## 3D holographic printer: Fast printing approach |

Optics Express, Vol. 22, Issue 3, pp. 2193-2206 (2014)

http://dx.doi.org/10.1364/OE.22.002193

Acrobat PDF (1756 KB)

### Abstract

This article describes the general operation principles of devices for synthesized holographic images such as holographic printers. Special emphasis is placed on the printing speed. In addition, various methods to increase the printing process are described and compared.

© 2014 Optical Society of America

## 1. Introduction

1. S.A. Benton and V.M. Bove Jr., *Holographic Imaging* (Wiley-Interscience, 2008), 1. [CrossRef]

2. H. Kogelnik, “Couple wave theory for thick hologram gratings,” Bell System Technical Journal **48**, 2909–2949 (1969). [CrossRef]

## 2. Principle of holographic printer

## 3. Quality of synthesized holographic image

*δγ*). In accordance with Eq. (1), the maximum size of an element in a holographic image (hogel) should be less than 300

*μm*with the observation distance (

*l*) equal to 300 mm

*d*,

*λ*, and

*α*represent the hogel size, wavelength of the reconstructing light radiation, and aberration coefficient, respectively. The estimated reduction of the angular resolution is a consequence of the synthesized image of the Fourier transforming optical system spatial spectrum formation.

*α*= 1.0, the minimal acceptable hogel size (

*d*) must be equal to 61

_{min}*μm*for the reconstructing light radiation of

*λ*= 0.532

*μm*.

8. Keehoon Hong, Soon-gi Park, Jiwoon Yeom, Jonghyun Kim, Ni Chen, Kyungsuk Pyun, Chilsung Choi, Sunil Kim, Jungkwuen An, Hong-Seok Lee, U-in Chung, and Byoungho Lee, “Resolution enhancement of holographic printer using a hogel overlapping method,” Opt. Express **21**, 14047–14055 (2013). [CrossRef] [PubMed]

## 4. Printing speed

### 4.1. Continuous printing

*ps*to tens of

*ns*and produce a few

*mJ*of energy. Therefore, as the energy of the generated pulse is increased, the volume of the laser active media also increases, while the pulse repetition frequency (

*f*) decreases. The minimum printing time,

_{pulse}*T*, can be determined using where

*A*,

*d*, and

*f*represent the total printing area, size of one hogel, and pulse repetition frequency, respectively.

_{pulse}*v*represents the speed of the material.

13. Horst Berneth, Friedrich-Karl Bruder, Thomas Fcke, Rainer Hagen, Dennis Hnel, Thomas Rlle, Gnther Walze, and Marc-Stephan Weiser, “Holographic recordings with high beam ratios on improved Bayfol HX photopolymer,”Proceedings of SPIE **8776**, 877603 (2013). [CrossRef]

*ps*, and exhibit a higher sensitivity compared to the photopolymer materials.

14. Viktor N. Mikhailov, K. T. Weitzel, Vitaly N. Krylov, and Urs P. Wild, “Pulse hologram recording in dupont’s photopolymer films,” Proc. SPIE **3011**, 200–202 (1997). [CrossRef]

15. Viktor N. Mikhailov, K. T. Weitzel, Tatiana Y. Latychevskaia, Vitaly N. Krylov, and Urs P. Wild, “Pulse recording of slanted fringe holograms in dupont photopolymer,” Proceedings of SPIE **3294**, 132–135 (1998). [CrossRef]

14. Viktor N. Mikhailov, K. T. Weitzel, Vitaly N. Krylov, and Urs P. Wild, “Pulse hologram recording in dupont’s photopolymer films,” Proc. SPIE **3011**, 200–202 (1997). [CrossRef]

15. Viktor N. Mikhailov, K. T. Weitzel, Tatiana Y. Latychevskaia, Vitaly N. Krylov, and Urs P. Wild, “Pulse recording of slanted fringe holograms in dupont photopolymer,” Proceedings of SPIE **3294**, 132–135 (1998). [CrossRef]

### 4.2. Step-by-step printing method

*μs*to tens or hundreds of

*ms*. This does not allow for the recording of micro-holograms without stopping the light-sensitive material during the exposure. As a result, the discontinuous movement of the material generates high levels of vibrations that cannot be ignored. In general, the time required for printing a synthetic hologram is determined by the diagram shown in Figure 2.

*τ*,

*t*, and

_{move}*t*represent the time required to expose one hogel, time required to move between two hogels, and waiting time after stopping the movement, respectively. Conversely, time required to expose one hogel according to [16] is determined by where

_{wait}*d*,

*S*,

*P*, and

*ε*respectively represent the hogel size, sensitivity of the material, laser output power, and efficiency of the optical system.

*a*is the acceleration. [17]

*Micos Scan Table MS-8*) with DC motors was used as a mechanical positioner. We used three DPSS lasers, separate for each color. All experiments were carried outed by using of Bayer Bayfol HX-102 photopolymer material. It should be noted that the waiting time for a red wavelength of light was nearly 5 times less than that for green and blue wavelengths. In addition, the blue wavelength had a much lower acceleration compared to the red and green wavelengths.

### 4.3. As intermediate conclusion

*Vibration sensitivity*may be reduced by using a more compact arrangement and lighter mechanical parts with a higher rigidity. One way to reduce the vibration influence is by the use of compact and inflexible optical parts, e.g., something similar to the integral optical recording device discussed in [19

19. Kyungsuk Pyun, Chilsung Choi, Alexander Morozov, Sunil Kim, Jungkwuen An, Hong-seok Lee, and Uni Chung, “Integrated Hologram Optical Head for Holographic Printer,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (online), Optical Society of America (2013), paper DW4A.2. [CrossRef]

*exposure time*may be reduced by using more powerful coherent light sources. However, this will cause the device size and power consumption to increase. An alternative solution to this problem can be increasing the optical efficiency because the exposure time is inversely proportional to the optical efficiency as shown in Eq. (9). In [19

19. Kyungsuk Pyun, Chilsung Choi, Alexander Morozov, Sunil Kim, Jungkwuen An, Hong-seok Lee, and Uni Chung, “Integrated Hologram Optical Head for Holographic Printer,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (online), Optical Society of America (2013), paper DW4A.2. [CrossRef]

*printing speed*depends on several factors. However, the factor that likely affects the printing speed the most is the waiting time. It is important that a moving material have a suf-ficient waiting time so that the vibration level can be sufficiently reduced (see Figure 2). A possible solution to the printing speed problem is the use of a multi-printing head. However, this method increases the overall device size as well as the number of coherent light sources. One of more the interesting ways to overcome the printing speed is to print several hogels at the same position of light sensitive material. This is called multi-hogel printing technology.

## 5. Multi-hogel printing technology

**I**record all hogels in a hogel cluster at the same time. However, during the recording, spatial splitting of its angular spectrum occurs due to multiple hogels sharing the single spatial light modulator (SLM) information. This approached reduces the image quality when compared to the conventional printing method (single hogel printing method). Conversely, methods belong to Group

**II**form images that are separated by time and spatial hogels at a fixed position on the light sensitive material. At the same time, the entire SLM resolution is used to form an angular spectrum of each hogel. In that case, it is possible to achieve the same image quality as the single hogel printing method.

### 5.1. Efficiency of multi-hogel printing technology

*M*

^{2}single hogels, where

*M*is positive integer greater than 1.

*K*are defined as

*M*

^{2}when compared to the single hogel printing method. At the same time, the overall moving time is reduced by [20

20. Note that, the total exposure time has not changed. However, the time required to record one hogel will depend on the number of simultaneous recorded hogels and will be equal to

*M*

^{3/2}. Furthermore, Eq. (13) describes a method from Group

**I**.

**II**can be defined as where

*t*represents the time required for the optical system to print the next hogel in hogel cluster. For the ideal case,

_{shift}*t*=

_{shift}*f*

_{SLM}^{−1}, where

*f*represents the SLM frame rate.

_{SLM}## 6. Spatial Splitting Technology

*σ*,

*h*, and

*f*represent the entire angle defined for a single hogel field of view, linear size of a SLM placed at front of the focal plane of Fourier transforming optical system, and focal distance of a Fourier transforming optical system, respectively. Meanwhile, the numerical aperture of the this optical Fourier transforming system (according to [6]) can be described using where

*D*is the diameter of the Fourier transforming optical system exit pupil.

*M*is positive integer greater than 1,

*M*

^{2}is the number of hogels in one hogel cluster (see Section 5), and

*f*

_{Σ}is the total focal distance of the optical system. The total focal distance of such a system according to [6] can be defined as where Φ

_{Σ}= 1/

*f*

_{Σ}is the optical power of the whole optical system, Φ

_{1}= 1/

*f*

_{1}is the optical power of the first component, Φ

_{2}= 1/

*f*

_{2}is the optical power of the second component, Φ

_{3}= 1/

*f*

_{3}is the optical power of the third component,

*d*

_{1}=

*f*

_{1}+

*f*

_{2}is the distance between first and second components, and

*d*

_{2}=

*f*

_{2}+

*f*

_{3}is the distance between the second and third components.

22. Eqs. (15), (17), and (19) are true for the case for the field of view of a synthesized holographic image recorded using the single hogel printing technique and is equal to the field of view of the image recoded using the spatial hogel spectra splitting technology if and only if both designs used the same SLM.

*M*times less than that of a single hogel printing optical system. We can define the numerical aperture for this case using of Eqs. (16) and (20) Notice that the numerical aperture of the Fourier transforming systems with spatial splitting of the angular spectra of separate hogels increase as the number of hogels in a hogel cluster increases. This causes a reduction in the synthesized image field of view. Table 4 shows dependency of the field of view and numerical aperture on the number of hogels in a hogel cluster [23]. Additionally, notice that the maximum Fourier objective numerical value can only provide a maximum field of view of 60°.

*N*,

*σ*, and

*M*

^{2}, represent the SML pixel number, SLM pixel number used for forming the hogel field of view, half angle of a hogel’s field of view, and number of hogels in a hogel cluster, respectively. We emphasize that Eq. (22) is valid only for

*f*-Theta Fourier lenses. Table 5 shows the variation of the angular resolution as a function of

*M*

^{2}for a VGA SLM holographic image formed by an

*f*-Theta Fourier objective.

*f*-Theta one, Eq. (22) becomes where

*N*,

*σ*, and

*M*

^{2}represent the SLM pixel number, half angle of a hogel’s field of view, and number of hogels in a hogel cluster. Table 6 shows the variation of the angular resolution as a function of

*M*

^{2}for a VGA SLM holographic image formed by a conventional Fourier objective. As one can see, spatial splitting technology can significantly reduce the printing time compared to the single hogel printing technology. However, serious limitations occur not only in the manufacturability but also in the image quality of the formed hologram.

## 7. Time sequential Technology

*γ*. This angle defines the shift of recording hogel position according to [6] using Meanwhile, the numerical aperture of the Fourier transformation objective can be defined as where

*h*,

*M*,

*f*, and

*d*represent the SLM linear size, square root of the number of hogels in a hogel cluster, Fourier transformation lens focal distance, and shift of the hogel position that is equal to size of a single hogel in a hogel cluster, respectively.

## 8. Comparison of different printing methods

**I**. The increase in the optical system complexity is due to the increasing hogel number in a hogel cluster. Thus, one cannot uniquely identify the optimal technology for each particular case.

*cm*

^{2}, 60°or 30°, and 0.2× 0.2

*mm*

^{2}, respectively. It is clear that at large viewing angles (60°) the synthesized image using the spatial multi-hogel method containing 4 (

*M*= 2) hogels has some advantages when compared to the time sequential method. For a larger amount of hogels, the time sequential method is advantageous due to the fact that this system with SLM spatial splitting requires a numerical aperture greater than 0.76 and cannot form more than 4 hogels in a hogel cluster. In addition, the spatial multi-hogel has the narrowest field of view, i.e., approximately 30° field of view for time and spatial multi-hogels. Conversely, the time sequential design exhibited a narrow field of view for high

*M*

^{2}, i.e., more than 16. In fact, for

*M*

^{2}≥ 16, there is no difference between the spatial and time multi-hogels. Therefore, the selection of holographic systems should be made based on economic considerations.

## 9. Conclusion

*cm*

^{2}. On the same time, spatial splitting technology allows to print four hogel in one time and reduce overall printing time till 67 minutes with small image quality reduction. The time sequential technology with 25 hogels in one hogel cluster will print same image just for 32 minutes without any image quality reduction.

## Acknowledgments

## References and links

1. | S.A. Benton and V.M. Bove Jr., |

2. | H. Kogelnik, “Couple wave theory for thick hologram gratings,” Bell System Technical Journal |

3. | Michael Klug, Mark Holzbach, and Alejandro Ferdman, “Method and apparatus for recording one-step, full-color, full-parallax, holographic stereograms,” (2001). US patent 6330088 B1, Dec. 11, 2001. |

4. | David Brotherton-Ratcliffe, Stanislovas J. Zacharovas, Ramunas J. Bakanas, Julius Pileckas, Andrej Nikolskij, and Jevgenij Kuchin, “Digital holographic printing using
pulsed RGB lasers,” Opt. Eng. |

5. | Craig Newswanger, Pankaj Lad, Robert L. Sitton, Qiang Huang, Michael A. Klug, and Mark E. Holzbach, “Pulsed-laser systems and methods for producing holographic stereograms,” (19-Oct.-2004). US 6806982 B2. |

6. | Michael J. Kidger, |

7. | Equation (2) is written in the square hogel form. |

8. | Keehoon Hong, Soon-gi Park, Jiwoon Yeom, Jonghyun Kim, Ni Chen, Kyungsuk Pyun, Chilsung Choi, Sunil Kim, Jungkwuen An, Hong-Seok Lee, U-in Chung, and Byoungho Lee, “Resolution enhancement of holographic printer using a hogel overlapping method,” Opt. Express |

9. | David Brotherton-Ratcliffe, Florian Michael Robert Vergnes, Alexey Rodin, and Mikhail Grichine, “Holographic printer,” (2005). US patent 6930811 B2, Aug. 16, 2005. |

10. | Equation (6) is written for the case when the speed of the material is the same in each direction. |

11. | H.I. Bjelkhagen, “Silver Halide Recording Materials for Holography and Their Processing,” |

12. | Friedrich-Karl Bruder, Francois Deuber, Thomas Fcke, Rainer Hagen, Dennis Hnel, David Jurbergs, Thomas Rlle, and Marc-Stephan Weiser, “Reaction-diffusion model applied to high resolution Bayfol HX photopolymer,”Proceedings of SPIE |

13. | Horst Berneth, Friedrich-Karl Bruder, Thomas Fcke, Rainer Hagen, Dennis Hnel, Thomas Rlle, Gnther Walze, and Marc-Stephan Weiser, “Holographic recordings with high beam ratios on improved Bayfol HX photopolymer,”Proceedings of SPIE |

14. | Viktor N. Mikhailov, K. T. Weitzel, Vitaly N. Krylov, and Urs P. Wild, “Pulse hologram recording in dupont’s photopolymer films,” Proc. SPIE |

15. | Viktor N. Mikhailov, K. T. Weitzel, Tatiana Y. Latychevskaia, Vitaly N. Krylov, and Urs P. Wild, “Pulse recording of slanted fringe holograms in dupont photopolymer,” Proceedings of SPIE |

16. | H.J. Caulfield, |

17. | The coefficient 2 before root sign takes into account the situation when the acceleration and deceleration are equal. |

18. | In our experimental setup we are using 4F optical system to be able to simple modify it for implementing different multi-hogel printing techniques. |

19. | Kyungsuk Pyun, Chilsung Choi, Alexander Morozov, Sunil Kim, Jungkwuen An, Hong-seok Lee, and Uni Chung, “Integrated Hologram Optical Head for Holographic Printer,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (online), Optical Society of America (2013), paper DW4A.2. [CrossRef] |

20. | Note that, the total exposure time has not changed. However, the time required to record one hogel will depend on the number of simultaneous recorded hogels and will be equal to |

21. | Andrew N. Putilin, Alexander V. Morozov, and Ivan V. Bovsunovskiy, “Optical device with Fourier transforming optical components for one step multi-micro-hologram recording using wedge system,” (2012). Russian Patent Application RU 2012127529, July 03, 2012. |

22. | Eqs. (15), (17), and (19) are true for the case for the field of view of a synthesized holographic image recorded using the single hogel printing technique and is equal to the field of view of the image recoded using the spatial hogel spectra splitting technology if and only if both designs used the same SLM. |

23. | The maximum permissible value of the numerical aperture for the Fourier transforming system containing a large linear field was 0.76. |

24. | For simplicity, a SLM with a pixel number equal to N and an aspect ratio of 1:1 is used. |

25. | Andrew N. Putilin, Alexander V. Morozov, and Ivan V. Bovsunovskiy, “Optical device with multi aperture Fourier transforming optical components for one step multi-micro-hologram recording,” (2012). Russian Patent Application RU 2012120356, May 17, 2012. |

26. | In the above calculations, the exposure time (τ), moving time (t |

**OCIS Codes**

(210.2860) Optical data storage : Holographic and volume memories

(230.3120) Optical devices : Integrated optics devices

(230.7370) Optical devices : Waveguides

**ToC Category:**

Holography

**History**

Original Manuscript: October 24, 2013

Revised Manuscript: December 13, 2013

Manuscript Accepted: December 15, 2013

Published: January 27, 2014

**Citation**

Alexander V. Morozov, Andrey N. Putilin, Sergey S. Kopenkin, Yuriy P. Borodin, Vladislav V. Druzhin, Sergey E. Dubynin, and German B. Dubinin, "3D holographic printer: Fast printing approach," Opt. Express **22**, 2193-2206 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-3-2193

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### References

- S.A. Benton, V.M. Bove, Holographic Imaging (Wiley-Interscience, 2008), 1. [CrossRef]
- H. Kogelnik, “Couple wave theory for thick hologram gratings,” Bell System Technical Journal 48, 2909–2949 (1969). [CrossRef]
- Michael Klug, Mark Holzbach, Alejandro Ferdman, “Method and apparatus for recording one-step, full-color, full-parallax, holographic stereograms,” (2001). US patent 6330088 B1, Dec. 11, 2001.
- David Brotherton-Ratcliffe, Stanislovas J. Zacharovas, Ramunas J. Bakanas, Julius Pileckas, Andrej Nikolskij, Jevgenij Kuchin, “Digital holographic printing using pulsed RGB lasers,” Opt. Eng. 50(9), 091307 (2011).
- Craig Newswanger, Pankaj Lad, Robert L. Sitton, Qiang Huang, Michael A. Klug, Mark E. Holzbach, “Pulsed-laser systems and methods for producing holographic stereograms,” (19-Oct.-2004). US 6806982 B2.
- Michael J. Kidger, Fundamental Optical Design (Society of Photo Optical, 2002).
- Equation (2) is written in the square hogel form.
- Keehoon Hong, Soon-gi Park, Jiwoon Yeom, Jonghyun Kim, Ni Chen, Kyungsuk Pyun, Chilsung Choi, Sunil Kim, Jungkwuen An, Hong-Seok Lee, U-in Chung, Byoungho Lee, “Resolution enhancement of holographic printer using a hogel overlapping method,” Opt. Express 21, 14047–14055 (2013). [CrossRef] [PubMed]
- David Brotherton-Ratcliffe, Florian Michael Robert Vergnes, Alexey Rodin, Mikhail Grichine, “Holographic printer,” (2005). US patent 6930811 B2, Aug. 16, 2005.
- Equation (6) is written for the case when the speed of the material is the same in each direction.
- H.I. Bjelkhagen, “Silver Halide Recording Materials for Holography and Their Processing,” Springer Series in Optical Sciences, Vol. 66(Springer-Verlag, Heidelberg, New York1993).
- Friedrich-Karl Bruder, Francois Deuber, Thomas Fcke, Rainer Hagen, Dennis Hnel, David Jurbergs, Thomas Rlle, Marc-Stephan Weiser, “Reaction-diffusion model applied to high resolution Bayfol HX photopolymer,”Proceedings of SPIE 7619, 76190I(2010). [CrossRef]
- Horst Berneth, Friedrich-Karl Bruder, Thomas Fcke, Rainer Hagen, Dennis Hnel, Thomas Rlle, Gnther Walze, Marc-Stephan Weiser, “Holographic recordings with high beam ratios on improved Bayfol HX photopolymer,”Proceedings of SPIE 8776, 877603 (2013). [CrossRef]
- Viktor N. Mikhailov, K. T. Weitzel, Vitaly N. Krylov, Urs P. Wild, “Pulse hologram recording in dupont’s photopolymer films,” Proc. SPIE 3011, 200–202 (1997). [CrossRef]
- Viktor N. Mikhailov, K. T. Weitzel, Tatiana Y. Latychevskaia, Vitaly N. Krylov, Urs P. Wild, “Pulse recording of slanted fringe holograms in dupont photopolymer,” Proceedings of SPIE 3294, 132–135 (1998). [CrossRef]
- H.J. Caulfield, Handbook of Optical Holography (Academic Press, 1980).
- The coefficient 2 before root sign takes into account the situation when the acceleration and deceleration are equal.
- In our experimental setup we are using 4F optical system to be able to simple modify it for implementing different multi-hogel printing techniques.
- Kyungsuk Pyun, Chilsung Choi, Alexander Morozov, Sunil Kim, Jungkwuen An, Hong-seok Lee, Uni Chung, “Integrated Hologram Optical Head for Holographic Printer,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (online), Optical Society of America (2013), paper DW4A.2. [CrossRef]
- Note that, the total exposure time has not changed. However, the time required to record one hogel will depend on the number of simultaneous recorded hogels and will be equal to τM2=d2SPεM2. Therefore, the required waiting time must be increased because of the increased single hogel exposure time. It is impossible to define the changes in the waiting time because it depends on the real exposure time, wavelength, and rigidity of the entire system. As such, in the future, we will not take into account the waiting time changes, which is true for very short exposure times as well as a low M.
- Andrew N. Putilin, Alexander V. Morozov, Ivan V. Bovsunovskiy, “Optical device with Fourier transforming optical components for one step multi-micro-hologram recording using wedge system,” (2012). Russian Patent Application RU 2012127529, July 03, 2012.
- Eqs. (15), (17), and (19) are true for the case for the field of view of a synthesized holographic image recorded using the single hogel printing technique and is equal to the field of view of the image recoded using the spatial hogel spectra splitting technology if and only if both designs used the same SLM.
- The maximum permissible value of the numerical aperture for the Fourier transforming system containing a large linear field was 0.76.
- For simplicity, a SLM with a pixel number equal to N and an aspect ratio of 1:1 is used.
- Andrew N. Putilin, Alexander V. Morozov, Ivan V. Bovsunovskiy, “Optical device with multi aperture Fourier transforming optical components for one step multi-micro-hologram recording,” (2012). Russian Patent Application RU 2012120356, May 17, 2012.
- In the above calculations, the exposure time (τ), moving time (tmove), waiting time (twait), and time for scheme shift (tshift) are 0, 10, 50, and 5 ms, respectively. The maximum numerical aperture of the Fourier transforming optical system was set to 0.76.

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