JP5257640B2 - Method for producing computer-generated hologram and computer-generated hologram produced by the method - Google Patents

Description

  The present invention relates to a method for producing a computer-generated hologram and a computer-generated hologram produced by the method.

  2. Description of the Related Art Conventionally, it is known that a hologram is provided on a cash voucher or a credit card to prevent forgery. As this hologram, there is a computer-generated hologram (CGH) that is produced by forming interference fringes on a predetermined recording surface by calculation using a computer (see Patent Document 1).

JP 2001-013858 A Japanese Patent No. 3810917 JP 2000-214750 A JP 2002-72837 A JP 2005-215570 A JP 2004-309709 A JP 2004-264839 A

A. W. Lohmann and D. P. Paris: "Binary Fraunhofer Holograms, Generated by Computer", Appl. Opt., 6, 10, pp. 1739-1748 (Oct. 1967) Wai Hon Lee: "Sampled Fourier Transform Hologram Generated by Computer", Appl. Opt., 9, 3, pp. 639-643 (Mar. 1970)

  However, the computer-generated hologram of Patent Document 1 described above has a small calculation load but a narrow vertical viewing area. For example, FIGS. 17 and 18 are diagrams showing a conventional technique. FIG. 17 shows a side view when the computer-generated hologram 101 is irradiated with the reproduction illumination light 102a made of monochromatic light. As shown in FIG. 17, the diffracted light 103 generated from the uppermost unit region is not diffracted in the direction of the viewpoint E. For this reason, at the position of the viewpoint E, the reproduced image of the uppermost stage of the computer-generated hologram 101 cannot be observed, and the vertical viewing area does not widen. FIG. 18 shows a case where the computer-generated hologram 101 is irradiated with reproduction illumination light 102b made of white light. As shown in FIG. 18, each unit area looks only a single color even though the reproduction illumination light 102 b made of white light is irradiated. For example, among the diffracted light 103 generated from the uppermost unit region, the light toward the viewpoint E is the blue component B in the incident white light 102b. For this reason, at the position of the viewpoint E, the reproduced image of the uppermost part of the computer-generated hologram 101 is observed in blue B. The central portion is observed in green G, and the lowermost portion is observed in red R (not shown).

  Patent Document 2 discloses a technique having a viewing area in the vertical direction (vertical direction) by using a point light source as a light source of object light from an original image. In the technique disclosed in Patent Document 2, the object light is a spherical wave that spreads from the point light source on the original image, and the viewing area in the vertical direction is widened. However, since the recording area on the hologram recording surface is limited in the vertical direction, the vertical viewing area changes depending on the depth position of the object.

  The present invention has been made in view of such problems of the prior art, and its purpose is to produce a computer-generated hologram that is easy to observe and has excellent security, and a computer-generated hologram produced by the method. Is to provide.

  A method for producing a computer-generated hologram of the present invention that achieves the above object is the method for producing a computer-generated hologram, wherein amplitude information and phase information are recorded on a predetermined recording surface by an operation using a computer. The hologram has each unit region having a parallax only in the first direction and a predetermined width in the second direction with respect to the first direction and the second direction orthogonal to the first direction, Within each unit region, gradually changing from one to the other, a diffraction pattern having a spatial frequency different in the second direction is produced, and spreads in the first direction from a linear light source set on the recording object, Recording is performed using object light having a constant width in the second direction, and using the reference light focused at a predetermined position determined for each unit region in the second direction as the reference light.

  Further, the diffraction pattern is characterized by comprising interference fringes.

  The diffraction pattern may be a pattern that modulates phase and amplitude.

  Furthermore, the computer-generated hologram is manufactured by the method for manufacturing the computer-generated hologram.

  According to the present invention, diffusion of diffracted light in the second direction is achieved by producing a computer-generated hologram having a parallax only in the first direction and having different spatial frequencies of diffraction patterns in the second direction in the unit region. Since the angle is changed, a computer-generated hologram with an enlarged viewing area in the second direction can be obtained. Further, since the spread of the object light in the second direction can be determined regardless of the position of the object, the viewing area in the second direction does not change depending on the depth position of the object. Further, when white light is used as the reproduction illumination light, the viewing area is enlarged and the reproduction image can be observed in white.

It is a perspective view which shows the concept of the recording method of the computer composition hologram which concerns on this invention. It is a figure which shows the specific example based on the concept of the arithmetic processing of FIG. It is a top view for demonstrating the concept of the arithmetic processing of FIG. It is a figure which shows the structure of the CGH original plate of this embodiment. It is a figure which shows the specific structure of the CGH original plate of this embodiment. It is a figure which shows the state at the time of CGH original plate preparation of Example 1 of this embodiment. It is a perspective view which shows the state at the time of CGH original plate preparation of Example 1 of this embodiment. It is a figure which shows the case where the reproduction illumination light which consists of monochromatic light is irradiated to the CGH original plate of Example 1. FIG. It is a figure which shows the state at the time of CGH original plate preparation of Example 2 of this embodiment. It is a figure which shows the other example of the divergence position Fm1 of a Y direction. It is a figure which shows the other example of the divergence position Fm1 of a Y direction. It is a figure which shows the other example of the divergence position Fm1 of a Y direction. It is a figure which shows the other example of the divergence position Fm1 of a Y direction. It is a figure which shows the case where the reproduction illumination light which consists of white light is irradiated to the CGH original plate of Example 1. FIG. It is a figure which shows the conditions which the CGH original plate can observe in white. It is a figure which shows the case where the reference light L is made into the light which converges to the predetermined condensing position G, and object light is made into the light which does not spread in a Y direction. It is a figure which shows the prior art. It is a figure which shows the prior art.

  Hereinafter, a method for producing a hologram of the present embodiment will be described with reference to the drawings.

  In this embodiment, first, the computer-generated hologram 1 is produced. 1 to 3 show a basic method for producing the computer-generated hologram 1.

  First, in the present embodiment, a computer-generated hologram that is recorded using object light that spreads only in a predetermined one-dimensional direction from a point light source set on an original image is used. This manufacturing method is a method based on the description in Patent Document 1. That is, as shown in FIG. 1, when object light Oi emitted from an arbitrary point light source Pi on the original image O spreads only in the horizontal direction (in a plane parallel to the XZ plane) in the present embodiment as shown. Assume. Then, the object light Oi reaches only the linear region B on the recording medium 1, and the object light Oi does not reach any other region of the recording medium 1. In the case of producing a hologram by an optical method, it is extremely difficult to limit the spread of object light in this way. However, if a hologram is produced using a computer, the object can be simply modified by correcting the arithmetic expression. Light can be easily controlled. Therefore, the same limitation is imposed on the object light emitted from all point light sources constituting the original image O (the limitation that the object light spreads only in a plane parallel to the XZ plane). The computer generated hologram produced in this embodiment is a computer synthesized hologram having only horizontal parallax.

  FIG. 2 is a perspective view showing a specific example of a recording method based on the basic concept described above. In this example, the original image O and the recording medium 1 (recording surface) are each divided in the horizontal direction by a large number of parallel planes to define a large number of linear unit areas. That is, as shown in the figure, the original image O is divided into a total of M unit areas A1, A2, A3,..., Am,... AM, and the recording medium 1 similarly has a total of M unit areas B1, B2. , B3,..., Bm,. When the original image O is a stereoscopic image, each of the unit areas A1, A2, A3,..., Am, ... AM is an area obtained by dividing this stereoscopic surface portion. Here, the M unit areas on the original image O and the M unit areas on the recording medium 1 have a one-to-one correspondence. For example, the mth unit area Am on the original image O corresponds to the mth unit area Bm on the recording medium 1.

  In the example shown in FIG. 2, the width of each unit area A1, A2, A3,..., Am,... AM is the Y direction of the point light source defined on the original image O (vertical direction in this embodiment). Each unit region is a linear region in which point light sources are arranged in a line. For example, in the illustrated example, N point light sources Pm1 to PmN are arranged in a line in the m-th unit region Am.

  Further, the width of each unit area B1, B2, B3,..., Bm,... BM is set equal to the pitch in the Y direction of the point light source defined on the original image O. The calculation point is a linear region arranged two-dimensionally. The illustrated calculation point Q (x, ym) indicates a calculation point located in the m-th unit region Bm, and is at a position indicated by a coordinate value (x, ym) in the XY coordinate system.

  In the case of this example, the interference wave intensity at the calculation point Q (x, ym) is obtained as follows. First, a unit area Am on the original image O corresponding to the unit area Bm to which the calculation point Q (x, ym) belongs is determined as a calculation target unit area. Then, the amplitude at the position of the calculation point Q (x, ym) for the interference wave formed by the object light Om1 to OmN emitted from the point light sources Pm1 to PmN and the reference light Lθm in the calculation target unit area Am. If the intensity is obtained, this amplitude intensity is the interference wave intensity at the target calculation point Q (x, ym). Here, the reference light Lθm is, for example, a monochromatic parallel light beam parallel to the YZ plane, and is incident on the recording medium 1 at the same angle at any position. Alternatively, the incident angle θm of the reference light Lθm is determined based on the setting of the virtual illumination and the virtual viewpoint assuming the observation environment. For example, when assuming a point light source from above at the time of observation, the unit region B1 at the upper end The incident angle θ1 of the reference light Lθ1 from the normal direction of the recording medium may be set to a small angle δ, and the incident angle θM of the reference light LθM to the lower unit region BM may be set to a large angle β. .

  FIG. 3 is a top view for explaining the concept of such arithmetic processing, and shows a state in which the original image O and the CGH original recording medium 1 shown in FIG. 2 are viewed from above. As shown in the figure, the object light necessary for obtaining the interference wave intensity at the calculation point Q (x, ym) is emitted from N point light sources Pm1,..., Pmi,. , Omi,..., OmN, and it is not necessary to consider object light from all point light sources constituting the original image O. In this way, if the predetermined interference wave intensity is obtained for each of the calculation points Q (x, ym) defined on the CGH original recording medium 1, the intensity distribution of the interference wave to be recorded on the CGH original recording medium 1 is obtained. If the intensity distribution of the obtained interference wave is physically recorded by some method, the CGH original plate 1 is obtained. Specifically, as described in Patent Document 3, the CGH original plate 1 can be produced by recording a rectangle having an occupation rate corresponding to the intensity of the interference wave at a position corresponding to the calculation point.

  As described above, with reference to FIGS. 1 to 3, the light source information on the m-th unit area Am defined on the original image O is the m-th unit defined on the CGH original recording medium 1. A method of recording on the area Bm has been described. In the model described in this method, each of the unit areas Am and Bm is an elongated strip-shaped area, and the point light sources are arranged one-dimensionally and the calculation points are arranged two-dimensionally.

  In the above method, the amplitude and phase of the object light at the calculation point Q on the divided area may be recorded in addition to the method of recording with interference fringes due to interference with the reference light as described above. As described in 4, 5, the phase may be recorded by the depth of the groove of the three-dimensional cell having a groove on one surface, and the amplitude may be recorded by the width of the groove.

  Alternatively, as described in A.N. W. The amplitude and phase may be recorded by the Lohmann method, the Lee method described in Non-Patent Document 2, or the like.

  FIG. 4 is a diagram showing a configuration of the CGH original plate 1 of the present embodiment. 4A is a view of the system shown in FIG. 2 observed from the X direction, and FIG. 4B is an enlarged view of the CGH original plate 1 observed from the X direction.

  The CGH original plate 1 of the present embodiment has a diffraction pattern so that the pitch intervals (spatial frequencies) in the Y direction are different in the unit regions B1, B2, B3,..., Bm, BM shown in FIG. As a result, the viewing area in the Y direction is changed. For example, the interference fringe spacings Cm1, Cm2, Cm3,..., CmT in the Y direction of the unit region Bm of the CGH original plate 1 can be produced in various patterns as shown in FIG. In FIG. 4 (b), the interference fringe spacings Cm1, Cm2, Cm3,..., CmT in the Y direction are illustrated as conceptual diagrams. It is formed as unevenness. In this case, as shown in FIG. 5, there are various methods such as a rectangular cross section (FIG. 5A) and a curved line (FIG. 5B). In addition, the interference fringe interval can be determined not by changing the cross section but by periodically changing the two-dimensional pattern in the Y direction. In FIG. 5, the interference fringe intervals that differ in the Y-th direction gradually change from one to the other in the unit region. However, the present invention is not limited to this, and various patterns can be produced.

  FIG. 6 is a diagram illustrating a state when the CGH original plate 1 of Example 1 of the present embodiment is manufactured. In the first embodiment, the divergence position in the Y direction of the light source of the object light Om is set to the divergence position Fm1 on the opposite side to the observer of the CGH original plate 1. Therefore, as shown in FIG. 7, the object light Om is emitted from the point light sources P1... Pm... PM in the X direction and is emitted without spreading in the Y direction, and the divergence positions F11. It is set to spread from FM1. For this reason, although some astigmatism occurs, since the distance between the original image O and the CGH original 1 is very short, there is almost no influence.

  When the light source is set in this manner, the reference light L is irradiated at a predetermined incident angle, and the object light Om and the reference light L are set to interfere with each other, interference fringes are formed in the unit area Bm of the CGH original plate 1 shown in FIG. Interference fringes with intervals Cm1, Cm2, Cm3,..., Cmt,. In the first embodiment, the interference fringe interval appears so as to spread from top to bottom with respect to the paper surface. That is, the CGH original plate 1 is manufactured so that the spatial frequency on the side of the interference fringe interval Cm1 is high and the spatial frequency on the side of the interference fringe interval CmT is low.

  FIG. 8 is a diagram showing a case where the reproduction illumination light 2 made of monochromatic light is irradiated to the CGH original plate 1 produced as in the first embodiment shown in FIGS. 6 and 7. When the reproduction illumination light 2 of monochromatic light is irradiated on the CGH original plate 1 shown in FIGS. 6 and 7, the diffracted light 3 diffracted by the CGH original plate 1 is circular when viewed from the side as shown in FIG. It spreads in an arc and proceeds while expanding the viewing zone in the Y direction.

  FIG. 9 is a diagram illustrating a state when the CGH original plate 1 of Example 2 of the present embodiment is manufactured. In the second embodiment, the focusing position in the Y direction of the object light Om is set to the focusing position Fm2 on the observer side with respect to the CGH original. Therefore, the object light Om is emitted from the point light sources P1... Pm... PM without spreading in the Y direction in the X direction perpendicular to the paper surface, and is emitted from the converging positions F12... Fm2. Is set. For this reason, although some astigmatism occurs, since the distance between the original image O and the CGH original 1 is very short, there is almost no influence.

  When the light source is set in this manner, the reference light L is irradiated at a predetermined incident angle, and the object light Om and the reference light L are set to interfere with each other, interference fringes are formed in the unit area Bm of the CGH original plate 1 shown in FIG. Interference fringes with intervals Cm1, Cm2, Cm3,..., Cmt,. In the second embodiment, the interference fringe interval appears so as to narrow from the top to the bottom with respect to the paper surface. That is, the CGH original plate 1 is manufactured so that the spatial frequency on the side of the interference fringe interval Cm1 is low and the spatial frequency on the side of the interference fringe interval CmT is high.

  10 to 13 are diagrams showing other examples of the diverging position Fm1 or the focusing position Fm2 of the object light in the Y direction. FIG. 10 is a diagram showing a case where the divergence position Fm1 is arranged near the CGH original plate 1. FIG. In this case, the spread of the viewing area in the Y direction is increased. FIG. 11 is a diagram showing a case where the divergence position Fm1 is arranged far away from the CGH original plate 1. FIG. In this case, the spread of the viewing area in the Y direction is reduced. FIG. 12 is a diagram showing a case where the positional relationship between the CGH original plate 1 and the diverging position Fm1 is constant with respect to all the unit areas B1, B2, B3,..., Bm,. In this case, the design becomes easy and the calculation load is small. FIG. 13 is a diagram showing a case where the positional relationship between the CGH original plate 1 and the diverging position Fm1 is different for each of the unit areas B1, B2, B3,..., Bm,. In this case, the viewing area in the Y direction can be changed for each of the unit areas B1, B2, B3,..., Bm,. In the example shown in FIG. 13, the range in which the reproduction light toward the observer from the upper and lower unit areas can be seen simultaneously is wide.

  FIG. 14 is a diagram showing a case where the reproduction illumination light 2 made of white light is irradiated to the CGH original plate 1 manufactured as in the first embodiment shown in FIG. When the CGH master 1 shown in FIG. 6 is irradiated with the white reproduction illumination light 2, different diffracted light 3 is generated from the CGH master 1 for each wavelength of light, as shown in FIG. 14. In the present embodiment, each diffracted light 3 corresponding to RGB travels in different directions as shown in FIG. 14, but appears white in a region S including all RGB of the diffracted light 3.

  Here, the conditions under which the CGH original plate 1 can be observed in white will be described in detail. FIG. 15 is a diagram showing conditions under which the CGH original plate can be observed in white.

In each unit region Bm of the CGH original 1, the direction in which the light having the shortest wavelength λB (for example, 380 nm) to be used is diffracted among the reproduction illumination light 2 incident on the highest spatial frequency (fmax) in the Y direction is defined as θBmax ( Within the ZY plane, the Z direction is 0 degree and a positive angle is set in a counterclockwise direction), and the longest wavelength to be used among the reproduction illumination light 2 that is incident on the lowest spatial frequency (fmin) in the Y direction When the direction in which the light of λR (for example, 780 nm) is diffracted is θRmin, there is a position where each unit region Bm of the CGH original plate 1 can be observed in white if the relationship of the following conditional expression (1) is satisfied. become.
θRmin <θBmax (1)
Here, the angle θ such as a diffraction angle is a positive angle counterclockwise with the Z direction in the ZY plane being 0 degree, and the possible range is −π / 2 <θ <π / 2.

Also, the diffraction formula 1 / f = λ / (sinθout−sinθin)
f: Spatial frequency in the Y direction of CGH λ: Wavelength θin: Incident angle of incident light θout: Using the exit angle of diffracted light, the incident angle of incident light is θL,
θRmin = sin ^-1 (fmin · λR + sinθL)
θBmax = sin ⁻¹ (fmax · λB + sinθL)
Therefore, in order to have a position where each unit region Bm of the CGH original plate 1 can be observed in white, θRmin and θBmax are substituted into the conditional expression (1), and the following conditional expression (2) is satisfied. In order to observe each unit region Bm of the CGH original plate 1 in white at the observation position, the intersection extending the arrow giving θBmax and the arrow giving θRmin is set to W, and the angle from the intersection W to the eye E is set to θE. The following conditional expression (3) may be satisfied.
fmin · λR <fmax · λB (2)
θRmin <θE <θBmax (3)

  Therefore, if the conditional expressions (2) and (3) are satisfied for every unit region Bm of the CGH original plate 1, the entire CGH can be observed in white at the observation position.

  FIG. 16 is a diagram illustrating a case where the reference light L is focused at a predetermined focusing position G for each unit region, and the object light does not spread in the Y direction. As shown in FIG. 16, when the reference light L is focused at a predetermined focusing position G in the Y direction for each unit region Bm, and the object light Om is set as a linear light source that does not spread in the Y direction, the unit of the CGH original 1 The interference fringes in the region Bm appear such that the interference fringe spacings Cm1, Cm2, Cm3,..., Cmt,. That is, the CGH original plate 1 is manufactured so that the spatial frequency on the side of the interference fringe interval Cm1 is high and the spatial frequency on the side of the interference fringe interval CmT is low. Further, the focusing position G in the Y direction may be on the side opposite to the observer of the hologram, and in this case, the interval in the Y direction is produced so that the spatial frequency on the Cm1 side is high and the spatial frequency on the CmT side is low. .

  In this way, the diffusion angle in the Y direction of the diffracted light 3 is changed by preparing the CGH master plate 1 so that the interference fringe intervals Cm1, Cm2, Cm3,..., CmT in the unit region are different. Therefore, the CGH original plate 1 with an enlarged viewing area in the Y direction can be obtained. Furthermore, when white light is used as the reproduction illumination light 2, the viewing area in the Y direction is enlarged, and it is possible to observe in white.

  As mentioned above, although the production method of the computer-generated hologram of the present invention and the computer-generated hologram produced by the method have been described based on the embodiments, the present invention is not limited to these embodiments, and various modifications are possible. For example, the computer-generated holographic stereogram technique as presented in Patent Document 6 and Patent Document 7 may be applied to the computer-generated hologram according to the present invention.

1 ... CGH master (recording medium for CGH master)
2 ... Reproduction illumination light 3 ... Diffracted light

Claims (4)

In a method for producing a computer-generated hologram that records amplitude information and phase information on a predetermined recording surface by calculation using a computer,
The computer-generated hologram is
For the first direction and the second direction orthogonal to the first direction,
Having parallax only in the first direction;
Each unit region having a predetermined width in the second direction,
In each unit region, a diffraction pattern having a spatial frequency of a concavo-convex pattern that is gradually changed from one to the other in the second direction is produced,
Extends from the linear light source set on the recording object in the first direction,
Using object light of a certain width in the second direction,
A method for producing a computer-generated hologram, wherein the reference light is recorded by using a reference light that converges at a predetermined position determined for each of the unit regions in the second direction.   The method for producing a computer-generated hologram according to claim 1, wherein the diffraction pattern is made of interference fringes.   The method for producing a computer-generated hologram according to claim 1, wherein the diffraction pattern is a pattern that modulates a phase and an amplitude.   A computer-generated hologram produced by the method for producing a computer-generated hologram according to any one of claims 1 to 3.

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