions vertically and horizontally. Then, a representative point is defined for each virtual cell. The position of the representative point may be an arbitrary point in the cell, but here, the representative point of the cell is defined at the center point position of the front surface of the cell (the surface facing the object image 10). For example, an XY coordinate system is defined on the front surface (the surface facing the object image 10) of the three-dimensional virtual cell set 30, and the representative point P (x, y) at the position of the coordinate (x, y) in this coordinate system is defined. If the virtual cell is called a virtual cell C (x, y), the representative point P (x, y) comes to the center point of the front surface of the virtual cell C (x, y).

  On the other hand, the object image 10 is defined as a set of point light sources. In the example shown in FIG. 5, the object image 10 is defined as a set of K point light sources O (1), O (2),..., O (k),. Each of these point light sources emits object light having a predetermined amplitude and phase, and a combined wave of these object lights reaches the representative point P (x, y). The complex amplitude of this composite wave can be calculated by the above-described equation, and is shown as a coordinate point Q in the complex coordinate plane shown in FIG. 4, and based on this coordinate point Q, the amplitude A (x, y) and phase As described above, θ (x, y) can be obtained. Here, the amplitude A (x, y) and phase θ (x, y) obtained for the representative point P (x, y) are used as the virtual cell C (x, y) including the representative point P (x, y). ) Will be referred to as a specific amplitude A (x, y) and a specific phase θ (x, y).

  The above procedure is actually executed as arithmetic processing using a computer. Eventually, the specific amplitude and the specific phase can be obtained for all the virtual cells constituting the three-dimensional virtual cell set 30 by this arithmetic processing. Therefore, if each of these virtual cells is replaced with a physical cell, an optical element (hologram recording medium on which the object image 10 is recorded) composed of a set of three-dimensional physical cells can be created. Here, the physical cell that replaces the virtual cell has optical characteristics such that the amplitude and phase of incident light can be modulated in accordance with the specific amplitude and specific phase defined in the virtual cell. Need to be. In other words, the replaced individual physical cell, when given incident light, depends on the amplitude and phase of the incident light according to the specific amplitude and specific phase defined in the virtual cell before the replacement. It is necessary to have a specific optical characteristic having a function of generating emission light by changing the angle.

  For an optical element composed of a set of physical cells having such specific optical characteristics, a predetermined reproduction illumination light (ideally, the same wavelength as the object light wavelength λ used in the above arithmetic processing) is used. If a single monochromatic light plane wave) is irradiated, since the reproduction illumination light is modulated by a specific amplitude and a specific phase in each physical cell, the wavefront of the original object light is reproduced. Thus, the hologram recorded on the optical element is reproduced.

<<< §2. Specific configuration of physical cell >>>
Next, a specific configuration of the physical cell used in the present invention will be described. The physical cell used in the present invention is a three-dimensional solid cell, each having a specific amplitude and a specific phase. When a predetermined incident light is given to each cell, the specific amplitude and the specific cell defined in the cell are specified. A cell having any configuration may be used as long as it has specific optical characteristics such that emission light in which the amplitude and phase of incident light are changed in accordance with the phase can be obtained. For example, assuming that an amplitude A (x, y) and a phase θ (x, y) are recorded in a three-dimensional cell C (x, y) as shown in FIG. 6, the amplitude Ain and phase θin are stored in this cell. When the incident light Lin is given, it is only necessary to obtain the emitted light Lout having the amplitude Aout = Ain · A (x, y) and the phase θout = θin ± θ (x, y). The amplitude Ain of the incident light is modulated by the specific amplitude A (x, y) recorded in the cell and changes to the amplitude Aout, and the phase θin of the incident light is changed to the specific phase θ (x , Y), the phase changes to the phase θout.

  One method of modulating the amplitude in the three-dimensional cell is a method in which an amplitude modulation unit having a transmittance corresponding to a specific amplitude is provided in the cell (the entire cell may be used as the amplitude modulation unit). An amplitude modulation unit may be provided in a part of the cell). For example, a cell having an amplitude modulation unit with a transmittance of Z% functions as a cell in which a specific amplitude of A (x, y) = Z / 100 is recorded, and incident light having an amplitude Ain is this cell. , The amplitude modulation is performed on the emitted light having an amplitude of Aout = Ain · Z / 100. Setting the transmittance of each three-dimensional cell to an arbitrary value can be dealt with, for example, by changing the content of the colorant.

  Another method for modulating the amplitude in the three-dimensional cell is a method in which an amplitude modulation unit having a reflectance corresponding to a specific amplitude is provided in the cell. For example, a cell having an amplitude modulation unit with a reflectance of Z% functions as a cell in which a specific amplitude of A (x, y) = Z / 100 is recorded, and incident light having an amplitude Ain is this amplitude. If the light is reflected and emitted from the modulation unit, the amplitude is modulated to emitted light having an amplitude of Aout = Ain · Z / 100. In order to set the reflectance of each three-dimensional cell to an arbitrary value, for example, a reflecting surface is prepared in the cell (this reflecting surface functions as an amplitude modulation unit), and the reflecting surface of this reflecting surface is set. What is necessary is just to set a reflectance to arbitrary values. Specifically, for example, the ratio of reflected light and scattered light can be adjusted by changing the surface roughness of the reflecting surface. Therefore, by adjusting the surface roughness, an arbitrary reflectance can be obtained. Cell can be prepared.

  Still another method of modulating the amplitude in the three-dimensional cell is a method of providing an amplitude modulation unit having an effective area corresponding to a specific amplitude in the cell. For example, when the area of all incident regions of incident light is 100%, it is possible to obtain emission light effective for reproducing an object image only from incident light incident on a portion having an effective area of Z%. A cell having an amplitude modulation unit having a simple structure functions as a cell in which a specific amplitude of A (x, y) = Z / 100 is recorded. That is, even if incident light having an amplitude Ain is incident on the amplitude modulation unit, only Z% of the light exits as effective emission light, so Aout = Ain · Z / 100. Amplitude modulation is performed on the emitted light having an amplitude. In order to obtain effective emission light only from such a region having a specific effective area, a cell having a physical uneven structure may be used. Specific examples thereof will be described in §3.

  On the other hand, one method of modulating the phase in the three-dimensional cell is a method in which a phase modulation unit having a refractive index corresponding to a specific phase is provided in the cell (even if the whole cell is used as the phase modulation unit). Alternatively, a phase modulation unit may be provided in a part of the cell). For example, in a cell having a phase modulation unit made of a material having a refractive index of n1 and a cell having a phase modulation unit made of a material having a refractive index of n2, even if incident light having the same phase is given, A difference occurs in the phase of the emitted light. Therefore, if the cell is made of various materials having different refractive indexes, it is possible to apply arbitrary phase modulation to the incident light.

  Another method for modulating the phase in the three-dimensional cell is a method in which a phase modulation unit having an optical path length corresponding to a specific phase is provided in the cell (the entire cell may be used as the phase modulation unit). A phase modulation unit may be provided in a part of the cell). For example, even in the case of a cell having a phase modulation unit made of the same material having a refractive index n, if the optical path length of the phase modulation unit is different, even if incident light having the same phase is given, There will be a difference in the phase. For example, if the optical path length of the phase modulation unit provided in the first cell is L and the optical path length of the phase modulation unit provided in the second cell is 2L, incident light having the same phase is given. Even so, compared to the light emitted from the first cell, the light emitted from the second cell has doubled the distance traveled in the material having the refractive index n, so that the phase difference is large. It is happening. In order to realize a phase modulation unit having an arbitrary optical path length, a cell having a physical uneven structure may be used. Specific examples thereof will be described in §3.

  Thus, a three-dimensional cell having an amplitude modulation function based on a specific amplitude and a three-dimensional cell having a phase modulation function based on a specific phase can be realized by several methods. The optical element according to the present invention can be realized by selecting an arbitrary method from the modulation method and the phase modulation method. For example, as an amplitude modulation method, a method in which an amplitude modulation unit having a transmittance corresponding to a specific amplitude is provided in a cell, and as a phase modulation method, a phase having a refractive index corresponding to a specific phase in the cell is adopted. If a method of providing a modulation unit is adopted and the entire cell is used as an amplitude modulation unit and a phase modulation unit, 16 kinds of physical cells as shown in the table of FIG. 7 are selectively arranged. An optical element can be formed. In this table, the horizontal axis corresponds to the amplitude A, and the vertical axis corresponds to the phase θ, and both the amplitude A and the phase θ are divided into four ranges.

  Here, the cell drawn in the range corresponding to the amplitude A of “0 to 25%” (the cell in the first column in the table) is a cell made of a material having a very low transmittance, and the amplitude A is “ The cells drawn in the range corresponding to “25 to 50%” (cells in the second column of the table) are cells made of a material having a slightly low transmittance, and the amplitude A corresponds to “50 to 75%”. The cells drawn in the range (cells in the third column of the table) are made of a material having a slightly higher transmittance, and the cells drawn in the range corresponding to the amplitude A of “75 to 100%” (tables). The cells in the fourth column) are cells made of a material having a very high transmittance. On the other hand, the cell drawn in the range corresponding to the phase θ of “0 to π / 2” (cell in the first row of the table) is a cell made of a material having a refractive index n1 very close to air. The cell drawn in the range corresponding to the phase θ of “π / 2 to π” (the cell in the second row of the table) is a cell made of a material having a refractive index n2 slightly larger than air, and the phase θ is A cell drawn in a range corresponding to “π to 3π / 2” (cell in the third row of the table) is a cell made of a material having a refractive index n3 that is considerably larger than air, and the phase θ is “3π / The cell drawn in the range corresponding to “2−2π” (the cell in the fourth row of the table) is a cell made of a material having a refractive index n4 that is much larger than air.

  As described above, in the example shown in FIG. 7, a total of 16 cells having four types of transmittance and four types of refractive index are prepared, but in order to record the amplitude and phase in the cell with higher accuracy. In this case, the steps of the transmittance and the refractive index should be set more finely, and more types of cells should be prepared. In order to replace a virtual cell using such 16 types of physical cells, the optical characteristics closest to the optical characteristics required for performing modulation with a specific amplitude and a specific phase defined for each virtual cell. May be selected.

<<< §3. Practical configuration of physical cell >>>
As described above, the physical cell used in the present invention may be realized in any configuration as long as it has a function of modulating incident light according to a specific amplitude and a specific phase. FIG. 7 shows an example in which the modulation according to the specific amplitude is controlled by the transmittance and the modulation according to the specific phase is controlled by the refractive index. As described above, there are theoretically various methods for modulating the amplitude and phase, but not all methods are practical in view of industrial mass production. In order to reproduce an object image having a certain level of resolution using the optical element according to the present invention, the size of each three-dimensional cell must be limited to a certain level (roughly speaking, the cell size). When the thickness is 100 μm or more, it is difficult to reproduce an object image with good visibility). Therefore, when an optical element is created by combining the 16 types of physical cells shown in FIG. 7, it is necessary to perform a two-dimensional arrangement of minute cells as parts, and there are 16 types of cells at specific positions. It is necessary to arrange a specific cell among the cells. Considering such work, it can be seen that the method of configuring an optical element using a physical cell as shown in FIG. 7 is not suitable for industrial mass production.

  The inventor of the present application can provide information on amplitude and phase in one physical cell, and an individual physical cell as a method of constructing an optical element suitable for industrial mass production by a set of such physical cells. A method of recording the amplitude information as the area of the concavo-convex structure portion and recording the phase information as the step length of the concavo-convex structure portion (depth of the concave portion or height of the convex portion). It was.

  FIG. 8 is a perspective view showing an example of the structure of a physical cell C (x, y) that is considered optimal for use in the present invention. As shown in the figure, this three-dimensional physical cell has a substantially rectangular parallelepiped block shape, and a groove G (x, y) is formed on the upper surface thereof. In this example, the dimensions of the physical cell C (x, y) are C1 = 0.6 μm, C2 = 0.25 μm, C3 = 0.25 μm in the figure, and the dimension of the groove G (x, y) is G1 = 0.2 μm, G2 = 0.05 μm, and G3 = C3 = 0.25 μm. If the physical cell C (x, y) having such a structure is used, the amplitude information can be recorded as the value of the lateral width G1 of the groove G (x, y), and the phase information is , And can be recorded as the value of the depth G2 of the groove G (x, y). In other words, when a virtual cell in which a specific amplitude and a specific phase are defined is replaced with a physical cell having such a structure, it has a dimension G1 corresponding to the specific amplitude and a dimension corresponding to the specific phase. Replacement with a physical cell having G2 will be performed.

  The reason why the amplitude information is recorded as the width G1 of the groove G (x, y) and the phase information is recorded as the depth G2 of the groove G (x, y) in the physical cell shown in FIG. 9 will be described with reference to the front view. Now, the physical cell C (x, y) is made of a material having a refractive index n2, and the outside of the physical cell C (x, y) is made of a material (for example, air) having a refractive index n1. It shall be configured. At this time, the refractive index n2 of the light L1 perpendicularly incident on the surface S1 inside the groove G (x, y) and the light L2 perpendicularly incident on the surface S2 outside the groove G (x, y) Comparing the optical path lengths passing through the medium, it can be seen that the optical path length of the light L1 is shorter than the optical path length of the light L2 by the depth G2 of the groove G (x, y). Therefore, if the refractive indexes n1 and n2 are different, a predetermined phase difference is generated between the light L1 and the light L2 emitted as transmitted light from the physical cell C (x, y).

  On the other hand, FIG. 10 is a front view showing a case where emitted light is obtained as reflected light from the physical cell C (x, y). In this example, the upper surface of the physical cell C (x, y), that is, the surfaces S1 and S2 are reflection surfaces, and the light L1 incident on the surface S1 inside the groove G (x, y) substantially perpendicularly. The light L2 incident substantially perpendicularly to the surface S2 outside the groove G (x, y) is reflected substantially perpendicularly to each surface and emitted. At this time, when comparing the total optical path length along the incident and reflection paths, the optical path length of the light L1 is twice the depth G2 of the groove G (x, y) than the optical path length of the light L2. It turns out that it becomes long by the corresponding amount. Therefore, a predetermined phase difference is generated between the light L1 and the light L2 emitted as reflected light from the physical cell C (x, y).

  As described above, regardless of whether the physical cell C (x, y) is a transmissive cell or a reflective cell, the light L1 incident on the surface S1 inside the groove G (x, y); A predetermined phase difference is generated between the light L2 incident on the surface S2 outside the groove G (x, y), and this phase difference depends on the depth G2 of the groove G (x, y). Will be determined. Therefore, of the light incident on the upper surface of the physical cell C (x, y), only the emitted light obtained based on the incident light on the surface S1 inside the groove G (x, y) is reproduced from the object image 10. (In other words, in FIG. 9 or FIG. 10, if only the light L1 is handled as the emission light effective for image reproduction), it is effective for image reproduction. The emitted light L1 has undergone phase modulation by a specific phase corresponding to the depth G2 of the groove G (x, y) in the physical cell C (x, y). Thus, the information on the phase of the object light can be recorded as the depth G2 of the groove G (x, y).

  Further, as described above, if only the emitted light obtained based on the incident light on the surface S1 inside the groove G (x, y) is handled as the emitted light effective for reproducing the object image 10, Information on the amplitude of the object light can be recorded as the width G1 of the groove G (x, y). This is because as the width G1 of the groove G (x, y) increases, the area of the surface S1 inside the groove G (x, y) also increases, and the proportion of the emitted light effective for reproducing the object image 10 increases. Because. That is, since the emitted light L2 shown in FIG. 9 or 10 does not include any meaningful phase component, even if the emitted light L2 is observed at the viewpoint position during reproduction, a so-called background noise component is used. It is not recognized as effective light for reproducing a meaningful image. On the other hand, since the output light L1 includes a meaningful phase component, it is observed as a signal component effective for image reproduction. Eventually, the width G1 of the groove G (x, y) is an element that determines the proportion of the light L1 observed as a signal component of the light emitted from the physical cell C (x, y). This parameter gives information on the amplitude of the signal wave.

  However, in general, the amplitude information is not expressed by the width G1 of the groove G (x, y), but by the area of the surface S1 inside the groove G (x, y). become. In the case of the embodiment shown in FIG. 8, it happens that the depth G3 of the groove G (x, y) is always set equal to the depth C3 of the physical cell C (x, y). The area of the surface S1 inside G (x, y) is proportional to the length of the width G1, but the depth dimension G3 of the groove G (x, y) is not necessarily constant, It is also possible to change both the width dimension and the depth dimension so that the area of the surface S1 inside the groove G (x, y) has a variation.

  As described above, the portion having the area corresponding to the specific amplitude (the portion corresponding to the surface S1 in FIG. 8) of the upper surface of the block-shaped physical cell is the depth corresponding to the specific phase (dimension G2 in FIG. 8). If a concave portion (groove G (x, y)) is formed by digging only by a depth corresponding to (a depth corresponding to), a specific amplitude is generated with respect to the reproduction illumination light by the physical cell having such a structure. It is possible to perform amplitude modulation according to the phase and phase modulation according to the specific phase. However, the same modulation processing can be performed by forming convex portions instead of forming concave portions in the block-like physical cells. That is, in the physical block shown in FIG. 8, even if the dimension G2 is set to a negative value and a protrusion is formed instead of the groove, an optical path difference corresponding to the height of the protrusion can be generated. And a phase difference can be generated. In other words, if the convex portion is formed by raising the portion having the area corresponding to the specific amplitude out of the upper surface of the block-shaped physical cell by the height corresponding to the specific phase, Even with a physical cell having such a structure, it is possible to perform amplitude modulation corresponding to a specific amplitude and phase modulation corresponding to a specific phase to the reproduction illumination light.

  In the physical cell C (x, y) having the groove G (x, y) as shown in FIG. 8, the groove width G1 and depth G2 can be continuously changed. An infinite variety of physical cells can be prepared. If such an infinite type of physical cell is used, the virtual cell has an accurate groove width G1 corresponding to the specific amplitude defined in the virtual cell and an accurate depth G2 corresponding to the specific phase. It is possible to replace the cell. However, in practice, a groove width and b depth are determined in advance, and a total of a × b physical cells are prepared, and optical characteristics required from these physical cells are obtained. It is preferred to select the closest physical cell. FIG. 11 is a perspective view showing an example in which seven kinds of groove widths and four kinds of depths are defined, and a total of 28 kinds of physical cells are prepared. These 28 physical cells are all block-like physical cells having the form shown in FIG. 8, and FIG. 11 shows a state in which these physical cells are arranged in a matrix of 4 rows and 7 columns. Yes.

  The seven columns of the matrix shown in FIG. 11 show variations of the amplitude A, and the four rows show variations of the phase θ. For example, the cell located in the column W1 is a cell corresponding to the minimum value of the amplitude A, and is a cell in which the groove width G1 = 0, that is, the groove G is not formed at all. As the line moves to the right side from the lines W2 to W7, the cell corresponds to a larger amplitude A, and the groove width G1 gradually increases. The cell located in the column W7 is a cell corresponding to the maximum value of the amplitude A, and the groove width G1 = cell width C1, that is, a cell in which the entire surface is dug. When attention is paid to the row of the matrix shown in FIG. 11, for example, the cell located in the row V1 is a cell corresponding to the minimum value of the phase θ, and the groove depth G2 = 0, that is, the groove G Is a cell that is not formed at all. As the cell moves downward to the rows V2 to V4, the cell corresponds to a larger phase θ, and the groove depth G2 gradually increases.

<<< §4. Method for creating optical element using practical physical cell >>
Here, a specific method for creating an optical element (hologram recording medium) on which the object image 10 is recorded using 28 physical cells as shown in FIG. 11 will be described. First, as shown in FIG. 5, an object image 10 composed of a set of point light sources and a three-dimensional virtual cell set 30 are defined using a computer. Here, each virtual cell constituting the three-dimensional virtual cell set 30 is a block-shaped cell as shown in FIG. 8 (at this time, no groove is formed yet). A three-dimensional virtual cell set 30 is formed by two-dimensionally arranging at a pitch. The dimensions of one virtual cell may be, for example, about C1 = 0.6 μm, C2 = 0.25 μm, and C3 = 0.25 μm. In this case, the horizontal pitch of the cell is 0.6 μm and the vertical direction If the pitch is set to 0.25 μm, the cells can be arranged without a gap. Of course, the dimension value of each cell introduced here is an example, and in practice, it can be set to an arbitrary dimension as required. However, the larger the cell size, the narrower the viewing angle at which a reproduced image of the object can be obtained, and the resolution of the object also decreases. Conversely, the smaller the cell dimensions, the more technically difficult it will be to form the concavo-convex structure of the physical cell. The cell arrangement is not necessarily performed at an equal pitch, but it is preferable to arrange the cells at predetermined equal pitches in the vertical and horizontal directions in consideration of the convenience of arithmetic processing and physical cell processing.

  Thus, when the definition of the object image 10 and the three-dimensional virtual cell set 30 is completed, a representative point is defined in each virtual cell, and as described in §2, a combined wave of each object light that has reached each representative point position And a specific amplitude and a specific phase are defined for each virtual cell. Subsequently, each virtual cell is replaced with one of the 28 physical cells shown in FIG. 11 (opticals required for performing modulation according to the specific amplitude and specific phase defined in each virtual cell) An optical element as a set of physical cells is created. At this time, the groove forming surface of each physical cell (upper surface in the case of the physical cell shown in FIGS. 8 and 11) faces the front surface (object image 10) of the three-dimensional virtual cell set 30 shown in FIG. Face) side.

  However, in practice, the operation of replacing the virtual cell with the physical cell is performed as a process of forming a predetermined concavo-convex structure on the medium surface to be an optical element. As described above, when replacing individual virtual cells in the three-dimensional virtual cell set 30 shown in FIG. 5 with physical cells, the physical cells are arranged so that the grooves face the front side. The optical element produced in (1) is a medium having a concavo-convex structure comprising a large number of grooves on the surface. Therefore, the work of replacing a virtual cell with a physical cell is performed by transferring data related to the concavo-convex pattern from the computer storing the information of each virtual cell (information indicating the specific amplitude and specific phase defined in each virtual cell) to the drawing device. Given this, this drawing apparatus carries out the process of drawing the concavo-convex pattern on the physical medium surface. The process of drawing a fine concavo-convex pattern can be performed using, for example, a patterning technique using an electron beam drawing apparatus. In addition, when mass-producing the same optical element, an original plate on which a desired concavo-convex structure is formed is created by a drawing process using an electron beam drawing apparatus, and the concavo-convex structure is formed by a stamping process using the original plate. What is necessary is just to make it transfer on many media.

  The optical element according to the present invention is basically composed of a main body layer obtained by two-dimensionally arranging physical cells as shown in FIG. 8, and if necessary, this main body layer. A protective layer may be formed on the surface. This protective layer serves to cover the uneven surface formed on the surface of the main body layer. The main body layer and the protective layer are made of different materials.

  In the case of a transmissive optical element in which incident light given to each physical cell becomes emission light by passing through the main body layer and the protective layer, the main body layer and the protective layer have different refractive indexes. It is necessary to comprise with a translucent material. Here, a specific relationship between the depth of the groove G and the phase in the case of producing a transmission type optical element (transmission type physical cell) having such a two-layer structure of the main body layer and the protective layer is examined. Try.

  Consider the case of a transmissive cell C (x, y) having a structure as shown in the upper cross-sectional view of FIG. This cell has a two-layer structure of a main body layer Ca in which a groove G of depth d (x, y) is formed and a protective layer Cb formed so as to fill the groove G on the upper surface thereof. Cell. Here, the refractive index of the material forming the protective layer Cb (in other words, the refractive index of the substance filled in the concave portion or the substance constituting the convex portion) is defined as n1, and the refractive index of the material forming the main body layer Ca. Is set to n2, the maximum depth of the groove G (the maximum depth of the concave portion or the maximum height of the convex portion) dmax is set to dmax = λ / | n1-n2 | A physical cell capable of performing phase modulation within the range of 0 to 2π can be realized. For example, assuming that the wavelength λ = 400 nm and the difference in refractive index | n1-n2 | = 2, dmax = 200 nm (0.2 μm) may be set.

In this case, the depth d (x, y) corresponding to the specific phase θ (x, y) is, as shown in FIG. 12, when n1> n2,
d (x, y) = λ · θ (x, y) / 2 (n1−n2) π
If n1 <n2,
d (x, y) = dmax−λ · θ (x, y) / 2 (n2−n1) π
Is obtained by the following formula. Therefore, when the specific amplitude and specific phase for one virtual cell C (x, y) are respectively determined as A (x, y) and θ (x, y), the specific phase θ (x, y) Substituting y), the corresponding depth d (x, y) is obtained by calculation, and is closest to the depth d (x, y) obtained by calculation from the 28 physical cells shown in FIG. If a physical cell having a depth and having a horizontal width closest to the dimension corresponding to the specific amplitude A (x, y) is selected, and the virtual cell C (x, y) is replaced with the selected physical cell, Good. If the protective layer Cb is not provided, the refractive index of air (approximately 1) may be used as the refractive index n1 of the protective layer.

  On the other hand, consider the case of a reflective cell C (x, y) having a structure as shown in the upper cross-sectional view of FIG. This cell has a two-layer structure of a main body layer Cα in which a groove G of depth d (x, y) is formed and a protective layer Cβ formed so as to fill the groove G on the upper surface thereof. Although it is a cell, the boundary between the main body layer Cα and the protective layer Cβ is a reflecting surface, and incident light that has entered the protective layer Cβ from the top to the bottom of the figure is reflected by the reflecting surface. It will inject toward the upper side of. Here, if the refractive index of the material forming the protective layer Cβ (in other words, the refractive index of the substance filling the concave part or the substance constituting the convex part) is n, the maximum depth of the groove G (recessed part) If the maximum depth or the maximum height of the projections) dmax is set to dmax = λ / 2n, a physical cell capable of performing phase modulation within a range of 0 to 2π with respect to light of wavelength λ. realizable. For example, if the wavelength λ = 400 nm and the refractive index n = 2, dmax = 100 nm (0.1 μm) may be set.

In this case, the depth d (x, y) corresponding to the specific phase θ (x, y) is as shown in FIG.
d (x, y) = λ · θ (x, y) / 4nπ
It is obtained by the following formula. If the protective layer Cβ is not provided, the refractive index n of the protective layer may be the refractive index of air (approximately 1), so the maximum depth of the groove G: dmax = λ / 2 is set and the specific phase is set. The depth d (x, y) according to θ (x, y) is
d (x, y) = λ · θ (x, y) / 4π
And it is sufficient.

<<< §5. Modified example considering convenience of playback environment >>
Here, consider an environment in which reproduction illumination light is applied to an optical element created by the method described so far, and the object image 10 recorded as a hologram is reproduced. FIG. 14 is a side view showing the relationship between the optical element 40 (hologram recording medium using a physical cell), the reproduction illumination light Lt or Lr, and the viewpoint E when performing such reproduction. When the optical element 40 is a transmissive type using a transmissive cell, as shown in the drawing, the surface opposite to the viewpoint E is irradiated with the reproduction illumination light Lt, and the light transmitted through the optical element 40 is converted into the viewpoint E. In the case where the optical element 40 is a reflection type using a reflection type cell, as shown in the figure, the surface on the same side as the viewpoint E is irradiated with the reproduction illumination light Lr and reflected from the optical element 40. The observed light is observed at the viewpoint E. In any case, when the optical element 40 is produced by the method described so far, the reproduction illumination light Lt or Lr is given as a plane wave of monochromatic light, and the recording of the optical element 40 is performed as shown in FIG. Irradiation light Lt or Lr for reproduction is irradiated from the normal direction of the surface (two-dimensional array surface on which physical cells are arrayed) (in other words, reproduction is performed so that the wavefront is parallel to the recording surface of the optical element 40). If the image is observed from the normal direction of the recording surface, the best reproduced image can be obtained.

  However, the actual reproduction environment of the optical element 40 in which the object image 10 is recorded as a hologram is not necessarily an ideal environment as shown in FIG. In particular, in the case of the reflection type, the observer's head is located at the position of the viewpoint E. Therefore, even if the reproduction illumination light Lr is irradiated from the direction shown in FIG. As a result, good reproduction cannot be performed. Therefore, as shown in FIG. 15, the actual reproduction environment irradiates the recording light of the optical element 40 with the reproduction illumination light Lt or Lr from an oblique direction, and displays a reproduction image at the viewpoint E located in the normal direction. Or irradiating the reproduction illumination light Lt or Lr from the normal direction of the recording surface of the optical element 40 and observing the reproduction image at the viewpoint E located in the oblique direction, as shown in FIG. In general, both the irradiation direction of the reproduction illumination lights Lt and Lr and the observation direction from the viewpoint E are set in an oblique direction.

  In order to create an optical element 40 capable of obtaining a good reproduction image in such an actual reproduction environment, each virtual image 40 is considered in consideration of the direction of illumination light irradiated during reproduction and the viewpoint position during reproduction. What is necessary is just to perform the phase correction process which corrects the specific phase defined about the cell.

  For example, as shown in FIG. 17, light LL1 to LL4 (objects from the object image 10) subjected to amplitude and phase modulation by irradiating the reproduction illumination lights L1 to L4 from an oblique direction and passing through the optical element 40. Let us consider the case of observing light (reproducing the wavefront of light) at a viewpoint E located in the normal direction. Assuming that the reproduction illumination lights L1 to L4 are monochromatic plane waves having a wavelength λ, and that the reproduction illumination light is irradiated to the optical element 40 from an oblique direction, the points P1 to P4 on the optical element 40 are applied to the points P1 to P4. At the time of arrival, an optical path difference has already occurred, and the incident light itself at each of the points P1 to P4 has already produced a phase difference. For example, the incident light at the positions of the points P2, P3, and P4 has an optical path length that is longer by d2, d3, and d4 than the incident light at the position of the point P1, and is incident by this optical path difference. The light itself has already produced a phase difference. Therefore, if it is assumed that “the optical element 40 capable of obtaining a good reproduction image in the reproduction environment as shown in FIG. 17 is created”, the specific phase is obtained for each virtual cell by the method described above. These specific phases may be corrected according to the cell position. For example, the cell at the point P1 in FIG. 17 need not be corrected, but the cell at the point P2 is corrected to a specific phase so that the phase difference caused by the optical path difference d2 can be canceled. Will be added. In this way, when the optical element 40 is created by correcting the specific phase, a good reproduced image is given by the lights LL1 to LL4 emitted in the direction of the viewpoint E.

  As shown in FIG. 18, such correction processing for a specific phase is performed by irradiating the reproduction illumination lights L1 to L4 from the normal direction and transmitting the light LL1 that has undergone amplitude and phase modulation by passing through the optical element 40. The same applies to LL4 (light that reproduces the wavefront of the object light from the object image 10) observed at the viewpoint E located in the oblique direction. That is, assuming that the reproduction illumination lights L1 to L4 are monochromatic plane waves having a wavelength λ and such reproduction illumination light is irradiated onto the optical element 40 from the normal direction, each point P1 on the optical element 40 When reaching ~ P4, no optical path difference occurs, and the phases of incident light at the points P1 to P4 are aligned. However, there is a difference in the optical path length until the emitted light emitted from the positions of the points P1 to P4 reaches the viewpoint E, and a phase difference occurs when observed at the viewpoint E. For example, the light emitted from the positions of the points P2, P3, and P4 has an optical path length that is longer by d2, d3, and d4 than the light emitted from the position of the point P1, so that the viewpoint is increased by this optical path difference. At the position E, a phase difference occurs. Therefore, if it is assumed that “the optical element 40 capable of obtaining a good reproduction image in the reproduction environment as shown in FIG. 18 is created”, the specific phase is obtained for each virtual cell by the method described above. These specific phases may be corrected according to the cell position. For example, the cell at the point P1 in FIG. 18 does not need to be corrected, but the cell at the point P2 is corrected to a specific phase so that the phase difference caused by the optical path difference d2 can be canceled. Will be added. In this way, when the optical element 40 is created by correcting the specific phase, a good reproduced image is given by the lights LL1 to LL4 emitted in the direction of the viewpoint E.

  As described above, the correction process for the specific phase has been described for the transmission type optical element 40, but the principle of the correction process is the same even for the reflection type optical element 40.

  On the other hand, when examining the wavelength of the illumination light for reproduction, in an actual reproduction environment, it is extremely rare that monochromatic light having a wavelength λ can be used as the illumination light for reproduction. It can be considered that the case where the reproduction is performed is generally. As described above, when reproduction is performed using reproduction illumination light including a plurality of wavelength components, different phase modulation is performed for each wavelength of light, so that a good reproduction image cannot be obtained. Specifically, a reconstructed image in which images having various colors are slightly shifted and overlapped is observed.

  Therefore, in order to obtain a somewhat good reproduction image even in a reproduction environment using white reproduction illumination light, a device as shown in FIG. 19 is used when calculating the complex amplitude distribution of object light. You just have to do it. The system shown in FIG. 19 defines the object image 10 and the three-dimensional virtual cell set 30 on the computer in the same manner as the system shown in FIG. 5, and the distribution of the total complex amplitude of each object light emitted from the object image 10 is determined. This is for performing an operation to be obtained on the three-dimensional virtual cell set 30. Here, the three-dimensional virtual cell set 30 is a cell set composed of virtual cells arranged on a two-dimensional matrix, which are configured by arranging virtual cells in the horizontal direction and the vertical direction. A representative point is defined for each virtual cell.

  When the method described here is used, the calculation of the total complex amplitude at each representative point position is performed by the following method. First, on the object image 10, a plurality of M point light source arrays, each extending in the horizontal direction and arranged in the vertical direction, are defined. In the illustrated example, three point light source arrays m1, m2, and m3 are defined with M = 3. Each point light source array includes a plurality of point light sources arranged in the horizontal direction. For example, the point light source array m1 includes j point light sources O (m1,1), O (m1,2),..., O (m1, j). On the other hand, on the three-dimensional virtual cell set 30 side, a total of M groups are defined by defining one group of virtual cell groups belonging to a plurality of rows adjacent in the vertical direction in the two-dimensional matrix. In the illustrated example, a total of three groups are defined with M = 3. That is, the first group g1 is composed of virtual cell groups belonging to the first row to the third row, the second group g2 is composed of virtual cell groups belonging to the fourth row to the sixth row, and the third The group g3 includes virtual cell groups belonging to the seventh to ninth rows.

  As described above, when M point light source arrays are defined on the object image 10 side and M groups are defined on the three-dimensional virtual cell set 30 side, the M point light source arrays and the M groups are vertically aligned. Corresponding to the order of arrangement. That is, in the illustrated example, the uppermost point light source array m1 corresponds to the uppermost group g1, the central point light source array m2 corresponds to the central group g2, and the lowermost point light source array m3. Corresponds to the bottom group g3. Then, it is assumed that the object light emitted from the point light source in the m-th (m = 1 to M) point light source array reaches only the virtual cell belonging to the m-th group at each representative point position. The total complex amplitude is calculated. For example, object light emitted from point light sources O (m1,1), O (m1,2),..., O (m1, j) belonging to the point light source array m1 in FIG. It is assumed that only the cells (virtual cells arranged in the first to third rows) are reached, and that the virtual cells belonging to the groups g2 and g3 are not reached, the total complex amplitude is calculated. . In other words, the calculation of the total complex amplitude at the representative point position of the virtual cell belonging to the group g1 is performed by calculating the point light sources O (m1,1), O (m1,2),. Only the object light emitted from m1, j) is considered, and the object light emitted from the point light sources belonging to the point light source arrays m2 and m3 is not considered.

  Actually, when the object image 10 is recorded under such conditions, the original hologram recording is not performed. In the first place, the basic principle of a hologram is that all the information of the object image 10 is recorded at any position on the recording surface. By performing such recording, a three-dimensional image is reproduced. It is. When the object image 10 is recorded under the above-described conditions, only the information of the part of the point light source array m1 (that is, a part of the upper part of the object image 10) is recorded in the group g1 region. As a result, a three-dimensional reproduction image cannot be obtained. Specifically, stereoscopic viewing in the horizontal direction is possible, but stereoscopic viewing in the vertical direction is insufficient. However, when the object image 10 is recorded under such conditions, in a reproduction environment using white reproduction illumination light, a better reproduction image (stereoscopic view in the vertical direction is insufficient, but clearer. (A reconstructed image) can be obtained. This is because the object image 10 is recorded separately for each part in the vertical direction, so that an effect of suppressing the wavelength dispersion of the reproduction light in the vertical direction during reproduction can be obtained.

  As mentioned above, although this invention was demonstrated based on some embodiment shown in figure, this invention is not limited to these embodiment, In addition, it can implement with a various form. For example, in the above-described embodiment, the three-dimensional virtual cell set 30 is defined by arranging individual three-dimensional cells in a two-dimensional matrix. However, as shown in FIG. It is also possible to define a three-dimensional virtual cell set 30 by preparing cells and arranging such three-dimensional cells in a one-dimensional matrix. In the example shown in FIG. 20, a three-dimensional virtual cell set 30 is formed by arranging vertically elongated cells C (1), C (2), C (3),. When the object image 10 is recorded on the optical element composed of cells arranged in a one-dimensional matrix in this way, only a reconstructed image that can be stereoscopically viewed in the vertical direction can be obtained. worth it.

  Needless to say, the optical element according to the present invention can be used as a “hologram recording medium” in which any object image 10 is recorded as a hologram and reproduced as a three-dimensional image. However, the present invention is not limited to the use as such a hologram recording medium, and can also be used when manufacturing general optical elements such as an optical filter, a polarizing element, and a light modulation element. For example, if a simple lattice pattern is used as the object image 10 and the complex amplitude distribution of the object light emitted from the pattern is recorded on a physical medium, an optical device having a specific optical action is obtained. An element can be realized.

  Further, the arrangement of the three-dimensional cells is not necessarily arranged along the orthogonal coordinate system, and can be arranged along the spherical surface using a polar coordinate system, for example. Furthermore, although the three-dimensional physical cells used in the above-described embodiments are all cells as passive elements, the physical cells used in the present invention are based on the refractive index, transmittance, and reflectance based on signals from the outside. It may be configured by an active element capable of controlling the above. For example, if each physical cell is made of a birefringent material such as a liquid crystal and the ratio of ordinary light and extraordinary light can be controlled by an external signal, each physical cell can be controlled based on an external signal. It becomes possible to determine the specific amplitude and specific phase of the physical cell. In an optical element using such an active element as a physical cell, a recorded image is not physically fixed, so that an arbitrary object image can be reproduced according to an external signal. become able to.

10: Object image (object)
20: Recording surface (recording medium)
30: Three-dimensional virtual cell set 40: Optical elements A, Ak, A (x, y): Amplitude Ain: Amplitude of incident light Aout: Amplitude of emitted light C (x, y): Virtual cell / physical cell C (1 ), C (2), C (3): elongated cells C1, C2, C3: cell dimensions Ca: body layer Cb: protection layer Cα: body layer Cβ: protection layer d (x, y): depth of groove G Dmax: maximum depth of groove G d2, d3, d4: optical path difference E: viewpoints G, G (x, y): grooves G1, G2, G3 formed in the cell: groove dimensions g1, g2, g3: Cell group Ixy: Imaginary part of complex amplitude i: Imaginary unit Lin: Incident light Lout: Emission light Lt: Reproduction illumination light Lr for transmission optical element: Reproduction illumination lights L1 to L4 for reflection optical element LL1 to LL4: light m1, m2, m3: point light source array n, n1 to n4: refractive indexes O, O (1), O (k), (K): Point light sources O (m1, 1), O (m1, j): Point light sources P (x, y), P (x ′, y ′) on the point light source array m1: Representative points P1 to P4: Point Q on optical element: Coordinate point R: Reference light Rxy: Real part of complex amplitude r, r1, rk, rK: Distance from point light source S1: Surface inside groove G (x, y) S2: Groove G External surfaces V1 to V4 of (x, y): Rows W1 to W7 corresponding to the phase θ: Columns θ, θk, θ (x, y) corresponding to the amplitude A: Phase θin: Phase θout of incident light: Ejection Phase λ of light: wavelength of light

Claims (11)

An optical element composed of a set of a plurality of three-dimensional cells,
Each cell has a specific amplitude and a specific phase defined, and the specific amplitude is expressed by any one of four or more ranges obtained by dividing a range of 0 to 100%. The specific phase is represented by any one of four or more ranges obtained by dividing a range of 0 to 2π.
Each cell has an amplitude modulator with transmittance or reflectance according to the specific amplitude defined in the cell, and phase modulation with a refractive index or optical path length according to the specific phase defined in the cell. And
The amplitude modulation part of each cell has a transmittance corresponding to each specific amplitude by changing the content of the colorant, or according to each specific amplitude by changing the surface roughness of the reflecting surface. Has reflectivity,
The phase modulation unit of each cell has a refractive index corresponding to each specific phase by changing the refractive index of the constituent material, or changes the traveling distance of light in the material having a predetermined refractive index. Has an optical path length corresponding to each specific phase,
When each cell is given a predetermined incident light, each cell has its own output so that the incident light can be obtained by changing the amplitude and phase of the incident light according to the specific amplitude and phase defined in the cell. An optical element having specific optical characteristics. The optical element according to claim 1,
An optical element in which individual cells are arranged one-dimensionally or two-dimensionally. The optical element according to claim 2,
An optical element, wherein the vertical pitches and the horizontal pitches of the individual cells are arranged at equal pitches. In the optical element in any one of Claims 1-3,
An optical element, wherein a complex amplitude distribution of object light from an object image is recorded so that the object image is reproduced when observed from a predetermined viewpoint position, and can be used as a hologram. A method of manufacturing an optical element in which a predetermined object image is recorded,
A cell definition stage for defining a set of a plurality of three-dimensional virtual cells;
A representative point definition stage for defining a representative point for each virtual cell;
An object image definition stage for defining an object image to be recorded;
By calculating a complex amplitude at each representative point position of the object light emitted from the object image, among the ranges of four or more stages obtained by dividing a range of 0 to 100% into individual virtual cells An amplitude phase definition stage that defines a specific amplitude expressed by any one and a specific phase expressed by any one of four or more ranges obtained by dividing a range of 0 to 2π. When,
A physical cell forming stage in which each virtual cell is replaced with a physical cell, and an optical element composed of a set of three-dimensional physical cells is formed;
Have
In the physical cell formation stage, when predetermined incident light is given to each physical cell, the amplitude and phase of the incident light are changed according to the specific amplitude and specific phase defined in the virtual cell corresponding to the physical cell. In order to obtain the emitted light, an amplitude modulator having a transmittance or reflectance corresponding to the specific amplitude defined in the virtual cell, and a refractive index or optical path length corresponding to the specific phase defined in the virtual cell A phase modulation unit, and each of which is replaced by a physical cell having specific optical characteristics ,
The amplitude modulation unit of each physical cell has a transmittance corresponding to each specific amplitude by changing the content of the colorant, or according to each specific amplitude by changing the surface roughness of the reflecting surface. Has a high reflectivity,
The phase modulation unit of each physical cell has a refractive index corresponding to each specific phase by changing the refractive index of the constituent material, or changes the traveling distance of light in the material having a predetermined refractive index. Therefore , the optical element manufacturing method has an optical path length corresponding to each specific phase . In the manufacturing method of the optical element according to claim 5,
A method of manufacturing an optical element, wherein a cell set is defined by arranging block-like virtual cells one-dimensionally or two-dimensionally in a cell definition stage. In the manufacturing method of the optical element according to claim 5 or 6,
In the amplitude phase definition stage, a plurality of point light sources are defined on the object image, and object light composed of spherical waves having a predetermined amplitude and a predetermined phase is emitted from each point light source. A method for manufacturing an optical element, characterized in that a total complex amplitude of object light from each point light source at a point position is calculated. In the manufacturing method of the optical element according to claim 7,
Define K point light sources that emit object light of wavelength λ on the object image, the amplitude of the object light emitted from the k-th (k = 1 to K) point light source O (k) is Ak, and the phase is θk. And the total complex amplitude of the object light from the K point light sources at the predetermined representative point P, where rk is the distance between the predetermined representative point P and the kth point light source O (k), A method of manufacturing an optical element, characterized in that it is obtained by calculation of Σ _{(k = 1 to K)} (Ak / rk · cos (θk ± 2πrk / λ) + iAk / rk · sin (θk ± 2πrk / λ)). In the manufacturing method in any one of Claims 5-8,
A method for manufacturing an optical element, further comprising a phase correction step of correcting a specific phase defined for each virtual cell in consideration of the direction of illumination light irradiated during reproduction or the viewpoint position during reproduction. In the manufacturing method in any one of Claims 5-9,
In the cell definition stage, by arranging virtual cells in the horizontal and vertical directions, a cell set consisting of virtual cells arranged on a two-dimensional matrix is defined,
In the amplitude phase defining step, a plurality of M point light source columns each extending in the horizontal direction and arranged in the vertical direction are defined on the object image, and the plurality of rows adjacent in the vertical direction in the two-dimensional matrix are defined. A total of M groups are defined by setting one virtual cell group to which the cell belongs, and M point light source columns and M groups are associated with each other according to the arrangement order in the vertical direction, and the mth (m = 1 to M), the object light emitted from the point light sources in the point light source array reaches only the virtual cell belonging to the mth group, and the total complex amplitude is calculated at each representative point position. A method for producing an optical element characterized by the above.   The optical element manufactured by the manufacturing method in any one of Claims 5-10.

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