[0001] The present invention relates to a device for processing digital optical signals.
More particularly, the present invention relates to an optical device for comparing
at least one sequence of N bits with at least one predetermined sequence of N reference
bits, an optical communication system in which this comparison is made, and a method
for making this comparison.
[0002] Conventionally, the pattern recognition is carried out by means of a conventional
operation of correlation between a reference pattern and a test pattern. The term
"reference pattern" denotes a predetermined pattern which is to be recognized. The
term "test pattern" denotes any other pattern which is to be compared with the reference
pattern. The correlation c(x,y) between a reference pattern s(x,y) and a test pattern
f(x,y) is defined thus:

where s(x,y) and f(x,y) are two-dimensional patterns, (x, y) are spatial coordinates
of the said two-dimensional patterns, (α,β) are conventional integration variables
and the asterisk indicates the complex conjugation.
[0003] This integral is conventionally represented as the convolution of the two patterns
s(x,y) and f(x,y):

where ⊗ represents the convolution operation.
[0004] As is known, in the domain of the Fourier transform this convolution operation becomes
a simple product of the Fourier transforms of the individual patterns (indicated in
upper-case letters):

where (ξ,η) are the spatial frequencies.
[0005] In order to find the correlation function c(x,y) in the spatial domain, therefore,
it is sufficient to calculate the spectrum C(ξ,η) and then to find its inverse Fourier
transform.
[0006] As is well known, in optics it is possible to carry out a highly complex operation
such as the two-dimensional Fourier transform in a simple way and in real time by
using an optical lens. This is because such a lens provides, on its rear focal plane,
the exact Fourier transform of a pattern located on its front focal plane.
[0007] There are known optical devices capable of carrying out an operation of correlation
between two patterns. For example, Figure 1 (in which, for greater clarity, the reference
axes x, y, z are also indicated) shows a conventional optical correlator according
to Vander Lugt (A. Vander Lugt, "Signal detection by complex spatial filtering", IEEE
trans. Inform. Theory, vol. 10, p. 139, 1964).
[0008] This device comprises a first lens 21 having a focal length f
1, an optical filter 22 and a second lens 23 having a focal length f
2. The two lenses 21 and 23 are at a distance of f
1+f
2 from each other, and the optical filter 22 is located in the rear focal plane of
the first lens 21, which corresponds to the front focal plane of the lens 23. In Figure
1, the second lens 23 has the same focal length f as the lens 21 (f
1=f
2=f). On the other hand, when the lens 23 has a focal length f
2 different from f
1, the optical field at the output of the correlator has an additional scaling factor
by comparison with the case in which f
1=f
2=f.
[0009] For the purposes of the present description, the input plane 11 and the output plane
14 of the device shown in Figure 1 are intended to indicate, respectively, the front
focal plane of the lens 21 and the rear focal plane of the lens 23.
[0010] The optical filter 22 may be, for example, a matched filter (MF) or a phase only
filter (POF).
[0011] The matched filter MF has a transfer function H(ξ,η) = kS*(ξ,η), where S*(ξ,η) denotes
the complex conjugate of the Fourier transform of the reference pattern s(x,y) and
k is a multiplication constant.
[0012] The phase only filter POF has a transfer function of

where S(ξ,η) is:

is the Fourier transform of the reference pattern s(x,y).
[0013] With reference to the operation of the Vander Lugt correlator,
a) the test pattern f(x,y) which is located on the input plane 11 is Fourier transformed
on the rear focal plane of the lens 21, thus producing the field distribution F(ξ,η);
b) on the said rear focal plane, this optical field distribution F(ξ,η) is filtered
by the optical filter 22, giving at its output an optical field distribution of F(ξ,η)H(ξ,η);
and
c) on the rear focal plane of the second lens 23, the optical field distribution F(ξ,η)H(ξ,η)
is Fourier transformed by the lens 23 to provide the convolution f(x,y)⊗h(x,y) of
the test pattern f(x,y) and the response to the impulse [h(x,y)] of the optical filter
22;
where h(x,y) is the inverse Fourier transform of the transfer function H(ξ,η) of
the filter [ζ
-1 H(ξ,η)] which, as shown above, contains the information relating to the reference
pattern s(x,y).
[0014] In the case of both the matched filter and the phase only filter, the intensity of
the field distribution on the output plane 14, measured at the origin (x=0, y=0),
takes a peak value when the test pattern coincides with the reference pattern [f(x,y)=s(x,y)],
and a smaller value when this is not the case. Thus by measuring the intensity of
the field distribution at the origin (x=0, y=0) of the output plane 14 it is possible
to determine whether or not the test pattern is identical to the reference pattern.
[0015] However, the matched filter and the phase only filter process the patterns in different
ways from each other.
[0016] In the case of a matched filter, the convolution f(x,y)⊗h(x,y) corresponds to the
correlation c(x,y) between the test pattern and the reference pattern as defined by
equation (2). Thus, when the test pattern coincides with the reference pattern [f(x,y)=s(x,y)],
the Vander Lugt correlator carries out an operation of the auto-correlation type:

and, when the test pattern f(x,y) is different from the reference pattern s(x,y),
it carries out an operation of the cross-correlation type:

[0017] However, in the case of a phase only filter, the convolution f(x,y)⊗h(x,y) does not
correspond to an operation of correlation c(x,y) between the test pattern and the
reference pattern, as conventionally defined in mathematics [equation (2)], and, when
the reference pattern [f(x,y)=s(x,y)] is present on the input plane 11, the said convolution
is of the type:

where ζ
-1 indicates the operation of the inverse Fourier transformation. On the other hand,
when the test pattern f(x,y) is different from the reference pattern s(x,y), this
convolution is of the type

[0018] Although the operation carried out by the Vander Lugt correlator with a phase only
filter is not a true correlation operation as conventionally defined in mathematics,
for the purposes of the present invention the functions ac'(x,y) and cc'(x,y) are
considered to be an autocorrelation and a cross-correlation respectively.
[0019] In the present description, among the various parameters identifying the performance
of a correlator with a phase only filter, reference will be made to a parameter D'
indicating the ratio between the intensity (|cc'(0,0) |
2) of the field distribution found at the origin (x=0, y=0) of the output plane 14
in a cross-correlation operation cc'(x,y) and that (|ac'(0,0) |
2) which is found in an autocorrelation operation ac'(x,y):

where cc'(0,0) and ac'(0,0) are the convolution operations defined previously in
equations (8) and (9), evaluated, for x=0 and y=0, on the output plane 14 of the correlator
shown in Figure 1.
[0020] However, in the case of a correlator with a matched filter, reference will be made
to a parameter D indicating the ratio between the intensity (|cc(0,0) |
2) of the field distribution found at the origin (x=0, y=0) of the output plane 14
in a cross-correlation operation cc(x,y) and that (|ac(0,0) |
2) which is found in an autocorrelation operation ac(x,y):

where ac(0,0) and cc(0,0) are the autocorrelation and cross-correlation defined previously
[equations (6) and (7)], evaluated, for x=0 and y=0, on the output plane 14 of the
correlator shown in Figure 1.
[0021] The parameters D and D' take a value of unity when a test pattern f(x,y) identical
to the reference pattern s(x,y) is present at the input of a correlator. However,
if a pattern different from the reference pattern is present at the input, these parameters
D and D' take a value of less than 1, and the discrimination capability CD of the
correlator, defined as

will increase as the value of D or D' decreases.
[0022] The parameters D and D' are therefore indicators of the discrimination capability
CD of a correlator device.
[0023] It is also known that the phase only filter has an overall performance which is better
than that of the matched filter when it is connected in a Vander Lugt correlator for
pattern recognition [K.C. Macukow et al., "Phase only filter as matched spatial filter
with enhanced discrimination capability", Optics communications, vol. 64, p. 224,
1987; L.P. Yaroslavsky, "Is the phase only filter and its modifications optimal in
terms of discrimination capability in pattern recognition?", Applied Optics, vol.
31, p. 1677, 1992; L.A. Romero et al., "Comparison between the peak-to-sidelobe ration
of the matched and the phase only filters", Optics Letters, vol. 16, p. 253, 1991;
B.V. Kumar et al., "Phase only filter with improved signal to noise ratio", Applied
Optics, vol. 28, p. 250, 1989].
[0024] US Patent 5 214 534 also describes a method for carrying out a correlation of a pattern
in a Fourier transform correlator. This method consists in encoding an input pattern
as a phase only object having a standardized amplitude and a phase which is a function
of the intensity of the said input pattern. The said method also consists in obtaining
the Fourier transform of this object, in filtering the Fourier transform of the said
object with a two-dimensional phase only filter in which a reference pattern has been
recorded, and, finally, in obtaining the inverse Fourier transform of the said object
which has been filtered in this way.
[0025] US Patent 5 523 881 describes an optical signal processor which uses a coherent light
source, a first and a second spatial light modulator and a beam splitter. The light
from the said source is reflected by the beam splitter and sent to the first spatial
light modulator where it is modulated by multi-phase modulation in accordance with
an input pattern. The said coherent light, modulated in this way, is then subjected
to the Fourier transform, sent to the said second spatial light modulator in which
it is modulated by multi-phase modulation in accordance with a reference pattern,
and then subjected to the inverse Fourier transform. A signal dependent on the correlation
operation between the said input pattern and the said reference pattern is thus obtained
at the output.
[0026] However, the problem of the recognition of digital optical signals, in other words
that of the discrimination of a sequence of N reference bits from any other sequence
of N bits, even in the case in which these sequences differ only by a single bit,
is much more complex than that of pattern recognition, in which the input patterns
generally differ from the reference pattern by much more than a single point.
[0027] In tackling the problem of the recognition of digital optical signals, in other words
of sequences of bits which carry a numerically encoded data element, the inventors
of the present invention have investigated, by means of computer simulations, the
performance of a Vander Lugt correlator with a phase only filter 22 and with binary
sequences of N bits (the bits had the value of 1 or 0) at the input. These simulations
commenced with the use of an amplitude modulation of the N bits, in which bit 1 was
associated with the presence of an optical field while bit 0 was associated with its
absence, or vice versa (modulation of the on/off type). Additionally, two reference
binary sequences of 8 bits (one byte) corresponding to 01000111 (the number 71 in
decimal notation) and 01001110 (the number 78 in decimal notation) were selected,
and the values of the parameter D' (defined above) were calculated for 256 different
input test bytes (all the possible bytes obtainable with binary sequences of N=8 bits,
i.e. 2
N).
[0028] Figures 14 and 15 show the values of the parameter D' found in this way for the reference
byte 01000111 (71) and 01001110 (78) respectively. In both cases, all the test bytes,
which were different from the reference byte, were discriminated (gave a value of
D' less than 1) from the reference byte, and the worst case (lowest CD') was found
with the test byte 01001111 (79), in other words with one of the bytes which differed
from the reference byte by one bit only. For the reference word 01000111 (71) and
the test byte 01001111 (79), the parameter D' was found to be 0.99, while for the
word 01001110 (78) and the byte 01001111 (79) it was found to be 0.87. This means
that the worst value of CD' was found to be less than 1% in the case of the reference
byte (71), and approximately 13% in the case of the reference byte (78).
[0029] In this connection, it should be noted that, in order to determine whether or not
a test sequence is identical to the reference sequence, it is also necessary to use
a device which is capable of analysing the value of the intensity of the signal provided
by the operation of comparison between the two sequences, and to determine whether
or not this value is equal to the maximum value which this intensity has when the
test sequence is identical to the reference sequence. As the value of the intensity
corresponding to the worst case approaches the said maximum value, the said device
has to be more sensitive to be able to distinguish the reference sequence from all
the possible input test sequences. For example, with a value of CD' (or CD) equal
to 1%, the said device has to be capable of detection variations of intensity of 1%,
provided that there is no background noise. However, since this is never the case,
a relatively very low noise is required in addition to the high sensitivity of the
device. These conditions, even if they can be met, require the construction of very
expensive devices. In order to be able to use inexpensive commercial devices, the
inventors tackled the problem of identifying the most favourable possible values of
CD' (or CD) for all the 2
N-1 test sequences which differ from the reference sequence.
[0030] Having found that the amplitude modulation of a numerical sequence was not suitable
for the discrimination of sequences of bits, the inventors decided to investigate
the performance of a Vander Lugt correlator with a phase only filter and sequences
of N input bits which were phase modulated (the bits having the same intensity and
a phase of 0/π for the 0 and 1 bits respectively, or vice versa).
[0031] Figures 4 and 5 show the values of the parameter D' which were obtained in the case
of the reference bytes 01000111 (71) and 01001110 (78) respectively for the 256 possible
input test bytes.
[0032] In this way the inventors found that the discrimination capability CD' had acceptable
values for all the input test bytes, except for the complementary bytes. This was
because the Vander Lugt correlator configured in this way (with a phase only filter
and conventional 0/π phase modulation) was unable to discriminate the reference byte
from its complementary.
[0033] The inventors therefore set up various other working hypotheses concerning the question
of how to distinguish a sequence of N reference bits from its complementary without
adversely affecting the capability of discriminating this reference sequence of N
bits from the other test sequences of N bits. In the course of this research, they
unexpectedly found that this could be achieved by using a suitable 0/απ phase modulation,
with 0<α<1, for the input bits.
[0034] In a first aspect, the present invention therefore relates to an optical device comprising
- a first element capable of supplying a digital optical signal comprising at least
one sequence of N bits modulated by a suitable phase modulation;
- a series-parallel converter for converting the said at least one sequence of N bits
into a spatial pattern of N bits in parallel, carrying the same information as the
said sequence of N bits; and
- a second element capable of carrying out an operation of comparison between the said
spatial pattern of N bits and a predetermined spatial reference pattern of N bits,
and of supplying at the output a signal having an intensity whose value depends on
the result of the said comparison operation,
characterized in that the said suitable phase modulation is 0/απ, in which 0<α<1.
[0035] The device according to the present invention is not only able to discriminate a
predetermined sequence of N reference bits from its complementary sequence, but can
also improve the mean capability of discrimination of the reference sequence of N
bits from all the other test sequences obtainable with the aforesaid N bits (that
is, it decreases the mean value of the parameter D or D'). In other words, it enables
the number of sequences of bits which can be recognized to be increased above the
level for known devices.
[0036] The device according to the invention also has the advantage of carrying out a discrimination
operation in real time, in other words in a period equal to the duration of the propagation
of the bits within the device. It therefore introduces no limitations of bit rate
when it is connected in an optical switching network or in an optical communication
system.
[0037] Typically, the said at least one sequence of N bits is also the complementary sequence
of the said predetermined spatial reference pattern of N bits.
[0038] Advantageously, the value of the parameter α is selected in such a way as to optimize
the discrimination of the said predetermined spatial reference pattern of N bits from
the said complementary sequence. More advantageously, the value of the parameter α
is selected in such a way as to optimize the discrimination of the said predetermined
spatial reference pattern of N bits from all the possible sequences of N bits.
[0039] Typically, the said value of the parameter α is from 0.3 to 0.95.
[0040] More typically, the said value of the parameter α is from 0.7 to 0.9.
[0041] Typically, the said first element comprises a laser source and a phase modulator
capable of carrying out the said 0/απ phase modulation.
[0042] In one embodiment, the said first element also comprises an opto-electronic device
capable of converting an input digital optical signal, having a modulation different
from 0/απ, into an electrical control signal for the said 0/απ phase modulator.
[0043] In one embodiment, the said series-parallel converter comprises a 1xN splitter for
cloning the said digital optical signal into N digital optical signals, and N delay
lines for delaying the said N digital optical signals by a predetermined delay for
each signal, in such a way as to supply the said spatial pattern of N bits at the
output of the said N delay lines.
[0044] More preferably, the said N delay lines comprise heater devices.
[0045] Typically, the said second element carries out an operation of convolution of the
said spatial pattern of N bits and the said predetermined spatial reference pattern
of N bits.
[0046] Preferably, the said second element capable of carrying out a comparison operation
is an optical element capable of supplying at its output an optical signal having
an intensity whose value depends on the result of the said comparison operation.
[0047] In one embodiment, the said second element is a Vander Lugt correlator.
[0048] Preferably, the said Vander Lugt correlator comprises a first optical lens, a second
optical lens and a phase only filter.
[0049] Preferably, the said optical device also comprises a detector element for detecting
the said intensity of the said signal at the output of the said second element, and
a comparator element capable of comparing the said intensity with a threshold of intensity
having a predetermined value, to determine whether or not the said spatial pattern
of N bits is identical to the said predetermined spatial reference pattern of N bits.
[0050] When the said signal at the output of the said second element is optical, the said
detector element is typically a photodetector for converting the said optical signal
into a corresponding electrical output signal having a predetermined voltage. Also,
the said comparator is typically an electronic threshold circuit capable of comparing
the said voltage with a voltage threshold having a predetermined value, to determine
whether or not the said spatial pattern of N bits is identical to the said predetermined
spatial reference pattern of N bits.
[0051] In one embodiment, the said optical device is operationally connected to a processor
capable of determining, for each predetermined spatial reference pattern, the value
of the said parameter α which optimizes the discrimination of the said predetermined
spatial reference pattern of N bits from its complementary sequence, and of causing
the said first element to carry out the said 0/απ phase modulation and causing the
said second element to optimize the said comparison operation.
[0052] Advantageously, the said processor determines, for each predetermined spatial reference
pattern, the value of the said parameter α which optimizes the discrimination of the
said predetermined spatial reference pattern of N bits from all the possible sequences
of N bits.
[0053] In a second aspect, the present invention relates to an optical communication system
comprising:
- at least a first apparatus comprising a light source and a phase modulator, for supplying
a digital optical signal comprising at least one sequence of N bits modulated by a
suitable 0/απ phase modulation, in which 0<α<1;
- an optical transmission line, optically connected to the said first apparatus, to
carry the said digital optical signal;
- a second apparatus, optically connected to the said optical transmission line, the
said second apparatus comprising:
i. a series-parallel converter for converting the said at least one sequence of N
bits into a spatial pattern of N bits in parallel carrying the same information as
the said sequence of N bits; and
ii. an element capable of carrying out an operation of comparing the said spatial
pattern of N bits with a predetermined spatial reference pattern of N bits and of
supplying at the output a signal having an intensity whose value depends on the result
of the said comparison operation;
iii. a detector element for detecting the said intensity of the said signal at the
output of the said element capable of carrying out a comparison operation; and
iv. a comparator element connected to the said detector element and capable of comparing
the said intensity with a threshold of intensity having a predetermined value, to
determine whether or not the said spatial pattern of N bits is identical to the said
predetermined spatial reference pattern of N bits.
[0054] For details of the determination of the said parameter α and the characteristics
of the said series-parallel converter, of the said element capable of carrying out
a comparison operation, of the said detector element and of the said comparator element,
reference should be made to the previous description of the device according to the
invention.
[0055] Typically, the said light source is a laser source.
[0056] Advantageously, the said optical transmission line comprises an optical fibre. More
advantageously, it comprises an optical cable.
[0057] In one embodiment, the said second apparatus comprises:
- a 1xM splitter for cloning the said digital optical signal, comprising at least one
sequence of N bits, into M optical signals, each comprising the said at least one
sequence of N bits,
- a series-parallel converter, for each of the said M optical signals, for converting
the said at least one sequence of N bits into a spatial pattern of N bits in parallel
carrying the same information as the said sequence of N bits, and
- an element capable of carrying out an operation of comparing the said spatial pattern
of N bits with one of M predetermined spatial reference patterns of N bits.
[0058] Typically, the said at least one sequence of N bits is also the complementary sequence
of one of the said M predetermined spatial reference patterns of N bits.
[0059] Preferably, the said parameter α is selected in such a way as to optimize the discrimination
of the said M predetermined spatial reference patterns from the said complementary
sequence. More preferably, the said parameter α is selected in such a way as to optimize
the discrimination of the said M predetermined spatial reference patterns from all
the possible sequences of N bits.
[0060] In a third aspect, the present invention relates to a method for comparing an optical
spatial pattern of N bits with a predetermined spatial reference pattern of N bits
comprising the phases of:
a) modulating the said N bits of the said optical spatial pattern by a suitable phase
modulation;
b) carrying out an operation of convolution of the said spatial pattern of N bits
and the said predetermined spatial reference pattern of N bits in such a way as to
supply a signal having an intensity whose value depends on the result of the said
convolution operation;
c) detecting the said intensity;
d) comparing the value of the said intensity with a threshold of intensity having
a predetermined value, to determine whether or not the said optical spatial pattern
of N bits is identical to the said predetermined spatial reference pattern of N bits,
characterized in that the said suitable phase
modulation is 0/απ, in which 0<α<1.
[0061] Preferably, the phase b) supplies an optical signal having an intensity whose value
depends on the result of the said convolution operation.
[0062] Typically, the phase c) consists in converting the said optical signal into a corresponding
electrical signal having a predetermined voltage, and phase d) consists in comparing
the value of the said voltage with a voltage threshold having a predetermined value
for determining whether or not the said optical spatial pattern of N bits is identical
to the said predetermined spatial reference pattern of N bits.
[0063] For information on the determination of the parameter α, reference should be made
to the previous description of the device according to the invention.
[0064] Characteristics and advantages of the invention will now be illustrated with reference
to embodiments represented by way of example, and without restriction, in the attached
drawings, in which:
- Figure 1 shows schematically a conventional Vander Lugt correlator;
- Figure 2 shows schematically an optical transmission system according to the invention;
- Figure 3 shows an embodiment of a series-parallel converter of the transmission system
shown in Figure 2;
- Figure 4 shows the values of the parameter D' which were obtained with a conventional
0/π phase modulation, 256 test bytes and the reference byte 01000111 (71);
- Figure 5 shows the values of the parameter D' which were obtained with a conventional
0/π phase modulation, 256 test bytes and the reference byte 01001110 (78);
- Figure 6 shows schematically an embodiment of an optical device according to the invention;
- Figure 7 shows, in curve A, the values of the parameter D' which were obtained with
a variation in the level of the φ phase modulation using the byte 01001110 as the
reference and the complementary byte as the test and, in curve B, the worst values
of the parameter D' which were obtained, for each value of the level of the φ phase
modulation, using the other test bytes;
- Figure 8 shows the value of the parameter D' which was obtained, for each of 256 test
bytes, with the reference byte 01001110 (78) and an optimal modulation equal, according
to the invention, to 0/0.72π;
- Figure 9 shows the values of the parameter D' which were obtained with the eight bytes
which differed from the reference byte 01001110 (78) by only one bit, and with its
complementary byte, with a level of modulation according to the prior art (curve E)
and also with a level of modulation according to the invention (curve F);
- Figure 10 shows, for each of 256 reference bytes, the value which was obtained for
the optimal level ϕ'o of modulation according to the invention;
- Figure 11 shows, for each of 256 reference bytes, the maximum value of the parameter
D' which was obtained with the optimal level ϕ'o of modulation;
- Figure 12 shows, for each of 256 reference bytes, the maximum value of the parameter
D' which was obtained for a modulation value of 0.83π;
- Figure 13 shows the relative variation of the parameter D' for each of the 256 bytes;
- Figure 14 shows the values of the parameter D' which were obtained with the reference
byte 01000111 (71), 256 test bytes and an amplitude modulation of the on/off type;
- Figure 15 shows the values of the parameter D' which were obtained with the reference
byte 01001110 (78), 256 test bytes and an amplitude modulation of the on/off type;
- Figure 16 shows schematically a second embodiment of an optical device according to
the invention;
- Figure 17 shows, for each of 256 reference bytes, the maximum value of the parameter
D' which was obtained for a conventional 0/π phase modulation;
- Figure 18 shows, for each of 256 reference bytes, the difference between the values
of the parameter D' of Figure 17 and those of Figure 12.
[0065] The embodiment of the optical device 500 according to the invention comprises a first
element 100 for supplying a digital optical signal comprising at least one serial
optical sequence 1000 of N binary bits, suitably phase modulated, a series-parallel
converter 6 and a second element 9 for carrying out an operation of convolution in
free space and in parallel of a predetermined reference sequence of N binary bits
and the said serial optical test sequence 1000 (Figure 6).
[0066] The said first element 100 for supplying the said optical sequence 1000 of N bits
comprises, for example, a laser source 120 and a phase modulator 130. The said laser
source 120 is, for example, a laser diode, emitting at the wavelengths of an optical
signal for telecommunications, for example in the range from approximately 1300 to
1600 nm, or, preferably, in the range from approximately 1500 to 1600 nm.
[0067] The phase modulator 130 is a conventional optical modulator, consisting, for example,
of a waveguide on an LiNbO
3 substrate associated with two electrodes. The said modulator 130 carries out a binary
phase modulation of the optical signal emitted by the laser source 120 according to
a digital electrical pilot signal 110 which carries the digital information to be
transmitted at a predetermined bit rate.
[0068] For example, the said phase modulator 130 associates with the optical signal emitted
by the laser source 120 a phase of
- ϕ=0 when the bit of the said electrical signal 110 is 0; and
- ϕ=απ when the bit of the said electrical signal 110 is 1,
where the value of the parameter α is preferably selected in such a way as to optimize
the discrimination of the predetermined reference sequence of N bits from its complementary
sequence, or, more preferably, to optimize the discrimination of the predetermined
reference sequence of N bits from all the possible 2
N test sequences with N binary bits.
[0069] In this way, at the input of the series-parallel converter 6, the said optical sequence
1000 of N bits is phase modulated by the 0-απ modulation.
[0070] The series-parallel converter 6 can convert the said serial sequence 1000 of N bits,
formed in the above way, into a spatial pattern 3000 of N bits carrying the same information
as the serial sequence 1000.
[0071] Figure 3 shows an example of a series-parallel converter 6 for N=8. The optical signal
carrying the said serial sequence 1000 of N bits at the input of the series-parallel
converter 6 is divided into N equal signals by a splitter 61 and subsequently the
i-th replica (i=1...N) is delayed by a period τ
i=(N-i)*T
b (T
b is the duration of the bit, in other words the inverse of the bit rate) by suitable
optical delay lines 62. In this way, the i-th bit of the serial sequence 1000 of N
bits is present at the i-th output of the converter 6, so that the corresponding spatial
pattern 3000 of N bits is formed.
[0072] The splitter 61 is, for example, a single 1xN fused-fibre coupler, or is formed from
an equivalent number of 1x2 fused-fibre splitters connected in cascade to form a 1xN
splitter. Alternatively, the splitter 61 may also be produced by other technologies
such as that of integrated optics or holographic diffraction.
[0073] The optical delay lines 62 are, for example, sections of optical fibre or waveguides
of suitable length.
[0074] Preferably, conventional thermo-optical phase controllers ("heaters"), not shown,
are located at the output of the optical delay lines 62 or, alternatively, along them,
and precisely regulate the phase lag of each of the N signals in such a way that the
phase relation between the N bits of the said spatial pattern 3000 is the same as
that between the N bits of the optical sequence 1000 at the input of the series-parallel
converter 6.
[0075] By means of a conventional electronic stabilization and control circuit, the said
heaters suitably regulate the temperature of the said delay lines 612 to adjust the
lengths of the said lines 612 and consequently the phases of the N bits of the said
spatial pattern 3000.
[0076] When the optical delay lines 62 consist of sections of optical fibre, a similar effect
may also be obtained with conventional piezoelectric devices (stretchers) capable
of regulating the lengths of the said sections of optical fibre.
[0077] In one embodiment, the said second element 9 for carrying out an operation of convolution
in free space and in parallel of the said reference sequence of N bits and the said
serial optical test sequence 1000 consists of a conventional Vander Lugt correlator
of the type described previously with reference to Figure 1, comprising a first convex
lens 21, a phase only filter 22 and a second convex lens 23. The lenses 21 and 23
have, for example, focal lengths of f
1=1000 mm and f
2=250 mm respectively.
[0078] The said second element 9 supplies at its output an optical signal 2000 having an
intensity whose value depends on the result of the operation of comparing the said
reference sequence of N bits with the said serial optical test sequence 1000.
[0079] The phase only filter 22 has a transfer function with a phase ϕ(ξ,η) substantially
equal to the conjugate phase of the optical field which is incident on the said filter
when the test sequence of N bits is equal to the reference sequence. More particularly,
this phase only filter 22 has a transfer function with a phase ϕ(ξ,η) substantially
equal to the conjugate phase of the Fourier transform of the reference sequence of
N bits [equation (4)].
[0080] For example, it consists of a conventional spatial light modulator (SLM) using liquid
crystals of the "twisted nematic" type.
[0081] This device consists of an array of N liquid crystal cells which impart a phase lag
to the incident optical field according to the conjugate of the phase information
contained in the Fourier transform of the reference sequence of N bits. The said phase
lag is obtained by controlling the electrical potential difference applied to the
said liquid crystal cells by an electrical control system. This is achieved because,
owing to the birefringent properties of the liquid crystals, it is possible to obtain
a rotation of the polarization plane of the light incident on the cells, in other
words a change of phase of the incident light, by applying a predetermined potential
difference to the said cells.
[0082] Alternatively, the phase only filter 22 may also consist of a conventional phase
mask made by known holographic or diffractive lithographic methods.
[0083] A similar effect may also be obtained with a Vander Lugt correlator comprising a
first and a second convex optical lens and a conventional matched filter.
[0084] In other embodiments, the said second element 9 may also consist of other types of
devices capable of carrying out an operation of convolution of two sequences of bits,
such as a conventional joint transform correlator (JTC), a correlator of the type
described in Patent Application No. 982002411.9 filed by the present applicant, or
suitable conventional electronic devices.
[0085] Figure 2 shows an embodiment of an optical transmission system according to another
aspect of the present invention. This system is suitable for transmitting at least
one digital optical signal carrying a certain number of serial optical sequences 1000
of N bits, each having a duration T
b and bit rate r
b = 1/ T
b. The optical transmission system in Figure 2 comprises a transmitter A, an optical
transmission line 4 and a receiver B.
[0086] In turn, the transmitter A comprises a laser source 2 connected optically to one
input of a phase modulator 3. The output of the phase modulator 3 is connected to
the optical transmission line 4 which, in turn, is connected optically to the input
of the receiver B.
[0087] The laser source 2 is, for example, a laser diode, emitting at the wavelengths of
an optical signal for telecommunications, for example in the range from approximately
1300 to 1600 nm, or, preferably, in the range from approximately 1500 to 1600 nm.
[0088] The phase modulator 3 is a conventional optical modulator, consisting, for example,
of a waveguide on an LiNbO
3 substrate associated with two electrodes. The said modulator 3 carries out a binary
phase modulation of the optical signal emitted by the laser source 2 according to
a digital electrical pilot signal 110 which carries the digital information to be
transmitted at a predetermined bit rate.
[0089] For example, the said phase modulator 3 associates with the optical signal emitted
by the laser source 2 a phase of
- ϕ=0 when the bit of the said electrical signal 110 is 0; and
- ϕ=απ when the bit of the said electrical signal 110 is 1,
where the value of the parameter α is preferably selected in such a way as to optimize
the discrimination of M predetermined spatial reference patterns of N bits from their
complementary sequences, or, more preferably, from all the possible 2
N test sequences which can exist with N binary bits.
[0090] The optical transmission line 4 typically comprises an optical fibre. Preferably,
it comprises an optical cable.
[0091] Preferably, in long-distance connections, the optical transmission line 4 comprises
at least one conventional optical amplifier, for example one of the erbium-doped fibre
type.
[0092] In the illustrated embodiment, the receiver B comprises a 1xM splitter 5 for separating
the input signal into M outputs. Each of the M outputs of the splitter 5 is connected
to a series-parallel converter 6, each comprising N outputs made, for example, from
optical fibre. The N outputs of each series-parallel converter 6 are optically connected
to one of M elements 9.1-9.M, of the type described previously, for carrying out an
operation of convolution in free space and in parallel of a spatial reference pattern
of N bits and a spatial test pattern of N bits (Figure 6). The output of each element
9.1-9.M is connected to a different photodetector 7 which in turn is connected to
a threshold circuit 8.
[0093] The splitter 5 is, for example, a single 1xM fused-fibre coupler, or consists of
a plurality of fused-fibre couplers (of the 1x2 type for example) connected in cascade
to form a 1xM splitter.
[0094] Alternatively, the splitter 5 may also be produced by other technologies such as
those of integrated optics or holographic diffraction.
[0095] The series-spatial converters 6 are, for example, of the type described previously
in relation to Figure 3.
[0096] In one embodiment, the devices 9.1-9.M may be, as stated previously, Vander Lugt
correlators (Figure 1), each comprising a first convex lens 21, a phase only filter
22 and a second convex lens 23. Alternatively, the devices 9.1-9.M may consist of
other types of conventional correlator, such as a conventional joint transform correlator
(JTC), a correlator of the type described in Patent Application No. 98202411.9 filed
by the present applicant, or conventional electronic devices capable of carrying out
an operation of convolution of a reference byte and a test byte.
[0097] Each of the devices 9.1-9.M is constructed in such a way that it recognizes a predetermined
binary reference sequence of N bits among all the possible sequences (2
N) arriving from the optical transmission line 4. The receiver B is thus capable of
discriminating, from all the 2
N possible sequences arriving at its input, those which are identical to at least one
of M reference sequences (where M≤2
N).
[0098] On the other hand, if it is necessary to recognize only one predetermined reference
sequence of N bits, the receiver B will comprise only one series-parallel converter
6, a single element 9, a single photodiode 7 and a single threshold circuit 8.
[0099] These reference sequences may be, for example, an address of a cell for a transmission
of the asynchronous type (asynchronous transfer mode, ATM) or a CDMA (code division
multiple access) transmission code.
[0100] The photodetector 7 is, for example, a PIN photodiode made from InGaAs, such as the
ETX75 FJ SLR model, marketed by Epitaxx Optoelectronics Devices, 7 Graphics Drive,
West Trenton, NJ, USA.
[0101] The threshold circuit 8 is, for example, a conventional electronic circuit.
[0102] The photodetector 7 detects the intensity of the optical signal 2000 at the output
of the corresponding element 9 and converts it into a corresponding value of voltage
V. The threshold circuit 8 compares this voltage value V with a threshold voltage
value which is selected in a conventional way to determine whether or not the sequences
of N bits arriving from the optical transmission line 4 are identical to the predetermined
reference sequence.
[0103] Figure 16, in which the same numerical references are used to indicate components
of the same type as those described previously, shows a second embodiment of the device
500 according to the present invention.
[0104] In the embodiment shown in Fig. 16, the device 500 in Fig. 6 also comprises an opto-electronic
circuit 43, a photodetector 7, a threshold circuit 8 and a processor 44. In turn,
the opto-electronic circuit 43 comprises, typically, a photodiode, a threshold circuit
and an electronic amplifier, all of conventional types (not shown).
[0105] The opto-electronic circuit 43 converts a digital optical signal, having a modulation
different from 0/απ and arriving from a transmission line (of the optical fibre type
for example) 41, into a corresponding electrical signal 110. This electrical signal
110 is used as the pilot signal of the phase modulator 130 of the device 500 which
modulates the optical signal generated by the laser source 120 by an 0/απ modulation.
[0106] The sequence of N bits 1000 modulated in this way by the phase modulator 130 is sent
to the series-parallel converter 6 and to the second element 9 in Figure 6.
[0107] The output optical signal 2000 of the second element 9 is then sent to the photodetector
7 and then to the threshold circuit 8.
[0108] For information on the determination of the parameter α and the characteristics of
the laser source 120, the phase modulator 130, the series-parallel converter 6, the
second element 9, the photodetector 7 and the threshold circuit 8, reference should
be made to the preceding descriptions.
[0109] The device in Figure 16 may be used, for example, in the receiver of a conventional
optical transmission system in which at least one digital optical signal comprising
sequences of N bits, modulated by a conventional modulation such as an NRZ (non return
to zero) or RZ (return to zero) amplitude modulation or a 0/π phase modulation, is
transmitted.
[0110] For the last-mentioned 0/π phase modulation, the opto-electronic circuit 43 is preferably
associated with a conventional device capable of carrying out a detection of the coherent
type.
[0111] The said at least one digital optical signal arrives along the transmission line
41 at the input of the device in Figure 16.
[0112] The circuit 43 carries out the optical-to-electrical conversion of the said digital
optical signal comprising the sequences of N bits, and thus supplies the electrical
pilot signal 110 to the phase modulator 130.
[0113] According to the predetermined reference sequence of N bits, the processor 44 determines
the parameter α, as described previously, and operates
- the phase modulator 130 so that it carries out a 0/απ modulation of the signal emitted
by the laser source 120; and
- the filter of the element 9 so that it changes the phase (in the case of a phase only
filter) or the phase and amplitude (in the case of a matched filter) of the incident
optical field in accordance with the information on the phase or on the phase and
amplitude respectively, present in the optical field incident on the said filter when
the test sequence of N bits is identical to the reference sequence.
[0114] The optical signal 2000 supplied by the second element 9 is then converted by the
photodiode 7 into an electrical signal whose voltage is compared by the circuit 8
with a threshold voltage which is selected in a conventional way to determine whether
or not the incoming test sequences are identical to the predetermined reference sequence.
[0115] Therefore, owing to the processor 44, the device in Figure 16 can recognize more
than one predetermined reference sequence of N bits among those arriving at the receiver.
[0116] The inventors have developed a computer program capable of simulating the behaviour
of a device according to the invention.
[0117] They have thus determined the values of the parameter D' which were obtained with
a variation of the level of ϕ phase modulation for the bit 1 (0≤ϕ≤π), in other words
with a variation of the parameter α (0≤α≤1), using:
- a reference sequence of 8 bits (N=8) which is 01001110 (78 in decimal notation);
- all the possible 256 test bytes; and
- a step of variation of 0.01 π of the level of ϕ phase modulation.
[0118] Figure 7, curve A, shows the values of the parameter D' obtained in this way, using
as the test sequence the complementary byte of the reference byte 78. In turn, Figure
7, curve B, shows for each value of a the highest value (worst case) of the parameter
D' which was obtained with all the 256 test bytes with the exception of those identical
to the reference byte 78 and its complementary. The curve B therefore represents,
for each value of the parameter α considered, the worst case of the discrimination
capability CD of a device according to the invention for all the test bytes with the
exception of those identical to the reference byte 78 and its complementary.
[0119] For each value of the parameter α, the point of the curve A or B corresponding to
the maximum value of the parameter D' was then considered, and the curve passing through
the points found in this way was plotted.
[0120] At this point, the level of modulation φ corresponding to the minimum point of this
curve was considered, and in this way the optimal modulation level ϕ
o, which optimized the discrimination of the reference sequence of bits 78 from all
the other test sequences, including the complementary, was found. As shown in Figure
7, for the reference sequence 01001110 (78) the optimal modulation level ϕ
o (corresponding in this case to the minimum point of the curve B) was found to be
equal to 0.72π; in other words, the optimal value α
o of the parameter α was found to be equal to 0.72. For this value of the level of
modulation, the parameter D' for the complementary sequence was found to be equal
to 0.4537 while, for the sequence with the worst discrimination, D' was found to be
equal to 0.6635 (see curves A and B).
[0121] Figure 8 shows the results of a further simulation carried out to determine the variation
of the parameter D', using:
- 256 test bytes,
- the byte 01001110 (78) as the reference sequence, and
- an optimal modulation level ϕo equal to 0.72π.
[0122] The results which were obtained show that the 0/απ modulation according to the method
of the invention provided a good value of the parameter D' for all the test bytes,
including the complementary.
[0123] Figure 9 shows the values of the parameter D' which were obtained with the test bytes
(206, 14, 110, 94, 70, 74, 76, 79) which differ from the reference byte 01001110 (78)
by only one byte, and with its complementary byte (177). The curve E shows the values
of the parameter D' obtained with level of modulation ϕ equal to π, in other words
with a conventional modulation, while the curve F shows the values of the parameter
D' obtained, according to the invention, with the optimal modulation level ϕ
o equal to 0.72π.
[0124] These curves show that the phase modulation according to the invention made it possible
to discriminate the numerical reference sequence from its complementary sequence and
to improve the discrimination (to decrease the value of the parameter D') from the
remaining most critical byte 01001111 (79). It should be noted that a very high value
of D' was obtained for this last byte with the conventional 0/π phase modulation.
[0125] The device according to the invention therefore made it possible to overcome the
problem of the inability to distinguish a predetermined reference sequence from its
complementary and, on average, to increase the ability to distinguish it from all
the other test sequences.
[0126] The same procedure was used to determine the optimal value of φ for each of 256 reference
bytes.
[0127] Figure 10 shows the optimal values φ (on the vertical axis) found in this way for
each reference byte (indicated in decimal values on the horizontal axis). It will
be noted from Figure 10 that the optimal modulation levels ϕ
o belong, for virtually all the bytes, to a limited set of values ranging from 0.7
π to 0.9 π, corresponding to 0.7 ≤ α
o ≤ 0.9.
[0128] In turn, Figure 11 shows the maximum value of the parameter D' which was obtained
for each of 256 reference bytes for the corresponding optimal modulation level ϕ
o found previously. From time to time, the test bytes did not include the one equal
to the selected reference byte.
[0129] Additionally, by means of a set of simulations executed on the computer, a modulation
level φ of 0.83 π (α=0.83) was found, which optimized the capability of discriminating
all the 256 reference bytes from all the possible test bytes.
[0130] Figure 12 shows the maximum values of the parameter D' obtained in this way for each
reference byte.
[0131] In this connection, it should be noted that, if it is necessary to recognize only
M (M<2
N) reference bytes from all the possible test bytes, it is preferable to determine
the modulation level φ which optimizes the capability of discriminating these M reference
bytes from all the possible test bytes. This modulation level will generally be different
from that which optimizes the capability of discriminating all the 2
N reference bytes.
[0132] The difference (the relative variation of the parameter D') between the maximum value
of the parameter D' obtained by using the said modulation level of 0.83 π and the
maximum value of the parameter D' obtained with the optimal modulation level of each
byte was then calculated for each byte.
[0133] Figure 13 shows the results obtained in this way for the relative variation of the
parameter D' (on the vertical axis). For each reference byte (shown on the horizontal
axis in decimal notation), the increase of the value of the parameter D' due to the
use of a modulation value of 0.83π instead of the optimal value was found to be contained
within 20%.
[0134] In turn, Figure 17 shows the worst value of the parameter D' which was obtained for
each of 256 reference bytes with a conventional 0/π modulation, considering all the
2
N test sequences with the exception of the complementary sequence and the sequence
identical to the reference sequence.
[0135] When comparing the results in Figures 11 and 12 with those in Figure 17, it should
be noted that the modulation according to the invention not only provided a good capability
of discriminating the complementary sequence but also made it possible to obtain,
on the average, much lower values of the parameter D' than those obtained with a conventional
modulation.
[0136] For example, Figure 18, which illustrates the difference between the values of D'
obtained in Figure 17 and those obtained in Figure 12, shows how the values of D'
obtained with the conventional modulation 0/π were found to be, on average, higher
than those obtained according to the invention.
[0137] The procedure of determining the parameter α and, consequently, the optimal modulation
level, is independent of the length (N) of the reference sequence of bits, and of
the particular embodiment of the second element 9. For example, further simulations
were carried out for different lengths of the numerical sequence, in other words for
values N equal to 7 and 5. In this case also, an optimal value α
o typically ranging from 0.7 to 0.9 was obtained.
[0138] In another embodiment of the invention, the device 500 in Figure 6 also comprises
a phase mask (not shown). Preferably the said phase mask is located at the input of
the second element 9. For example, it may be located on the input plane 11 of the
Vander Lugt correlator shown in Figure 1.
[0139] Examples of conventional phase masks suitable for the purposes of the invention are
those produced by Lasiris, which uses laser scribing methods, or by RPC, which uses
lithographic methods with ultraviolet radiation. These methods of scribing and the
performance of the diffractive optical elements thus produced are described, for example,
by A. Asselin et al. ("Diffractive optics at NOI", National Optics Institute, vol.
5, pp. 1-8, 1994).
[0140] The said phase mask may accentuate the existing differences between sequences of
N bits which are very similar to each other (for example, in the case of sequences
which differ from each other by one bit only) and is preferably carried out in such
a way as to imprint a predetermined phase shift on the bits which in the input test
sequence occupy the same position, in the plane x,y, as the bits set to 1 in the reference
sequence of N bits.
[0141] By using such a mask, the phase only filter 22 of the Vander Lugt correlator shown
in Figure 1 is preferably operated in such a way that the phase ϕ(ξ,η) of its transfer
function [equation (4)] is equal to the sum of the conjugate phase of the Fourier
transform of the reference sequence of N bits and the phase shift introduced by the
mask.
[0142] To determine the optimal phase shift value which is to be introduced by the said
phase mask, simulations were executed using the byte 01001110 (78) as the reference
sequence of N bits.
[0143] In an initial stage, the said optimal phase shift value of the phase mask was calculated
by using, for the input sequence, a conventional phase modulation level ϕ (equal to
π).
[0144] In this way an optimal phase shift level ϕ
M of the mask, equal to 0.29π, was obtained. With this value it was possible to improve
by approximately 21% the discrimination of all the sequences of N bits with the exception
of the complementary of the reference sequence (78) which, on the other hand, was
not discriminated.
[0145] Consequently, the said optimal phase shift value of the phase mask was then calculated
by using, for the input sequence, a phase modulation level ϕ equal to απ according
to the invention.
[0146] In this way a combination of values ϕ
0, ϕ
0M was found, which was capable of discriminating the reference sequence from its complementary
while simultaneously optimizing its discrimination from the other test sequences.
[0147] In this way, an optimal modulation value ϕ
0, equal to approximately 0.78π, and an optimal phase shift value ϕ
0M, equal to approximately 0.45π, were obtained.
[0148] For these values of ϕ
0, ϕ
0X, the highest value of the parameter D' (corresponding to the worst case) was found
to be equal to 0.6416 for the numerical test sequence 00001110 (14).
[0149] Thus the phase mask provided values of D' which were similar overall to those obtained
in the absence of a phase mask and with an optimal modulation of 0.72π of the bits
of the input sequence (Figure 8).