Publication : SPIE Proc. Practical Holography XX: Materials and Applications, SPIE#6136, San Jose, 347–354(2006).

1A high-resolution fringe printerfor studying synthetic holograms
K. Matsushimaa , S. Kobayashia , H. Miyauchiaa Department of Electrical Engineering and Computer Science, Kansai University

Yamate-cho 3-3-35, Suita, Osaka 564-8680, Japan
ABSTRACT
A high resolution fringe printer developed for driving the research in computer-generated holograms is presented.
This fringe printer consists of a rotation drum and a laser diode and is capable of printing elliptical dots of
1.5 times 3.0 microns in diameter on photosensitive ﬁlms. These dot sizes are approximately converted intoresolutions of 17,000dpi × 8,500dpi. The horizontal and vertical angles of viewing-zone of holograms printed by
the printer reach 24 and 12 degrees, respectively. The designed maximum scan speed is more than 200mm/s, andat current stage of development, a hologram of approximately 50 mm square can be printed in approximately 2hours.
Keywords: Digitally synthetic hologram, Computer-generated hologram, CGH, 3-D image, Fringe printer1. INTRODUCTION
Computer-generated holograms (CGH), sometimes called digitally synthetic holograms, are one of candidates forsophisticated three-dimensional digital imaging system in the future. But the CGHs at current stage are suﬀeringfrom twin problems before growing into practical use. One is the problem of its computation. Generation ofCGHs is, in general, much time-consuming process even in modern CPU technology.1, 2 The other is the problemof its fabrication. Resolution of printed fringe pattern of CGHs directly leads to angle of its viewing-zone. For
example, a laser printer in resolution of 1,200 dpi can generate a hologram that has only an angle of viewingzone of 1.7 degrees. If we can use micro-processing technology such as e-beam writing3 or photo-lithography
for fabricating LSI device, we can print CHGs of which viewing zone is larger than that of conventional analog
holograms. However, these high-technologies are, in general, too expensive to print only a piece of 3-D picture.
Furthermore, time necessary for fabricating a hologram is usually too long to fabricate experimental holograms
to verify algorithm for its computation.
This printing-problem has blocked progress in computer algorithm for synthetic holograms. For example,
even if someone invents an algorithm to calculate ﬁne holograms very fast, they can not verify their idea becauseof no instrument to print the synthetic hologram.
To overcome this situation, i.e. lack of easy printing equipments for CGHs, some low-cost fringe printersystems have been reported. Sakamoto et al. proposed to use a speciﬁc CD-R writer available on the market
as fringe printer for CGHs.4 However, the CD-R writer they reported is not available at the present time.
Yoshikawa et al. also reported a fringe printer, in which a LCD is used as SLM and images displayed on theLCD are transferred to photosensitive materials.5, 6 This is very fast printing system. The only drawback in thefringe printer is that resolution of the printed fringe pattern is determined by quality of optics for transferring
images.
We also presented fringe printer system in former reports.7, 8 The fringe printer can print fringe patterns
dot by dot by focusing single laser beam onto photosensitive plate, and therefore optical system is simple andinexpensive. But its printing speed was very slow. The new printer system reported in this article is animprovement on the previous one. In the new printer, the improvement is made on the mechanism for scanningthe laser spot, i.e. a rotation drum is introduced into the new printer and plays an important roll to increasescan speed drastically.
Further author information:
E-mail: matsu@kansai-u.ac.jp, Telephone/Fax: +81-6-6368-0933

Publication : SPIE Proc. Practical Holography XX: Materials and Applications, SPIE#6136, San Jose, 347–354(2006).

2L a se r B e a m
O b je c tiv e L e n sD ru m
R o ta tio nXF ilm
YFigure 1. The basic structure of the fringe printer. Fringe patterns are printed dot by dot using a rotation drum.

2. PRINTER SYSTEM
2.1. Basic Structure
Mechanism of the fringe printer is shown in Fig. 1. This printer is nothing more than an extraordinary highresolution laser printer in a sense. The fringe patterns of a hologram are formed from many small dark dots
printed on photosensitive ﬁlm used in recording analog holograms by focusing a laser beam. However, rotational
polygon mirrors and f − θ lens system used in ordinary laser printers are not used in this printer. Instead of thesecomplicated optomechanical mechanism, the photo-sensitive ﬁlm is directly pasted on a drum and a laser beam
is focused on the ﬁlm by objective lens. A laser diode is used as the laser source, and its output is modulated
to give diﬀerent gray-level to each printed dot. Rotation of the drum provides X-scan of the laser spot, while
Y-scan is given by translational movement of objective lens and laser spot along the rotation axis of the drum.

2.2. Optics and the rotation drum
Optics of the fringe printer is shown in Fig 2. Output of the laser diode is reﬂected by the surface of a glass
prism to attenuate the power to one or two order of magnitude, because intensity of the focused laser spot is toostrong to expose photosensitive ﬁlm properly and control gray-level of printed dots. All optical instruments areinstalled on a base plate loaded on a pulse-motor translational stage to provide Y-scan.
The rotation drum is driven by AC servomotor and supported by a rigid and precision shaft bearing mechanism. Photographs of printer system is shown in Fig. 3

2.3. Control system
Fig. 4 shows the block diagram of a circuit controlling the printer. Y- and Z-stage are controlled by a PC via
the stage controller connected by the serial interface. AC servomotor is also controlled by the PC via the motor
driver installed in PCI bus. A build-in rotary encoder in the servomotor triggers the pulse generator, and thepulse generator generates a series of pulse corresponding to a line in X-scan. This pulse string triggers one-shot
pulse generator and D/A converter installed in PCI bus. Finally, a height-controlled pulse string is generated bya C-MOS switch and fed to LD driver.

3. RESOLUTION AND PRECISION OF THE CONSTRUCTED PRINTER
3.1. The size of a dot
Dot size printed on the ﬁlm gives the resolution of the printer. Fig. 5 shows the photomicrograph of a dot string
printed with laser irradiation at intervals of 2 µm. Each dot has elliptical shape owing to the elliptical beammode of the LD output and its size (diameter) measures approximately 1.5 µm in the direction of X-scan andPublication : SPIE Proc. Practical Holography XX: Materials and Applications, SPIE#6136, San Jose, 347–354(2006).

L aP ris msioer Dd e

L a se r B e a m
6 3 2 n m
Z -S ta g e
O b je c tiv e L e n sZ

Y -S ta g e
YX

A C
S e rv oM o to r

F ilm

D ru mFigure 2. Optics of the fringe printer.

L a s e r D io d eP ris m

A C S e rv o m o to r

O b je c tiv e L e n s

P ris mZ -S ta g e

S h a ft B e a rin g

D ru mY -S ta g e

Figure 3. Photographs of the constructed fringe printer.

3Publication : SPIE Proc. Practical Holography XX: Materials and Applications, SPIE#6136, San Jose, 347–354(2006).

L D

Y -S ta g e

4

L D D riv e r

A C S e rv o m o to r
VS ta g e
C o n tro lle r
R S -2 3 2 CP CZ -P h a seT rig g e r
M o to r
D riv e r

D ru mC lo c k
D /A
C o n v e rte r

M o tio n
C o n tro lle ro u t

S in g le -S h o t
P u ls e

P u ls e
G e n e ra to r
C -M O S S W

P C I B u s
Figure 4. The block diagram of control system.

3.0 µm in the direction of Y-scan. As a result, the resolution of the printer is estimated to be approximately
17,000 dpi × 8,500 dpi.

3.2. Precision of dot positions
Precision of dot positions in the direction of Y-scan is given by that of the Y-stage, while precision in the directionof X-scan is aﬀected by several factors such as jitter of encoder signals or unevenness of rotational speed of theAC servomotor. Fig. 6 shows the photomicrograph of some lines of printed dot string in the X direction. Theinterval in the X direction is 2 µm again.
Fluctuation of dot positions in X-scan is approximately 1 µm at the starting point of the scan, while it reaches
approximately 5 µm at the end of the scan. The former ﬂuctuation is attributed to jitter of the encoder signal.
The latter ﬂuctuation is larger than that of the former and most likely caused by ﬂuctuation of the rotational
speed of the servomotor.

3.3. Eccentricity of rotation of the drum
Any mechanism for automatic focus adjustment is not installed in this fringe printer at this stage. Therefore,
eccentricity of rotation of the drum directly leads to focus error. As shown in Fig. 7, an overhung drum andprecision shaft bearing designed to keep eccentricity to minimum are adopted in this printer. Values of eccentricity

2 [m m ]Figure 5. The photomicrograph of a dot string. Dots are printed at an interval of 2 µm. The speed of rotation is 2 rps(220 m/s).

Publication : SPIE Proc. Practical Holography XX: Materials and Applications, SPIE#6136, San Jose, 347–354(2006).

1 [m m ]55 [m m ]1 0 [m m ]1 0 [m m ]S ta rtE n d

R u n n in g

Figure 6. The photomicrograph of some lines of dot strings in the direction of X-scan. The speed of rotation is 2 rps(220 m/s).

S h a ft b e a rin g
R e d u c tio n g e a rs
S e rv o m o to r

D ru m
1 2 0 m m
3 5 m m) S id e v ie w

* + P o s itio n S e n s o r

Figure 7. Structure of the overhung drum. Eccentricity of the drum was measured around points of (A)–(C).

Publication : SPIE Proc. Practical Holography XX: Materials and Applications, SPIE#6136, San Jose, 347–354(2006).

tn (A)em
2.3 [µm]
ecal
psi
D

Angle of rotation [a.u.]

(B)

(C)

4.2 [µm]

Angle of rotation [a.u.]

67.2 [µm]Angle of Rotation [a.u.]

Figure 8. Eccentricity measured by eddy-current position sensor around points of (A)–(C) shown in Fig. 7

at the several distances from the bearing were measured by an eddy-current position-sensor, installed right under
the drum. Fig. 8 shows displacement of the drum surface in rotating the drum. It is conﬁrmed that measured
eccentricity are not lager than the depth of focus (∼ 10 µm) in any position along the rotation axis.

3.4. Printing a test patternFig. 9 (b) is the photomicrograph of a printed test pattern, whose original image is shown in Fig. 9 (a). This
test pattern with 480 × 200 multi-gray level pixels was printed in pitches of 1.5 × 3.0 µm. It is veriﬁed by thisphotograph that the multi-gray level image is successfully drawn by the constructed fringe printer.

4. RECONSTRUCTION OF PRINTED HOLOGRAMSFringe patterns of computer-generated holograms (CGH) were calculated and printed by the constructed fringe
printer to verify its optical reconstruction. Table 1 shows the common parameters used for calculating andprinting holograms.
Fig. 10 is optical reconstruction of the wire frame of a globe. The wire frame is composed by point sources oflight in a density of 5,000 point/m. The fringe pattern with 16384 × 8192 sampling points (pixels) was printed
in 1 hour and 9 minutes.

(a)

(b)

100[µm]Figure 9. The photomicrograph of a test pattern (b) and its original image (a).

Publication : SPIE Proc. Practical Holography XX: Materials and Applications, SPIE#6136, San Jose, 347–354(2006).

7

Table 1. Parameters and methods used for calculating and printing holograms.

Pixel size

1.5 µm × 3.0 µmReconstruction wavelength632.8 nmObject position from hologram

100 mmDensity of point sources

5,000 points/m (wire frame)
10,000 points/m (surface)Calculation of spherical waves

Recurrence formula1

CodingPoint oriented coding

1 4 [m m ]Figure 10. Optical reconstruction of the wire frame of a globe.

Fig. 11 is for a hexadecimal prism in the wire frame model again. This hologram consists of 32768 × 16384
pixels, and its dimension is approximately 50 mm square. The fringe printer ﬁnish printing the hologram in 2 h24 m.
In the hologram shown above the object is a simple wire frame, i.e. spherical waves emitted from point
sources placed along the wire frame are calculated and simply superimposed on the hologram plane. Fig. 12 also
shows optical reconstruction of printed holograms but its object wave was numerically synthesized by anotheralgorism. Objects of the hologram in Fig. 12 is composed of small planar surfaces, i.e. polygons. Furthermore,
the hidden surfaces is removed by using the method of silhouette approximation.9 The hologram consist of
16384 × 8192 pixels in Fig. 12 (a), while 32768 × 16384 pixels in (b).

5. CONCLUSION
We developed a printer system to print fringe patterns of digitally synthetic hologram, i.e. computer-generatedholograms. The fringe pattern is printed on a photosensitive ﬁlm pasted on a drum. Rotation of the drum
provides raster-scan of laser spot. Optics of the fringe printer is simple and inexpensive, and therefore, a highresolution can be obtained easily. The constructed fringe printer actually reaches approximately 17,000 dpi ×8,500 dpi in resolution and is capable of printing a gray-level hologram of 5 cm square in 2 h 24 m.

ACKNOWLEDGMENTS
This work was partly supported by JSPS Grant-in-Aid for Scientiﬁc Research (15300025). Authors would liketo give special thanks to M. Inoue for assistance in fabricating holograms and Y. Oshima for calculating fringe
patterns.

Publication : SPIE Proc. Practical Holography XX: Materials and Applications, SPIE#6136, San Jose, 347–354(2006).

8(a )1 4 [m m ](b )2 5 [m m ]2 0 [m m ]Figure 11. Optical reconstruction of the wire frameof a hexagonal prism.

Figure 12. Optical reconstruction of surface-modeledspirals. The hologram is printed in 16384 × 8192 pixels(a) and 32768 × 16384 pixels (b).

REFERENCES
1. K. Matsushima and M. Takai, “Recurrence formulas for fast creation of synthetic three-dimensional holograms,” Appl. Opt. 39, pp. 6587–6594, 2000.
2. K. Matsushima, “Computer-generated holograms for three-dimensional surface objects with shade and texture,” Appl. Opt. 44, pp. 4607–4614, 2005.
3. T. H. M. Kitamura, “Computer-generated holograms for multilevel 3d images with complex amplitude modulation,” SPIE Proc. Practical Holography XVI and Holographic Materials VIII #4659, pp. 196–204, 2002.
4. Y. Sakamoto, M. Morishima, and A. Usui, “Computer-generated holograms on a CD-R disk,” SPIE Proc.
Practical Holography XVIII: Materials and Applications #5290, pp. 42–49, 2004.
5. H. Yoshikawa and K. Takei, “Development compact direct fringe printer for computer-generated holograms,”
SPIE Proc. Practical Holography XVIII and Holographic Materials X #5290, pp. 114–121, 2004.
6. H. Yoshikawa and M. Tachinami, “Development compact direct fringe printer for computer-generated holograms,” SPIE Proc. Practical Holography XIX: Materials and Applications #5742, pp. 259–266, 2005.
7. K. Matsushima and A. Joko, “High-resolution printer for fabricating computer-generated display holograms(in Japanese),” J. of the Institute of Image Information and Television Engineers 56, pp. 1989–1994, 2002.
8. S. Yamanaka and K. Matsushima, “A new high-resolution printer for digitally synthetic holograms (inJapanese),” J. of the Institute of Image Information and Television Engineers 58, pp. 1665–1668, 2004.
9. K. Matsushima and A. Kondoh, “A wave optical algorithm for hidden-surface removal in digitally synthetic
full-parallax holograms for three-dimensional objects,” SPIE Proc. Practical Holography XVIII #5290, p. 90,
2004.