The Use of Holographic Optical Elements in Optical Systems Sights

Abstract

Objectives: This paper presents several variants of stable optical schemes of sight with Holographic Optical Element to solve a problem of changing direction of diffracted by it. Methods/Statistical Analysis: Optical scheme of holographic sight is presented where the transmission hologram together with mirror is working like the reflection one. Transmission hologram with mirror can be used to stabilize beam position for much bigger wavelength shift, than it is possible with reflection hologram. Findings: Results of calculations show that using of optical systems with a mutually inclined HOE and ADG allows reducing size of scheme with acceptable shift of image. Also it should be noted that the beneficial properties of reflection holograms can be realized using transmission holograms. Application/Improvements: Our results can be useful in devices with Holographic Optical Elements such as display systems and especially for development of holographic sight.

Full text

Indian Journal of Science and Technology, Vol 9(47), DOI: 10.17485/ijst/2016/v9i47/104552, December 2016
ISSN (Print) : 0974-6846
ISSN (Online) : 0974-5645
* Author for correspondence
1. Introduction
Holographic Optical Elements (HOE) are widely used in
techniques to form wave-fronts of special kind, the typical
example of such elementary HOE is Fresnel zone plate,
which in simple case collimates laser light in a point1. One
of the most famous areas of application of holograms is
developing of holographic storage devices. Holograms
are used as optical elements in the systems, which are
used for generation of wave fronts of specic types. HOE
is used in information display systems. One of practical
applications of the Holographic Optical Elements is their
usage for development of holographic sight2,3.
Holographic sight is used to generate the virtual
image of the aiming mark on the axis, which coincides
with the axis of the gun barrel and at a distance equal to
the distance to the object of sighting. e luminous sign
of the impact point located on the optical axis is the main
element of the aiming mark. e hologram of such sign is
a diraction grating - a hologram, being recorded as the
result of interference of two plane waves - plane reference
wave and plane object wave (because the displayed object
- point - is located at big distance).
Semiconductor lasers, which can signicantly reduce
weight and size of the device, are frequently used as the
light source in holographic sights. A disadvantage of these
lasers is changing of the wavelength of the emitted light, if
the ambient temperature changes. When the temperature
changes from -500С to + 500С the wavelength changes from
0.62 μm to 0.68 μm. As a result, direction of propagation
of diracted by the hologram beam is changed, causing
fails of the device operation.
In this article we will discuss ways how to stabilize
direction of the diracted by HOE beam, if the laser beam
wavelength is unstable (achromatization of the optical
circuit), as the object of study here is considered optical
circuit of the holographic sight.
In many cases HOE is recorded on media with a
certain thickness of the photosensitive layer, so it is
volume hologram. Operation principle of hologram is
based not on laws of the geometrical optics, but on laws
of diraction and interference of light and, in particular,
Abstract
Objectives: This paper presents several variants of stable optical schemes of sight with Holographic Optical Element to
solve a problem of changing direction of diffracted by it. Methods/Statistical Analysis: Optical scheme of holographic

hologram with mirror can be used to stabilize beam position for much bigger wavelength shift, than it is possible with
Findings: Results of calculations show that using of optical systems with a mutually inclined HOE and

   Application/Improvements: Our results can be
useful in devices with Holographic Optical Elements such as display systems and especially for development of holographic
sight.
Keywords: Diffraction, Holography, Holographic Sight
The Use of Holographic Optical Elements
in Optical Systems Sights
V. I. Bobrinev, Ya. A. Grad, M. S. Kovalev, P. I. Malinina*, V. V. Nikolaev,
S. B. Odinokov, A. B. Solomashenko and N. G. Stsepuro
Department of Electronics and Laser Technology, Bauman Moscow State Technical University, Moscow,
Russian Federation; vbobr2008@yandex.ru, y.gradinka@rambler.ru, m.s.kovalev@gmail.com,
pi.malinina@mail.ru, vnikolaev@hololab.ru, odinokov@bmstu.ru, art_s87@mail.ru, sng.bmstu.rl@gmail.com

Vol 9 (47) | December 2016 | www.indjst.org Indian Journal of Science and Technology
2
The Use of Holographic Optical Elements in Optical Systems Sights
light dispersion has a strong inuence on operation of
hologram.
e sight optical scheme should ensure stability of the
direction of propagation of a plane wave, diracted on
the holographic elements of the circuit and carrying the
virtual image of the aiming mark.
To solve the achromatization problem optical circuit
of holographic sight is formed using two Holographic
Optical Elements, one of them (HOE) forms a virtual
image of the aiming mark, and the second – Achromatic
Diraction Grating (ADG) is used to compensate the
image shi when the wavelength of the reading light
beam is changed from nominal value
0
λ
4.
e optical circuit of device, which can be used to
provide stabilized position of the image of the aiming
mark, is shown in Figure 1. ere ADG is achromatic
grating, HOE - Holographic Optical Element with a
recorded aiming mark hologram. e angle between
the planes of the ADG and the HOE is
ϕ
. Interference
fringes in the two holograms are directed horizontally
perpendicular to the plane of the Figure.
Figure 1. Principal optical scheme of holographic sight.
Dotted lines N1 and N2 are normal to surfaces of
holograms,
1
α
- incidence angle of the laser beam to
the ADG,
1
β
-deection angle from the normal N1 of
beam, diracted by the ADG. is beam becomes to be
the reading beam for HOE,
2
α
- incidence angle of this
beam to HOE.
2
β
- angle between the normal N2 and diracted by
the HOE beam, which is carrying the virtual image of the
aiming mark,
10 10 20 20
,,,abab
- the magnitude of these
angles at a nominal wavelength of light
0
λ
corresponding
to the center of the tuning range,
21
d,d
- period of
gratings recorded on ADG and HOE.
e achromatization condition of optical scheme is
constant value of
2
β
angle, when the wavelength of laser
beam is changed and
1
α
is constant.
Light propagation of the light beams in the optical
circuit on Figure 1 is described by diraction of light by
gratings formulas5.
111
d/sinsin λ=β+α
(1)
111 sind/sin α−λ=β
(2)
222
d/sinsin λ=β+α
(3)
222
sind/sin α−λ=β
(4)
e value of angle
2
α
is determined by considering
the triangle BCD:
21
90 90 180a bj- + + +=
 
or
ϕ+β=α 12
(5)
Corresponding to (4) and (5), we obtain:
112122 sincoscossind/)sin(d/sin
βϕ−βϕ−λ=β+ϕ−λ=β
(6)
If the wavelength of laser beam is changed by
λ∆
from the nominal value
0
λ
, the angle
1
β
is changed in
accordance with Equation (1) as:
1 10 1
cos /dbb lD =D
or 1 1 10
/ 1/( cos )dbl bD D=
(7)
Assuming that
2
β
does not change (it is possible, if the
scheme is achromatized), consider the beam diraction
through the HOE with the formula (6). We will get:
1 10
2
0 cos( )
d
l
b jb
D
= -D + or 1
2 10
1
cos( )d
b
jb l
D
=
+D
(8)
Joining (7) and (8), we will obtain the achromatization
condition:
1 2 10 2 2
cos( ) cosdd djb a= +=
(9)
From (5), (6) and (9) we can get the simplest scheme
of achromatization. If

0=ϕ
, then according to (9) there
should be
21
dd =
and
12
β=α
.
Second simple option of achromatization can be
realized, if 10
0b=
and
ϕ= cosdd
21
. (10)
According to (5) we have additionally
20
aj=
.

V. I. Bobrinev, Ya. A. Grad, M. S. Kovalev, P . I. Malinina, V. V. Nikolaev, S. B. Odinokov, A. B. Solomashenko and N. G. Stsepuro
Vol 9 (47) | December 2016 | www.indjst.org Indian Journal of Science and Technology 3
e third option is implemented if
10
/2bj=-
. In this case, the diracted by ADG beam is directed
perpendicular to the bisector of the angle between
ADG and HOE and the angle of incidence of the
beam on the HOE at a nominal wavelength
0
λ=λ
is
20 10
/2a jb j=+ =
.
Let us consider in details the capabilities of these
achromatization options.
1.1 Option 1. (φ = 0o , d1 = d2)
According to the rst option if ADG and HOE planes are
parallel to each other and the periods of gratings, being
recorded on them, are equal, the output beam direction
coincides with the direction of the input laser beam and
does not change when the wavelength is changed (see.
Figure 2. As can be seen from the gure, the output beam
is displaced parallel to itself.
Figure 2. Scheme with parallel arrangement of ADR
and HOE (by thick lines are presented rays passing at a
nominal wavelength and by dotted lines - rays with changed
wavelength).
Oset of beam parallel to itself does not aect seriously
position of the image of the aiming mark, since the
magnitude of this shi is much less than the dimensions
of the hologram.
Additional scheme option with parallel arrangement
of ADG and HOE is presented on Figure 3.
Figure 3. e waveguide achromatization scheme.
e scheme represents a glass plate on which two
diraction gratings with the same period are plotted
(d.gr.1 and d.gr.2), the lines are directed perpendicular
to the plane of the Figure. Gratings period is selected
so that the incidence angle on the back surface of the
glass plate of the wave, diracted on a lattice 1, is greater
than the angle of total internal reection. Aer a few
reections inside the plate, this wave is incident on the
second diraction grating 2 and the diracted by this
grating beam is carrying the virtual image of the aiming
mark, which remains stationary when the wavelength is
changed.
Optical schemes with parallel arrangement of ADR
and HOE can operate over a wide wavelength range,
but they have a signicant drawback - their vertical size
should be more than two times bigger than the hologram
size (and accordingly the pupil of the sight).
To reduce the size of the sight let us consider possibility
of other achromatization options, when φ ≠ 0. In this case
dependence
2
β
of
λ
cannot be completely excluded;
however, in this case, there is a limited range of allowable
wavelength variations.
1.2 Option 2. (β10 = 0o)
Let us consider the second achromatization option when
10
0b=

,
20
aj=
and
ϕ= cosdd
21
(Figure 4). Here
the thick arrows show optical path of the laser beam,
being diracted by ADR and HOE. Dotted arrow from
eye shows direction to the aiming object. It is clear that
this line cannot go through ADR.
If 10 , the Equation (2) will be
11
d/sin λ=α
.
In addition, the value of
1
d
should be chosen due the
condition
ϕ= cosdd
21
to stabilize the angle
2
β
.
Figure 4. Holographic sight scheme with β10=0
Taking into account that
10
0b=

, we can get
20
aj=
.

Vol 9 (47) | December 2016 | www.indjst.org Indian Journal of Science and Technology
4
The Use of Holographic Optical Elements in Optical Systems Sights
Now to calculate dependence of
2
β
from
λ
it is
necessary to choose
1
α
and then make calculation, using
(2), (4) and (10) formulas. Let us consider the examples of
optical schemes, where
10
0b=

.
Example 1:
40j=

,
0
0.65 mlm=
,
10
0b=

.
Choose
1
60a=

. en
10,75055dmm=
,
2
0,9798dmm=
,
20
1,1819b=

0
20
1.1819b=
.
For
2
β
dependence on
λ
we have in Table 1.
Table 1. For β2 dependence on λ (option 2, example 1)
,m
λµ
0,60 0,62 0,64 0,65 0,66 0,68 0,70
2,dgr
β
1,264 1,211 1,185 1,182 1,185 1,211 1,264
2
,min utes
∆β
4,9 1,76 0,2 0 0,2 1,76 4,9
To have possibilities see together aiming mark and
aiming object it is necessary to have
20
b
not too small.
is angle determines direction of the view and must be
such that it does not go through ADG (dotted line from
the eye in Figure 4). It is possible to make calculation,
using
20
β
as assigned.
Example 2:
40j=

,
0
0.65 mlm=
,
10
0b=

40j=

,
m65.0
0
µ=λ
,
10
0b=

,
20 5b=
.
Using (4) and (5) we have:
m8905,0d
2
µ=
, using
(10):
m6822,0d
2
µ=
,
172,34a=
For
2
β
dependence on
λ
we obtain Table 2.
Table 2. For β2dependence on λ (option 2, example 2)
,m
λµ
0,60 0,62 0,64 0,65 0,66 0,68 0,70
2,dgr
β
5,0994 5,0358 5,004 5 5,004 5,0358 5,0995
,min utes
∆β
5,8 2,1 0,24 0 0,24 2,1 5,8
It is seen from the table, that if the wavelength dri
is ± 50 nm, a beam shi is less than 6 minutes. us, the
considered optical scheme can be used in practice.
1.3 Option 3 (β2 = α20)
Of interest is a situation where the beam, diracted
on ADG, is perpendicular to the bisector of the angle
between the ADG and the HOE and, accordingly are of
the same value on the angles of inclination to the ADG
and HOE, when the wavelength of the reading light beam
( Figure 5).
Figure 5. Optical scheme when β10=α20
e angles
10 20
/2baj==
. As a result of the formula
(9), it follows that the periods of gratings, recorded on the
ADG and HOE should be equal
When calculating
2
β
dependence on the wavelength
it is necessary to remember that in the scheme of Figure
5 ADG operates by formula
11 1
sin sin /da bl-=
and
HOE – by
2 21 2
sin sin /da bl-=
.
Below are presented calculations of value of
2
β
dependence on wavelength for the scheme with the
following parameters:
20
40 , 15jb==

.
In this case  537,70,m08182,1dd,20 11220 =αµ===α
. For
2
β
dependence on
λ
we obtain Table 3.
A number of publications were published, where it was
proposed to use reective hologram for achromatization
of optical scheme6. However, the allowable shi of the
laser wavelength when such holograms are used is
smaller than ±10 nanometers due to the fact that in the
reection holograms violation of Bragg law is observed
at much smaller displacements of wavelength than in the
transmission holograms7.
It should be noted that the reection holograms,
which are recorded on a photographic emulsion, have
another drawback. e photo emulsion is good absorber
of moisture and it changes thickness of the emulsion layer,
causing more strong violation of Bragg law.
It should be noted that the benecial properties of
reection holograms can be realized using transmission
holograms. To do this, it is necessary to apply a mirror
coating on the back surface of the photographic plate,
with recorded on it hologram, as shown in Figure 6.

V. I. Bobrinev, Ya. A. Grad, M. S. Kovalev, P . I. Malinina, V. V. Nikolaev, S. B. Odinokov, A. B. Solomashenko and N. G. Stsepuro
Vol 9 (47) | December 2016 | www.indjst.org Indian Journal of Science and Technology 5
Figure 6. Transmission hologram with mirror reector.
Hologram should be recorded in such way that the
incident reading beam does not satisfy Bragg condition.
is condition is satised for the beam passing through the
hologram and reected from the mirror 2. Reconstructed
by the hologram beam is used to read the image of the
aiming mark from HOE.
Previously transmission holograms with a mirror
were used to make holographic screen, which can display
the stereoscopic images8,9.
For example, there is shown on Figure 7 scheme of
a holographic sight, which uses transmission hologram
with a mirror.
Figure 7. Optical scheme of rear sight with using
transmission hologram with mirror as ADG.
Here 1 – transmission holographic diraction
grating, which one together with mirror 2 is used as
achromatization element, 3 – HOE with recorded on it
image of aiming point.
If 10 1 0
40 , 0 , 70 , 0,65
mjba l m
= == =
 
, then

2,4,m903,0d,m692,0d 2021 =βµ=µ= Calculated stability
of the reconstructed image is shown in Table 4. If laser
beam wavelength is changed from 0,6 μm to 0,7 μm,
image displacement doesn’t exceed 5,8 minute. Overall
size of such scheme is 4,5 x 3,6 cm when HOE size is 2,5
cm.
Table 4. For β2dependence on λ
,m
λµ
0,60 0,62 0,64 0,65 0,66 0,68 0,70
2,dgr
β
4,516 4,454 4,423 4,419 4,423 4,454 4,516
2
,min utes
∆β
5,8 2,1 0,24 0 0,24 2,1 5,8
Presented in Table 4 results of calculations show that
using of optical systems with a mutually inclined HOE
and ADG allows reducing size of scheme with acceptable
shi of image.
2. Conclusion
ere exist several options how to solve problem of image
stabilization in the holographic sights by using additional
transmission holographic elements for compensation of
image shi.
Sight optical scheme is presented, where the
transmission hologram with mirror, installed behind of
hologram is used analogous to the reection hologram.
3. Acknowledgments
e research was carried out at BMSTU. is work
was supported by a grant # 14.574.21.0066 (Project ID
Table 3. For β2dependence on λ (option 3)
,m
λµ
0,60 0,62 0,64 0,65 0,66 0,68 0,70
2,dgr
β
15,050 15,018 15,002 15 15,002 15,017 15,048
2
,min utes
∆β
3 1,1 0,12 0 0,12 1,05 2,9

Vol 9 (47) | December 2016 | www.indjst.org Indian Journal of Science and Technology
6
The Use of Holographic Optical Elements in Optical Systems Sights
RFMEFI57414X0066) and by a grant of the main part of
the state order “Organization of scientic research” and
“Providing of scientic research” from the Ministry of
Education and Science of the Russian Federation.
4. References
1. Shei HJ. e tolerance of linear scanning and the scan-
ning angle of holographic zone plate in optical thin-lm
elements. Indian Journal of Science and Technology. 2012
Dec; 5(12):1–5.
2. Salakhutdinov VK. Holographic sight. Russian Federation
Patent No. 2034321; 1995.
3. Kovalev MS, Kozintsev VI, Lushnikov DS, Markin VV,
Odinokov SB. e method of compensation changes the
position of the impact mark and a holographic collimating
sight. Russian Federation Patent No. 2355989; 2007.
4. Betin AY, Dontchenko SS, Kovalev MS, Odinokov SB, Sol-
omashenko AB, Zlokazov EY. A combination of comput-
er-generated Fourier holograms and light guide substrate
with diractive optical elements for optical display and
sighting system. Digital Holography and ree-Dimen-
sional Imaging; 2015. p. 410.
5. Kolyer R, Berhart K, Lin L. Optical holography. Moscow:
Mir; 1973.
6. Sieczka EJ, Tai AM, Fish RH. Low prole holographic sight
and method of manufacturing same. United States Patent
US2006/0164704 A1; 2006.
7. Bobrinev VI, Kovalev MS, Odinokov SB, Sagatelyan GR.
Investigation of the properties of a beam reconstructed
from volume Holographic Optical Elements used in op-
tical observation devices. Russian Physics Journal. 2016;
58:1457–66.
8. Hwang SH, Bobrinev VI, Son JY. Achromatized transmis-
sion type holographic screen for a multiview stereoscopic
image system. Applied Optics. 1997; 36(26):6605–10.
9. Son JY, Bobrinev VI. Method of producing a holographic
projection screen for displaying a three-dimensional color
images. United States Patent No US 6211977 B1; 2001.