Analysis of multichannel optical rotary connectors based on the compensation operating principle with mirror and prismatic optical compensators (Part 1)
Performed in this work is a comprehensive theoretical computer analysis of performances inherent to two types of multichannel optical rotary connectors (ORC of compensation operation based on mirror and prismatic compensators. This analysis relies on exact analytical expressions obtained for light r...
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| Опубліковано в: : | Semiconductor Physics Quantum Electronics & Optoelectronics |
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| Дата: | 2017 |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2017
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| Цитувати: | Analysis of multichannel optical rotary connectors based on the compensation operating principle with mirror and prismatic optical compensators (Part 1) / V.M. Shapar, V.S. Lysenko, A.V. Savchuk // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2017. — Т. 20, № 1. — С. 1-18. — Бібліогр.: 58 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860279378381897728 |
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| author | Shapar, V.M. Lysenko, V.S. Savchuk, A.V. |
| author_facet | Shapar, V.M. Lysenko, V.S. Savchuk, A.V. |
| citation_txt | Analysis of multichannel optical rotary connectors based on the compensation operating principle with mirror and prismatic optical compensators (Part 1) / V.M. Shapar, V.S. Lysenko, A.V. Savchuk // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2017. — Т. 20, № 1. — С. 1-18. — Бібліогр.: 58 назв. — англ. |
| collection | DSpace DC |
| container_title | Semiconductor Physics Quantum Electronics & Optoelectronics |
| description | Performed in this work is a comprehensive theoretical computer analysis of performances inherent to two types of multichannel optical rotary connectors (ORC of compensation operation based on mirror and prismatic compensators. This analysis relies on exact analytical expressions obtained for light ray paths in ORC models with a mirror compensator made in the form of a bilateral mirror placed between two optical hemispheres and with a prismatic compensator made in the form of a Dove prism placed between two non-aberrational elliptic lenses. Found in ORC with the mirror compensator is the essential deficiency inherent to all these constructions, which is related to considerable rotary oscillations in the value of optical signals in mirror angular positions when the mirror halves the input light beam. In these mirror positions, the amplitude value of optical signal oscillations exceeds 95%, and optical losses are higher than –13 dB when the rotor turns. One deficiency more in these constructions is also strict technical requirements for the accuracy of making the optical components and mechanisms at the level of 1…2 µm. Concerning the ORC construction with a prismatic compensator as well as collimator and focusing lenses common for all the channels, one should note the inadmissibly high optical losses of the signal value (higher than –30…40 dB) in the case of construction with fiber-optic interfaces, and large dimensions and mass in the case of active construction with optoelectronic transducers at the inputs and outputs of ORC. For example, when the number of channels N = 10, the longitudinal dimension of the optical transfer channel (prism and lenses) exceeds 300 mm, and this dimension increases with increasing the number of channels. When this dimension is lower than 100 mm, the facility can be equipped with only one optical communication channel containing one LED and one photodiode located on the rotation axis. Optical losses in these constructions cannot be considered as satisfactory ones, since the respective loss value is higher than 18 dB for the number of channels N = 10.
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| first_indexed | 2026-03-21T13:44:24Z |
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| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 1. P. 1-18.
doi: https://doi.org/10.15407/spqeo20.01.001
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
1
PACS 42.15.Eq, 42.74.-e, 85.60.-q
Analysis of multichannel optical rotary connectors
based on the compensation operating principle
with mirror and prismatic optical compensators (Part 1)
V.M. Shapar1, V.S. Lysenko1, A.V. Savchuk2
1V. Lashkaryov Institute of Semiconductor Physics, NAS of Ukraine,
41, prospect Nauky, 03028 Kyiv, Ukraine, e-mail: v_shapar@rambler.ru
2International center “Institute for Applied Optics”, NAS of Ukraine,
10-g, Kudryavska str., 04053 Kyiv, Ukraine
Abstract. Performed in this work is a comprehensive theoretical computer analysis of
performances inherent to two types of multichannel optical rotary connectors (ORC) of
compensation operation based on mirror and prismatic compensators. This analysis relies
on exact analytical expressions obtained for light ray paths in ORC models with a mirror
compensator made in the form of bilateral mirror placed between two optical
hemispheres and with prismatic compensator made in the form of Dove prism placed
between two non-aberrational elliptic lenses.
Found in ORC with the mirror compensator is the essential deficiency inherent to all
these constructions, which is related with considerable rotary oscillations in the value of
optical signals in mirror angular positions when the mirror halves the input light beam. In
these mirror positions, the amplitude value of optical signal oscillations exceeds 95%,
and optical losses are higher than –13 dB, when the rotor turns. One deficiency more in
these constructions is also strict technical requirements to the accuracy of making the
optical components and mechanisms at the level of 1…2 µm.
Concerning the ORC construction with a prismatic compensator as well as collimator and
focusing lenses common for all the channels, one should note the inadmissibly high
optical losses of the signal value (higher than –30…40 dB) in the case of construction
with fiber-optic interfaces, and large dimensions and mass in the case of active
construction with optoelectronic transducers at the inputs and outputs of ORC. For
example, when the number of channels N = 10 the longitudinal dimension of optical
transfer channel (prism and lenses) exceeds 300 mm, and this dimension increases with
increasing the number of channels. When this dimension is lower than 100 mm, the
facility can be equipped with only one optical communication channel containing one
LED and one photodiode located on the rotation axis. Optical losses in these
constructions cannot be also considered as the satisfactory ones, since the respective loss
value is higher than –18 dB for the number of channels N = 10.
Keywords: optical rotary connector, fiber-optic rotary connector, fiber-optic
communication, optical compensator, optoelectronic.
Manuscript received 12.09.16; revised version received 25.01.17; accepted for
publication 01.03.17; published online 05.04.17.
1. Introduction
To transfer information signals from rotating objects to
the stationary ones in various branches of science and
technique, different contact, capacitive and inductive
current-collecting connectors (e.g., of the “Slip ring” type)
are widely used up to date. The contact connectors are the
most often applied, since they are more simple and cheap.
Also, with development of information technolo-
gies and impetuous growth of information volumes that
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 1. P. 1-18.
doi: https://doi.org/10.15407/spqeo20.01.001
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
2
should be transferred from rotating objects to the stable
ones, implementation of fiber-optic transducers for
physical quantities into rotating objects as well as fiber-
optic transmission lines, traditional application of
contact current collectors in many cases of up-to-date
technique is not only problematic but sometimes
impossible in general because of principal physical
deficiencies inherent to current-collecting facilities.
Among these deficiencies, it should be noted first of all
the limited frequency band of electric transmission
channels based on contact rings, high sensitivity to
external electromagnetic interference as well as great
mass and considerable sizes of these facilities.
A low frequency band of electric transmission
channels and sizeable mass/dimension characteristics
(e.g., of Sleep rings) in the multichannel version cause
especial difficulties when using them in the objects
intended for transferring huge information signal
massifs. For instance, the mass of information parts of
contact current collectors used in observational radars is
approximately 200–300 kg, and their dimensions reach
several meters in length and 0.5 m in diameter [1].
In up-to-date radar complexes with phased-array
antennas, which are characterized by considerably
higher information fluxes that should be transferred from
radio-electronic facilities mounted on the rotating
antenna-spinning column of the complex to stationary
modules, the amount of rotary current collectors must
reach several thousands units instead of hundred ones, as
earlier. It will result in further complication of current
collectors that are already over-saturated by the amount
of electrical channels, without this addition. In this case,
the mass of cable assemblies intended for transferring all
the sets of electric signals between radio-electronic
modules operating in the observational radar will reach
more than ten tons.
The same difficulties arise when using the current-
collecting facilities in modern systems for
reconnaissance, surveillance and target acquisition as
well as for vehicle navigation technologies [2].
Optimal solution of the problem of transferring
huge massifs of high-frequency wide-band signals from
rotating objects to the stationary ones is now possible by
using, instead of the above current-collecting facilities,
their functional contactless analogs – optic rotary
connectors (ORC), and applying optical communication
channels for this process of information transfer.
Optic rotary connectors are delivered from the
above deficiencies of current collectors and possess a set
of unique properties and advantages over the previous
ones.
Their main advantages are as follows:
• absence of frictional contacts;
• wide frequency band of the transmission channel,
which exceeds the frequency band of electric
channels by thousand times;
• mass and dimensions of ORC are hundreds times
lower than those of their electric analogs.
Besides, ORC
• provide galvanic separation between input and
output of the communication channel in ORC,
which enables to connect radio-electronic units that
are under electric potentials with the difference of
tens or hundreds kilovolts;
• allow transferring the optical signals within the
frequency range from direct current up to super-
high frequencies even simultaneously in both
directions;
• are absolutely insensitive to actions of external
electromagnetic interference;
• do not create electric reactivity in communication
channels;
• guarantee safety of their application at the objects
operating in dangerous explosive conditions, which
has its great social implication.
The above mentioned advantages of ORC as well
as their high reliability and longevity, absence of any
needs in preventive maintenance for 3 to 5 years corres-
pond to requirements of up-to-date technique, and owing
to it ORC can be undoubtedly related to one of the most
promising facilities for signaling between movable and
stationary objects and find their more and more wide use
in various branches of surface and space technique.
Unfortunately, up to now considerable achieve-
ments are only reached in development of single- and
two-channel ORC [3-6]. The frequency band of the opti-
cal channel in them comprises the range 0.1–10 Gbit/s,
and in some facilities can even exceed the latter value.
The channel can be bi-directional and full-duplex, i.e., it
can transfer information in both directions simul-
taneously. For this case, they use the technique of using
two different wavelengths for transferred signals (most
often they are λ = 1550 nm in one direction and λ =
1310 nm in the opposite one) [2].
Single-channel facilities can be also used in the
multichannel regime. In this case, they use the technique
of wavelength division multiplexing (WDM) [2, 7-10].
However, there is a considerable amount of cautions
when multiplexing is not desirable. Namely: when one
should provide secrecy in channels operating in parallel
with channels transmitting unclassified information;
when there is a necessity to have an additional cashed
circuit aimed at providing high reliability of data
transfer; to avoid cross-interference between channels;
when the data are received from different places; when it
is necessary to have a free space at the device axis to
provide allocation of additional facility inside ORC, e.g.,
SHF-waveguide, etc [2, 11].
Therefore, many researches in the leading countries
all over the world perform intense investigations for
creation of multichannel ORC with parallel independent
physical channels. They study possibilities for using
various physical principles and optical elements aimed at
creating ORC.
Beside traditional geometrical optics, there studied
are the possibilities to apply holographic, Fresnel, fiber
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 1. P. 1-18.
doi: https://doi.org/10.15407/spqeo20.01.001
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
3
and gradient optics, as well as electro- and magneto-
optics. In these cases, they use various optical facilities
and elements, namely: ring fiber-optic transducers of the
light beam shape [12-20], holographic Fresnel lenses
[21-25], focusing facilities [26, 27], light-guide facilities
based, in particular, on optical fibers and hollow mirror
toroids [28-32], mirror systems that revolve
synchronically [2, 33, 34], etc. As a separate direction,
one should name development of facilities based on the
principle of compensation [35-50]. From the viewpoint
of reaching the maximum possible number of optical
channels, the latter are the most promising ones up to
date.
ORC based on the compensation principle of action
essentially differs, from the construction viewpoint, from
other ORC types in that the latter contain an additional
slide assembly for optical interconnection, the rotation
velocity of which differs from that of the ORC rotor
part. On the one hand, availability of this additional
movable compensation assembly is a deficiency of these
devices, since complicates the facility, but on the other
hand, the very compensation principle enables to create
ORC designed for tens of optical channels as opposite to
the other ORC types where the amount of optical
channels does not exceed 3 to 8 channels, in practice.
Optical-and-technical characteristics of ORC with a
compensator mainly depend on properties of the
compensator used in it. Known up to date is a set of
technical solutions for ORC with prismatic [35-43],
reflective [44-47] and fiber-optic compensators [48-51].
A considerable amount of these technical solutions are
studied neither experimentally nor theoretically and need
a deep theoretical analysis.
Shown in this analytical review are the results of
computer simulation only part of the known technical
solutions ORC based on the compensation principle
realized with a mirror compensator and that with the
Dove prism, including the focusing and collimating
lenses that serve as the collective ones in all the
channels.
2. Multichannel ORC with prismatic compensators
One of the first constructions of ORC with prismatic
compensator was offered yet in 1977 by Myren L.
Iverson who used the Dove prism [35]. This facility
should be related to active constructions [52], inputs and
out puts of which are provided with respective
optoelectronic transducers for conversion of the electric
signal into the optical one in the transmitting part of the
communication channel and, vice versa, of the optical
signal into the electric one in the receiving part (for
example, LEDs in the transmitting part and
photodetectors in the receiving part). Active facilities do
not operate in the composition of fiber-optic
transmission lines but only in the composition of electric
lines. Therefore, their advantages over other collectors
lies only in the fact that they are less sensitive to external
electromagnetic interferences and are more reliable.
The essential feature of the Iverson construction is
that for focusing and collimating the light beams there
used are focusing and collimating collective lenses for
all the transmission channels. As it will be shown below,
the principle for image formation at the output ORC
interface by using the collective lens has essential
deficiencies, namely: the amount of optical channels in
the active design with optoelectronic transducers is
limited by only a few channels, because of a high level
of the cross-interference between them and, in the case
of passive variant used for facility composition with
optical interfaces designed for operation directly in the
composition of fiber-optic transmission lines, very
rigorous requirements to the facility components and
their assemblage.
Also, there exists a number of technical solutions for
ORC with prismatic compensators, where individual
focusing and collimating lenses are used in each optical
channel [36-43]. These constructions possess better
technical performances as compared with those mentioned
above, in particular, the amount of optical channels can be
increased here. Since the mentioned constructions have
structural peculiarities that essentially influence on their
technical performances, it seems reasonable to consider
them as typical representatives of two different directions
for creation of multichannel ORC with prismatic
compensators. Analysis of these constructions will be
presented in the following publication.
2.1. Multichannel ORC with prismatic compensators and
lenses for focusing and collimation that serve as the
collective ones in all the channels
Let us consider this ORC type by using, as an example,
the construction [35] schematically depicted in Fig. 1.
5
1
7
3
4
8
6
2
Fig. 1. Schematic view of the active optical rotary connector
with the Dove prism and photoelectric transducers. 1 – rotary
part; 2 – stationary part; 3 – Dove prism; 4 – reduction
mechanism with the ratio 1:2; 5 – optical radiators (LEDs); 6 –
optical detectors (photodiodes); 7 – collimating lens; 8 –
focusing lens.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 1. P. 1-18.
doi: https://doi.org/10.15407/spqeo20.01.001
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
4
The depicted in this figure multichannel optical
rotary connector includes two parts – rotary 1 and
stationary 2 – mounted on the common rotation axis as
well as the compensator 3 placed in alignment between
them and based on the Dove prism for turning the light
beams. The Dove prism is mechanically related with the
rotary part 1 via the tooth reducing motion 4 possessing
the reduction ratio 1:2.
In every optical channel of ORC, placed on the
rotary part 1 are the sources of radiation 5 (LEDs), while
the detectors of radiation (p-i-n-photodiodes) are
mounted in the stationary part 2. Besides, the rotary part
1 includes the collimating lens 7, in the focal plane of
which the LEDs 5 are located, while the stationary part 1
includes the focusing lens 8 with photodiodes 6 in its
focal plane.
The lens 7 is intended to form parallel light beams
at the input into the Dove prism, which is aimed at
elimination of the influence of prism astigmatism on the
formed image. The lens 8 focuses the optical beams at
the prism output onto the respective photodetectors.
The Dove prism is an isosceles prism of right
vision with one reflective and two refractive faces placed
at the angles 45° relatively to the reflective one [53, 54].
The prism has the mirror plane of symmetry, axis of
symmetry of the first order and inversion center. When
the prism is fixed, and entering beams turn around the
optical axis, the prism inverts direction of beam turn.
And while the prism turns around the optical axis, the
input beams are turned at the output by the double angle
as compared to that of the prism turn.
Owing to these properties, the prism can be used as
an optical compensator of light beam rotation, if the prism
turns with the speed two times less than that of beams.
With this purpose, in the facility (Fig. 1) the reducing
motion 4 with the reducing ratio 1:2 is used, which
provides connection between the prism and rotary part 1.
To determine the most important characteristics of
this ORC (value of optical losses in the transmitting
channels, depth of modulation in the optical signal
amplitude when the prism turns around the axis, value of
cross-interference between channels, and the maximum
amount of optical channels available in this facility), we
performed theoretical investigations of this facility
behavior in various constructive solutions.
In what follows, we have considered the active
ORC construction with optoelectronic transducers as
well as the passive ORC construction with optical
interfaces.
2.1.1. Active construction of ORC with the Dove prism
and collective lenses for focusing and collimation of
beams
Active construction of ORC with optoelectronic
transducers at its inputs and outputs connected with
electric transmission lines was created using thin non-
aberrational elliptical lenses instead of the spherical
ones. The former provide considerably lower aberrations
as compared with biconvex thick lenses with spherical
surfaces that were used in the facility [35].
The results of these investigations showed that
application of a prism as a compensator of light beam
rotation in ORC with collimating and focusing lenses,
which are common for all the optical transmission
channels, is related with a number of technical
difficulties.
The matter is that direct-vision prisms, e.g. the
Dove or Pehan ones, operate without astigmatism
exclusively in parallel optical beams [53, 54], while the
angular dispersion of beams from semiconductor light
sources (laser diodes) used in wide-band channels for
optical transmission comprises the range from several
degrees up to several tens degrees. If using these light
sources, the collimation lens cannot form a light beam
with necessary parallelism, and the focusing lens is
unable to provide necessary focusing on the detector. It
is the reason for a considerable part of non-focused light
to fall into adjacent receiving channels, which causes a
noticeable cross-interference between channels.
To avoid this cross-interference caused by
overlapping images created by adjacent light sources at
the receiving side of ORC, the optical sources and
respective optical detectors should be mounted at
sufficient distances between them. At least, this distance
should correspond to the dimension of the source image
created by the lens in its focal plane. Due to increasing
the distance between light sources, the component of
cross-interference caused by overlapping between
diffuse images can be considerably reduced. But
moreover, in this case the total amount of optical
detectors that can be mounted in the facility (i.e., optical
channels, the amount of which corresponds to that of
light sources).
At the first glance, it seems sufficient to increase
transverse dimensions of the prism, which will result in
the increased amount of channels. But since the
dimension of the astigmatic image (scattering circle)
grows with the prism dimensions, the amount of
channels increased in this way grows only
insignificantly. An optimal solution of this task needs a
mathematical analysis that has been performed in the
work [55].
Shown in Fig. 2 is the path of light rays in the
facility for a point source in the principal plane of
facility (in the mirror plane of prism symmetry).
The prism optical axis and principal optical axes of
the lenses are related with the rotation axis. Light
sources are placed along the circle in the focal plane of
the collimation lens at the distance h from its optical
axis. Detectors are placed in the focal plane of focusing
lens symmetrically to the light sources.
When deducing the equations describing the path
of rays in the optical system shown in Fig. 2, we
assumed that the light sources are point. To plot the
images created by real sources, calculations are usually
performed for a set of point sources placed along the
peripheral contour line of source.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 1. P. 1-18.
doi: https://doi.org/10.15407/spqeo20.01.001
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
5
2.1.2. Mathematical model of the active ORC facility
with the Dove prism and collective optical means for
focusing the beams
Solving the task of determination of ray paths can be
separated by three stages. It means that light ray paths in
collimation lens, Dove prism and focusing lens can be
considered separately.
Let us consider the light ray paths in the
meridional plane of the collimation lens.
Let us assume that the optical axis of the lens
coincides with the OX axis, while the OY axis is
directed along the perpendicular to the lens optical axis.
The prism is placed in such a manner that its optical axis
also coincides with the OX axis, and the OY axis of the
coordinate system lies in the prism principal plane and
passes through the middle of the prism edge along the
perpendicular to it (Fig. 2).
The equation of projectively-equivalent surface for
the elliptic lens in the rectangular coordinate system with
its origin superposed on the lens apex, when the lens
optical axis coincides with the OX axis, is as follows
[56]:
( ) ( ) 0/11211 2
1
22
1 =+⋅⋅−⋅−⋅− yxfnxn , (1)
where f is the lens focal distance, n1 – lens refraction
index, and x,y are the coordinates of the elliptic lens
surface.
Let us write the equation for the ray going out of
the point located in the lens focal plane at the distance h
from the OX axis
( ) 1tgβ⋅−+= xfhy , (2)
where β1 is the angle of incidence for the rays relatively
to the OX axis.
Solving the expression (1) in combination with (2),
one can obtain a quadratic equation, solution of which is
the х1 coordinate of intersection of the ray with lens
111
2
111 24 acabbx ⎟
⎠
⎞
⎜
⎝
⎛ ⋅−−−= , (3)
where
1
22
11 tg11 β+−= na ,
( ) 11
2
111 tg2tg/112 β⋅+β+−⋅= hnfb ,
11
22
1
2
1 tg2tg β⋅+α⋅+= hffhc .
The у1 coordinate for the same point can be found by
substitution of the obtained х1 value into the equation (2)
( ) 111 tgβ⋅−+= xfhy . (4)
Let us find the angle θ1 inherent to the ray refracted
by lens relatively to the optical axis of the lens. To do it,
one can use the non-aberrational property of the elliptic
lens, physical essence of which is that the light rays,
going out of the principal focal point of lens, propagate
after refraction on its surface in parallel to its principal
optical axis.
This condition allows finding the angle α between
the straight line normal to the lens surface at the point
(х1, у1) and the OX axis, as well as to determine the
angle θ for the rays going out of the lens, for the light
source located off-axis by using the law of light
refraction at the optical surface.
With account of the mentioned above, it can be
shown that the angle θ1 for the refracted ray 1 can be
found from the following relations:
( )[ ] 11111 sinarcsin α−β−α⋅=θ n , (5)
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−β⋅
β⋅
=α
1cos
sinarctg
111
111
1 n
n
, (6)
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−
=β
11
1
11 arctg
xf
y
, (7)
where β11 is the slope angle for the ray relatively to the
OX axis, when this ray goes out of the lens focal point to
the point with coordinates (х1, у1), α1 – slope angle
relatively to the OX axis for the normal to the lens
elliptical surface at the same point (х1, у1).
Xh
1
12
2
у'у
θΙ
2
γ
H
x1 x11
β1
α1 x'
f2
h
f1
y1
y2
1
12
2
у'у
θ 1
θΙ
1θ2
Δy2
Δy1γ1
γ
H
β'11
β11
β'1
β'2
o'
L
h1'
h2 '
O
Fig. 2. The scheme of ray paths in ORC with the Dove prism and optical means (elliptical non-aberrational lenses) for focusing
the rays.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 1. P. 1-18.
doi: https://doi.org/10.15407/spqeo20.01.001
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
6
By analogy, one can find the angle θ2 for another
extreme ray (ray 2 in Fig. 2 with the maximum aperture),
then he can determine the coordinates у11, у22 of the
intersection points of respective rays with the OY axis
11111 tgθ⋅+= xyy , (8)
22222 tgθ⋅+= xyy . (9)
Let us consider the light ray paths in the Dove
prism.
It should be noted that the rays falling onto the
prism in parallel to it optical axis at the distance h1 from
it go out of the prism at the distance minus h1 not
changing their initial direction. The rays falling at the
angle θ to the prism optical axis change their initial
direction by that inherent to mirror reflection when
going out of the prism. It is accompanied by ray shifts
along the OY axis by the value Δy. This value consists of
three components, namely: δY1 – for the air space at the
input to the prism, Δpr – for the prism bulk, and δY2 – for
the air space at the prism output.
The Δy value for the ray total shift can be
determined using the following expressions describing
the ray paths in the prism:
θ⋅Δ+Δ+θ⋅=Δ tgtg prprHy , (10)
( )
( )1
1
tg1tg
tgtgtg
γ+⋅γ
γ−γ⋅α
⋅=Δ Hïð , (11)
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
⋅
−°=γ
prn2
2arcsin45 , (12)
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛ θ+°
−°=γ
prn
45sin(arcsin451 , (13)
where H is the height of the Dove prism, npr – prism
refraction index, θ – slope angle for the ray falling onto
the prism relatively to the OX axis, γ, γ1 are the angles of
incidence for the rays relatively to the prism base
(Fig. 2), α is the angle between the prism input face and
its base, which is equal to 45° in the Dove prism.
In Fig. 2, for the upper ray θ = θ1, while for the
lower one θ = θ2 . The sign for the angle θ is chosen
using the general rule. In our case, this sign is negative
for both rays.
Let us consider the light ray paths in the
meridional plane of the focusing lens.
Let a new rectangular coordinate system Х′О′Y′
has its О′Х′ axis directed along the principal optical axis
of another elliptic lens and its О′Y′ axis directed along
the normal to the lens and prism optical axes and passing
through the middle of the edge between the prism output
refractive face and its base (reflective face). The apex of
this elliptic lens is located in the origin of the coordinate
system Х′О′Y′.
Having determined the Δу1 and Δу2 values for the
ray shifts at the prism output, one can find the
coordinates у′11 and у′22 of the intersection points for the
rays with the О′Y′ axis that lies in the plane х′ = 0
11111111 tgθ⋅+Δ+=′ xyyy , (14)
22222222 tgθ⋅+Δ+=′ xyyy . (15)
Further, one can determine the coordinates х′1, у′1
and х′2, у′2 inherent to the points of intersection between
these rays and lens surface. Here, it is pertinent to use
Eq. (1) for the surface of elliptic lens in the new
coordinate system Х′О′Y′ as well as equations for rays
going out of the points у′11 and у′22 identical to Eq. (2).
For the ray going out of the point у′11, one can
obtain the following relations:
( )
( )1
22
2
1
22
2
2
11
2
22
1
tg112
tg114
θ+−
θ+−′−−−
=′
n
nybb
x , (16)
11111 tgθ⋅′+′=′ xyy , (17)
where ( ) 1111
2
222 tg2tg112 θ⋅+θ+−= ynfb , n2 –
refraction index for the focusing lens, f2 – focal distance
of this lens.
For the second ray, there exist analogous relations
where, instead of the angle θ1 and ordinate у′11, the angle
θ2 and ordinate у′22 take place.
The light rays 1 and 2 after refraction at the
external surface of the focusing lens further propagate
under the angles β′1 and β′2 relatively to the lens optical
axis and intersect the lens focal plane in the points
located at the distances h′1 and h′2 from its optical axis,
respectively.
The values of angles β′1 and β′2 as well as distances
h′1 and h′ can be calculated using the following
equations:
( )[ ]21111 sinarcsin nθ+α′−α′=β′ , (18)
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−β′⋅
β′⋅
=α′
1cos
sinarctg
112
112
1 n
n , (19)
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
′−
′
=β′
12
1
11 arctg
xf
y , (20)
( )
( ) ⎭
⎬
⎫
⎩
⎨
⎧
β′⋅′−−′=′
β′⋅′−−′=′
22222
11211
tg
tg
xfyh
xfyh
. (21)
The difference (h′1 – h′2) is the highest dimension
of the image spot in the principal optical section of a
facility (in the direction of О′Y′ axis) in the lens focal
plane, this section being created by the rays with the
highest aperture.
When the prism rotates, the image spot also moves
– precesses around some point h′. Therefore, when the
facility operates, the maximum radius of spot scattering is
defined by the highest distance between the point, around
which this precession is realized, and the points h′1 or h′2.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 1. P. 1-18.
doi: https://doi.org/10.15407/spqeo20.01.001
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
7
2.1.3. Results of theoretical studying the active ORC
with the Dove prism and lens collimating optics common
for all optical channels
Using the obtained above expressions (1) to (21), in
[55] we performed calculation for the radius of the
confusion circle as a function of the aperture inherent to
point source radiation for the number of real
construction parameters of facility.
Fig. 3 shows a family of calculated dependences
for the diameter of confusion circle on the distance h
between the point radiation source and the lens optical
axis for elliptic lenses with the focal distances f = 25, 50,
75 and 100 mm. The refraction index of the prism and
lenses was assumed to be equal to 1.7. The aperture
angle value of the radiation source was β = 6º.
When performing calculations, the height of the
prism Н was chosen as the minimum possible one for the
set aperture angle β of the optical source and focal
distance of lenses by using the condition that high-
aperture rays should not exceed the transverse
dimensions of the prism and propagate outside it.
Also, there is a limitation for the acceptable prism
dimension. The rays should propagate inside the prism
without any vignetting. However, when these
dimensions are large this condition is not performed.
The rays incident onto the prism at various angles,
during their propagation inside the prism, obtain at the
prism output some additional shift Δу (see Exps (10) to
(13)) proportional to the prism height and the angle θ of
ray incidence onto the prism.
In its turn, the angle θ is in proportion to the
distance between the source and axis (see Exps (5) to
(7)). When the prism height is larger than some critical
value or the source is located off-axis above some
critical distance, then inclined rays inside the prism
obtain so considerable additional shift Δpr that after
reflection from the prism base they fall not onto the
output face but onto the upper face of the prism oriented
in parallel to the base, and go out of the prism.
Distance h of the point source to the optical axis, mm
Ra
di
us
o
f t
he
c
on
fu
si
on
c
irc
le
, m
m
0 4 8 12
0
1
2
3
n=1.7
β=6°
f=50 mm
Н=22 mm
L=81 mm
f=75 mm
Н=32 mm
L= 118 mm
f=100 mm
Н=42 mm
L= 155 mm
f=25 mm
Н=11 mm
L= 40,5 mm
n=1.5
Fig. 3. Calculated dependences for the radius of radiation
confusion circle on the distance h of the point source to the
optical axis of elliptical lenses with various focal distances f.
It is noteworthy that with increasing the distance
between the light source and prism axis there arises a
situation when the transfer of rays through the prism
become impossible without vignetting for any arbitrary
prism dimensions. Therefore, when calculating the
maximum possible amount of channels in ORC the prism
height was chosen with account of the condition that the
point source is located at the maximum possible distance
from the axis, for which the rays pass inside the prism yet.
Calculations of the limiting distance between the
point source and axis as well as the choice of the prism
height for this distance were performed using the method
of step-by-step approximation. The distance source-to-
axis was increased successively with the step 0.1 mm up
to the moment when further increasing by this step
resulted in impossibility for rays to pass through the
prism without vignetting.
The calculated acceptable limiting distances h
between the source and axis for various lens focal
distances f and optimal height of the Dove prism are
shown in Fig. 3 with dash-dotted lines drawn to the
horizontal axis of the figure. Fig. 4 shows the
dependences for the radius value of the confusion circle
on the angle of ray incidence for various distances
between the point source and axis in the facility with
lenses of the focal distance f = 50 mm.
To obtain real practical results, let us consider
these dependences by using the available elemental base
with account of existing discrete semiconductor
radiation sources.
Shown in Figs 5a-5d are the contours of light
beams for the light source of the type L3989-01
(Hamatsu) and contour lines of images at the facility
output, which are created by elliptic lenses with various
focal distances. The certified value of the aperture angle
β inherent to the LED L3989-01 is 6°. When calculating
the maximum possible distances h between this point
source and axis (see Fig. 4), the angle of ray incidence
was assumed to be 6°, too.
Angle of incidence for the source rays, deg.
0 2 4 6
0
0.2
0.4
0.6
0.8
1
f = 50 mm
Н = 22 mm
L = 81 mm h=6 mm
h=4 mm
h=2 mm
Ra
di
us
o
f t
he
c
on
fu
si
on
c
ir
cl
e,
m
m
Fig. 4. Calculated dependences for the radius of radiation con-
fusion circle on the aperture angle β of rays for various dis-
tances h of the point source to the optical axis of elliptical lens.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 1. P. 1-18.
doi: https://doi.org/10.15407/spqeo20.01.001
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
8
In what follows, the obtained data for the
maximum acceptable h values (Fig. 4) were used to
calculate coordinates for location of centers of real
sources L3989-01, which were determined as the
difference (h – r), where r is the radius of the case of this
light source.
In Figs 5a-5d, the annular lines shown in diagrams
with dots are related to dimensions of the LED case, the
diameter of which is close to 5.4 mm. The lines
designated with small rings are related to the diameter of
source light beam equal to 3.72 mm in accord with the
LED L3989-01 certificate. The peripheral lines looking
as ellipses plotted with asterisks (Figs. 5a-5d) are related
to calculated contour lines for source images on the
receiving side of facility.
The contour lines of optical images for light
sources on the receiving part of ORC are plotted using
superposition of images corresponding to point light
sources located along the contour of radiator at different
distances from the rotational axis.
Using the method described above for each variant
of chosen lenses with different focal distances, we
calculated optimal dimensions for the prism in such a
manner that they provide to reach the largest amount of
channels in this facility, when cross-interference
between these channels is practically absent. As seen
from Fig. 5, in the case of LED L3989-01 the maximum
amount of optical channels for the lenses with focal
distances 50, 75 and 100 mm is equal to 2, 6 and 9
channels, respectively. Concerning the lens with the
focal distance 25 mm, the respective facility can contain
only one channel located on the axis of rotation (diagram
for this case is not shown in Fig. 5).
The results of calculations aimed at determination
of the maximum possible amount of channels N for the
discussed above light sources in dependence on lens
dimensions are adduced in Table 1. The represented data
show that the maximum amount of optical channels that
can be reached in ORC with the Dove prism, when all
the channels use the same ways for collimation and
focusing the beams, depends on the light source aperture
angle and dimensions of the ORC optical system. In
particular, in the case of using the elliptical lenses with
the focal distance 100 mm and the source with the
aperture angle β = 2°, for example LED SV5637-001,
the amount of channels can reach 21, while for the
source with β = 6º – only 9 channels.
However, it should be noted that in the case of
using lenses with the focal distance 100 mm, the total
length of optical section in ORC (prisms with lenses)
exceeds 355 mm. It is clear that these dimensions are not
suitable for many practical applications of these
facilities.
For the lenses with the focal distance 50 mm, the
length of optical section can be reduced down to
180 mm, but the maximum amount of channels in this
case will be only 7 channels for the sources with the
aperture angle β = 2° and only 2 channels when this
angle will be β = 6°. If the lens focal distance is lower
than 25 mm, then in this facility only one optical channel
on the axis of rotation can be mounted.
The value of optical losses can be estimated if
using high-frequency photodetectors possessing the
frequency band 100 MHz as an example. As a rule, these
photodetectors have the diameter of photosensitive area
no larger than 1 mm. It is clear from Fig. 5 that the
diameter of light spot from the light source at the plane
of photodetector reaches approximately 8 mm. Thereof,
rude estimation of the optical loss value is close to
18 dB, which is caused by mismatch between the
diameters of photodetector and light beam incident on
this detector.
The obtained results of calculations, performed for
the active ORC construction based on the compensation
principle with the Dove prism and general for all the
transmission channels way of collimation and focusing
the beams, enables to draw the following conclusions:
1. The maximum amount of channels in this facility
reaches practically the value approximately 10
channels, because of inadmissibly large sizes and
mass of a facility with larger amount of channels.
In particular, the length of the optical system in the
10-channel ORC reaches approximately 300 mm
and grows in proportion to the amount of channels.
Table 1. The maximum possible amount of optical channels in ORC with LEDs of different types.
Focal distance of the lens f, mm
25 50 75 100
(LED type)
Aperture angle β
N H,
mm
L,
mm N H,
mm
L,
mm N H,
mm
L,
mm N H,
mm
L,
mm
(SV5637-001) β = 2° 1 8 30 7 18,5 69 14 29.6 109 21 37.5 140
(SV2637-001) β = 4° 1 11 40 5 20 74 10 31 114 17 41 151
(L3989-01) β = 6° 1 11 40 2 22 81 6 32 118 9 42 155
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 1. P. 1-18.
doi: https://doi.org/10.15407/spqeo20.01.001
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
9
(a)
Distance Z from the optical axis, mm
D
is
ta
nc
e
Y
,
m
m
(b)
Distance Z from the optical axis, mm
D
is
ta
nc
e
Y
,
m
m
(c)
Distance Z from the optical axis, mm
D
is
ta
nc
e
Y
,
m
m
(d) Distance Z from the optical axis, mm
D
is
ta
nc
e
Y
,
m
m
Fig. 5. Diagrams for location of radiation sources L3989-01 on the ORC transmitting part and their contoured images within
the plane of detectors on the receiving part, which are created by the ORC optical system based on the Dove prism and
elliptical lenses with different focal distances.
2. In the facility with the optical system of the length
shorter than 70 mm, only one optical channel
mounted on the axis of rotation can be available.
3. In the facility even with ideal connection between
channels, there is noticable cross-interference
caused by light scattering on non-homogeneities
inside the prism and optical surfaces of prism and
lenses, the value of which is in proportion to the
amount of channels.
These conclusions also concern other constructions
of the ORC with prismatic compensators, in particular,
the known from [35] ORC based on the Pehan prism,
since astigmatism and aberrational image blurring in this
prism are not lower than those in the Dove one.
2.2. Passive construction of ORC
with the Dove prism and collective lenses
for focusing and collimation of beams
The course of rays in the construction of ORC with
fiber-optic transmission lines was calculated using the
mathematical solutions obtained by the methods of
analytic geometry, being based on geometric optics laws
for reflection and refraction of light at optical surfaces.
The value of optical losses in the transmission channels
was computed using the method of numeric integration
based on Fresnel equations. The respective program for
modeling the facility was developed using the software
package Mathlab.
Adduced below are the results of studying ORC
made in the variant when its transmission and receiving
parts are equipped with optical light guides serving as
radiators and receivers.
Shown in Fig. 6 are the calculated dependences of
the optical loss value in ORC transmission channels on
the butt radius of the receiving light guide for various
distances h of this butt from the rotation axis. The
calculations were performed for two cases, namely: i) in
the absence of prism angular beating; ii) when the prism
angular beating reaches the value ∆ = 0.06°.
Fig. 7 shows the calculated dependences of the
optical loss value in the ORC optical channel on the
prism angular beating for various values of the receiving
light guide butt: 50, 100, 200 та 400 μm. These
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 1. P. 1-18.
doi: https://doi.org/10.15407/spqeo20.01.001
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
10
calculations were performed for spherical lenses with the
following parameters: lens thickness is equal to 10 mm,
focal distance – f = 50 mm, refraction index of the prism
and lenses – n = 1.7. The butt diameter and numeric
aperture of the transmitting light guide were assumed to
be typical for multichannel fiber-optic cables: the butt
diameter – 50 μm, numeric aperture – NA = 0.2.
To minimize the sizes of the aberration scattering
circle, the height of prism was chosen as low as possible
for the given aperture of input beams and sizes of the
collimating lens. The height was calculated with account
of the condition that the extreme rays at the output of the
collimating lens should not be blinded by the prism. For
the above set lens and light guides characteristics, the
optimal prism sizes were as follows: the height – 27 mm,
and length 100 mm.
b)
h=0 mm
h=2 mm
h=3.5 mm
0
25
50
75
0.00 0.04 0.08 0.12 0.16 0.20
a)
Radius of optical detector, mm
O
pt
ic
al
lo
ss
v
al
ue
,
dB
Fig. 6. Calculated dependences of optical loss values in the
ORC optical channels with the Dove prism on the radius of
receiving channel. a) ∆ = 0°; b) ∆ = 0.06°.
0.00 0.01 0.02 0.03 0.04 0.05 0.06
10
0
20
30
40
50
d=100 km
d=50 km
d=200 km
d=300 km
Fig. 7. Calculated dependences of optical loss values in the
transmitting optical channel located on the rotation axis (h = 0)
on the value of the prism angular beating for various values of
the butt diameter d in the receiving light guide.
As seen from Figs 6 and 7, the essential
deficiencies of this ORC are high optical losses and
considerable oscillations of the signal amplitude during
prism rotation, which is caused by prism beating. For
instance, when prism angular beating is as low as
0.06°, modulation rotational oscillations of the optical
signal amplitude reach the value 30 dB for the light
guide of 100-μm diameter and 40 dB for that of 50-μm
diameter. Optical losses for the above light guides are
40 and 54 dB, respectively. If one takes into account
the losses by Fresnel for this case as well as the losses
caused by non-ideal mutual arrangement of lenses and
light guides in ORC transmitting channels, the total
losses will exceed 50 dB in the first case and 60 dB in
the second one. Thus, such facility is unfit to be used in
circuits of fiber-optic transmission lines with standard
cables.
Thereof, the ORC construction with collective
lenses for focusing and collimation of beams can be used
in the multichannel variant only as an active construction
in the composition with electrical transmission lines. In
the passive variant with optical interfaces based on light
guides without additional focusing and collimating
lenses, there take place inaccessibly high optical losses.
In particular, for the standard optical cables with the core
diameter 50 μm, the value of optical losses exceeds
36 dB, and for the non-standard cables with the core
diameter 100 μm this value exceeds 30 dB.
3. Multichannel ORC with a mirror compensator
When creating the multichannel ORC with a mirror
compensator, the mirror needs to satisfy two specific
requirements: it should be double-sided and as far thin as
possible. To make a facility with such mirror and, being
more exact, to mount it in such a manner that external
harmful factors (vibrations, temperature) could not have
any effect on it, is very difficult. In the most optimal and
original form, these tasks are solved in the technical
solution patented by [44]. In their facility schematically
depicted in Fig. 8, the optical compensator 4 consists of
two optical hemispheres separated between each other
with the thin double-sided mirror 5 that is not affected
by any external harmful factors.
The optical compensator 4 is mounted on the
rotation axis 3 between the rotor 17 and stator 16
through the insert 9. The rotational axis of the ORC rotor
3 passes through the center of the optical sphere and lies
within the plane of the mirror 5. The insert 9 is
articulationly joined with the case 6 due to bearings 10
and coupled with inserts 16, 17 via the conical gears 12,
14, 15 possessing the reduction coefficient 1:2.
Two groups of optical fibers (transmitting 1А-1N
and receiving 2A-2N) are located in the respective
inserts 16, 17 along the arc around the compensator
sphere and are oriented relatively to the mirror in such a
way that the butts of one group are the mirror images for
respective butts of another group. The lenses 18 serve as
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 1. P. 1-18.
doi: https://doi.org/10.15407/spqeo20.01.001
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11
the collimator ones for the transmitting group and as the
focusing ones for the receiving group.
The insert 16 is placed in the case 6, while the
insert 17 – in the case 7 that is articulationly joined with
the case 6 via the bearings 8, 11, which enables it to
freely rotate around the axis 3, together with the insert
17 and a group of light guides 2А-2N mounted in it.
When the insert 17 together with the group of light
guides 2А-2N rotates by an arbitrary angle φ relatively
to the insert 16, the optical sphere 4 with the mirror 5
also rotate in the same direction by the halved angle φ/2
due to a gear mechanism.
Compensation of the beam turn in the facility is
reached by the following way.
Let us assume that, in one of the azimuthal
positions of the insert 17 relatively to the insert 16, the
light guide group 2А-2N is optically connected with that
1А-1N due to the mirror 5.
Fig. 8. Optical rotary connector with mirror compensator [44]:
1А-1N – group of transmitting light guides; 2А-2N – group of
receiving light guides; 3 – axis of rotation; 4 – optical sphere;
5 – double-sided mirror.
Fig. 9. Paths of rays in ORC for one of mirror positions, when
the mirror crosses the input light flow.
When the mirror does not move, and light guides
2А-2N with the insert 17 turn by the arbitrary angle φ,
the beams radiated by the light guides 2А-2N are
reflected by the mirror in the direction opposite to the
rotation direction of the incident beams by the angle
“– φ”. Since the mirror also rotates, then its turn by the
angle +φ/2 causes the turn of the reflected beams by the
angle +φ. As a result, at the output of the optical sphere
the position of beams remains unchanged. In other
words, there takes place compensation of beam
movement, and from a theoretical viewpoint the facility
is functionally capable.
At the same time, when thoroughly considering
operation of this facility there arises a controversial
question related with the possibility to avoid here
significant optical losses as well as considerable
rotational vibrations in the value of optical losses in
those mirror angular positions when the mirror crosses
the input light flow and separate it by two ones (see
Fig. 9). It causes the following question: is it allowed to
practically use the facility with these deficiencies?
Since the description for the USA patent №4447114
does not contain any optical characteristics of the respective
facility, to determine them in [57] there were performed
detailed theoretical investigations of this facility behavior
by using the method of computer modelling.
Studying the facility was performed for two in
principle different variants of its realization. First, in the
variant with fiber-optic collimators that provide a wide
collimated optical beam with the diameter 1 to 4 mm.
These collimators are designed being based on fiber-optic
light guides and quarter-wave gradient plates or spherical
lenses. Second, in the variant with fiber-optic collimator
that provides a narrow optical beam with the diameter
lower than 0.2 mm. The latter can be created on the base
of single-mode light guides and spherical microlenses.
Fig. 9 illustrates the calculated beam course in
ORC. There used is the constructive variant with wide
collimated light beams. To image in one figure the
focused optical patterns of small sizes, which are created
by light beams at the output of optical sphere, as well as
the course of beams through the constructive elements of
considerably larger sizes (optical sphere with the mirror,
focusing and collimating lenses) this sphere and mirror
are depicted in Fig. 9 in a slightly deformed look. Along
the Х axis, the picture dimensions are elongated, while
along the Z axis they are squeezed. Besides, for
simplicity Fig. 9 shows only those input rays that
contour the light flow incident on the optical sphere
from the lens fiber-optic collimator.
Calculations of ray courses were performed in the
facility model with the following parameters: the radius
of optical sphere R = 10 mm, refractive index of the
sphere n = 1.5, diameter of input light beam d = 1 mm,
aperture angle of the input light beams Ψ = 0.6°. The
diameter of light beam and aperture of rays are taken as
those for typical multi-mode light guides with the
diameter 50 µm and the collimating gradient quarter-
wave lens with the diameter 1 mm.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 1. P. 1-18.
doi: https://doi.org/10.15407/spqeo20.01.001
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
12
Fig. 10. 3D image of the optical sphere, mirror, input light
beam of ring shape, and spot of focused beams at the output of
optical sphere.
To provide more obvious reception, shown in
Fig. 10 are the 3D image of the optical sphere, plain
mirror, contour of the collimated optical beam
possessing the ring shape at the sphere input and the
light beam at the sphere output, which is split by the
double-sided mirror. This figure is plotted when
calculating the facility with the following parameters:
radius of the optical sphere R = 1 mm, refraction index
of the sphere n = 1.5; radius of the input beam r = 1 mm;
aperture angle of the collimated beams Ψ = 1°.
As seen from Figs 9 and 10 in angular positions of
the mirror when it splits the input light beam the part of
rays inside the optical sphere is reflected from the
mirror, while another part freely passes along the mirror.
At the output of optical sphere, the light beam is separa-
ted by several light beams. The beams reflected from the
mirror in accord with the mentioned above principle of
compensation are focused onto the butt end of receiving
light guide, while the beams that pass along the mirror
do not change their initial direction. It is obvious that in
above mentioned positions of the mirror in the facilities
with the mirror compensator there take place specific,
inherent to these constructions optical losses of signals
as well as rotational dependence of the transfer
coefficient for the optical signal, when the mirror rotates.
Investigated in [57] was the influence on ORC opti-
cal characteristics from various constructive factors, na-
mely: the diameter and refractive index of the optical
sphere, diameters and refractive indexes of spherical
collimating and focusing lenses, diameter of light guide
core and its numeric aperture. Also, the authors studied
the influence ORC characteristics from exactness of ma-
nufacturing the construction elements and their com-
position, which plays the principal role in determination
of technological effectiveness inherent to the facility.
The method of calculations performed in [57] for
the transfer coefficient and the value of optical losses
can be briefly described as follows.
The optical losses between the butts of transmitting
and receiving light guides were calculated with account
of the ratio between the number of beams focused on the
butt of receiving light guide and total amount of beams
radiated by the transmitting light guide, taking into
account the intensity of each beam and numeric aperture
NA of light guides.
The intensity of beams was determined in assump-
tion that the surface brightness of light at the butt of light
guide is homogeneous over the butt area and obeys the
Lambert law, which is close to the real distribution of
the light intensity at the output butt of a light guide,
when one uses a light source with a high aperture, for
instance, LED.
The source of radiation (in our case, it is the radia-
ting butt of a light guide) was separated by l ring zones,
each of them, in its turn, was separated by m sectors. Cen-
ters of these sectors were defined as points (coordinates)
of output for homocentric light beams, the intensity of
which was conditionally considered as the total intensity
that can be radiated by the respective sector of the light
guide butt in all the possible directions with the boundary
angle corresponding to the light guide numeric aperture.
In its turn, the homocentric beams from each sector
were separated by n conical beams each of them was
additionally separated by g azimuthal sectors.
Thus, after partitioning the light beam by the
elementary ones the intensity of one beam was
considered as the intensity that corresponds to radiation
from the elementary area of the light guide butt in a set
direction within the limits of an elementary solid angle.
Before calculation of the intensity for this elementary
beam Рelem, they calculated the total intensity Рik of all the
beams that propagate between two conical surfaces from
the following mathematical expression [58]:
( ) ( )[ ]kiik IP α−α⋅⋅π= coscos2 , (1.1)
( )iII α⋅= cos0 , (1.2)
where I0 is the intensity of light beam along the cone
axis, αi and αk are the plain angles at the apexes of
respective cones.
The intensity of one beam was calculated using
division of the total intensity of beams Рik on the amount
of ring zones and sectors corresponding to the number of
elementary parts with account of their areas by using the
following mathematical relation
( ) gmrrrPP qqikelem ⋅⋅−⋅= −
22
1
2 , (1.3)
where r is the light guide butt radius, rq and rq-1 are
external and internal radii of the respective butt ring zone.
When the light guide butt surface is divided by
sufficiently small areas of elementary sectors and the
solid angle is divided by elementary solid angles, then
the accuracy of calculations for the transfer coefficients
can be made as high as one likes. Using the iteration
method, one can ascertain that, to reach the accuracy of
calculations at the level 0.2%, it is sufficient to choose
l = 10, m = 36, g = 36, αi = αk = 0.25°.
X, mm
Z
, m
m
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 1. P. 1-18.
doi: https://doi.org/10.15407/spqeo20.01.001
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
13
3.1. Optical losses and rotational dependence for the
coefficient of optical transfer inherent to ORC with
mirror compensator and fiber-optic collimator, which
provide wide optical beams
Depicted in Fig. 11 are the angular dependences for the
ORC transfer coefficients calculated for the facility with
the optical sphere of the radius R = 10 mm with single-
mode and multimode light guides in optical receiving
channels. These calculations were performed for ORC
with ideally exact geometry of construction (transverse
shift of the light guide butt Δx, transverse shift of the
sphere center δXc and angular beating Δβ of the mirror in
the horizontal plane were assumed to have zero value).
At the transmitting side of the optical channel,
fiber-optic collimators are used, they are based on a
spherical lens of the radius r = 2 mm.
As to the receiving side, we considered two
variants of: multimode fiber-optic light guide
(d = 50 μm, NA = 0.19) and single-mode light guide
(d = 7 μm, NA = 0.13). The focusing lenses were
assumed to be analogous to the collimating ones
(r = 2 mm, n = 1.5).
It is seen from Fig. 11 that in angular positions of the
mirror β when it crosses the light beam (near 90° in the
figure) one can observe a sharp drop of the transfer
coefficient down to the value lower than 5%. In this
moment, the value of modulation amplitude reaches 95%.
The angle β is conditionally assumed to be equal to
90° for the mirror position, when its normal lies along the
perpendicular to the plane where the axes of transmitting
and receiving light guides lie, these guides being placed
along the ring around the compensator optical sphere
(Fig. 9). In other words, when the mirror plane and the
plane where axes of light guides lie coincide.
87 88 89 90 91 92 93
0
0.2
0.4
0.6
0.8
1
K1
K2
R=10 mm
r=2 mm
n=1.5
Δx=0
Δβ°=0
δXc=0
Angle of mirror turn, β°
Tr
an
sf
er
c
oe
ff
ic
ie
nt
K
, r
el
. u
n
Fig. 11. Rotational dependences for the transfer coefficient in
the ORC optical channel with a lens fiber-optic collimator,
which are calculated in the model of facility with spherical
focusing and collimating lenses for two types of light guides in
the receiving channels. K1 is the relative transfer coefficient
for ORC with single-mode light guides in the receiving
channels; K2 – relative transfer coefficient for ORC with
multimode light guides in the receiving channels.
The same results were obtained when calculating the
construction with light beams of the diameters 1 and 2 mm.
3.2. Information capacity of ORC with the mirror
compensator and fiber-optic collimators that provide
wide optical beams
As seen from Fig. 8, the amount of optical channels in
ORC directly depends on the diameter of compensator
optical sphere. The larger is the sphere diameter, the
higher is the amount of channels that can be placed on
its surface along the arch around the sphere. On the other
hand, as calculations show, optical characteristics of the
facility are worsened with increasing the compensator
dimensions. I.e., the higher the amount of channels in
the designed facility, the worse are optical characteristics
of ORC for the set accuracy of manufacturing it.
For instance, if the diameters of holes for lenses in
the inserts 16, 17 (Fig. 8) are assumed to be 1.5 –
2.0 mm, and the distance between holes is 0.5 mm
(which is necessary to provide needed durability of
construction), then the diameter of optical sphere 5 mm
allows placing only three channels along the arc around
the sphere (one – on the rotation axis, and two – on both
sides of the axis under the angles 45°).
If the sphere diameter is increased up to 10 mm,
then there may be placed 5 optical channels. However, it
considerably increases requirements to the accuracy of
making the construction. For example, when the sphere
diameter is 10 mm, and with the same errors in the
construction assemblage as in the construction with the
5-mm optical sphere (Δx = 1 μm, δXc = 5 μm and
Δβ = 0.15°), optical losses will increase from 75 up to
90% in the variant of construction with collimating and
focusing lenses of the diameter 1 mm and multimode
light guides in optical channels of the facility.
Being based on the results of theoretical
investigations [57], one can make the following
conclusions. If the construction of movable transmitting
mechanism contains tooth gears, then making the facility
with the above mentioned accuracy is practically
impossible. Especially, when it concerns the facility that
designed to operate in harsh conditions of exploitation
within a wide temperature range. Even for this practically
unattainable accuracy, the values of optical losses and
modulation distortions in the amplitude of optical signals
during rotation of the rotor part remain too high.
3.3. Optical characteristics of ORC with the mirror
compensator and micro-lens optics
Let us consider the variant of facility with application of
micro-lenses on the butts of light guides.
Micro-optics allows realization of a narrow light beam
with a small diameter at the output of single-mode light
guide. In the case of narrow light beam, the optical rays
after their splitting by the mirror pass near the optical
axis of the system and are focused by the compensator
optical sphere into the spot of small sizes (see Fig. 12).
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 1. P. 1-18.
doi: https://doi.org/10.15407/spqeo20.01.001
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
14
Fig. 12. Spatial distribution of rays in the ORC construction with microlenses for one of mirror positions: a) diagram of ray paths
in ORC; b) distribution of ray coordinates within the plane of receiving light guide butt; c) distribution of ray angles of incidence
onto the light guide butt. 1 and 7 – point light source and its image at the receiving light guide butt; 2 and 6 – ray paths in
collimating and focusing lenses; 3 and 5 – ray paths between the optical sphere and microlenses; 4 – path of the part of rays that
pass near the mirror.
Adduced in Fig. 12a is the calculated diagram of
ray paths in the facility with the point source of light.
Application of the point source of light instead of the
long one allows revealing the typical features in
behavior of this facility independently of source
dimensions as well as saving the time for calculations.
Figs 12b and 12c illustrate distributions for
coordinates and angles of ray incidence onto the butt of
receiving light guide for the construction with the
following parameters: the radius of optical sphere
R = 2.5 mm, radius of the micro-lens r = 0.2 mm,
transversal shift of the point light source relatively to its
nominal position ΔX = −2 μm, the maximum aperture
angle of point source radiation is 7.5°.
As seen from Fig. 12a, in the case of micro-lenses
all the rays pass near the optical axis (both those
reflected from the mirror and those passing aside of the
mirror) and, therefore, are focused into a spot of small
sizes, the diameter of which is lower than 20 μm (see
Fig. 12b).
At the same time, despite sharp focusing the rays in
this variant of construction one can also observe
considerable losses and rotational oscillations in the
optical signal value in ORC optical channels. In this
case, the facility is exceedingly sensitive to the accuracy
of making the construction and its assemblage. Even a
small error in making the fiber-optic collimator results in
the transverse shift of a point source relatively to the
optical axis of collimating lens at the level of several
micrometers, which increases optical losses and signal
modulation up to the values higher than 90%. The main
reason for optical losses and additional modulation in
this case is related with high angles of ray incidence onto
the butt of receiving light guide after output from the
short-focus lens when the rays exceed the aperture
parameters of light guide.
As seen from Fig. 12c, when the transverse shift of
the point light source reaches only 2 μm, a considerable
part of rays at the output of short-focus lens falls onto
the light guide butt under the angles 16 to 20 degrees,
which essentially exceeds the operation aperture of
fiber-optic cable.
The influence of the transverse shift ΔX of the point
light source relatively to the center of the collimating
micro-lens as well as radial beating δXc of the sphere on
the transfer coefficient K in ORC with multimode light
guides (Ø = 50 μm, NA = 0.19) at the receiving side of
ORC are shown in Fig. 13a. The calculated curves for
the dependence of the transfer coefficient on the value
Δβ for angular beating of the mirror in the case of
transverse shift of the point source ΔX = −3 μm and
radial beating of the sphere δXc = ±10 μm is shown in
Fig. 13b. The calculations were performed for the mirror
angular position β = 89.8°.
As seen from the adduced figures, the radial shift of
the point source by 3 μm in the case of optical sphere
radial beating δXс ± 10 μm leads to the value of optical
losses at the level 50%. The angular beating of the
mirror with the value 0.3° introduces additional optical
losses and respective amplitude modulation of optical
signals during mirror rotation from 50 up to 80%.
Thus, being based on the considered dependences
for the value of optical losses on the value of transverse
shifting the point light source relatively to the microlens
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 1. P. 1-18.
doi: https://doi.org/10.15407/spqeo20.01.001
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
15
-5 -2.5 0
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
ΔX, μm.
Tr
an
sf
er
c
oe
ff
ic
ie
nt
K
, r
el
. u
n.
β°=89.8
Δβ°=0
0 0.25 0.5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Mirror angular beating, Δβ°.
Tr
an
sf
er
c
oe
ff
ic
ie
nt
K
, r
el
. u
n.
ΔX=-3 μm °
δXc=+10 μm
δXc=-10 μm
δXc=0
(а) (b)
Fig. 13. Calculated dependences for the relative transmission coefficient in ORC with a point light source on the indexes of
manufacturing accuracy.
89 90 91
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
∅=7 μm
∅=50 μm
δXc=-5 μm
Δx=+1 μm
β°
89 90 91
0
0.1
0.2
0.3
0.4
0.5
∅=7 μm
∅=50 μm
δXc=-5 μm
Δx=-1 μm
β°
89 90 91
0.2
0.25
0.3
0.35
0.4
0.45
0.5
∅=7 μm
β°
Tr
an
sf
er
c
oe
ffi
ci
en
t K
, r
el
. u
n.
NA=0.19
NA=0.13
∅=50 μm
(a) (b) (c)
Fig. 14. Dependences of the signal transfer coefficient on the angle of mirror turn in ORC with microlenses of the diameter
0.4 mm and single-mode light guides in transmission channels as well as single-mode and multimode light guides in receiving
channels: (a) for a geometrically ideal ORC; (b) for ORC with a light-guide butt shifted along the radius (Δx = +1 μm,
δXc = –5 μm); (c) for ORC with a light-guide butt shifted along the radius (Δx = –1 μm, δXc = –5 μm).
center, one can draw an important conclusion, namely:
in optical channels of ORC of compensation operation
with the mirror compensator and micro-optics, it seems
reasonable to use optical sources only of small sizes that
do not exceed 7 μm.
Depicted in Fig. 14 are the calculated charac-
teristics for the transmission coefficient K for ORC with
the micro-lens of the diameter 0.4 mm and single-mode
light guides having the diameter Ø = 7 μm (NA = 0.13)
(lower curves in the figure). Also adduced in this figure
are the K dependences on the angle of mirror turn in the
case of using multimode light guides with the core
diameter 50 μm in the receiving channels, NA = 0.19
(upper curves).
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 1. P. 1-18.
doi: https://doi.org/10.15407/spqeo20.01.001
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
16
Fig. 14a shows the characteristics for an ideal
(from the geometrical viewpoint) facility. Depicted in
Figs 14b and 14c are the ORC characteristics typical for
the optical sphere center shifted by the value
δXc = −5 μm and the transverse shift of the transmitting
light guide butt by ΔX = ±1 μm. These calculations were
performed for the construction with parameters:
R = 2.5 mm, r = 0.2 mm, n = 1.5.
It is seen from Fig. 14a that in the geometrically
ideal facility optical losses reach 80% of those in fiber-
optic channels based on single-mode light guides, and
60% of those in optical channels where multimode light
guides are used.
The latter variant could be considered as the
acceptable one, but it is prevented by high sensitivity of
facility performances to the construction assemblage.
For instance, a small transverse shift of the transmitting
light guide butt by 1 μm reduces the transfer coefficient
down to 10% in the optical channels with single-mode
light guides, and does it down to 26% in those with
multimode light guides at the receiving side (see
Fig. 14c). In this case, modulation of the signal transfer
coefficient during rotor rotation reaches the value 50%
in the channel with the multimode light guide.
Thus, being based on the results obtained by using
computer theoretical analysis of ORC construction
known from the USA patent No 4447114 and containing
the mirror compensator, one can draw the following
conclusions:
1. ORC with mirror compensators can be capable
only in the variant of using micro-optics, they are
extremely sensitive to the accuracy of manufacturing the
mechanism and optical components of the facility, a
number of which should be made and mounted with the
accuracy not worse than 1…2 μm.
With this accuracy, the facility is low-technological
and expensive, and its optical characteristics remain
middling.
With increasing the diameter of compensator
optical sphere, the ORC optical characteristics are
worsened. So, the calculations indicate that, when the
diameter of compensator optical sphere grows from 5 up
to 14 mm, optical losses increase from 80 up to 96% for
the geometrically ideal construction with single-mode
light guides, and from 60 up to 85% for the construction
with multimode light guides.
2. Optical channels of the facility are one-
directional, since in the transmitting part only single-
mode light guides with a small butt diameter can be
applied, while in the receiving part multimode light
guides with a large diameter of butt should be used.
3. The maximum amount of physical channels that
can be really provided using this technical solution does
not exceed 5–7 identities, since for larger amount of
channels the requirements to ORC construction accuracy
can be unreal.
4. The construction is not protected from mutual
cross-interference between channels, which is caused by
light scattering on optical inhomogeneities inside the
sphere as well as on its surface.
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(To be continued).
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| id | nasplib_isofts_kiev_ua-123456789-214918 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1560-8034 |
| language | English |
| last_indexed | 2026-03-21T13:44:24Z |
| publishDate | 2017 |
| publisher | Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| record_format | dspace |
| spelling | Shapar, V.M. Lysenko, V.S. Savchuk, A.V. 2026-03-03T11:11:04Z 2017 Analysis of multichannel optical rotary connectors based on the compensation operating principle with mirror and prismatic optical compensators (Part 1) / V.M. Shapar, V.S. Lysenko, A.V. Savchuk // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2017. — Т. 20, № 1. — С. 1-18. — Бібліогр.: 58 назв. — англ. 1560-8034 PACS: 42.15.Eq, 42.74.-e, 85.60.-q https://nasplib.isofts.kiev.ua/handle/123456789/214918 https://doi.org/10.15407/spqeo20.01.001 Performed in this work is a comprehensive theoretical computer analysis of performances inherent to two types of multichannel optical rotary connectors (ORC of compensation operation based on mirror and prismatic compensators. This analysis relies on exact analytical expressions obtained for light ray paths in ORC models with a mirror compensator made in the form of a bilateral mirror placed between two optical hemispheres and with a prismatic compensator made in the form of a Dove prism placed between two non-aberrational elliptic lenses. Found in ORC with the mirror compensator is the essential deficiency inherent to all these constructions, which is related to considerable rotary oscillations in the value of optical signals in mirror angular positions when the mirror halves the input light beam. In these mirror positions, the amplitude value of optical signal oscillations exceeds 95%, and optical losses are higher than –13 dB when the rotor turns. One deficiency more in these constructions is also strict technical requirements for the accuracy of making the optical components and mechanisms at the level of 1…2 µm. Concerning the ORC construction with a prismatic compensator as well as collimator and focusing lenses common for all the channels, one should note the inadmissibly high optical losses of the signal value (higher than –30…40 dB) in the case of construction with fiber-optic interfaces, and large dimensions and mass in the case of active construction with optoelectronic transducers at the inputs and outputs of ORC. For example, when the number of channels N = 10, the longitudinal dimension of the optical transfer channel (prism and lenses) exceeds 300 mm, and this dimension increases with increasing the number of channels. When this dimension is lower than 100 mm, the facility can be equipped with only one optical communication channel containing one LED and one photodiode located on the rotation axis. Optical losses in these constructions cannot be considered as satisfactory ones, since the respective loss value is higher than 18 dB for the number of channels N = 10. en Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України Semiconductor Physics Quantum Electronics & Optoelectronics Analysis of multichannel optical rotary connectors based on the compensation operating principle with mirror and prismatic optical compensators (Part 1) Article published earlier |
| spellingShingle | Analysis of multichannel optical rotary connectors based on the compensation operating principle with mirror and prismatic optical compensators (Part 1) Shapar, V.M. Lysenko, V.S. Savchuk, A.V. |
| title | Analysis of multichannel optical rotary connectors based on the compensation operating principle with mirror and prismatic optical compensators (Part 1) |
| title_full | Analysis of multichannel optical rotary connectors based on the compensation operating principle with mirror and prismatic optical compensators (Part 1) |
| title_fullStr | Analysis of multichannel optical rotary connectors based on the compensation operating principle with mirror and prismatic optical compensators (Part 1) |
| title_full_unstemmed | Analysis of multichannel optical rotary connectors based on the compensation operating principle with mirror and prismatic optical compensators (Part 1) |
| title_short | Analysis of multichannel optical rotary connectors based on the compensation operating principle with mirror and prismatic optical compensators (Part 1) |
| title_sort | analysis of multichannel optical rotary connectors based on the compensation operating principle with mirror and prismatic optical compensators (part 1) |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/214918 |
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