CN104407485B - A kind of Quantum Correlation imaging method tangled based on Angle Position - Google Patents
A kind of Quantum Correlation imaging method tangled based on Angle Position Download PDFInfo
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- CN104407485B CN104407485B CN201410724877.5A CN201410724877A CN104407485B CN 104407485 B CN104407485 B CN 104407485B CN 201410724877 A CN201410724877 A CN 201410724877A CN 104407485 B CN104407485 B CN 104407485B
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- G02F—OPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
- G02F1/00—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
- G02F1/35—Non-linear optics
Abstract
The invention discloses a kind of Quantum Correlation imaging method tangled based on Angle Position, this method is the angle seam that object to be imaged information is encoded into different angles, and different angle seams is loaded on light beam.Due to there is the functional relation of dullness between coincidence counting and angle seam angle, the information of object can be obtained in reference path according to coincidence counting value, the imaging of object is obtained, a kind of Quantum Correlation imaging method tangled based on Angle Position is obtained.This new relevance imaging method：On the one hand concept Angle Position tangled introduces relevance imaging field, the research direction of relevance imaging is extended, while also having obtained good imaging effect；On the other hand, the research that diagonal position is tangled also provides a new approaches for follow-up study, such as multiple access optic communication, the field such as optical identification.This method is realized simply, has good imaging effect for multi-grey image object.
Description
Technical field
The present invention relates to a kind of Quantum Correlation imaging method tangled based on Angle Position, belong to quantum optices and imaging technique
Interleaving techniques field.
Background technology
Relevance imaging (Correlated Imaging, be abbreviated as CI), also referred to as (Ghost Imaging, are abbreviated as ghost imaging
GI), it is one of forward position and focus for studying in the last few years in quantum optices field.Relevance imaging can be in the ginseng without object
Examine light path and obtain object picture rich in detail.It can break through classical diffraction limit, with high-resolution and high-visibility, there is wide answer
With prospect, such as satellite remote sensing, laser radar, medical imaging is military, the various fields such as industry imaging and survey of deep space, at present
Extensive concern is obtained.
1988, Klyshko tangled behavior according to conversion (SPDC) photon pair under Spontaneous Parametric, it is proposed that relevance imaging
Scheme.Nineteen ninety-five, Pittman et al. is completed based on quantum entanglement using the entangled photon pairs that generation is changed under Spontaneous Parametric
" ghost " imaging experiment checking.Or subsequent correlation theory and experiment show the characteristic for tangling relevance imaging be embodied in momentum-
The momentum of position Heisenberg uncertainty relation is tangled, otherwise the position for being embodied in momentum-position Heisenberg uncertainty relation is tangled.Photon trajectory
Angular momentum (OAM) and (angle) position are also that one kind tangles source.Compared with photon polarization state only has two kinds of values, single photon
OAM values can substantially increase the ability of single photon transmission information from negative infinite to just infinite., Back et al. in 2009
Use for reference photon polarization state and tangle relevance imaging method, complete the relevance imaging experiment tangled based on OAM, and carried in terms of OAM
The quantum essence of relevance imaging is shown.On this experiment basis, we proposed a kind of ash more tangled based on OAM in 2011
Spend the method and experimental verification of " ghost " imaging.This provides a kind of scheme simple and easy to apply for the imaging process of phase object.The opposing party
Face, Jha et al. is a pair of indeterminacy physical quantitys in experimental verification Angle Positions in 2010 and angular momentum, can pass through double angle seams and obtain base
In the interference of Angle Position.Compared with angular momentum is tangled, the relation between the coincidence counting and angle seam angle tangled based on Angle Position will
It is simpler.Therefore, the present invention proposes a kind of relevance imaging scheme tangled based on Angle Position, and object to be imaged information is encoded
It is loaded into the angle seam of different angles, and by different angle seams by phase on light beam.Due between coincidence counting and angle seam angle
The functional relation of dullness is there is, the information of object can be obtained in reference path according to coincidence counting value, the imaging of object is obtained.
The present invention gives it is a kind of it is new tangle relevance imaging method, with important theory significance and application value.
The content of the invention
Present invention aims at a kind of Quantum Correlation imaging method tangled based on Angle Position is provided, this method is first by angle
Position is tangled applied to relevance imaging technology.In the method, a Gauss pump light carries out changing under parameter by bbo crystal,
Produce an entangled photon pairs.If signal light path is LG-l,0Pattern, then light path of leaving unused will be LG+l,0Pattern.By object to be imaged
Different information are encoded into the angle seam θ of different angles, and different angle seams is loaded into the phase of signal beams.Due to meeting
The functional relation that dullness is there is between angle seam θ is counted, by setting specific region, can be obtained between coincidence counting and object information
One-to-one relationship.Then, the information of object can be obtained according to coincidence counting in reference path, obtains the imaging of object, should
Method is realized simply, has good imaging effect for multi-grey image object.
The technical scheme adopted by the invention to solve the technical problem is that：Tangled the invention provides one kind based on Angle Position
Quantum Correlation imaging method, this method comprises the following steps：
Step one：A branch of Gauss pump light passes through Ι type degenerate non-linear phase matcher crystal, is produced by parametric down conversion
Tangle for raw a pair pair.The photon entanglement of generation is to being represented byWherein s and i representation signals light path and
Idle light path；|l>Represent eigenstate of the exponent number for l orbital angular momentum；|cl|2It is general under l and-l patterns to be that exponent number is respectively
Rate.
Step 2：Set up it is as shown in Figure 1 schematic diagram is realized based on the Quantum Correlation imaging method that Angle Position is tangled, order is not busy
Putting light path is |+l>Pattern, signal light path is |-l>Pattern.
Step 3：First by the gray-coded of the object to be imaged into different angle seam θ in signal light path, and with fan-shaped phase
Form be loaded into signal light path.The value of present invention selection angle seam angle arrives π for 0, if the tonal gradation of object is M, into
As the gray value of object corresponds to the M different angle seams such as 0, π/(M-1), 2 π/(M-1) ..., (M-2) π/(M-1), and π respectively
θ, different gray values are encoded into different angle seam θ.
Step 4：By the information of the object to be imaged, i.e., different angle seam angle, θs are loaded into signal light path, and to signal
Light path and idle light path carry out coincidence measurement, obtain coincidence counting.From Such analysis, the fan-shaped phase of signal light path loading
Angle theta and coincidence counting value there is single-valued relationship,clWith A all
It is constant.The angle seam θ sizes of loading are resulted in by coincidence counting value.
Step 5：The gray value and the coding corresponding relation of angle seam produced by step 3, is recovered often in idle light path
The gray value of individual pixel, obtains object to be imaged information.
The method of the invention be by the Angle Position of entangled photon pairs tangle theory based on a kind of relevance imaging method；
Premised on there is single-valued relationship between the fan-shaped angle seam phase carried according to added by coincidence counting value and signal light path.
The method of the invention can be adapted to the relevance imaging of many gray scale object to be imaged.
Exist between the method for the invention coincidence counting value and the added fan-shaped angle seam phase carried of signal light path strict single
Tune relation, imaging precision is high.
Beneficial effect：
1st, the concept that the present invention first tangles Angle Position introduces relevance imaging field, extends the research side of relevance imaging
To.
2nd, good imaging quality of the invention, high resolution has general applicability for the image of different gray scales.
Brief description of the drawings
Fig. 1 is imaged scheme schematic diagram for the present invention based on the Quantum Correlation that Angle Position is tangled.
Fig. 2 is the phase diagram that signal light path of the present invention is loaded.
Fig. 3 is | Ψs>With | Ψi>Degree of conformity C (Ψs,Ψi) and fan-shaped angle graph of a relation.
Fig. 4 is 2 gray scales " NUPT ", 4 gray scales " LENA ", the numerical simulation of the present invention of the object to be imaged such as 8 gray scales " LENA ".
Fig. 5 is 8 gray scales " LENA " figure (signal to noise ratio) under different noise conditions, the peak value noise of imaging object of the present invention
Compare variation diagram.
Fig. 6 is the flow chart of the inventive method.
Embodiment
Patent of the present invention is described in further detail below in conjunction with Figure of description.
Embodiment one
A kind of schematic diagram of the Quantum Correlation imaging method tangled based on Angle Position of the present invention is as shown in figure 1, idle light path
For LG+l,0Pattern, signal light path is LG-l,0Pattern, wherein LG+l,0And LG-l,0Pattern is that a branch of Gauss pump light is moved back through Ι types
Change nonlinear phase adaptation, produced by parametric down conversion process.Selected in signal light path according to the different gray value of object
Different angle seam θ fan-shaped phase is selected, and is loaded into signal light path.For example, it is assumed that the tonal gradation of the object to be imaged is M, i.e.,
The gray scale value of the object to be imaged is 0,1 ... M-2, M-1.Selecting angle seam θ angle change to arrive π for 0, this is interval (because of 0
It is a monotonic function to the coincidence counting corresponding to π intervals), the M angle seam θ value from 0 to π will be obtained, i.e. angle seam θ can distinguish
It is set to 0, π/(M-1), 2 π/(M-1) ..., (M-2) π/(M-1), and π, M gray value of imaging object and M angle seam θ mono-
One correspondence.Then signal light path and idle light path are subjected to coincidence measurement and obtain coincidence counting, finally according to coincidence counting and angle
Dull functional relation obtains the half-tone information of the object to be imaged between seam angle, so as to be recovered in reference path by imaging thing
Body.
In theory, conversion obtains signal photon and idle photon entanglement pair under a Gauss pump light is by Spontaneous Parametric
When, two-photon state can be expressed as：
Wherein, | n>The orbit angular momentum state (LG patterns) of l=n patterns is represented, | cn|2Represent converted under Spontaneous Parametric
A pump photon is converted into the probability of ± n-photon in journey.Because conversion has symmetry under Spontaneous Parametric, have：
cn=c-n, (2)
In order to provide the corresponding relation of coincidence counting and different angle seam information, derive load difference in signal light path below
The expression-form of coincidence counting during angle seam phase.
Assuming that the basic state of signal light path and idle light path is respectively |-l>With |+l>, in the loading of signal light path such as Fig. 2
Shown angle seam phase, wherein white portion phase value are 0, and grey parts phase value is π, the angle seam angular dimension of grey parts
For θ, then the phase corresponding to angle seam can be expressed as：
Wherein θ is the angle for representing angle seam, the π of 0≤θ of its transformation range≤2；r0It is angle seam radial direction radius size.Due to letter
The OAM states that the initial pattern of number light path input is-l, its mathematical form is |-l>=Aexp (- il φ), wherein Α are LG patterns
Radial distribution, the value with l is unrelated.Therefore, OAM states after signal light path loads angle seam θ | Ψs>For：
|Ψs>=Ae-ilφeiM(φ) (4)
Because different l values LG patterns are mutually orthogonal, therefore the signal state after loading angle seam θ is deployable for various l values LG moulds
Formula, i.e.,
Wherein Al′For：
The further abbreviation of above formula can be obtained：
Due to light path OAM states of leaving unused | Ψi>For+l OAM states, it is represented by
|Ψi>=|+l>, (8)
According to coincidence counting formula, the coincidence counting C (Ψ of signal light path and idle light path can be obtaineds,Ψi) be：
C(Ψs,Ψi)=|<Ψs|<Ψi|Ψ>|2, (9)
Wherein：
It can be obtained by two formulas above：
Wherein, clAll it is constant with A, therefore：
Fig. 3 is | Ψs>With | Ψi>Degree of conformity graph of a relation, it is shown that C (Ψs,Ψi) and angle theta relation.Can from figure
With find out with angle theta from 0 change to π when, C (Ψs,Ψi) minimum value is reduced to from maximum, as angle theta from π changes to 2
During π, C (Ψs,Ψi) increase to maximum from minimum value.
It can be found that when the primary input state of signal light path and idle light path is in Fig. 3 |-l>With |+l>When, arrive π 0
Interval coincidence counting value is the monotonous descending function of loading fan-shaped phase angle theta.If signal light path is |-l>The OAM light of pattern,
Idle light path input |+l>The OAM light of pattern.When loading the fan-shaped phase of different angle thetas in signal light path, in idle light
Road will obtain different coincidence counting values, and the functional relation of dullness is there is between coincidence counting value and angle seam angle, θ.Due to not
The different gray scales of the object to be imaged are correspond to angle seam, therefore the area of the different gray values of imaging object can be realized in idle light path
Point, obtain image objects.The present invention to implement step as follows：
Step one：A branch of Gauss pump light passes through Ι type degenerate non-linear phase matchers, is produced by parametric down conversion process
Give birth to a pair and tangle light, respectively flashlight and idle light.The photon of generation is to being represented byWherein s
Represent signal light path and idle light path respectively with i, | l>Represent eigenstate of the exponent number for l orbital angular momentum.|cl|2It is two photons
Exponent number is respectively l and-l patterns probability.
Step 2：Set up the Quantum Correlation imaging scheme tangled based on Angle Position as shown in Figure 1, light path of leaving unused input
LG+l,0Pattern, signal light path input LG-l,0Pattern.The different gray value of object is first encoded into different angles in signal light path
Angle, θ is stitched, and to be loaded into the form of fan-shaped phase in signal light path, (0 is right to π intervals for this interval of present invention selection 0 to π
The coincidence counting answered is in a monotonic function with angle seam angle, θ).If the tonal gradation of imaging object is M, i.e. value 0,1 ..., M-
2, M-1, then corresponding angle seam angle, θ is 0, π/(M-1), 2 π/(M-1) ..., (M-2) π/(M-1) and π, i.e., by 0 to π interval
M parts are uniformly divided into, M angle seam θ value is corresponding with M gray value.
Step 3：Signal light path and idle light path are subjected to coincidence measurement, coincidence counting is obtained.By foregoing
Analysis understands that the angle theta of the fan-shaped phase of signal light path loading has one-to-one relationship with coincidence counting value,clAll it is constant with A, by coincidence counting value, results in correspondence and add
The fan-shaped phase theta size of load.
Step 4：Relation between the angle seam size and gray value that are obtained by step 2, obtains the ash of each pixel
Angle value, image is recovered by computer.
Embodiment two
In order to verify the Quantum Correlation imaging method proposed by the invention tangled based on Angle Position, now pass through numerical simulation
Verified.The wavelength for the Gauss pump light source that this numerical simulation is used is λ=633nm.In order to more objectively and accurately illustrate base
The performance for the relevance imaging method tangled in Angle Position, present invention introduces Y-PSNR (peak signal-to-noise
Rate, PSNR), wherein PSNR is defined as：
Wherein,The gray scale maximum of original objects is represented, MSE is defined as：
Wherein, Xi,jWith X 'i,jOriginal objects are represented respectively and recover the half-tone information value of image.
As shown in figure 1, the present invention provides a kind of Quantum Correlation imaging method tangled based on Angle Position, this method is with light
Based on sub- Angle Position is tangled, different angle seam θ (fan-shaped phases are loaded according to the tonal gradation of imaging object in signal light path
Position), using the monotonic functional relationship between angle seam θ and idle light path and signal light path coincidence counting value, idle light path according to
Coincidence counting value adjudicates angle seam θ sizes, recycles angle seam θ and imaging object gray value one-to-one relationship, it is determined that imaging thing
Body.Methods described includes：
1) a branch of wavelength is that λ=633nm Gausses pump light passes through Ι type degenerate non-linear phase matchers, is passed through
Parametric down conversion process produces a pair and tangles light, respectively flashlight and idle light.The photon of generation is to being represented byWherein s and i represent signal light path and idle light path respectively, | l>Represent the track angular motion that exponent number is l
The eigenstate of amount.|cl|2Be two photon exponent numbers be respectively l and-l patterns probability.
2) light path of leaving unused input LG+l,0Pattern, signal light path input LG-l,0Pattern.It is first that object is different in signal light path
Gray value be encoded into different angle seam angle, θs, and to be loaded into the form of fan-shaped phase in signal light path, present invention choosing in text
Select 0 to π this interval (0 to π interval corresponding coincidence counting and angle seam angle, θ are in a monotonic function).If the ash of imaging object
Degree grade is M, i.e. value 0,1 ..., M-2, M-1, then corresponding angle seam angle, θ is 0, π/(M-1), 2 π/(M-1) ..., (M-
2) π/(M-1) and π, i.e., be uniformly divided into M parts, M angle seam θ value is corresponding with M gray value by 0 to π intervals.In order to illustrate to difference
Gray scale has a general applicability, the present invention respectively with 128 × 128 " NUPT ", " LENA " of 4 gray scales " LENA " and 8 gray scales
Carry out simulating, verifying.
3) signal light path and idle light path are subjected to coincidence measurement, obtain coincidence counting.By formulaUnderstand, coincidence counting value and angle seam θ are one dull in [0, π] interval
Function, as shown in Figure 3.
4) because the gray value and loading angle seam θ of the object to be imaged have one-to-one relationship, one can be entered by step 2
Step obtains the corresponding relation between the gray value of coincidence counting value and the object to be imaged.Receiving terminal, quilt is determined according to coincidence counting value
The gray value of each pixel of imaging object, recovers imaging object.
In order to verify the validity of this method, " NUPT " the 2 gray scale object of the present invention respectively to 128 × 128,4 gray scales
" LENA " object and " LENA " object of 8 gray scales carry out numerical simulation.As a result as shown in figure 4, wherein Fig. 4 (a) is 2 gray scales
" NUPT " artwork, Fig. 4 (b) is its recovery figure, and the PSNR values after imaging are 78.0744.Fig. 4 (c) is 4 gray scales " LENA " original
Figure, it is recovery figure to Fig. 4 (d), and the PSNR after imaging is 14.1949.Fig. 4 (e) is 8 gray scales " LENA " artwork, and Fig. 4 (f) is it
Recover figure, the PSNR after imaging is 13.9295.As can be seen here, the present invention effectively can obtain the object to be imaged in reference path
Information.Either image this method of 2 gray scales, 4 gray scales or 8 gray scales can be carried out clearly being imaged.
The present invention is further tested the noise resisting ability of the present invention.Fig. 5 is that 8 gray scales " LENA " figure is adding difference
After noise (signal to noise ratio), the change curve of reconstruction image Y-PSNR after imaging.As seen from the figure, SNR and PSNR exists dull
Relationships of increase function, SNR value is bigger, and image Y-PSNR PSNR is also bigger after being imaged, and represents that noise is got in imaging object
Greatly, the quality of imaging is poorer.
Claims (6)
1. a kind of relevance imaging method tangled based on Angle Position, methods described is comprised the following steps：
Step one：A branch of Gauss pump light passes through Ι type degenerate non-linear phase matcher crystal, and one is produced by parametric down conversion
To tangling pair, the photon entanglement of generation is to being represented byWherein s and i representation signals light path and idle
Light path；| l ＞ represent the eigenstate for the orbital angular momentum that exponent number is l；|cl|2It is that exponent number is respectively l and the probability under-l patterns；
Step 2：Set up and schematic diagram realized based on the Quantum Correlation imaging method that Angle Position is tangled, the idle light path of order is |+l>Mould
Formula, signal light path is |-l>Pattern；
Step 3：First by the gray-coded of the object to be imaged into different angle seam θ in signal light path, and with the shape of fan-shaped phase
Formula is loaded into signal light path；The value of angle seam angle is selected to arrive π for 0, if the tonal gradation of object is M, the ash of imaging object
Angle value corresponds to the M different angle seam θ such as 0, π/(M-1), 2 π/(M-1) ..., (M-2) π/(M-1), and π, different gray scales respectively
Value is encoded into different angle seam θ；
Step 4：By the information of the object to be imaged, i.e., different angle seam angle, θs are loaded into signal light path, and to signal light path
Coincidence measurement is carried out with idle light path, coincidence counting is obtained；The angle theta and coincidence counting value of the fan-shaped phase of signal light path loading
There is single-valued relationship,clAll it is constant with A；Pass through coincidence counting
Value obtains the angle seam θ sizes of loading；
Step 5：The gray value and the coding corresponding relation of angle seam produced by step 3, each picture is recovered in idle light path
The gray value of vegetarian refreshments, obtains object to be imaged information.
2. a kind of relevance imaging method tangled based on Angle Position according to claim 1, it is characterised in that：Methods described
Be by the Angle Position of entangled photon pairs tangle theory based on a kind of relevance imaging method；According to coincidence counting value and flashlight
Premised on there is single-valued relationship between the fan-shaped angle seam phase that road is loaded.
3. a kind of relevance imaging method tangled based on Angle Position according to claim 1, it is characterised in that：Methods described
Suitable for the relevance imaging of many gray scale object to be imaged.
4. a kind of relevance imaging method tangled based on Angle Position according to claim 1, it is characterised in that：Methods described
There is strictly monotone relation between coincidence counting value and the added fan-shaped angle seam phase carried of signal light path.
5. a kind of relevance imaging method tangled based on Angle Position according to claim 1, it is characterised in that：Methods described
A Gauss pump light pass through bbo crystal carry out parameter under change, produce an entangled photon pairs；If signal light path is LG-l,0Mould
Formula, then light path of leaving unused will be LG+l,0Pattern；The different information of object to be imaged are encoded into the angle seam θ of different angles, and will
Different angle seams are loaded into the phase of signal beams；Due to there is the functional relation of dullness between coincidence counting and angle seam θ, lead to
Setting specific region is crossed, the one-to-one relationship between coincidence counting and object information is obtained；In reference path according to coincidence counting
The information of object can be obtained, the imaging of object is obtained.
6. a kind of relevance imaging method tangled based on Angle Position according to claim 1, it is characterised in that：Methods described
Angle Position is tangled applied in relevance imaging technology.
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