The present disclosure relates to a holographic printer, and more particularly, to a holographic printer for manufacturing by printing a holographic optical element (HOE) on a holographic material.
Related-art holographic printing is a method for reproducing a hologram image that has a large amount of information equivalent to an analogue hologram from digital information, by demagnifying digital image information displayed on a spatial light modulator (SLM) having a small amount of information as shown in
In particular, when information on the SLM is demagnified to hogels, a complex field value having both an amplitude and a phase may be recorded by performing spatial bandpass filtering through a 4f-system. In addition, an HOE that requires only phase information without amplitude information may be manufactured through holographic printing.
However, the related-art holographic printing may use a first-order diffraction component of the SLM in order to represent a complex field value, and in this process, a DC value where most of energy is concentrated may be discarded and thus very low light efficiency may be provided.
As a result, energy transmitted to a holographic material when hologram printing is performed may be reduced and time required to record per hogel may increase, which results in problems of degradation of hologram recording quality caused by a vibration, increase of total recording time.
The present disclosure has been developed in order to address the above-discussed deficiencies of the prior art, and an object of the present disclosure is to provide a holographic printer which is capable of representing phase information without a DC value that should be filtered, by using a combination of a tunable focus lens and a rotating mirror, instead of using an SLM, and a HOE printing method thereof, as a solution for enhancing quality of the HOE, reducing a printing time per hogel, and greatly reducing a total recording time, in manufacturing the HOE by holographic printing.
According to an embodiment of the present disclosure to achieve the above-described object, there is provided a holographic printer including: a first optical engine configured to adjust a phase of an incident collimated beam and emit the collimated beam; a first reduction optical system configured to reduce the beam emitted from the first optical engine and to allow the beam to enter a holographic material; a second optical engine configured to adjust a phase of an incident collimated beam and emit the collimated beam; and a second reduction optical system configured to reduce the beam emitted from the second optical engine and to allow the beam to enter the holographic material, wherein each of the first optical engine and the second optical engine includes: a rotating mirror configured to reflect while adjusting the phase of the incident collimated beam through rotation; and a tunable focus lens configured to refract while adjusting the phase of the incident collimated beam reflected from the rotating mirror through focus tuning.
Each of the first optical engine and the second optical engine may further include an aperture configured to limit a width of the incident collimated beam to a defined width, and to transmit the collimated beam toward the rotating mirror, and the defined width may be equal to an effective width of the tunable focus lens.
Each of the first optical engine and the second optical engine may further include a beam splitter configured to reflect the collimated beam passing through the aperture and transmit the collimated beam to the rotating mirror, and to pass the collimated beam reflected from the rotating mirror toward the tunable focus lens.
Each of the first optical engine and the second optical engine may further include an optical system configured to transmit the collimated beam passing through the beam splitter to the tunable focus lens.
The holographic printer according to an embodiment of the disclosure may further include a beam splitter configured to split a collimated beam generated from a light source into the first optical engine and the second optical engine.
A first collimated beam split at the beam splitter may directly enter the first optical engine, and a second collimated beam split at the beam splitter may be reflected through at least one mirror and may enter the second optical engine.
The tunable focus lens may be an ETL.
A rotation angle of the rotating mirror and a focus of the tunable focus lens may be adjusted according to information of each hogel to be recorded on the holographic material. Each hogel to be recorded on the holographic material may constitute an HOE.
According to another embodiment of the present disclosure, there is provided a holographic printing method including: adjusting, by a first optical engine, a phase of an incident collimated beam and emitting the collimated beam; reducing, by a first reduction optical system, the beam emitted from the first optical engine and allowing the beam to enter a holographic material; adjusting, by a second optical engine, a phase of an incident collimated beam and emitting the collimated beam; and reducing, by a second reduction optical system, the beam emitted from the second optical engine and allowing the beam to enter the holographic material, wherein each of the first optical engine and the second optical engine includes: a rotating mirror configured to reflect while adjusting the phase of the incident collimated beam through rotation; and a tunable focus lens configured to refract while adjusting the phase of the incident collimated beam reflected from the rotating mirror through focus tuning.
According to another embodiment of the present disclosure, there is provided a holographic printer including: a light source configured to generate a collimated beam; a first optical engine configured to adjust a phase of the collimated beam generated at the light source, and to emit the collimated beam; a first reduction optical system configured to reduce the beam emitted from the first optical engine and to allow the beam to enter a holographic material; a second optical engine configured to adjust a phase of the collimated beam generated at the light source, and to emit the collimated beam; and a second reduction optical system configured to reduce the beam emitted from the second optical engine and to allow the beam to enter the holographic material, wherein each of the first optical engine and the second optical engine includes: a rotating mirror configured to reflect while adjusting the phase of the incident collimated beam through rotation; and a tunable focus lens configured to refract while adjusting the phase of the incident collimated beam reflected from the rotating mirror through focus tuning.
According to another embodiment of the present disclosure, there is provided a holographic printing method including: generating, by a light source, a collimated beam; adjusting, by a first optical engine, a phase of the collimated beam generated at the light source, and emitting the collimated beam; reducing, by a first reduction optical system, the beam emitted from the first optical engine and allowing the beam to enter a holographic material; adjusting, by a second optical engine, a phase of the collimated beam generated at the light source, and emitting the collimated beam; and reducing, by a second reduction optical system, the beam emitted from the second optical engine and allowing the beam to enter the holographic material, wherein each of the first optical engine and the second optical engine includes: a rotating mirror configured to reflect while adjusting the phase of the incident collimated beam through rotation; and a tunable focus lens configured to refract while adjusting the phase of the incident collimated beam reflected from the rotating mirror through focus tuning.
According to embodiments of the present disclosure as described above, phase information may be represented without a DC value that should be filtered, by using a combination of a tunable focus lens and a rotating mirror, instead of using an SLM of a holographic printer, so that quality of an HOE may be enhanced, a printing time per hogel may be reduced and a total recording time may be greatly reduced when holographic printing of the HOE is performed.
Hereinafter, the present disclosure will be described in more detail with reference to the drawings.
An ETL is a tunable focus lens that has the form of a lens with a thin polymer membrane being filled with a liquid, and is able to change a focal distance by changing the shape of the lens by moving a peripheral circular ring according to an electrical signal.
As shown in
ϕ(x,y)=ϕM(x,y)+ϕL(x,y)
In this case, if rotation angles of the rotating mirror 120 in x, y directions are θx, θy, angles of reflection on an optical axis of the collimated beam are expressed by 2θx, 2θy, and accordingly, the phase ϕM(x, y) by the rotating mirror 120 may be calculated by the following equation:
ϕM(x,y)=k(x sin 2θx+y sin 2θy)
The phase ϕL(x, y) by the ETL 160 may be calculated by the following equation if a focal distance of the ETL 160 is fL:
When the focal distance is long enough, the above-described equation may be approximated as follows through paraxial approximation:
Accordingly, the rotating mirror 120 reflects the beam while adjusting the phase of the beam entering through rotation, and the ETL 160 refracts the collimated beam entering after being reflecting from the rotating mirror 120 while adjusting the phase of the collimated beam by tuning a focus.
The collimated laser beam passing through the aperture 110 is reflected by a beam splitter 130 and then is reflected on the rotating mirror 120 again, and passes through the beam splitter 130 and arrives at a lens-1140 having a focal distance f.
In this case, a distance between the rotating mirror 120 and the lens-1140 is equal to the focal distance f of the lens. An optical path after passing through the lens-1140 propagates by a distance of 2f, and then, meets a lens-2150 of the focal distance f, and passes through the lens-2150, travels by a distance of f, and then, arrives at the ETL 160. Due to the above-described optical path, the two lenses 140, 150 form a 4f system.
More specifically, a laser constituting a light source 210, a collimated laser beam generated by a spatial filter and a collimating lens are split into two optical paths through a beam splitter 220. The two beams are referred to as a signal beam 1 and a signal beam 2 as shown in
The signal beam 1 enters an aperture 110-1 of the optical engine 100-1 which emits an incident collimated beam while adjusting the phase of the beam, and passes through the optical path as described in
In this case, a mirror 170-1 is positioned at a front end of the ETL-1160-1 to bend the optical path by 90 degrees and to easily form the optical path, which is different from
The beam outputted in this way may reduce phase distribution of the surface of the ETL-1160-1 at a ratio of fo/fin through a reduction optical system, which includes a lens 230 having a focal distance of fin and a lens 240 having a focal distance of fo, and may image phase information on a surface of the holographic material 300. The phase information imaged in this way may be recorded on the surface of the holographic material as one hogel through interference with the signal beam 2.
The signal beam 2 also reduces phase distribution of a surface of the ETL 160-2 and images phase information on a surface of the holographic material through the same process as the signal beam 1.
Specifically, the signal beam 2 is reflected through mirrors 250, 260, 270 and enters an aperture 110-2 of the optical engine 100-2, which emits an incident collimated beam while adjusting the phase of the collimated beam, and passes through the optical path as described in
A mirror 170-2 is positioned at a front end of the ETL-2160-2 to bend the optical path by 90 degrees and to easily form the optical path, which is different from
The beam outputted in this way may reduce phase distribution of the surface of the ETL-2160-2 at a ratio of fo/fin through a reduction optical system, which includes a lens 280 having a focal distance of f in and a lens 290 having a focal distance of fo, and may image phase information on a surface of the holographic material 300. The phase information imaged in this way may be recorded on the surface of the holographic material as one hogel through interference with the signal beam 1.
In this case, a reduction ratio of the reduction optical system may be different from that of the signal beam 1. When each hogel is recorded, hogel information to be recorded may be modulated by adjusting rotation angles of the rotating mirror-1120-1 and the rotating mirror 120-2 and adjusting the focal distances of the ETL-1160-1 and the ETL-2160-2.
That is, an incident beam may be modulated by adjusting an amount of phase adjustment of each optical engine 100-1, 100-2 according to information of each hogel constituting an HOE to be recorded on the holographic material 300, that is, characteristics of the HOE.
In this case, if the reduction ratio of the reduction optical system is high enough to reduce the size of each hogel to be small enough and a difference between grating vectors in each hogel is not great, an optimal combination of rotation angles of the rotating mirror-1120-1 and the rotating mirror-2120-2 and focal distances of the ETL-1160-1 and the ETL-2160-2 that can record close to a desired grating vector may be found.
For easy explanation, if changes in an angle with an axis perpendicular to the surface of the holographic material 300, which are caused by rotation of the rotating mirrors 120-1, 120-2 after beams pass through the reduction optical systems, are θSx, θSy and a focal distance value of the ETL 160-1, 160-2 that meaningfully influences on the surface of the holographic material 300 by the reduction optical system is fs, a complex field made by each signal beam on the surface of the holographic material 300 may be calculated by the following equation:
In this case, the last line is an expression when paraxial approximation is applied. A phase value regarding this may be calculated by the following equation:
The last line is also an expression that reflects paraxial approximation. In order to acquire a corresponding local k-vector, a given phase ϕ(x, y) is converted into a continuous phase function {tilde over (ϕ)}(x, y) through phase-unwrapping, and the local k-vector is obtained by applying a first order partial differentiation equation presented below:
If expressions corresponding to respective signal beam paths are re-written by using subscripts 1, 2, complex fields made by the signal beam 1 and the signal beam 1 on the surface of the holographic material may be written as follows, respectively;
h
S1(x,y;kS1x,kS1y,fS1)=hM1(x,y;kS1x,kS1y)·hL1(x,y;fS1)
h
S2(x,y;kS2x,kS2y,fS2)=hM2(x,y;kS2x,kS2y)√hL2(x,y;fS2)
Phases may be written as follows, respectively;
ϕS1(x,y;kS1x,kS1y,fS1)=S1(x,y;kS1x,kS1y,fS1)
ϕS2(x,y;kS2x,kS2y,fS2)=S2(x,y;kS2x,kS2y,fS2)
If distribution of the complex fields and the phases obtained thereby is sampled by M×N and is given as a discrete signal indexed like (m, n), a local grating vector at each position (m, n) may be expressed in the form of a matrix as follows:
In this regard, a k-vector in a z-direction may be determined by the following equations:
Local grating vectors recorded by the local k-vectors on an inside of the holographic material 300 may be expressed by the following equations:
K
Gx
=K
S1x
−K
S2x)
K
Gy
=K
S1y
−K
S2y)
K
Gz
=K
S1z
−K
S2z)
The aim of designing for optimization is to diffract and output a target beam of KT(m,n)=(KTx(m,n), KTy(m, n), KTz(m,n)) when a probe beam KP(m,n)=(KPx(m, n), KPy(m, n), KPz(m, n)) enters the local grating vector written as de scribed above. The k-vector KD(m,n)=(KDx(m, n), KDy(m, n), KDz(m, n)) regarding a beam diffracted and outputted by the recorded local grating vector may be obtained by the following equations:
K
Dx
=K
Px
+K
Gx
=K
Px
+K
S1x
−K
S2x,
K
Dy
=K
Py
+K
Gy
=K
Py
+K
S1y
−K
S2y,
K
Dz=√{square root over (k2−KDx2−KDy2)}
In this case, an error of directions of the k-vectors of the diffracted beam and the target beam may be an L2-norm therebetween, and may be defined by the following equation:
In addition, it may be seen that degradation of diffraction efficiency caused by a k-vector different from that intended when a probe beam is recorded is proportional to a z component of the k-vector of the diffracted beam and a z component of the recorded grating vector, as indicated by the following expression:
Δη∝|KDz(m,n)−KGz(m,n)|
Accordingly, the optimization may be performed for the purposes of minimizing both the direction error of the diffracted beam and the degradation of diffraction efficiency, and may be achieved by finding a combination of (θS1x, θS1y, θS2x, θS2y, fS1, fS2) for minimizing the two factors. However, these parameters are in a boundary condition in which they should be found within an operation range of each rotating mirror 120-1, 120-2 and ETL 160-1, 160-2. Accordingly, an optimization method reflecting all of these parameters may be expressed by the following expression:
s.t. θS1x, θS1y, θS2x, θS2y, fS1, fS2 inside the system working range
In this case, a is a coefficient that determines which of the direction of the diffracted beam and the degradation of the diffraction efficiency influences the optimization more greatly.
Up to now, a holographic printer which is capable of representing phase information without a DC value that should be filtered, by using a combination of a tunable focus lens and a rotating mirror, instead of using an SLM, and a HOE printing method thereof have been described as a solution for enhancing quality of the HOE, reducing a printing time per hogel, and greatly reducing a total recording time, in manufacturing the HOE by holographic printing.
The technical concept of the present disclosure may be applied to a computer-readable recording medium which records a computer program for performing the functions of the apparatus and the method according to the present embodiments. In addition, the technical idea according to various embodiments of the present disclosure may be implemented in the form of a computer readable code recorded on the computer-readable recording medium. The computer-readable recording medium may be any data storage device that can be read by a computer and can store data. For example, the computer-readable recording medium may be a read only memory (ROM), a random access memory (RAM), a CD-ROM, a magnetic tape, a floppy disk, an optical disk, a hard disk drive, or the like. A computer readable code or program that is stored in the computer readable recording medium may be transmitted via a network connected between computers.
In addition, while preferred embodiments of the present disclosure have been illustrated and described, the present disclosure is not limited to the above-described specific embodiments. Various changes can be made by a person skilled in the art without departing from the scope of the present disclosure claimed in claims, and also, changed embodiments should not be understood as being separate from the technical idea or prospect of the present disclosure.
Number | Date | Country | Kind |
---|---|---|---|
10-2021-0177358 | Dec 2021 | KR | national |
Filing Document | Filing Date | Country | Kind |
---|---|---|---|
PCT/KR2021/019023 | 12/15/2021 | WO |