JP5516957B2 - Hologram generating apparatus, method thereof, and program - Google Patents

Description

  The present invention relates to a hologram generation technique used for electronic holography.

  In recent years, research on electronic holography has been made for the purpose of being used for playback of stereoscopic television and stereoscopic movies, and for use in stereoscopic video equipment and stereoscopic video providing services such as stereoscopic television and stereoscopic movies. In addition, the electronic holography is also expected to be applied to, for example, stereoscopic video games, educational equipment, medical equipment, sightseeing guidance, procedure explanations, exhibitions, two-way communication, and the like.

  Conventionally, a method of recording a hologram on a photographic plate or reproducing an image recorded on the hologram is known (see Non-Patent Document 1). In the field of electronic holography, for example, an electronically generated hologram (interference fringes) is displayed on a display panel such as a liquid crystal panel, and recording is performed by irradiating the display panel on which the hologram is displayed with a laser beam or the like. There is also known a stereoscopic display device for reproducing the generated stereoscopic image. As the hologram, there are an off-axis hologram in which the inclination θ of the reference light is not 0, and an in-line hologram in which the reference light is perpendicularly incident on the hologram surface (the inclination θ of the reference light is 0). A method for generating a hologram will be outlined with reference to FIG.

  The coordinate space shown in FIG. 5 has an X axis in the in-plane direction along the hologram surface 4 and a Z axis in the normal direction of the hologram surface 4 for simplicity. Further, the object 2 on which the hologram is to be recorded is at a predetermined position separated from the hologram surface 4 in the Z-axis direction. In FIG. 5, the reference light 3 is displayed by a two-dot chain line, and the object light 5 is displayed by a one-dot chain line. The reference light 3 is irradiated to the object 2 in a direction from the upper right to the lower left in FIG.

  The hologram irradiates the object 2 with the reference light 3 having the same phase, and the object light 5 formed by scattering the reference light 3 from the object 2 and the irradiated reference light 3 interfere with each other. The fringes are recorded on the hologram surface 4.

  A general method for obtaining the interference fringes is as follows. As a premise, an object light 5 that comes out of an object point on the object 2 and reaches a point B on the hologram surface 4 is assumed. That is, in FIG. 5, a point on the object 2 (first predetermined point: object point A) and a point on the hologram surface (second predetermined point: point B) are set as predetermined points. Here, the object point is defined as a point A (object point A) on the Z axis. Further, a reference point C is provided at an arbitrary position on the hologram surface 4. Here, the intersection (origin) of the X axis and the Z axis is defined as the reference point C. That is, in this example, the reference point C is provided on a normal passing through the object point A among the normals of the hologram surface 4. On the hologram surface 4, the distance from the reference point C to the point B is X, and the distance from the hologram surface 4 to the object point A is Z.

In the conventional method, the interference fringe value H is obtained from the difference value between the phase φ _o of the object beam 5 shown in FIG. 5 and the phase φ _r of the reference beam 3 passing through the point B to obtain a hologram. Here, the phase φ _o of the object light 5 is determined by the optical path length d of the object light 5. The optical path length d of the object light 5 is the distance from the object point A to the point B shown in FIG. 5 and is expressed by the equation (1). Z and X in the formula (1) are distances shown in FIG. The rightmost side of equation (1) represents the result of approximation in which the middle equation of equation (1) is Taylor-expanded and the second term is adopted. This is based on the fact that the diffusion range X of the object light 5 is sufficiently smaller than the distance Z from the hologram surface 4 to the object point A.

Further, the phase φ _o of the object light 5 is expressed by the equation (2) by the optical path length d of the object light 5. Here, λ indicates the wavelength of light. However, the initial phase of the object light was set to zero.

Further, the interference fringe value H is obtained by the equation (3) based on the difference between the phase φ _o of the object light 5 and the phase φ _r of the reference light 3 passing through the point B. Here, O represents the brightness or color value of the object point A.

As a premise of Expression (3), the phase of the reference light 3 passing through the reference point C on the hologram surface 4 is regarded as 0. In FIG. 5, the reference light 3 is shown as three light beams for the sake of explanation. However, the reference light 3 is integrally irradiated onto the object 2 as a sharp coherent light like a laser beam. The
Here, in the case of an in-line hologram, the reference light 3 is perpendicularly incident on the hologram surface 4, so that the phase is 0 everywhere on the hologram surface 4. However, in the case of the off-axis hologram assumed here, the phase θ of the reference light 3 differs depending on the position on the hologram surface 4 because the inclination θ of the reference light is not zero.

Therefore, in the case of an off-axis hologram, at this time, the phase at the point B is considered in consideration of the difference from the reference phase, and the reference light 3 passing through the point B (the three references schematically shown in FIG. 5). It is determined as the phase φ _r of the leftmost reference light). For example, in FIG. 5, the broken line in the direction inclined by the angle θ (reference light angle) from the reference point C indicates the position where the phases of the three reference lights schematically shown in FIG. Therefore, the reference light 3 passing through the point B (leftmost reference light in FIG. 5) is compared with the reference light 3 passing through the reference point C (rightmost reference light in FIG. 5) to the optical path length to the hologram surface 4. Is longer by Xsinθ. When this optical path length difference is reflected in the phase delay, the phase φ _r at the point B that is separated from the reference point C by the distance X is expressed by equation (4).

Yoshikawa, Hakura translation, P.K. Hariharan, 1st edition, "Principles of Holography", Optronics, March 30, 2004, p.7-9

However, in the conventional method, the phase difference of the interference fringes, that is, the phase difference (φ _o −φ _r ) between the object beam 5 and the reference beam 3 passing through the point B is expressed by Expression (5).

As shown in Expression (5), the phase difference (φ _o −φ _r ) between the object beam and the reference beam includes Z and X. To obtain this phase difference, the values of Z and X are used. It is necessary to perform four arithmetic operations. Of these, the value Z corresponds to the distance from the hologram to the object. Further, the value X may be the same as the value of the hologram size at the maximum. These values of Z and X are usually on the order of several tens of mm. This order is about 100,000 times larger than the wavelength λ of light (which is about 0.5 μm). In addition, the value of the phase difference is degenerated at a period of 2π≈6.28 in the calculation of cos (φ _o −φ _r ) in Expression (3). Therefore, unless the value of the phase difference in Expression (5) is obtained with sufficiently high accuracy with respect to the precision of 2π, the value H of the interference fringe in Expression (3) cannot be obtained accurately. That is, the operation word length for accurately performing the calculation within the parentheses on the right side of the expression (5) and the calculation of λ outside the parentheses needs to be about 20 bits or more.

  In order to increase the speed of the hologram calculation, a calculator and a calculation means having a sufficiently long calculation word length are necessary particularly when making dedicated hardware. For this reason, there is a problem that the hologram generating apparatus having the arithmetic unit having the long arithmetic word length and the arithmetic means and the constituent means thereof become large and cost increases. In addition, there is a problem that the calculation speed is slowed down by an arithmetic unit or calculation means having a sufficiently long calculation word length for performing calculation accurately, and real-time operation such as reproduction of a moving image hologram becomes difficult. In particular, when the hologram display device is an ultra-high-definition liquid crystal panel having 8K × 4K pixels, it is necessary to perform a large amount of high-precision calculations at high speed. Therefore, in the case of an ultra-high definition liquid crystal panel, it has been difficult to realize a real-time hologram moving image.

  Therefore, the present invention solves the problem that the conventional apparatus is increased in size and cost, and the problem that the calculation speed of the conventional apparatus is slow, and the problem is to reduce the operation word length related to the hologram calculation. To do.

  In order to solve the above problems, a hologram generating apparatus according to a first aspect of the present invention includes object data including information on a position of an object and complex amplitude as object light, a wavelength of reference light, and an inclination angle with respect to the hologram surface. A hologram generating apparatus for generating a hologram of the object using reference light data including information on a hologram, wherein a hologram in-plane component calculating means, a hologram normal component calculating means, a phase difference calculating means, and a real component calculation Means.

According to such a configuration, the hologram generating device causes the hologram in-plane component calculation means to generate the object light generated at the first predetermined point of the object based on the position of the object and the wavelength of the reference light. An optical path length of object light that represents a distance to reach a second predetermined point on the surface, and a phase of the reference light when the reference light hits the first predetermined point of the object As a difference between the optical path length of the reference light representing the distance between the position where the phase of the reference light reaching the second predetermined point on the hologram surface is equal to the reference phase and the second predetermined point. As one value when the optical path length difference shown is formally divided into two values, the intersection point where the normal line drawn from the first predetermined point of the object intersects the hologram surface and the second predetermined point Hologram in-plane component showing the value related to the distance between Calculated to. Then, the hologram generation device uses the hologram normal component calculation means as the other value when the optical path length difference is formally divided into two values based on the position of the object and the wavelength of the reference light. A hologram normal component indicating a value related to a distance from the hologram surface to the first predetermined point of the object is calculated. Then, the hologram generating device adds the hologram in-plane component of the optical path length difference and the hologram normal component of the optical path length difference by the phase difference calculation means, and based on the addition result and the wavelength of the reference light Then, a phase difference indicating a difference between the phase of the object light and the phase of the reference light is calculated. Then, the hologram generation device calculates the real component of the complex amplitude as the value of the interference fringe of the hologram based on the position of the object, the complex amplitude, and the phase difference by the real component calculation means. Here, the hologram in-plane component calculation means is the object data when the position of the object is represented by (X, Y, Z), and the tilt angle information with respect to the hologram surface is represented by θ. The input of reference light data is received, the second term on the right side of the expression (12a) described later is calculated, and the hologram normal component calculation means receives the input of the object data and the reference light data, and the expression described later The first term on the right side of (12a) is calculated.

  Therefore, the hologram generation apparatus obtains a hologram from the result of separately calculating and adding the optical path length difference between the object beam and the reference beam into the hologram in-plane component and the hologram normal component, and thus reducing the operation word length. Can do. Therefore, the hologram generation apparatus does not require high-precision calculation for hologram calculation, and can increase the calculation speed, so that the hologram can be generated at high speed. Further, since the hologram generation apparatus does not require a high-precision calculation means, it can be manufactured in a small size and at a low cost.

  In addition, the hologram generating apparatus according to the second aspect of the present invention includes object data including information on the position of an object and complex amplitude as object light, and reference including information on the wavelength of reference light incident perpendicularly to the hologram surface. A hologram generation apparatus that generates a hologram of the object using optical data, and includes hologram in-plane component calculation means, phase difference calculation means, and real number component calculation means.

According to such a configuration, the hologram generating device causes the hologram in-plane component calculation means to generate the object light generated at the first predetermined point of the object based on the position of the object and the wavelength of the reference light. An optical path length of object light that represents a distance to reach a second predetermined point on the surface, and a phase of the reference light when the reference light hits the first predetermined point of the object As a difference between the optical path length of the reference light representing the distance between the position where the phase of the reference light reaching the second predetermined point on the hologram surface is equal to the reference phase and the second predetermined point. As an optical path length difference, a hologram in-plane component indicating a value related to a distance between an intersection point where a normal line drawn from the first predetermined point of the object intersects the second predetermined point is formed on the hologram surface. calculate. Then, the hologram generation apparatus is configured to cause the phase difference calculation means to indicate a difference between the phase of the object light and the phase of the reference light based on the hologram in-plane component of the optical path length difference and the wavelength of the reference light. Calculate the phase difference. Then, the hologram generation device calculates the real component of the complex amplitude as the value of the interference fringe of the hologram based on the position of the object, the complex amplitude, and the phase difference by the real component calculation means. Here, the hologram in-plane component calculation means accepts input of the object data and the reference light data when the position of the object is represented by (X, Y, Z), and the following equation (15) Calculate

  Therefore, the hologram generation apparatus calculates the optical path length difference between the reference light incident perpendicularly to the hologram surface and the object light from the hologram in-plane component to obtain the hologram, so that the operation word length is reduced as a dedicated device for inline holograms. be able to. Therefore, the hologram generation apparatus does not require high-precision calculation for hologram calculation, and can increase the calculation speed, so that the hologram can be generated at high speed. Further, since the hologram generation apparatus does not require a high-precision calculation means, it can be manufactured in a small size and at a low cost.

  In order to solve the above-described problem, a hologram generation method according to the first aspect of the present invention relates to object data including information on the position of an object and complex amplitude as object light, the wavelength of reference light, and the hologram surface. A hologram generation method of a hologram generation apparatus for generating a hologram of the object using reference light data including information on an inclination angle, the hologram generation apparatus comprising: a hologram in-plane component calculation step; and a hologram normal component calculation The steps, the phase difference calculation step, and the real number component calculation step are executed.

According to such a procedure, in the hologram generation method, in the hologram in-plane component calculation step, the object light generated at the first predetermined point of the object is based on the position of the object and the wavelength of the reference light. Based on the optical path length of the object light that represents the distance to reach the second predetermined point on the hologram surface, and the phase of the reference light when the reference light hits the first predetermined point of the object The difference between the optical path length of the reference light representing the distance between the position at which the phase of the reference light reaching the second predetermined point on the hologram surface is equal to the reference phase and the second predetermined point as the phase As one value when the optical path length difference indicating the above is formally divided into two values, the intersection point where the normal line drawn from the first predetermined point of the object intersects the hologram surface and the second place Hologram in-plane component showing the value related to the distance to a fixed point Calculated to. In the hologram generation method, the other value when the optical path length difference is formally divided into two values based on the position of the object and the wavelength of the reference light in the hologram normal component calculation step. Then, a hologram normal component indicating a value related to a distance from the hologram surface to the first predetermined point of the object is calculated. Then, in the phase difference calculation step, the hologram generation method adds the in-plane component of the optical path length difference and the hologram normal component of the optical path length difference, and based on the addition result and the wavelength of the reference light Then, a phase difference indicating a difference between the phase of the object light and the phase of the reference light is calculated. Then, in the real number component calculating step, the real number component of the complex amplitude is calculated as the interference fringe value of the hologram based on the position and complex amplitude of the object and the phase difference. Here, in the hologram surface component calculation step, the object data when the position of the object is represented by (X, Y, Z) and the information on the tilt angle with respect to the hologram surface are represented by θ. The input of reference light data is received, the second term on the right side of the expression (12a) described later is calculated, and the hologram normal component calculation step receives the input of the object data and the reference light data, and the expression described later The first term on the right side of (12a) is calculated. Therefore, according to the hologram generation method according to the first aspect of the present invention, the hologram is obtained from the result of separately calculating and adding the optical path length difference between the object beam and the reference beam separately to the hologram in-plane component and the hologram normal component. Therefore, the operation word length can be reduced.

  The method of adding each value of the interference fringes obtained as described above is not particularly limited. For example, the hologram in-plane component calculation step, the hologram normal component calculation step, and the phase difference calculation step The real component calculation step is executed for all the first predetermined points of the object that are included in the diffusion range determined by the maximum diffraction angle of the reference light passing through the second predetermined point of the hologram surface. The result obtained by adding all the obtained values is used as the interference fringe value of the second predetermined point on the hologram surface, and the above processing is executed for all of the second predetermined points in the hologram surface. The result can be generated as a hologram of the object. Further, for example, for each object point, the real component of the phase difference of the object light within the light diffusion range is recorded at each point in the hologram surface, and the object light obtained in the same manner every time the object point is changed. The real component of the phase difference may be added to the value recorded at each point in the hologram plane.

  Further, the hologram generation method according to the second aspect of the present invention is a reference including object data including information on the position of an object and complex amplitude as object light, and information on the wavelength of reference light incident perpendicularly to the hologram surface. A hologram generation method of a hologram generation apparatus that generates a hologram of the object using optical data, the hologram generation apparatus comprising: a hologram in-plane component calculation step, a phase difference calculation step, and a real component calculation step It was decided to include and execute.

According to such a procedure, in the hologram generation method, in the hologram in-plane component calculation step, the object light generated at the first predetermined point of the object is based on the position of the object and the wavelength of the reference light. Based on the optical path length of the object light that represents the distance to reach the second predetermined point on the hologram surface, and the phase of the reference light when the reference light hits the first predetermined point of the object The difference between the optical path length of the reference light representing the distance between the position at which the phase of the reference light reaching the second predetermined point on the hologram surface is equal to the reference phase and the second predetermined point as the phase A hologram in-plane component indicating a value relating to a distance between an intersection point where a normal line drawn from the first predetermined point of the object intersects the second predetermined point on the hologram surface Is calculated. In the phase difference calculation step, the hologram generation method indicates a difference between the phase of the object light and the phase of the reference light based on the hologram in-plane component of the optical path length difference and the wavelength of the reference light. Calculate the phase difference. Then, in the real number component calculating step, the real number component of the complex amplitude is calculated as the interference fringe value of the hologram based on the position and complex amplitude of the object and the phase difference. Here, the hologram in-plane component calculation step accepts input of the object data and the reference light data when the position of the object is represented by (X, Y, Z), and the following equation (15) Calculate Therefore, according to the hologram generation method according to the second aspect of the present invention, the hologram is obtained from the result of calculating the optical path length difference between the object beam and the reference beam as the hologram in-plane component, so that the operation word length can be reduced. In addition, the calculation speed can be further increased. In addition, the method of adding together each value of the interference fringe calculated | required as mentioned above is not specifically limited.

  In order to solve the above-described problem, a hologram generation program according to the first aspect of the present invention provides object data including information on a position of an object and complex amplitude as object light, a wavelength of reference light, and a hologram surface. In order to generate a hologram of the object using reference light data including information on an inclination angle, the computer is used as a hologram in-plane component calculation unit, a hologram normal component calculation unit, a phase difference calculation unit, and a real component calculation unit. It was decided to be a program for functioning.

According to this configuration, the hologram generation program causes the hologram in-plane component calculation means to generate object light generated at the first predetermined point of the object based on the position of the object and the wavelength of the reference light. An optical path length of object light that represents a distance to reach a second predetermined point on the surface, and a phase of the reference light when the reference light hits the first predetermined point of the object As a difference between the optical path length of the reference light representing the distance between the position where the phase of the reference light reaching the second predetermined point on the hologram surface is equal to the reference phase and the second predetermined point. As one value when the optical path length difference shown is formally divided into two values, the intersection point where the normal line drawn from the first predetermined point of the object intersects the hologram surface and the second predetermined point Hologram surface showing the value related to the distance between To calculate the component. Then, the hologram generation program uses the hologram normal component calculation means as the other value when the optical path length difference is formally divided into two values based on the position of the object and the wavelength of the reference light. A hologram normal component indicating a value related to a distance from the hologram surface to the first predetermined point of the object is calculated. Then, the hologram generation program adds the in-plane hologram component of the optical path length difference and the hologram normal component of the optical path length difference by the phase difference calculation means, and based on the addition result and the wavelength of the reference light Then, a phase difference indicating a difference between the phase of the object light and the phase of the reference light is calculated. Then, the hologram generation program calculates the real component of the complex amplitude as the interference fringe value of the hologram based on the position and complex amplitude of the object and the calculated phase difference by the real component calculation means. To do. Here, the hologram in-plane component calculation means is the object data when the position of the object is represented by (X, Y, Z), and the tilt angle information with respect to the hologram surface is represented by θ. The input of reference light data is received, the second term on the right side of the expression (12a) described later is calculated, and the hologram normal component calculation means receives the input of the object data and the reference light data, and the expression described later The first term on the right side of (12a) is calculated.

  In addition, the hologram generation program according to the second aspect of the present invention is a reference including object data including information on the position of an object and complex amplitude as object light, and information on the wavelength of reference light incident perpendicularly to the hologram surface. In order to generate a hologram of the object using optical data, the computer program is made to function as hologram in-plane component calculation means, phase difference calculation means, and real number component calculation means.

According to this configuration, the hologram generation program causes the hologram in-plane component calculation means to generate object light generated at the first predetermined point of the object based on the position of the object and the wavelength of the reference light. An optical path length of object light that represents a distance to reach a second predetermined point on the surface, and a phase of the reference light when the reference light hits the first predetermined point of the object As a difference between the optical path length of the reference light representing the distance between the position where the phase of the reference light reaching the second predetermined point on the hologram surface is equal to the reference phase and the second predetermined point. As an optical path length difference, a hologram in-plane component indicating a value related to a distance between an intersection point where a normal line drawn from the first predetermined point of the object intersects the second predetermined point is formed on the hologram surface. calculate. Then, the hologram generation program is configured to cause the phase difference calculation means to indicate a difference between the phase of the object light and the phase of the reference light based on the hologram in-plane component of the optical path length difference and the wavelength of the reference light. Calculate the phase difference. Then, the hologram generation program calculates the real component of the complex amplitude as the value of the interference fringe of the hologram based on the position and complex amplitude of the object and the phase difference by the real component calculation means. Here, the hologram in-plane component calculation means accepts input of the object data and the reference light data when the position of the object is represented by (X, Y, Z), and the following equation (15) Calculate

  According to the hologram generating apparatus, the method, and the program according to the first aspect of the present invention, the difference between the optical path length of the object light and the reference light is obtained with the phase when the reference light passes through the object point as the reference phase. Since the hologram is obtained from the result of separately calculating and adding the hologram in-plane component and the hologram normal component, the operation word length can be reduced.

  In addition, according to the hologram generating apparatus, the method, and the program according to the second aspect of the present invention, the optical path lengths of the object light and the reference light are set based on the phase when the reference light passes through the object point as the reference phase. Since the hologram is obtained from the result of calculating the hologram in-plane component for the difference, the calculation word length can be reduced and the calculation speed can be further increased.

  Moreover, according to the hologram production | generation apparatus which concerns on the 1st and 2nd viewpoint of this invention, the hardware for exclusive use of the small, low-cost and high-speed hologram production | generation apparatus can be comprised by shortening the calculation word length. Further, according to the hologram generation method according to the first and second aspects of the present invention, a high-speed hologram generation method can be provided. Therefore, a real-time hologram moving image can be realized even if an ultra-high definition liquid crystal panel is used.

It is a block diagram which shows the structure of the hologram production | generation apparatus which concerns on embodiment of this invention. It is explanatory drawing of the method of obtaining an off-axis hologram with the hologram production | generation method which concerns on embodiment of this invention. It is a flowchart at the time of implementing the hologram production | generation method which concerns on embodiment of this invention as a computer program. It is explanatory drawing of the method of obtaining an in-line hologram with the hologram production | generation method which concerns on embodiment of this invention. It is explanatory drawing of the method of obtaining a hologram by a prior art.

  DESCRIPTION OF EMBODIMENTS A hologram generating apparatus and method for carrying out the method of the present invention will be described in detail with reference to the drawings. Below, for convenience of explanation, 1. 1. Outline of hologram generating apparatus 2. Principle of hologram generation method Each embodiment of the hologram generation apparatus will be described sequentially.

[1. Overview of hologram generator]
As shown in FIG. 1, the hologram generator 1 generates a hologram 4d of an object using object data 2d and reference light data 3d, and a holo in-plane component of an optical path length difference between the object light and the reference light. A calculator 10 (hereinafter abbreviated as a holo in-plane component calculator 10) and a holo normal component calculator 20 (hereinafter abbreviated as a holo normal component calculator 20) of the optical path length difference between the object beam and the reference beam. And a phase difference calculator 30 and a real component calculator 40. Details of each of the calculators 10 to 40 will be described later. In the following, the normal component of the hologram surface is referred to as a hologram normal component, and the hologram surface is abbreviated as a holo surface and the hologram as a holo as appropriate.

  The object data 2d includes three-dimensional coordinate data (X, Y, Z) as information on the position of the object to be generated by the hologram 4d and complex amplitude information such as color and brightness as object light. It includes color data O (X, Y, Z). The complex amplitude includes amplitude information and phase information.

  The reference light data 3d is data including information on the wavelength λ of the reference light, information on the tilt angle θ with respect to the hologram surface, information on the light source position of the reference light, and the like. The tilt angle θ is an angle measured from the normal direction of the hologram surface.

  When calculating the phase difference between the object beam and the reference beam, the hologram generator 1 separately calculates the hologram in-plane component of the optical path length difference between them and the hologram normal component, Is significantly different from the prior art in that the phase difference is obtained by adding. Thereby, the hologram production | generation apparatus 1 enabled reduction of operation word length. Here, the component means each value of the optical path length difference indicating the distance, which is formally divided into two values, details of which will be described later. The hologram in-plane component, which is one of these, is the point at which the normal drawn from the object point intersects on the hologram surface and the point at which the object light generated by scattering the reference light at that object point hits the hologram surface The value which concerns on the distance between is shown. Further, the hologram normal component which is the other of the optical path length differences divided into two values form a value related to the distance from the hologram surface to the object point.

  The hologram generating apparatus 1 is greatly different from the conventional one in that the reference phase of the reference light is set to the phase when the reference light hits the object point. Thereby, in the calculation of the optical path length that determines the phase of the reference light and the object light, the normal components with respect to the hologram surface are substantially canceled from each other. As a result, the calculation word length of interference fringe calculation can be reduced, the calculation is simplified, and high-speed calculation is possible. Here, although details will be described later, in the calculation of the optical path length that determines the phase of the reference light and the object light, the optical path length of the reference light is set as the following distance. That is, the phase of the reference light at the time when the reference light hits the object point is used as a reference phase, and the reference light is scattered from the object point. The distance between the position at which the phase of the reference light that reaches the reference phase becomes equal to the reference phase and the point at which the object light hits the hologram surface was taken as the optical path length of the reference light.

[2. Principle of hologram generation method]
Next, the principle of the hologram generation method according to the embodiment of the present invention will be described with reference to FIG. 2 (refer to FIG. 5 as appropriate).

  The coordinate space shown in FIG. 2 has an X axis in the in-plane direction along the hologram surface 4 and a Z axis in the normal direction of the hologram surface 4 for simplicity. Further, the object 2 on which the hologram is to be recorded is at a predetermined position separated from the hologram surface 4 in the Z-axis direction. In FIG. 2, the reference light 3 is displayed by a two-dot chain line, and the object light 5 is displayed by a one-dot chain line.

  A method for obtaining interference fringes according to the present embodiment is as follows. As a premise, an object light 5 that comes out of an object point A on the object 2 and reaches a point B on the hologram surface 4 is assumed. That is, in FIG. 2, a point on the object 2 (first predetermined point: object point A) and a point on the hologram surface (second predetermined point: point B) are set as predetermined points. Here, it differs from FIG. 5 in that point B on the hologram surface 4 is the intersection (origin) of the X axis and the Z axis. Further, a reference point C is provided on the hologram surface 4 at the intersection where the normal line drawn from the object point A intersects. That is, in the prior art, once the reference point C is determined, the reference point is not changed while calculating the interference fringes at all points on the hologram surface. It differs from the prior art in that the perpendicular foot down to the X axis is the reference point C. On the hologram surface 4, the distance from the reference point C to the point B is X, and the distance from the hologram surface 4 to the object point A is Z. The reference light 3 is irradiated to the object 2 from the upper right in FIG.

  The optical path length d of the object light 5 is the distance from the object point A to the point B shown in FIG. 2, and is represented by the equation (6).

  The pixel size of the currently available hologram display liquid crystal panel is about P = 5 to 10 μm, and the maximum diffraction angle α of light that can be diffracted by this panel is given by equation (7). That is, the maximum diffraction angle α is determined by the pixel size of the hologram.

  However, λ is the wavelength of the illumination light having the same wavelength as the reference light 3 and is about 0.5 μm. At this time, α = 1.5 to 3 °. In the case of an off-axis hologram in which the inclination θ of the reference light is not 0, the inclination θ is about twice the maximum diffraction angle α of the hologram display panel. Therefore, the value of the diffusion range X of the object light 5 diffusing to both sides α of the reference light is expressed by the equation (8) since ∠BAC = α + θ = 3α from FIG.

  The value of X shown in this equation (8) is about X ≦ 0.15Z. More specifically, for example, when the pixel size P = 5 μm and the wavelength λ = 0.5 μm, X is about 0.1511992Z.

  Accordingly, the diffusion range X of the object light 5 is sufficiently small compared to the distance Z from the hologram surface 4 to the object point A, and the expression (9) is obtained by Taylor expansion of Expression (6) and adopting the second term. ).

  As described above, when the reference light 3 is tilted by the angle θ = 2α with respect to the hologram surface, the reference light 3 having the same phase as the light hitting the object point A (the three light beams schematically shown in FIG. 2). The optical path length r until the leftmost reference light of the reference light reaches the point B on the hologram surface 4 is expressed by equation (10) from FIG.

As a premise of Expression (10), the reference light 3 (the reference light in the middle of the three reference lights schematically shown in FIG. 2) has a phase at the time when it hits the object point A as a reference phase. Is different from the conventional method. That is, in this hologram generation method, the distance between the point B where the phase of the reference light 3 (the leftmost reference light shown in FIG. 2) reaching the point B on the hologram surface 4 is equal to the reference phase is The optical path length r of the reference light 3 was set. Then, the reference phase is set to 0, and the phase at the position of the point B in consideration of the difference from the reference phase is set to the phase φ _{r of the} reference light 3 (the leftmost reference light shown in FIG. 2) passing through the point B. Decided as

  For example, in FIG. 2, a broken line in a direction perpendicular to the direction of the reference light 3 at the object point A indicates a position where the phases of the three reference lights schematically shown in FIG. Therefore, the reference light 3 passing through the point B (the leftmost reference light in FIG. 2) has an optical path length r from the position where the phase of the reference light is equal (position corresponding to the object point A) to the hologram surface 4. When the optical path length r is translated in FIG. 2, the right side of Expression (10) is obtained. The first term on the right side of Equation (10) is that the reference light 3 (the rightmost reference light shown in FIG. 2) passing through the reference point C on the hologram surface 4 is the reference point C on the hologram surface 4. It is the optical path length to reach.

  In the conventional method described with reference to FIG. 5, if the reference point C is provided at an arbitrary position on the hologram surface 4, the interference fringe value H is correctly calculated according to the equations (3) and (5). It was supposed to be required. This is correct, but it was difficult to intuitively understand the mechanism by which the phase difference of the light causing the interference fringes occurs. However, as in the hologram generation method according to the present embodiment, interference fringes are generated by setting a point at a position equal to the reference phase of the reference light 3 on the object 2 instead of on the hologram surface 4 so far. Intuitively understands the mechanism of light phase difference generation. That is, in the object light 5 and the reference light 3 starting from the same object point A, the difference between the optical path length d of the object light 5 and the optical path length r of the reference light 3 causes a phase difference between the object light and the reference light. Since the phase of the object light and the reference light are out of phase, the principle of hologram that forms interference fringes has become easier to understand intuitively.

  And in the hologram production | generation method which concerns on this embodiment, the difference (dr) of the optical path length of the object light 5 and the reference light 3 is used for Formula (11) by using above-mentioned Formula (9) and Formula (10). ).

Here, the calculation in the first parenthesis on the right side of the equation (11) appeared in the equation (5) in the conventional calculation. In the calculation in the parentheses, the value of the second term (X ² / 2Z) is very small compared to the value of the first term (Z) in the parenthesis because it is the second term of the Taylor expansion. Therefore, the sum of the first term and the second term adds a huge value and a minute value. Conventionally, these are calculated in the same order as shown in Equation (5). However, when a huge value and a minute value are added, the accuracy of the calculation result is not good. Therefore, in the hologram generation method according to the present embodiment, each term on the right side of Expression (11) is rearranged and transformed into Expression (12a) before calculation.

Here, the first term on the right side of Equation (12a) is a value that is 2-3 orders of magnitude smaller than the first term on the right side of Equation (11). Although details will be described later, the calculation result in the parenthesis of the first term on the right side of the equation (12a) is a minute value of almost zero. In other words, in the coordinate space shown in FIG. 2, the "Z" of the hologram normal component of the optical path length d (d _Z component), the hologram normal component of the optical path length r of (r _Z component) "Zcosθ" and is very A value close to is canceled. The reason why cos θ is almost 1 is that a condition of maximum diffraction angle α = 1.5 to 3 ° and inclination θ = 2α is assumed. Similarly, sin θ of the second term on the right side of Expression (12a) is also a very small value of zero.

Further, the value of Z in the first term on the right side of the expression (12a) and the value of X in the second term are usually on the order of several tens of mm. For this reason, the value of the first term and the value of the second term of the expression (12a) are each a minute value. Therefore, the expression (12a) is replaced with an expression (12b). The first term delta _Z of formula (12b), Z components of the phase difference between the object beam and the reference beam, or, that the hologram normal component of the phase difference. Further, the second term Δ _X on the right side of Expression (12b) is referred to as an X component of the phase difference between the object beam and the reference beam, or a hologram in-plane component of the phase difference.

A hologram normal component delta _Z of the phase difference, the hologram plane component delta _X of the phase difference, the same degree of order. The addition of the first term and the second term of the equation (12b) is more accurate than the case of adding a huge value and a minute value as in the conventional equation (5). Will be better. This addition result is simply expressed as Δ as shown in the equation (12c).

Next, a specific example when using formulas (12a) to (12c) in this way will be described. Here, as an example, a case where the pixel size P = 5 μm and the wavelength λ = 0.5 μm is assumed. At this time, the maximum diffraction angle is α = 2.8659 ° ≈2.9 °.
Further, the inclination is θ = 2α = 5.7319 ° ≈5.7 °.

In the first term of the equation (12b), cos θ≈0.995.
Further, (1−cos θ) ≈0.005.
Therefore, the value of the first term, that is, Δ _Z = Z (1-cos θ) is a value on the order of 0.005 times the value of Z.

In the second term of the formula (12b), X satisfies the relationship of the formula (8).
Therefore, the value of X is about X ≦ Ztan (3α) = 0.15Z.
In the second term, sin θ = 0.099874≈0.1.
The second term, that is, the value of Δ _X = X (X / 2Z−sin θ) is calculated as follows.
0.15Z (0.075−0.1) = − 0.00375≈−0.004Z.
Therefore, the second term, i.e., the value of delta _X becomes -0.004 times the value of the order of the values of Z.

Therefore, the value of Δ in equation (12c) is the sum of a value on the order of 0.005 times the value of Z and a value on the order of −0.004 times the value of Z. As a result, the value of Z The value is on the order of 0.001 times. If the value of Δ in Expression (12c), that is, the difference in optical path length (dr) is obtained, the phase difference φ _Δ between the object light and the reference light can be obtained from Expression (13).

Here, (Δ _Z + Δ _X) is of the order of 0.001Z.
Therefore, when the value of Z is, for example, 40 mm, which is about the same as the size of a currently available hologram display panel, the value of the phase difference φ _Δ between the object beam and the reference beam is on the order of 40 μm. A value obtained by dividing the 40 μm order by the wavelength λ = 0.5 μm is the 80 order.
The order of 80 is a value of about 7 bits in binary.

From this phase difference φ _Δ , the interference fringe value H is obtained by the equation (14) as the real component of the complex amplitude light having the phase φ _Δ .

  Here, the interference fringe value H indicates the brightness (intensity) of the position of the point B on the hologram surface. This H is obtained using the object point and the point B on the hologram surface. Therefore, a hologram as an interference fringe can be generated by changing the position of the object point A in various ways on the object and adding them all together. Specifically, in the process of addition, a diffusion range determined by the maximum diffraction angle α of the hologram display panel is considered.

  As shown in Expression (14), the interference fringe value H degenerates with a period of 2π. Here, O / Z is obtained by determining the brightness of the object light on the hologram surface from the brightness O of the object point and the distance Z to the hologram surface.

In order to accurately obtain the value of the interference fringes, it is necessary to keep the value of the phase difference φ _Δ sufficiently high with respect to 2π. For that purpose, in the prior art, an arithmetic word length of about 20 bits or more is required, and therefore, fixed point arithmetic with an arithmetic word length of 32 bits was used. However, the hologram generation method according to the present embodiment does not require a fixed-point operation with an operation word length of 32 bits, and a fixed-point operation with an effective number of digits of about 16 bits is sufficient.

  The hologram generation method and apparatus according to the present embodiment are configured so that a hologram can be obtained with high accuracy with a short operation word length by using the operations shown in the equations (6) to (14). .

[3. Embodiments of Hologram Generation Device]
(First embodiment)
As shown in FIG. 1, a hologram generating apparatus 1 according to the first embodiment of the present invention generates a hologram 4d of an object using object data 2d and reference light data 3d. A calculator 10, a holo normal component calculator 20, a phase difference calculator 30, and a real component calculator 40 are provided. The hologram generating apparatus 1 is a dedicated device configured in hardware by, for example, a semiconductor memory or an electric circuit.

The holo in-plane component calculator 10 indicates the difference between the optical path length d of the object light and the optical path length r of the reference light based on the position (X, Y, Z) of the object and the wavelength λ of the reference light. and it calculates the hologram plane component delta _X of the difference (d-r). This holo in-plane component calculator 10 receives the input of the object data 2d and the reference light data 3d, and calculates the second term on the right side of the equation (12a). Calculated hologram plane component delta _X is input to the phase difference calculator 30.

The holo normal component calculator 20 indicates the difference between the optical path length d of the object light and the optical path length r of the reference light based on the position (X, Y, Z) of the object and the wavelength λ of the reference light. and it calculates the hologram normal component delta _Z difference (d-r). The holo normal component calculator 20 receives the input of the object data 2d and the reference light data 3d, and calculates the first term on the right side of the equation (12a). Calculated hologram normal component delta _Z is input to the phase difference calculator 30.

The phase difference calculator 30, a hologram plane component delta _X of the optical path length difference (d-r), the optical path length difference by adding the hologram normal component delta _Z of (d-r), the addition result and the reference beam The phase difference φ _Δ indicating the difference between the phase of the object light and the phase of the reference light is calculated on the basis of the wavelength λ. The phase difference calculator 30 receives an input of the hologram plane component delta _X from holo-plane component calculator 10 receives an input of the hologram normal component delta _Z from holo normal component calculator 20, the equation ( 13) is calculated. The calculated phase difference φ _Δ is input to the real component calculator 40.

Real component calculator 40, data of the position of the object (X, Y, Z) and the complex amplitude of the data O (X, Y, Z) and, on the basis of the phase difference phi _delta, the interference fringes of the hologram values H As above, the real component of the complex amplitude is calculated. The real component calculator 40 receives the input of the object data 2d, receives the input of the phase difference φ _Δ from the phase difference calculator 30, and calculates the above-described equation (14). The calculated interference fringe value H is output as a hologram 4d. The interference fringe values H obtained for all the object points A may be stored in a storage means (not shown), and the result of adding them may be output as the hologram 4d.

Next, the operation of the hologram generator 1 will be described.
First, the hologram generating apparatus 1 has three-dimensional coordinate data (X, Y, Z) of a sample point (object point A) of an object for which a hologram is to be generated, and color data O (X, Y, Z) of the point. The input of the object data 2d such as is accepted. Further, the hologram generation apparatus 1 accepts input of reference light data 3d such as an inclination angle θ of a reference light that gives a reference phase for generating a hologram with respect to the normal of the hologram surface, and a wavelength λ of the reference light.

Next, the hologram generating apparatus 1 uses the holo in-plane component calculator 10 to generate a hologram in-plane component d _X = X ² / 2Z of the optical path length d of the object light 5 and an in-plane hologram of the optical path length r of the reference light 3. The component r _X = _X sin θ is calculated. The holo-plane component calculator 10 calculates the respective differences as a hologram plane component delta _X.
That is, Δ _X = d _X −r _X = X (X / 2Z−sin θ) is calculated.

Next, the hologram generating apparatus 1 uses the holo normal component calculator 20 to generate the hologram normal component d _Z = Z of the optical path length d of the object beam 5 and the hologram normal component r _Z of the optical path length r of the reference beam 3. = Zcosθ is calculated. The holo-normal component calculator 20 calculates the respective differences as a hologram normal component delta _Z.
That is, to calculate the _{Δ Z = d Z -r Z =} Z (1-cosθ).

Next, the hologram generation apparatus 1 calculates the phase difference φ _Δ between the object light 5 and the reference light 3 from the two differences Δ _X and Δ _Z by the phase difference calculator 30.
That is, φ _Δ = 2π (Δ _X + Δ _Z ) / λ is calculated.

Next, the hologram generation apparatus 1 uses the real component calculator 40 to calculate interference fringes from the phase difference φ _Δ , the color data O (X, Y, Z) of the object point A, and the wavelength λ of the reference light 3. Is calculated as the interference fringe value H.
That is, O × cos (φ _Δ ) / Z is calculated.

  The hologram generating apparatus 1 performs the above operation for all the object points A within the diffusion range determined by the maximum diffraction angle α around the reference light passing through the point B for each point B on the hologram surface. A value obtained by adding the values of the expression (14) is output as the interference fringe value of the point B. The hologram generating apparatus 1 performs the above processing for all points B on the hologram surface.

  According to the first embodiment, the hologram generation apparatus 1 performs hologram generation with dedicated hardware, and by reducing the operation word length, the data bus width can be shortened, so the hardware size is reduced. Can be small. Moreover, since the hologram production | generation apparatus 1 does not require a high precision calculation and can raise calculation speed, it can produce | generate a hologram at high speed. Therefore, the hologram generation apparatus 1 can realize a reduction in size and cost of a real-time moving image hologram generation apparatus.

  Further, according to the hologram generation apparatus 1, when performing hologram display using an ultra-high-definition liquid crystal display having 8K × 4K pixels, a small, low-cost and high-speed hologram generation apparatus can be configured. Therefore, the hologram generating apparatus 1 is effective for generating a moving image hologram in real time.

(Second Embodiment)
Below, the form which implements the hologram production | generation method based on this invention with the program of a computer is demonstrated as 2nd Embodiment. In addition, the same code | symbol is attached | subjected to the same structure as 1st Embodiment, and description is abbreviate | omitted suitably.

  In the second embodiment, the hologram generating apparatus 1 shown in FIG. 1 transmits / receives various information input or output to / from an arithmetic device such as a CPU and a storage device such as a memory and a hard disk, not dedicated hardware. The computer includes an interface device, a display device, and an input device, and a program installed in the computer.

  The hologram generating apparatus 1 is realized by the hardware device and software cooperating to control the hardware resources described above by a program. As shown in FIG. A holo normal component calculator 20, a phase difference calculator 30, and a real component calculator 40.

  The operation of the hologram generating apparatus 1 according to the second embodiment will be described with reference to FIG. 3 (refer to FIGS. 1 and 2 as appropriate). FIG. 3 is a flowchart when the hologram generation method according to the present invention is implemented as a computer program.

In FIG. 3, steps S4 to S6 are processing (hologram normal component calculation step) executed by the holo in-plane component calculator 10.
Steps S <b> 7 to S <b> 9 are processing (hologram normal component calculation step) executed by the holo normal component calculator 20.
Step S10 is a process (phase difference calculation step) executed by the phase difference calculator 30 that calculates the phase difference between the object light and the reference light from these optical path length differences.
Steps S11 and S12 are processing (real component calculation step) executed by the real component calculator 40 that calculates the real component of the interference light obtained from the obtained phase difference as the value of the interference fringe of the hologram.

  First, the hologram generation apparatus 1 receives, from an input device (not shown), object data 2d which is position data (X, Y, Z) and color data O (X, Y, Z) of the object 2 for which the hologram 4d is obtained, An input of reference light data 3d that gives information on the wavelength λ of the reference light and the angle θ of the inclination is received (step S1). Note that the storage unit (not shown) stores the object data 2d and the reference light data 3d, and a calculation device such as a CPU reads the object data 2d and the reference light data 3d from the storage unit. It is also possible.

  Next, the hologram generation apparatus 1 performs the following calculation for all points on the hologram surface 4 in the processing loop of steps S2 to S15 (step S2). A point on the hologram surface focused on in the following calculation is defined as a point B.

  In the processing loop of Steps S3 to S13, the hologram generation apparatus 1 is configured to include all object points included in the diffusion range determined by the maximum diffraction angle α of the reference light 3 around the reference light 3 passing through the point B on the hologram surface 4. In contrast, the following calculation is performed (step S3). Hereinafter, such an object point is denoted by A.

The holo in-plane component calculator 10 generates a hologram in-plane component d _X = X ² / 2Z having an optical path length d until the object light 5 formed by scattering the reference light 3 at the object point A reaches the hologram surface 4. Is calculated (step S4).

The holo in-plane component calculator 10 calculates the hologram in-plane component r _X = _X sin θ of the optical path length r until the reference light 3 having the same phase as the reference light 3 at the object point A reaches the point B on the hologram surface 4. Calculate (step S5).

The holo in-plane component calculator 10 includes a hologram in-plane component (d _X component) of the optical path length d obtained in step S4, a hologram in-plane component (r _X component) of the optical path length r obtained in step S5, and The difference Δ _X = d _X −r _X is calculated (step S6).

The holo normal component calculator 20 generates a normal component d _Z = Z of the hologram surface 4 having an optical path length d until the object beam 5 generated by scattering the reference beam 3 at the object point A reaches the hologram surface 4. Is calculated (step S7).

The holo normal component calculator 20 calculates the normal component r _Z of the hologram surface 4 having the optical path length r until the reference beam 3 having the same phase as the reference beam 3 at the object point A reaches the point B on the hologram surface 4. = Zcos θ is calculated (step S8).

Holo normal component calculator 20 includes a hologram normal component of the optical path length d (d _Z component) obtained in step S7, the hologram normal component of the optical path length r obtained in step S8 (r _Z component) calculating the difference Δ _Z = _{d Z} -r _Z (step S9).

The phase difference calculator 30, the phase difference and the difference value delta _X obtained in step S6, the sum of the difference value delta _Z obtained in step S9, the object beam 5 and the reference beam 3 at the reference point C [phi] [ _Delta] = 2 [pi] ([Delta] _X + [Delta] _Z ) / [lambda] is calculated (step S10).

The real component calculator 40 calculates the point difference from the phase difference φ _Δ obtained in step S10, the color data O (X, Y, Z) of the object point, and the distance Z from the hologram surface 4 of the object point A. As a real component of the interference fringe at B, H = O × cos (φ _Δ ) / Z is calculated as the interference fringe value H (step S11).

  For each point (point B) on the hologram surface 4, the real number component calculator 40 sets the interference fringe value obtained this time in step S 11 to the interference fringe value calculated so far by setting the initial value of the interference fringe to 0. The value H is added (step S12).

  The hologram generation apparatus 1 calculates interference fringe values H for all object points A within the diffusion range determined by the maximum diffraction angle α of the reference light 3 around the reference light 3 passing through the point B on the hologram surface 4. Whether or not (step 13). When the interference fringe value H has not yet been calculated for all object points A within the diffusion range determined by the maximum diffraction angle α (step S13: No), the hologram generating apparatus 1 returns to step S3.

  In step S13, when the interference fringe value H is calculated for all object points A within the diffusion range determined by the maximum diffraction angle α (step S13: Yes), the hologram generating device 1 The addition result obtained for B is output as an interference fringe value at the reference point C (step S14).

  The hologram generation apparatus 1 determines whether or not the interference fringe value H has been calculated at all hologram points (point B) in the hologram surface 4 (step 15). Here, every time the point B is changed, the new point B is set as the coordinate origin and the same calculation is performed. When the interference fringe values H have not yet been calculated for all points B (step S15: No), the hologram generating apparatus 1 returns to step S2. On the other hand, when the interference fringe values H are calculated for all points B (step S15: Yes), the hologram generating apparatus 1 ends the process. In this case, the obtained addition result is the hologram 4d.

  According to the second embodiment, the same effect as that of the first embodiment can be obtained, and a general computer can be connected to the above-described holo in-plane component calculator 10, holo normal component without constructing dedicated hardware. By using a program (hologram generation program) that functions as the calculator 20, the phase difference calculator 30, and the real component calculator 40, the hologram generation apparatus 1 shown in FIG. 1 can be realized. This program (hologram generation program) can be distributed via a communication line, or can be distributed by writing on a recording medium such as a CD-ROM.

(Third embodiment)
In the first and second embodiments, the case of an off-axis hologram in which the reference light is tilted with respect to the hologram surface has been described. However, the present invention can also be applied to the case of an inline hologram perpendicular to the hologram surface. . The first and second embodiments can be applied as they are as long as the inclination θ of the reference light is 0. However, a form dedicated to inline holograms will be described as a third embodiment.

  Since the hologram generating apparatus of the third embodiment is the same as that of the first embodiment except that the inclination angle θ of the reference light is 0, the drawings and description will be omitted as appropriate. Specifically, the holo normal component calculator 20 of FIG. 1 may be omitted. In the third embodiment, the reference light data 3d does not need to include information on the inclination angle θ of the reference light.

  In the third embodiment, since the inclination of the reference light is θ = 0, FIG. 4 shows a coordinate space when θ = 0 is formally set in the coordinate space shown in FIG. When θ = 0, the angle α is ∠BAC shown in FIG. The coordinate space shown in FIG. 4 is the same as the coordinate space shown in FIG. In FIG. 4, a part of the Z axis is indicated by a two-dot chain line to indicate that the reference light 3 overlaps the Z axis.

Further, in the formula, by substituting θ = 0 in the above-described formula (12a) used when obtaining the optical path length difference between the object beam and the reference beam, the following formula (15) is simplified. Incidentally, delta _X of formula (15) is obtained by redefinition.

According to the equation (15), unlike the above equation (12a), the optical path length difference (dr) between the object beam and the reference beam does not include the normal component (Δ _Z ) of the hologram surface. That is, when calculating the optical path length difference between the object beam and the reference beam, only the in-plane component (Δ _X ) of the hologram surface needs to be calculated.

On the other hand, in the case of the conventional inline hologram, as described with reference to FIG. 5, the phase of the reference light 3 (the rightmost reference light in FIG. 5) passing through the reference point C on the hologram surface 4 is set to 0. The phase is assumed to be 0 everywhere on the hologram surface 4. That is, the phase value of the reference light for obtaining the phase difference from the object light is set to zero. Then, the hologram in-plane component (d _X ) and the hologram normal component (d _Z ) of the optical path length until the object light reaches the hologram surface are respectively calculated to obtain the sum.

In contrast, in the hologram generation method according to each embodiment, as described with reference to FIG. 2, the reference phase of the reference light 3 that has reached the point B on the hologram surface 4 is changed to the reference light that has reached the point B. 3 is regarded as a phase at the time when the reference light 3 having the same phase as 3 (the middle reference light shown in FIG. 2) hits the object point A. Note that the reference phase is similarly set in the coordinate space shown in FIG. That is, in the hologram generation method according to the present embodiment, the phase of the reference light for obtaining the phase difference from the object light is set to “a value other than 0”. Thus, in the third embodiment, is canceled hologram normal component of the optical path length d of the object beam (d Z _{= Z)} is, delta since _Z term becomes 0, X ^{2 /} 2Z of delta _X section only The calculation of As a result, it has become possible to perform hologram calculation at higher speed.

  Note that the hologram generation apparatus of the third embodiment may be configured by a general computer in which a hologram generation program is installed in the same manner as in the second embodiment. In this case, the processing of step S7 to step S9 can be omitted.

  The preferred embodiments of the present invention have been described above, but the hologram generating apparatus and method of the present invention are not limited to the embodiments. For example, in each embodiment, the initial phase of the object light is set to “0” for easy understanding, but the interference fringes generated by the light from the adjacent points of the object are the same, and the interference fringes are mutually In order to avoid canceling, for each object point A, a random initial phase value between 0 and 2π may be added. The reason why the hologram can be obtained correctly even in this way is that the interference fringe condition necessary to bend the illumination light in the direction of the original object light is only the fringe interval and is not related to the fringe phase. is there. The interval between the interference fringes is determined only by the optical path difference of the object light at adjacent points on the hologram surface, regardless of the initial phase of the object light.

Further, in the coordinate spaces shown in FIGS. 2, 4 and 5, the distance X in the hologram plane direction, the distance Z between the hologram plane and the object point, the angle θ, the angle α, etc. are clearly arranged. Since it is exaggerated for explanation, it is not limited to this. In each embodiment, for the sake of simplicity, the Y coordinate value of the object point in the three-dimensional space is set to 0, but may be a value other than 0. In this case, for example, X ² may be replaced with X ² + Y ² in the hologram calculation formulas after the above formula (6). In each embodiment, for each point (point B) on the hologram surface, the real number component of the phase difference of the object light within the light diffusion range is added to obtain the interference fringe value. It is not limited to this. For example, for each object point (point A), the real component of the phase difference of the object light within the light diffusion range is recorded at each point in the hologram plane, and the object obtained in the same manner every time the object point is changed The real component of the phase difference of the light may be added to the value recorded at each point in the hologram plane.

  The present invention can be used not only in the field of stereoscopic video technology, but also in the medical technology field, the education field, and the like.

DESCRIPTION OF SYMBOLS 1 Hologram production | generation apparatus 10 Holo in-plane component calculator of optical path length difference of object beam and reference beam 20 Holo normal component calculator of optical path length difference of object beam and reference beam 30 Phase difference calculator 40 Real component calculator

Claims (6)

Hologram generating apparatus for generating hologram of object using object data including information of position of object and complex amplitude as object light and reference light data including information of wavelength of reference light and inclination angle with respect to hologram surface Because
Based on the position of the object and the wavelength of the reference light, the object light representing the distance until the object light generated at the first predetermined point of the object reaches the second predetermined point on the hologram surface With reference to the optical path length and the phase of the reference light when the reference light hits the first predetermined point of the object, the reference light reaching the second predetermined point on the hologram surface One value when the optical path length difference indicating the difference between the position where the phase is equal to the reference phase and the optical path length of the reference light representing the distance between the second predetermined point is formally divided into two values A hologram surface for calculating a hologram in-plane component indicating a value relating to a distance between an intersection point where a normal drawn from the first predetermined point of the object intersects the second predetermined point on the hologram surface Internal component calculation means;
Based on the position of the object and the wavelength of the reference light, as the other value when the optical path length difference is formally divided into two values, from the hologram surface to the first predetermined point of the object Hologram normal component calculation means for calculating a hologram normal component indicating a value related to the distance;
The hologram in-plane component of the optical path length difference and the hologram normal component of the optical path length difference are added, and based on the addition result and the wavelength of the reference light, the phase of the object light and the phase of the reference light are A phase difference calculating means for calculating a phase difference indicating the difference between
Real number component calculating means for calculating the real number component of the complex amplitude as the value of the interference fringe of the hologram based on the position and complex amplitude of the object and the phase difference;
Equipped with a,
The hologram in-plane component calculation means includes the object data when the position of the object is represented by (X, Y, Z), and the reference light data when the tilt angle information with respect to the hologram surface is represented by θ. And calculate the second term on the right side of the following equation (12a),
The hologram normal component calculation means receives an input of the object data and the reference light data, and calculates the first term on the right side of the following equation (12a) .

Here, d is the optical path length of the object light, r is the optical path length of the reference light, and α is the maximum diffraction angle of light that can be diffracted by the hologram display panel placed on the hologram surface. Hologram generating apparatus for generating hologram of object using object data including information of position of object and complex amplitude as object light and reference light data including information of wavelength of reference light perpendicularly incident on hologram surface Because
Based on the position of the object and the wavelength of the reference light, the object light representing the distance until the object light generated at the first predetermined point of the object reaches the second predetermined point on the hologram surface With reference to the optical path length and the phase of the reference light when the reference light hits the first predetermined point of the object, the reference light reaching the second predetermined point on the hologram surface As the optical path length difference indicating the difference between the optical path length of the reference light indicating the distance between the position where the phase is equal to the reference phase and the second predetermined point, the first location of the object is set on the hologram surface. Hologram in-plane component calculating means for calculating a hologram in-plane component indicating a value related to a distance between the intersection point of the normal line drawn from the fixed point and the second predetermined point;
A phase difference calculating means for calculating a phase difference indicating a difference between the phase of the object light and the phase of the reference light based on the hologram in-plane component of the optical path length difference and the wavelength of the reference light;
Real number component calculating means for calculating the real number component of the complex amplitude as the value of the interference fringe of the hologram based on the position and complex amplitude of the object and the phase difference;
Equipped with a,
The hologram in-plane component calculation means receives input of the object data and the reference light data when the position of the object is represented by (X, Y, Z), and calculates the following equation (15). <br/> A hologram generator characterized by the above.

Here, d is the optical path length of the object light, r is the optical path length of the reference light, and α is the maximum diffraction angle of light that can be diffracted by the hologram display panel placed on the hologram surface. A hologram generating apparatus for generating a hologram of an object using object data including information on the position of the object and complex amplitude as object light, and reference light data including information on a wavelength of reference light and an inclination angle with respect to the hologram surface A hologram generation method comprising:
The hologram generation apparatus includes:
Based on the position of the object and the wavelength of the reference light, the object light representing the distance until the object light generated at the first predetermined point of the object reaches the second predetermined point on the hologram surface With reference to the optical path length and the phase of the reference light when the reference light hits the first predetermined point of the object, the reference light reaching the second predetermined point on the hologram surface One value when the optical path length difference indicating the difference between the position where the phase is equal to the reference phase and the optical path length of the reference light representing the distance between the second predetermined point is formally divided into two values A hologram surface for calculating a hologram in-plane component indicating a value relating to a distance between an intersection point where a normal line drawn from a first predetermined point of the object intersects the second predetermined point on the hologram surface An internal component calculation step;
Based on the position of the object and the wavelength of the reference light, as the other value when the optical path length difference is formally divided into two values, from the hologram surface to the first predetermined point of the object Hologram normal component calculation step for calculating a hologram normal component indicating a value related to the distance;
The hologram in-plane component of the optical path length difference and the hologram normal component of the optical path length difference are added, and based on the addition result and the wavelength of the reference light, the phase of the object light and the phase of the reference light are A phase difference calculating step for calculating a phase difference indicating the difference between
A real component calculation step of calculating a real component of the complex amplitude as a value of an interference fringe of the hologram based on the position and complex amplitude of the object and the phase difference;
Run contains,
The hologram in-plane component calculation step includes the object data when the position of the object is represented by (X, Y, Z), and the reference light data when the tilt angle information with respect to the hologram surface is represented by θ. And calculate the second term on the right side of the following equation (12a),
The hologram normal component calculation step receives an input of the object data and the reference light data, and calculates the first term on the right side of the following equation (12a) .

Here, d is the optical path length of the object light, r is the optical path length of the reference light, and α is the maximum diffraction angle of light that can be diffracted by the hologram display panel placed on the hologram surface. Hologram generating apparatus for generating hologram of object using object data including information of position of object and complex amplitude as object light and reference light data including information of wavelength of reference light perpendicularly incident on hologram surface The hologram generation method of
The hologram generation apparatus includes:
Based on the position of the object and the wavelength of the reference light, the object light representing the distance until the object light generated at the first predetermined point of the object reaches the second predetermined point on the hologram surface With reference to the optical path length and the phase of the reference light when the reference light hits the first predetermined point of the object, the reference light reaching the second predetermined point on the hologram surface As the optical path length difference indicating the difference between the optical path length of the reference light indicating the distance between the position where the phase is equal to the reference phase and the second predetermined point, the first location of the object is set on the hologram surface. A hologram in-plane component calculation step for calculating a hologram in-plane component indicating a value relating to a distance between an intersection point of normal lines drawn from a fixed point and the second predetermined point;
A phase difference calculating step for calculating a phase difference indicating a difference between the phase of the object light and the phase of the reference light based on the hologram in-plane component of the optical path length difference and the wavelength of the reference light;
A real component calculation step of calculating a real component of the complex amplitude as a value of an interference fringe of the hologram based on the position and complex amplitude of the object and the phase difference;
Run contains,
The hologram in-plane component calculation step receives the input of the object data and the reference light data when the position of the object is represented by (X, Y, Z), and calculates the following equation (15). A method for generating a hologram.

Here, d is the optical path length of the object light, r is the optical path length of the reference light, and α is the maximum diffraction angle of light that can be diffracted by the hologram display panel placed on the hologram surface. A computer for generating a hologram of the object using object data including information on the position of the object and complex amplitude as object light, and reference light data including information on a wavelength of the reference light and an inclination angle with respect to the hologram surface The
Based on the position of the object and the wavelength of the reference light, the object light representing the distance until the object light generated at the first predetermined point of the object reaches the second predetermined point on the hologram surface With reference to the optical path length and the phase of the reference light when the reference light hits the first predetermined point of the object, the reference light reaching the second predetermined point on the hologram surface One value when the optical path length difference indicating the difference between the position where the phase is equal to the reference phase and the optical path length of the reference light representing the distance between the second predetermined point is formally divided into two values A hologram surface for calculating a hologram in-plane component indicating a value relating to a distance between an intersection point where a normal drawn from the first predetermined point of the object intersects the second predetermined point on the hologram surface Inner component calculation means,
Based on the position of the object and the wavelength of the reference light, as the other value when the optical path length difference is formally divided into two values, from the hologram surface to the first predetermined point of the object Hologram normal component calculation means for calculating a hologram normal component indicating a value related to the distance,
The hologram in-plane component of the optical path length difference and the hologram normal component of the optical path length difference are added, and based on the addition result and the wavelength of the reference light, the phase of the object light and the phase of the reference light are A phase difference calculating means for calculating a phase difference indicating the difference between
A real component calculation means for calculating a real component of the complex amplitude as a value of an interference fringe of the hologram based on the position and complex amplitude of the object and the calculated phase difference;
Is a program for functioning as
The hologram in-plane component calculation means includes the object data when the position of the object is represented by (X, Y, Z), and the reference light data when the tilt angle information with respect to the hologram surface is represented by θ. And calculate the second term on the right side of the following equation (12a),
The hologram normal component calculation means receives an input of the object data and the reference light data, and calculates the first term on the right side of the following equation (12a) .

Here, d is the optical path length of the object light, r is the optical path length of the reference light, and α is the maximum diffraction angle of light that can be diffracted by the hologram display panel placed on the hologram surface . In order to generate a hologram of the object using object data including information on the position of the object and complex amplitude as object light, and reference light data including information on the wavelength of the reference light incident perpendicularly to the hologram surface, Computer
Based on the position of the object and the wavelength of the reference light, the object light representing the distance until the object light generated at the first predetermined point of the object reaches the second predetermined point on the hologram surface With reference to the optical path length and the phase of the reference light when the reference light hits the first predetermined point of the object, the reference light reaching the second predetermined point on the hologram surface As the optical path length difference indicating the difference between the optical path length of the reference light indicating the distance between the position where the phase is equal to the reference phase and the second predetermined point, the first location of the object is set on the hologram surface. Hologram in-plane component calculation means for calculating a hologram in-plane component indicating a value relating to a distance between an intersection where a normal drawn from a fixed point intersects and the second predetermined point;
A phase difference calculating means for calculating a phase difference indicating a difference between the phase of the object light and the phase of the reference light based on the hologram in-plane component of the optical path length difference and the wavelength of the reference light;
Real number component calculating means for calculating a real number component of the complex amplitude as a value of the interference fringe of the hologram based on the position and complex amplitude of the object and the phase difference;
Is a program for functioning as
The hologram in-plane component calculation means receives input of the object data and the reference light data when the position of the object is represented by (X, Y, Z), and calculates the following equation (15). A hologram generation program characterized by the above .

Here, d is the optical path length of the object light, r is the optical path length of the reference light, and α is the maximum diffraction angle of light that can be diffracted by the hologram display panel placed on the hologram surface.

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