Anamorphic holographic lenses composed by two volume holographic elements

Abstract

We design and construct anamorphic holographic lenses composed by two volume holographic elements. We study their efficiency and their capability to perform the multi-channel Fourier transformation. We test the behavior of an anamorphic optical processor constructed with these holographic lenses.

Full text

Anamorphic holographic lenses composed by two volume holographic
elements
M. V. Collados, J. Atencia, J. Tornos and M. Quintanilla
Departamento de FIsica Aplicada-13A, Universidad de Zaragoza, Facultad de Ciencias,
Pedro Cerbuna 12, 50009 Zaragoza, Spain
atencia@unizar.es
ABSTRACT
We design and construct anamorphic holographic lenses composed by two volume holographic elements. We study their
efficiency and their capability to perform the multi-channel Fourier transformation. We test the behaviour of an
anamorphic optical processor constructed with these holographic lenses.
Keywords: anamorphic holographic lenses, optical processing.
1. INTRODUCTION
A holographic lens is a special type of diffractive optical element generated by the holographic recording of the
interference of light wavefronts. Holographic lenses are thinner and lighter than conventional refractive optics. Their
construction can be accomplished in a conventional holography laboratory and can be adapted for specific uses with
great accuracy.
To obtain high efficiency lenses it is necessary to record volume holograms which are biaxial elements with different
input and output optical axes. These elements present poor aberration performing. To solve this problem we design and
construct compound uniaxial holographic lenses, which exhibits smaller aberration than biaxial elements but keep high
efficiency [1]. In that case we used spherical and plane wavefronts to record the elements, so the compound lens behaved
like spherical lenses.
In the present work we apply the previous design to construct anamorphic lenses. In this case we use plane and spherical
wavefronts or plane and cylindrical wavefronts to record the elements. This kind of lenses, like other types of diffractive
elements [2], can be included in the design of optical anamorphic processors which can be applied to local pattern
recognition [3], speckle metrology and velocimetry [4], readout optical systems [5] or hologram memories [6]. We
construct an anamorphic optical processor with anamorphic compound holographic lenses which performs multi-channel
Fourier transformation.
2. CONSTRUCTION OF ANAMORPHIC LENSES
We construct anamorphic lenses by joining two holographic elements: a biaxial lens registered with plane and spherical
wavefronts and a biaxial lens registered with plane and cylindrical wavefronts (figure 1). Both elements are phase
volume holograms, which guarantees high efficiency. We place the focal line ofthe cylindrical wavefront perpendicular
to the register plane z (the plane formed by the propagating directions of the recording beams). By joining these
elements, as shown in figure 1, we obtain an uniaxial anamorphic lens withf, =2f, beingf, andf the focal distances in
liz plane and z planerespectively.
We record the lenses with an He-Ne laser (632.8 nm) in Slavich PFG-O1 plates. The plates are processed with an
optimised silver halide sensitised gelatin method [7] which lets us obtain high efficiencies without displacements of the
efficiency maximum direction after processing. The cylindrical wavefront for the recording is provided by a refractive
cylindrical lens with a focal distance of 100 mm. Although a cylindrical wavefront do not have a symmetry axis, we refer
to these lenses as biaxial lenses.
The recording parameters shown in figure 1 are: r1 = r2 = -200 mm, a = 30°; r1 and r2 arethe distances from the origin of
cylindrical or spherical wavefront to the centre of the plate and a is the interbeam angle. In this way the final anamorphic
compound lens have focal distancesf 2f =200 mm.
The zero-order efficiency of biaxial cylindrical lens is shown in figure 2. We also show the transmittance curve of glass
substrate. By comparing these curves we can obtain the first order efficiency. As we can see in figure 2, there is a highly
5th Iberoamerican Meeting on Optics and 8th Latin American Meeting on Optics, Lasers,
and Their Applications, edited by A. Marcano O., J. L.Paz, Proc. of SPIE Vol. 5622
(SPIE, Bellingham, WA, 2004) · 0277-786X/04/$15 · doi: 10.1117/12.591654
1365

efficient second harmonic grating due to non-linear effects (corresponding to B and B' minima). This second harmonic
grating does not affect the behaviour of the final compound lens as we will see in the following sections. The efficiency
curve for the spherical lens is similar, so it is not shown here.
We present in table 1 the mean values of maximum efficiency and angular selectivity of several cylindrical biaxial lenses
and spherical biaxial lenses. The differences on diffraction efficiency and angular selectivity of the same type of lenses
are due to the fact that it is difficult to keep the same development conditions in each exposition. In figure 3 the first
order efficiency of the compound anamorphic lens is shown. The maximum efficiency is around 60%, according to the
values of efficiency of each lens separately.
+ rotation
around 17
Figure 1 : Recording andreconstruction geometry ofthe compound lens.
C2 Z
0.8
0.6
111
0.4
0.2o±-30 -20 -10 010
iiridenceang1e()
20 30
Figure 2: Zero order efficiency and glass transmittance as a
function of incidence angle of a cylindrical lens. Figure 3 : First order efficiency of a compound anamorphic
lens.
emulsion
-80 -60 -40 -20 020 40 60 80
iirid.encecng1e()
1366 Proc. of SPIE Vol. 5622

spherical lens Maximum efficiency (%)
79 5 Angular selectivity (°)
10.6 0.8
cylindrical lens 77 5 10.1 0.3
Table 1 : Angular selectivity and maximum efficiency values for spherical and cylindrical lenses.
3. MULTI-CHANNEL FOURIER TRANSFORMATION AND ANAMORPHIC PROCESSING WITH
HOLOGRAPHIC LENSES
We study the suitability of holographic anamorphic lenses constructed in the previous section to implement an optical
anamorphic processor. First we study the behaviour of the lenses to perform the multi-channel Fourier transformation.
We use a transparent periodic object illuminated with a plane wave from an He-Ne laser. The object consist in four
bands of 1 .5 mm width, each one with a binary transmittance pattern of different spatial frequencies ( around 4, 6, 8 and
16 lines/mm), as the one shows in figure 4. We place the object at a distance of -200 mm from the anamorphic lens, so
the lens performs the Fourier transform of the object in ijdirection and forms image in direction at a distance of 200
mm. This process correspond to the left part ofscheme at figure 6.
Figure 5 shows the Fourier plane captured with a CCD array when we use a pupil size of 0=20 mm on the lens plane.
We check that the same result is obtained if we rotate the lens 180° around the ijaxis, incising on the other side of the
lens. As we can see in figure 5, the contrast of the image is not diminished by the zero-order light or other diffraction
orders (minima B and B' offigure 2).
To perform the inverse Fourier transform we place an anamorphic holographic lens similar to the former (right part of
figure 6). The entire pupil of this lens (around 40 mm) is used to avoid vigneting on the image. The processor is similar
to 4f configuration in ij direction but it performs the image twice in direction. In both directions the processor operates
with unity magnification. To illustrate a simple one-dimensional spatial filtering we use as object a grating of
continuously variable frequency in i direction, from 7 lines/mm to 14 lines/mm approximately. Figure 7a shows the
image plane at processor output captured by a CCD array. In figure 7b we show the Fourier plane, in which we have the
Fourier transform ofthe object in ij direction and image in c direction. As the lens performs a Fourier transform only in
one direction, we can manipulate the frequencies in different ways along the direction with a simple filter.
In figure 8a we show the image ofthis object at the image plane when we place the V-shaped transmittance filter shown
in figure 8b at Fourier plane. With this filter, we eliminate information of left side of image, double the frequencies of
central part of image and let whole the information on right part.
Yo -' :::====
(mm) .%%%%%%%%%%%%%%%%%%%%%%%%%%%%'%':: :: : :
2.
.———
I I I
036 X() XF 6
(—
Figure 4: Part of the test to perform the multi-channel Fourier Figure 5: Multi channel Fourier transformation
transform of frequencies around 4 lines/mm, 6 lines/mm, performed by a compound anamorphic lens.
8 lines/mm and 16 lines/mm.
YF
(mm)
2
0
30
Proc. of SPIE Vol. 5622 1367

LENS I LENS2
x1
z
f,,=2f f,=21
Figure 6: Arrangement to form the multi-channel Fourier transform and perform the image of the object plane
y1
(mm)
9
(mm)
b
' YF(mm)
-1.8
-o
Figure 7: (a) Image of a continuously variable frequency
object in the image plane of the processor of figure 6, limited
by the CCD size, (b) Fourier transform of the object captured
at the Fourier plane of the processor of figure 6.
Figure 8: (a) Image of the object of continuously variable
frequency, limited by the CCD, obtained in the image plane of
processor of figure 6 when we place the V-shaped filter of
figure 8(b) on Fourier plane.
9xi(mm) 0-
1-
2-
3.
4
Xp*i I
(mm) 6(b) 0XF I
(mm) 6(b)
. -1.8
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4. CONCLUSIONS
We construct uniaxial anamorphic holographic lenses composed of two biaxial holographic elements, applying the
design of compound lenses presented in previous works [1]. We have characterized the lenses by measuring the zero
order efficiency. The lenses have been made with focal distances f =2f,to construct an anamorphic optical processor
with two lenses, working on axis and with unity magnification in both directions. We show that these lenses perform
properly the onedimensional multi-channel Fourier transform. We also show an example of image formation and spatial
filtering in the Fourier plane with the anamorphic processor.
5. ACKNOWLEDGEMENTS
This research was supported by the DiputaciOn General de Aragón (G.I.A. 2002, Holografia y Metrologla Opticas) and
by Comisión Interministerial de Ciencia y TecnologIa Programa Nacional de Materiales (Spain) under grant MAT2002-
041 18-C02-02.
REFERENCES
1 . J. Atencia and M. Quintanilla, "Ray tracing for holographic optical element recording with non-spherical waves",
J. Opt. A: Pure App!. Opt. 3, 387-397 (2001).
2. P. Liang, J. Ding, Z. Jin, G. Wenqi, "Composite binary optical elements used for multi-channel spectrum analysis",
IofMod Opt. 50, 141 1-1417 (2003).
3. LU. Almi and J. Shamir, "Pattern recognition using one-dimensional Fourier transformation", Opt. Comm. 18, 304-
306 (1976).
4. S. H. Collicott and L. Hesselink, "Analysis and design of an anamorphic optical processor for speckle metrology and
velocimetry", App!. Opt. 31, 1646-1659 (1992).
5. P. J. Marchand, P. C. Harvey, and S. C. Esener, "Motionless-head parallel-readout optical-disk system: experimental
results", App!. Opt. 34, 7604-7607 (1995).
6. K. Kubota, M. Kondo, S. Sugama and S. Takahashi, "Hologram memory using one-dimensional Fouried-transformed
image hologram", E!ectronics and Communications in Japan 61-C, 108114 (1978).
7. M. V. Collados, I. Arias, A. Garcia, J. Atencia and M. Quintanilla, "Silver Halide sensitised gelatin process effects in
holographic lenses recorded on Slavich PFG-01 plates". App!. Opt. 42, 805-8 10 (2003).
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