Kinoform syntesis as an improved method to form a concealed image in optical security devices
It is well known that one of the basic functions of security holograms is the maximal complication of their non-authorized reproduction, in other words – counterfeiting. To solve the problem, concealed images that can be observed only under special conditions are placed into a structure of the holog...
Gespeichert in:
| Datum: | 2006 |
|---|---|
| Hauptverfasser: | , , , , , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2006
|
| Schriftenreihe: | Semiconductor Physics Quantum Electronics & Optoelectronics |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/121642 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Kinoform syntesis as an improved method to form a concealed image in optical security devices / E.V. Braginets, V.I. Girnyk, S.A. Kostyukevych, V.N. Kurashov, N. Moskalenko, A.A. Soroka // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2006. — Т. 9, № 4. — С. 85-90. — Бібліогр.: 19 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-121642 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1216422017-06-16T03:03:06Z Kinoform syntesis as an improved method to form a concealed image in optical security devices Braginets, E.V. Girnyk, V.I. Kostyukevych, S.A. Kurashov, V.N. Soroka, A.A. Moskalenko, N. It is well known that one of the basic functions of security holograms is the maximal complication of their non-authorized reproduction, in other words – counterfeiting. To solve the problem, concealed images that can be observed only under special conditions are placed into a structure of the hologram. A popular way to place concealed image in Diffractive Optically Variable Image Device (DOVID) is integration into DOVID's structure of a Concealed Laser-Readable Image (CLRI). Traditionally CLRI is a 2D Computer-Generated Hologram (2D CGH), which is a digitized Interference Fringe Data (IFD) structure, computed under the scheme of Fourier-hologram synthesis. Such hologram provides inspection of the second level with portable laser reading devices. While it is being read, two (+/– 1 order of diffraction) identical images are formed. It is very interesting to achieve a CGH, which restores the image only in one diffractive order or two different images in +1 and –1 orders of diffraction. 2006 Article Kinoform syntesis as an improved method to form a concealed image in optical security devices / E.V. Braginets, V.I. Girnyk, S.A. Kostyukevych, V.N. Kurashov, N. Moskalenko, A.A. Soroka // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2006. — Т. 9, № 4. — С. 85-90. — Бібліогр.: 19 назв. — англ. 1560-8034 PACS 42.40.Jv http://dspace.nbuv.gov.ua/handle/123456789/121642 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
It is well known that one of the basic functions of security holograms is the maximal complication of their non-authorized reproduction, in other words – counterfeiting. To solve the problem, concealed images that can be observed only under special conditions are placed into a structure of the hologram. A popular way to place concealed image in Diffractive Optically Variable Image Device (DOVID) is integration into DOVID's structure of a Concealed Laser-Readable Image (CLRI). Traditionally CLRI is a 2D Computer-Generated Hologram (2D CGH), which is a digitized Interference Fringe Data (IFD) structure, computed under the scheme of Fourier-hologram synthesis. Such hologram provides inspection of the second level with portable laser reading devices. While it is being read, two (+/– 1 order of diffraction) identical images are formed. It is very interesting to achieve a CGH, which restores the image only in one diffractive order or two different images in +1 and –1 orders of diffraction. |
| format |
Article |
| author |
Braginets, E.V. Girnyk, V.I. Kostyukevych, S.A. Kurashov, V.N. Soroka, A.A. Moskalenko, N. |
| spellingShingle |
Braginets, E.V. Girnyk, V.I. Kostyukevych, S.A. Kurashov, V.N. Soroka, A.A. Moskalenko, N. Kinoform syntesis as an improved method to form a concealed image in optical security devices Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Braginets, E.V. Girnyk, V.I. Kostyukevych, S.A. Kurashov, V.N. Soroka, A.A. Moskalenko, N. |
| author_sort |
Braginets, E.V. |
| title |
Kinoform syntesis as an improved method to form a concealed image in optical security devices |
| title_short |
Kinoform syntesis as an improved method to form a concealed image in optical security devices |
| title_full |
Kinoform syntesis as an improved method to form a concealed image in optical security devices |
| title_fullStr |
Kinoform syntesis as an improved method to form a concealed image in optical security devices |
| title_full_unstemmed |
Kinoform syntesis as an improved method to form a concealed image in optical security devices |
| title_sort |
kinoform syntesis as an improved method to form a concealed image in optical security devices |
| publisher |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| publishDate |
2006 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/121642 |
| citation_txt |
Kinoform syntesis as an improved method to form a concealed image in optical security devices / E.V. Braginets, V.I. Girnyk, S.A. Kostyukevych, V.N. Kurashov, N. Moskalenko, A.A. Soroka // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2006. — Т. 9, № 4. — С. 85-90. — Бібліогр.: 19 назв. — англ. |
| series |
Semiconductor Physics Quantum Electronics & Optoelectronics |
| work_keys_str_mv |
AT braginetsev kinoformsyntesisasanimprovedmethodtoformaconcealedimageinopticalsecuritydevices AT girnykvi kinoformsyntesisasanimprovedmethodtoformaconcealedimageinopticalsecuritydevices AT kostyukevychsa kinoformsyntesisasanimprovedmethodtoformaconcealedimageinopticalsecuritydevices AT kurashovvn kinoformsyntesisasanimprovedmethodtoformaconcealedimageinopticalsecuritydevices AT sorokaaa kinoformsyntesisasanimprovedmethodtoformaconcealedimageinopticalsecuritydevices AT moskalenkon kinoformsyntesisasanimprovedmethodtoformaconcealedimageinopticalsecuritydevices |
| first_indexed |
2025-07-08T20:16:06Z |
| last_indexed |
2025-07-08T20:16:06Z |
| _version_ |
1837111200690733056 |
| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2006. V. 9, N 4. P. 85-90.
© 2006, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
85
PACS 42.40.Jv
Kinoform synthesis as an improved method
to form a concealed image in optical security devices
Eu. Braginets1, V. Girnyk2, S. Kostyukevych3, V. Kurashov1, N. Moskalenko3, A. Soroka1
1Taras Shevchenko Kyiv National University (Ukraine)
2Optronics (Ukraine)
3V. Lashkaryov Institute of Semiconductor Physics, NAS of Ukraine (Ukraine)
Abstract. It is well known that one of the basic functions of security holograms is the
maximal complication of their non-authorized reproduction, in other words –
counterfeiting. To solve the problem, concealed images that can be observed only under
special conditions are placed into a structure of the hologram. A popular way to place
concealed image in Diffractive Optically Variable Image Device (DOVID) is integration
into DOVID's structure of a Concealed Laser-Readable Image (CLRI). Traditionally
CLRI is a 2D Computer-Generated Hologram (2D CGH), which is a digitized
Interference Fringe Data (IFD) structure, computed under the scheme of Fourier-
hologram synthesis. Such hologram provides inspection of the second level with portable
laser reading devices. While it is being read, two (+/– 1 order of diffraction) identical
images are formed. It is very interesting to achieve a CGH, which restores the image only
in one diffractive order or two different images in +1 and –1 orders of diffraction.
Keywords: concealed image, kinoform methods, 2D CGH, CLR.
Manuscript received 20.09.06; accepted for publication 23.10.06.
1. Introduction
Computer generated Fourier holograms (Fourier CGH)
are widely used for the concealed image recording in
holographic protective elements. Decoding of such
holograms is realized in an optical way with use of
coherent decoders. It allows to strengthen a resistance of
protective elements to forgery and increase an object-
tivity of their identification procedure.
Generally, a problem of synthesis and Fourier
spectrum recording comes to calculation of A(ξ,η)
function in the frequency plane by specified distribution
of complex amplitudes a (x, y) in the coordinate area and
to record the received distribution of complex wave field
on a real physical carrier.
A ∫ ∫
∞
∞−
ηξ=ηξ dxdyyixiyx )π2exp()π2exp(),(),( a , (1)
where a )),(exp(),(),( yxiyxayx ϕ= .
One of the main problems, which we face with
when recording Fourier holograms, is a recording of
complex value.
There are two in principle different ways to solve
this problem, namely: use of various methods to encode
the Fourier spectrum, which allows to proceed from the
complex quantity of field distribution in a hologram
registration plane to the real quantity [1-3]. The methods
in which the phase is encoded by means of space carrier,
is of the largest interest. They combine more naturally
with modern recording devices. We call this the
holographic methods optimized for digital synthesis. The
second way is direct recording the Fourier spectrum on
double-layer amplitude-phase registering media [4-5].
This method is technologically possible, but it is not
acceptable for integration of such structures into the
holographic protective elements. However, it is possible
its cut-down version when in the computed Fourier
spectrum the amplitude is forcibly assumed to be equal
to a constant and phase recording is realized, for
example, by phase modulation of a geometric relief of
the recording medium.
This method was called as a kinoform by creators.
Kinoform transmission can be recorded in the following
form:
]},[exp{const],[ srisrA ϕ⋅= (2)
where π≤ϕ≤ 2],[0 sr along all plane [r,s].
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2006. V. 9, N 4. P. 85-90.
© 2006, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
86
It is necessary to mention that digital Fourier
holograms are flat and act as a flat 2D diffraction
grating. Thus, they restore two diffraction orders – two
conjugated images. It applies restriction on the recorded
object – the function a (x, y) must satisfy the causality
condition and turn into zero at x < 0:
a 0)),(exp(),(),( =ϕ= yxiyxayx at х < 0. (3)
Otherwise, mutual overlay of the real and
conjugated images will occur.
Studied in this work is the possibility to enlarge
opportunities of synthesis and recording the digital
Fourier spectra removing restrictions connected with the
causality condition.
From the practical standpoint, it will allow to
increase the resistance of the hologram to falsification
(synthesis algorithm changes, demands to the
technological process and materials are increased), to
increase the intensity of the image restored (owing to
energy re-distribution) and to enlarge the possibilities for
design solutions (owing to removing the restrictions (3)).
Below we examine two approaches for solution of
this problem: use of quadrature holograms and kinoform
methods of encoding.
2. Use of quadrature holograms for elimination of
conjugated images
When recording a traditional Fourier hologram on
registering medium in accordance with a computed
interference fringe data (IFD) an intensity distribution is
recorded [7]
( ) ))cos(1(2)exp(1 0
2
0 xxixΙ ω+=ω−+= . (4)
When restoring this interferogram with a plane
wave falling normally, two images of the object appear –
a conjugated image and a real one. The physical reason
of twin-image appearance is explained by the fact that
such hologram has no information about the direction
from which the object wave felt on the hologram (in
contrast, for example, to Denisyuk thick-layer hologram
where the direction of wave propagation is
unambiguously registered in the medium).
From the mathematical point of view, appearance
of two conjugated waves at the stage of hologram
restoring (instead of one wave when recording) is
explained by cos(ωx) function parity that is integral part
of the registered value. Fig. 1 shows the recording of the
point-like light source (PLS) object hologram in the
Leith scheme. k is the wave vector of the object wave
and k0 is the wave vector of the reference wave. It is not
possible to determine a growth direction of complex
components ехр(+іω0x) and ехр(–іω0x), IFD for cases of
the object wave falling at θ and –θ angles will be the
same.
Fig. 1. Scheme of elementary Leith hologram recording. k0 is
the wave vector of the reference wave, k is the wave vector of
the object wave, І (x) is the distribution of the light intensity in
the hologram registration plane.
It is logically to suppose that, if to insert an optical
element in this recording scheme, which would shift a
phase of the reference wave by π/2 radian, the same
hologram of PLS contained already the sine (odd)
function.
Such a hologram, where intensity distribution is
described by sin(ω0x) function, is called a quadrature
hologram. The diagram of recording of a primitive
quadrature hologram according to the Leith scheme is
shown in Fig. 2. Intensity distribution in this hologram is
described by the following expression (5)
))sin(1(2)exp()2/exp()( 0
2
0 xxiixI ω+=ω±+π= .
(5)
Fig. 2. Scheme of 2D quadrature hologram recording. A phase
plate shifting wavefront phase on π/2 is placed in the reference
beam. In the upper picture the reference wave falls at +θ
angle, in the lower one – at –θ angle. An appearance of the
interference pattern depends on that, from which direction the
reference wave comes.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2006. V. 9, N 4. P. 85-90.
© 2006, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
87
Eq. (5) shows that in any point with x = 0, cor-
responding to the intensity maximum in the traditional
hologram, the intensity in quadrature hologram will
increase or fall depending on that, at which positive or
negative angle the object wave falls on the hologram. To
restore both holograms [8-10] (traditional or quadrature)
are used, the wave phase restored by the quadrature
hologram must be additionally shifted on λ/4, thus, the
total wave field will be as follows:
).exp()1(
)sin1()cos1()(
0
00
xi
xixxur
ω±++=
=ω±+ω+=
(6)
As indicated in (6), when restoring, only one
diffraction order remains. Combination of the traditional
and quadrature holograms allows to register different
intensity distribution in hologram plane depending on
mutual source location of the object and reference waves.
Below you can see a computer algorithm flowchart
for computation of such combined hologram (Fig. 3) and
the results of the computer modelling (Fig. 4).
Fig. 3. Algorithm of computation and modelling of restoring of
the combined hologram.
Fig. 4. Screen shot of the program on modelling restoration of
the combined hologram. As object, words “FOURIER” and
“GILBERT” in opposite semiplanes (left top figure) were
used. The Fourier-interferogram with diffuser is shown in the
top right image. Mathematically restored image shown in the
left bottom figure (we can see two overplaced images), in the
right bottom figure – image restored from the combined
hologram (one order is restored only, overplacing is absent).
3. Use kinoform methods for twin-image elimination
As was mentioned above, the kinoform [6, 11, 12]
represents a special type of a thin-layer hologram, where
a complex amplitude of an object light wave a (x, y) =
= A (x, y) × exp [iϕ (x, y)] in the plane of hologram
registration is almost constant on the module. In practice
this situation takes place, when object has a diffused
surface, or lighted with a diffused light or diffuser is
installed on the way of object wave propagation. In such
cases, the image of the object can be restored with use of
the phase information φ(x, y) only.
3.1. Synthesis of the kinoform
Synthesis of the kinoform was carried out according to
the scheme of calculation of the Fourier-hologram. The
object was defined in the object plane as a set of point
light sources. Then, after the Fourier transformation, a
mathematical analogue of the object wave in the
hologram plane was calculated. As a basic assumption, a
constancy of the module complex amplitude of the
object wave )],(exp[const),( yxiyx ϕΔ⋅=a was made,
in addition for minimization losses related with rejection
of the amplitude information in the algorithm of
calculations a block of diffuser optimization was added.
After calculation of the phase difference between object
and reference waves in every point (х, y) of the
hologram plane, the result was normalized in such a
manner that the phase function (x, y) varies within 0-2π.
As a result, we obtained 2D array consisting of phase
discrete values
...,2,1,0,2)1(2
,2)2(mod
)7(,),()2(mod),(~
=π+≤ϕ≤π
π−ϕ=πϕ
Δ−Δ−δπϕ=ϕ ∑ ∑
−= −=
jjj
j
ymyxnxyx
nm
N
Nn
M
Mm
nm
The obtained array of phase values was used for
kinoform recording on the phase recording medium.
The quality of the image restored from the
kinoform mainly depends on two factors – value
constancies of the module in the complex amplitude
object wave and a performance of a condition of the
phase coordination (2). The performance of a condition
of the phase matching depends on accuracy of the
transfer of calculated discrete values of the phase on the
recording medium. The constancy of the amplitude value
of the field in the plane of registration is provided owing
to the insertion of the object diffuser. As a first
approximation, the diffuser represents an array with
random values of a phase (from 0 up to 2π).
This object-independent diffuser provides a rather
constant object wave amplitude value in the field of the
hologram registration, allows to obtain the value of SNR
about 20 for the restored image. However, the granular
structure of the image and a speсkle around of the image
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2006. V. 9, N 4. P. 85-90.
© 2006, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
88
remains. To eliminate these phenomena an algorithm of
diffuser optimization was applied.
For the first time, this algorithm was described in
[13, 14], where it is called an iterative algorithm of
diffuser optimization. An essence of this algorithm is in
the following: in the iterative cycle the initial array of
the amplitude and phase values, which describes object
is multiplied by the set of random values of the phase
(diffuser).
The Fourier transform from the object (actually,
mathematically restored image) is calculated. Then SNR
at this step of iteration is calculated. The value of SNR is
saved, then, after it, the next iteration step is made. If
after the next iteration, SNR value is higher than the
saved one, value of a phase diffuser in the given point is
accepted corresponding to maximal SNR. The iterative
cycle repeats itself or given number of times (or till
achievement of the given SNR value). As a result SNR
value was increased up to 30.
With the purpose to get more constant values of the
amplitude complex field in the hologram plane, we
proposed to supplement this algorithm with an additional
emphasis of the object amplitude [15-19].
3.2. Mathematical modelling of image restoring
processes
A direct analysis of total influence of all CGH's
parameters (parameters of the calculated IFD, para-
meters of e-beam litography, modes of electronic- and
photoresists developing etc.) is extremely difficult and
impossible in most cases.
The method of numerical modelling allows to
bypass this difficulty and with use of a quite simple
methods to receive exact quantitative results at any
intermediate stage of holographic process.
A characteristic full enough for phase recording
medium is a transmission function that can be presented
as follows:
)]}],([),({exp[),( 0 μξΔψΔ+ηξψ=ηξ Egitt n . (8)
For existing phase recording medium (electronic
resist) it is possible to consider amplitude t0 as a
constant, phase variation Ψn(ξ, η) caused by
heterogeneity of a substrate causes only a slight
alteration of the diffraction angle for the restoring beam,
forming a low-frequency component of noise. A
component ΔΨ[ΔEg(ζ,η)] depends in the complex way
on the changes of operating exposition ΔEg(ζ, η) and
can be expressed as:
ΔΨ[ΔEg(ζ, η)=
λ
π2 (n – 1) L[gEn[r, s] × h1(ζ, η) ×
× h2(ζ, η)] =
λ
π2 (n – 1) L[ΔL (ζ, η) ], (9)
where g is a constant of this material describing a level
of the dependence ΔL from ΔE; n is a factor of medium
refraction; L is the operator considering nonlinearity of
the relief-exposure characteristic; ΔL (ζ, η) – geometrical
distribution relief modulation; En [r, s] – distribution of
the imposed exposition (a calculated exposition of
resolution elements of the hologram); h1(ζ, η) – point
spread function; h2(ζ, η) – point spread function. When
numerical modeling, we can assume h(ζ, η) = h1(ζ, η) ×
× h2(ζ, η).
Parameter of modulation 2π/λ (n – 1) that describes
sensitivity of the recording medium during numerical
modelling can be replaced with a parameter of the
maximal phase shifting value Ψm, and the imposed
exposition – distribution of phase shift Ψn [r, s]. In view
of it, it is possible to write down the next expression:
)]}],(],[[{exp[),( ηξ⋅ψψψ=ηξ hsrit nm , (10)
where Ψ is the operator of transformation considering
nonlinearity of the phase-exposing characteristic.
Eq. (10) is the initial one to construct a digital model of
the system.
Result of a synthesis operation is the matrix of
numbers T [r, s] that defines phase modulation for each
element of the recorded hologram, the value of which is
represented in (10) instead of Ψn [r, s], thus Ψm Ψn [r, s]
varies from 0 up to Ψm. Taking into account that when
modeling, only numerical analysis is used, so for
performance of convolution (10), the continuous
function h(ζ, η) should be replaced with its discrete
analogue h [p, g] with the step of digitization δζ, δη,
defined according to the Nyiqist theorem. It is necessary
to note that the function h [p, g] and Т [r, s] have
the different periods of digitization δζ = δη < Δζ = Δη.
For the coordination of it, we set δζ so δζζΔ / = P,
δηηΔ / = Q, where Р and Q are integers for the counts
of the function h[p, g] inside the cell Δζ × Δη. As a
result of performance of linear convolution the new
sequence expressed below is formed:
Ψg [p, g]NP×MQ = T[r, s]N×M × h[p, g]P×Q. (11)
After execution of the operation (10), the hologram
is described by the following expression:
t[p, g] = exp[i{Ψ[Ψm Ψg [p, g]]}]. (12)
The expression (12) is a digital model of a real digi-
tal hologram registered on the phase recording medium.
When machine modelling of the recording medium and
recording device, the following parameters were set:
N = M = 64; P = Q + 8; Ψm = 0 – 6.28 rad,
h [p, g] was set by the table, its type was defined by the
type of the recording medium;
[Ψ] was set by table, its type was defined by
empiric data.
Analysis of the digital Fourier-hologram was
carried out in the following way. The hologram designed
according to (12) was lighted with normally falling flat
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2006. V. 9, N 4. P. 85-90.
© 2006, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
89
wave with the amplitude е = 1. Above the received
distribution of field amplitudes, behind the hologram
near to its plane, RFT was carried out using the FFT
algorithms, thus there was a discrete distribution of the
intensity in the plane of the restored image
g[n, m] = |F-1{t[p, g]}|2 . (13)
In view of periodicity of function g [n, m] =
= g [n + Z × P, m + Z × Q], the calculation and the
further analysis of the restored image was carried out
only for one period (Z = 0) – “zero” order of digitization
with quantity of samples NP × MQ.
For modelling the kinoform restoration processes, a
program utilizing described algorithms was written. The
block diagram of the program (Fig. 5) is shown below.
When modelling, boundary values for observation
conditions (2) were explored. To define a necessity of
condition of the phase matching, hologram restoration
with different values of c factor (c < 1, c = 1, c > 1) was
simulated. Before restoration of the image, the array of the
calculated phase values was multiplied by the factor c. At
с = 1, the phase matching condition is carried out, at c < 1
or с > 1, accordingly, it is not carried out. In Fig. 6, the
results of modelling for different c values are showed.
3.3 Kinoform recording by electron-beam litography
We used a method of electron-beam lithography for
recording the kinoform on a phase recording medium
(electron-sensitive PMMA resist).
When recording the kinoform, the use of the
methods of lithograph digitization for the continuous
function Δφ(x, y) is required. So, it is replaced by a
discrete function with the step 2π/N, where N is a
maximal possible number of levels for the phase relief in
the given recording method. Thus, the diffraction
efficiency is less than the theoretical one 100%, but with
growth of N it increases – for example, at N = 2; 3 or 10
the diffraction efficiency is equal accordingly 41; 81 and
97 %. In our case, the quantity of levels is chosen to be
equal to 16 (as a most simple way for realization).
Fig. 5. Algorithm of synthesis and modelling the restoration of
the kinoform hologram.
a) b) c)
Fig. 6. Results of modelling for factor с = 0.7 (a), с = 1 (b),
с = 1.3 (c).
Prepared in that way kinoform has the following
reflection function:
.),(
)]2(modexp[~),(
∑ ∑
−= −=
Δ−Δ−δ×
×πϕ±⎥
⎦
⎤
⎢
⎣
⎡
Δ⎥⎦
⎤
⎢⎣
⎡
Δ
N
Nn
M
Mm
ynyxnx
ic
y
y
rect
x
x
rectyxt
(14)
The sign of exponent in the exponential factor is
defined by that whether a negative or a positive image
for kinoform is used. Accordingly, the image restored by
kinoform will be real or virtual.
From consideration of the transmission function of
the kinoform, it follows that for restoration of the initial
wave front without distortions that the constant c is
required to be equaled to unity. It means that the light
falling on the hologram sample with a phase 0~ =ϕ , will
delays equally for one wavelength in comparison with the
light falling on the other sample with a phase π=ϕ 2~ . For
example, in case of the reflective hologram for a sample
with a phase π=ϕ 2~ at the wavelength λ = 630 nm, the
depth of a maximal relief modulation will be equal to λ/2,
i.e. 315 nm. If such phase matching has been achieved, all
light falling on kinoform will participate in formation of
the unique (real or imaginary) image of the object.
Otherwise, the kinoform is similar to an axial hologram,
where real and virtual images are partially superposed;
some light diffracted into zero order will create a bright
spot in the center of the image.
We preliminary recorded a series of tests to find
pulse response characteristic of the recording system to
choose optimum parameters for kinoform registration
(Fig. 7).
Fig. 7. Test structure, recorded for building the pulse-response
curve of the recording system.
Object assignment O = A(x,y)
Applying diffuser
FT
Calculating phase distribution
Phase normalization to interval [0, 2π]
Restoration image from kinoform
Diffuser optimization iterative
algorithm
Amplify preemphasis
algorithm
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2006. V. 9, N 4. P. 85-90.
© 2006, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
90
a) b) c)
Fig. 8. Restored images с = 0.7 (a), с = 1.3 (b), с = 1 (c).
Fig. 9. Surface and profile of the kinoform (obtained with
AFM ).
3.4. Analysis of results
As a result of using the described algorithms, test samples
of the kinoform (with various values of parameter c – less,
more or equal to unity) have been recorded.
Photos of the restored images (Fig. 8) and the
image of a phase relief (Fig. 9) made using an atomic
force microscope are shown below.
4. Conclusions
In this paper, a problem of twin-image elimination in 2D
digital holograms is considered. Two approaches to
solve this problem are proposed: using quadrature
holograms and kinoform methods. As shown above, use
the kinoform for this purpose allows (without essential
technology complexity of synthesis and record) to
receive required result that is shown in photos of the
images restored by recorded samples.
References
1. W.H. Lee, Sampled Fourier-transform hologram
generated by computer // Appl. Opt. 9(3), p. 639-
643 (1970).
2. W.H. Lee, Computer-generated holograms: Tech-
niques and application, Ed. E. Wolf. N.Y. // Progr.
Opt. 16, p. 119-132 (1978).
3. L.P. Jaroslavski, N.S. Merzlyakov, Comparison of
the methods of recording the computer-generated
holograms // Abstr. Symp. “Optika-80”, 1980, p. 86.
4. D.C. Chu, J.F. Fienup, J.W. Goodman, Recent
approaches to computer generated holograms //
Opt. Eng. 13, (3), p. 189-195 (1974).
5. B.R. Brown, Computer synthesis of holograms and
spatial filters // Application of holography, Ed. by
Barrekette. N.Y.; L.1971, p. 215-227.
6. I.B. Lesem, P.M. Hirch, J.A. Jordan. The kinoform
a new wave-front reconstruction device // IBM
Journal of Research and Develop. 13, 2 (1969).
7. L.M. Soroko, Gilbert-optics. M., 1981, p. 21-25.
8. D. Gabor, W. Goss, Interference microscope with
total wave-front reconstruction // J. Opt. Soc. Amer.
56, No 7, p. 849 (1966).
9. Baltiyskiy et al., Contemporary methods of digital
holography. In: Problems of coherent and
nonlinear optics, S.-Pt., 2004, p. 91-117.
10. E. Cuche, P. Marquet, Ch. Depeursinge, Spatial
filtering for zero-order and twin-image elimination
in digital off-axis holography // Applied Optics 39,
No. 23, 2000.
11. A.I. Fishman, The phase optical elements –
kinoforms // Soros Review Journal (Sorosovskij
obrazovatel'nyj zhurnal) No. 12, p. 76-83, 1999.
12. T.I. Kuznecova, About the phase problem in optics
// Uspekhi fiz. nauk 154(4), p. 677-690 (1988).
13. B. Chhetri, S. Serikawa, S. Yang, et al., Binary
phase difference diffuser: Design and application in
digital holography // Opt. Eng. 41(2), p. 319-327,
2002.
14. V.I. Girnyk, V. Kurashov, A. Makarovsky, Synthesis
of a kinoform with improved intensity transmission in
restored image. Proc. 3-rd Union School on
Holography – Riga, 1980, part II, p. 274.
15. V.I. Girnyk, V. Kurashov, A. Makarovsky, Amp-
litude preamphasis algorithm. Proc. 3-rd Union
School on Holography. – Riga, 1985, p. 315-316.
16. V. Girnyk, S. Kostyukevych, A. Kononov, I.
Borisov, Multilevel computer-generated holograms
for reconstructing 3D images in combined optical-
digital security devices // SPIE Proc. 4677, p. 255-
266, 2002.
17. V. Girnyk, S. Kostyukevych, E. Braginets, A. So-
roka, 3D CGH registration on organic and non-
organic resists: comparative analysis // SPIE Proc.
6136, p. 6136OP, 2006.
18. E.V. Braginets, V.I. Girnyk, S.A. Kostyukevych,
Computer-generated holograms of 3D images in
optical security devices // SPIE Proc. 5742, p. 33-
40, 2005.
19. V.I. Girnyk, S.O. Kostyukevich, P.Ye. Shepeliavyi,
Multilevel computer-generated holograms for
reconstructing 3-D images in combined optical-
digital security devices // Semiconductor Physics,
Quantum Electronics & Optoelectronics 5(1),
p. 106-114 (2002).
|