CN115166988B - Low-overhead quantum imaging method based on entangled light - Google Patents
Low-overhead quantum imaging method based on entangled light Download PDFInfo
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- 238000003384 imaging method Methods 0.000 title claims abstract description 36
- 239000011159 matrix material Substances 0.000 claims abstract description 27
- 238000005259 measurement Methods 0.000 claims abstract description 20
- 230000009466 transformation Effects 0.000 claims abstract description 5
- 238000000034 method Methods 0.000 claims description 10
- 238000006243 chemical reaction Methods 0.000 claims description 6
- 239000013078 crystal Substances 0.000 claims description 6
- 230000002269 spontaneous effect Effects 0.000 claims description 6
- 230000010287 polarization Effects 0.000 claims description 3
- WYOHGPUPVHHUGO-UHFFFAOYSA-K potassium;oxygen(2-);titanium(4+);phosphate Chemical compound [O-2].[K+].[Ti+4].[O-]P([O-])([O-])=O WYOHGPUPVHHUGO-UHFFFAOYSA-K 0.000 claims description 3
- 239000004065 semiconductor Substances 0.000 claims description 3
- 238000005314 correlation function Methods 0.000 claims description 2
- 230000003190 augmentative effect Effects 0.000 abstract 1
- 230000014759 maintenance of location Effects 0.000 abstract 1
- 230000001131 transforming effect Effects 0.000 abstract 1
- 238000005070 sampling Methods 0.000 description 6
- 238000001514 detection method Methods 0.000 description 3
- 238000010586 diagram Methods 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 238000003331 infrared imaging Methods 0.000 description 1
- 230000003287 optical effect Effects 0.000 description 1
- 238000012634 optical imaging Methods 0.000 description 1
- 238000011084 recovery Methods 0.000 description 1
- 239000000779 smoke Substances 0.000 description 1
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- G—PHYSICS
- G02—OPTICS
- G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
- G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
- G02B27/09—Beam shaping, e.g. changing the cross-sectional area, not otherwise provided for
- G02B27/0938—Using specific optical elements
- G02B27/095—Refractive optical elements
- G02B27/0955—Lenses
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
- G01J1/00—Photometry, e.g. photographic exposure meter
- G01J1/42—Photometry, e.g. photographic exposure meter using electric radiation detectors
- G01J1/44—Electric circuits
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- G—PHYSICS
- G02—OPTICS
- 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
- G02F1/353—Frequency conversion, i.e. wherein a light beam is generated with frequency components different from those of the incident light beams
-
- G—PHYSICS
- G02—OPTICS
- 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
- G02F1/355—Non-linear optics characterised by the materials used
- G02F1/3551—Crystals
- G02F1/3553—Crystals having the formula MTiOYO4, where M=K, Rb, TI, NH4 or Cs and Y=P or As, e.g. KTP
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
- G01J1/00—Photometry, e.g. photographic exposure meter
- G01J1/42—Photometry, e.g. photographic exposure meter using electric radiation detectors
- G01J1/44—Electric circuits
- G01J2001/4413—Type
- G01J2001/442—Single-photon detection or photon counting
Abstract
The invention provides a quantum imaging method based on entangled light correlation characteristics, which realizes low-cost imaging. Firstly, carrying out coincidence measurement on two paths of photons detected by a single photon detector to obtain a coincidence count value; then, decomposing the coincidence count value by wavelet transformation, and transforming the coincidence count value into a sparse domain; then, a random Bernoulli matrix is selected as a measurement matrix to ensure accurate retention of effective information in the sparse image; and finally, reconstructing the sparse coefficient of the target from a few measured values by using an augmented Lagrangian total variation algorithm, and introducing a relaxation variable to separate the variable under the condition of sparse target to obtain a reconstruction model so as to recover the original image from the few measured values.
Description
Technical Field
The invention belongs to the technical field of quanta, and particularly relates to a combination of a compressed sensing method and a quantum imaging method based on entangled light so as to reduce imaging cost and improve imaging quality.
Background
Quantum Imaging (QI) differs from classical optical Imaging in that it performs associative detection by extracting the fluctuation characteristics of photons to achieve non-localized Imaging of the target. The quantum imaging can overcome the limitation of the resolution ratio by the optical diffraction limit in the traditional imaging by utilizing the characteristics of quantum entanglement state and the like, and effectively inhibit the influence of atmospheric turbulence, smoke and the like on the imaging quality by separating the detection and the imaging process. Therefore, the quantum imaging technology has important application value in the fields of aviation detection, military reconnaissance, far infrared imaging and the like. Although the quantum imaging can realize anti-interference imaging to a certain extent, the quantum imaging can obtain a better imaging result by a large amount of sampling, and time cost is increased. Aiming at the problems of insufficient quality and long imaging time of the existing quantum imaging, the invention provides a low-overhead imaging method based on entangled light quanta by utilizing entanglement property, inaccurate measurement property and delocalization of entangled light quanta so as to make up a short plate of the traditional quantum imaging. Therefore, the invention proposes to apply compressed sensing to entangled light quantum imaging, enabling low overhead imaging. The earliest proposal of the compressed sensing method is that in the sampling problem, with the proposal of the compressed sensing method and the continuous promotion of related algorithms, the subsequent research is developed into the field of image restoration. Compressed sensing can accurately restore original signals by increasing constraint conditions under the condition that the compressed sensing is far smaller than Nyquist sampling samples. In compressed sensing theory, the object to be recovered is required to be sparse, and a sparse matrix can be obtained through wavelet transformation or discrete Fourier transformation. Meanwhile, the selection of a proper observation matrix can improve the recovery precision and reduce the sampling times, and the selection of the observation matrix is most typically a Gaussian random matrix, a random Bernoulli matrix, a local Hadamard matrix and the like. Therefore, the compressed sensing theory and the entangled light quantum imaging method are combined, so that the sampling times can be effectively reduced, the imaging time is shortened, and the real requirements are better met.
Disclosure of Invention
The invention aims to provide a low-overhead quantum imaging method based on entangled light. Compared with the traditional quantum imaging method, the method combines the compressed sensing theory with the entangled light quantum imaging method, can effectively reduce sampling times and shortens imaging time. The method comprises the following specific steps:
step one: generating pump light by using a semiconductor laser with a wavelength of 405 nm;
step two: a telescope system is formed by lenses with focal lengths of 300mm and 75mm respectively so as to shrink the generated pump light, so that the energy of the pump light is concentrated on periodically polarized potassium titanyl phosphate (Periodically poled KTiOPO, PPKTP) crystals, and stray light in the pump light is filtered by a high-pass filter with the wavelength of 810nm to obtain pure pump light;
step three: the pump light is incident into the PPKTP crystal, and photons in the light beam generate spontaneous parameter down-conversion (Spontaneous parametric down-conversion, SPDC) process with a certain probability, so as to obtain entangled two-photon pairs;
step four: the unconverted pump light is reflected by a high-pass total reflection mirror with a reflection wavelength of 405nm and the two photons of the entangled photon pair (i.e. the reference photon and the signal photon) are separated by a polarizing beam splitter (Polarization beam splitter, PBS) allowing passage of the wavelength of 810 nm;
step five: transmitting signal photons to a target to be imaged through a spatial channel, wherein reference photons are left locally;
step six: detecting signal photons transmitted by an object to be imaged by using the single photon detector 1, and detecting reference photons scanned by the DMD by using the single photon detector 2;
step seven: and carrying out coincidence measurement on the two paths of photons detected by the single photon detectors 1 and 2, and realizing imaging of a target according to a coincidence count value.
Drawings
FIG. 1 is a schematic diagram of the low overhead quantum imaging principle of the present invention;
fig. 2 is a flow chart of low overhead quantum imaging of the present invention.
Detailed description of the preferred embodiments
The invention is further described below with reference to the accompanying drawings:
the method comprises the following specific steps:
step one: generating pump light by using a semiconductor laser with a wavelength of 405 nm;
step two: a telescope system is formed by lenses with focal lengths of 300mm and 75mm respectively so as to shrink the generated pump light, so that the energy of the pump light is concentrated on periodically polarized potassium titanyl phosphate (Periodically poled KTiOPO, PPKTP) crystals, and stray light in the pump light is filtered by a high-pass filter with the wavelength of 810nm to obtain pure pump light;
step three: the pump light is incident into the PPKTP crystal, and photons in the light beam generate spontaneous parameter down-conversion (Spontaneous parametric down-conversion, SPDC) process with a certain probability, so as to obtain entangled two-photon pairs;
step four: the unconverted pump light is reflected by a high-pass total reflection mirror with a reflection wavelength of 405nm and the two photons of the entangled photon pair (i.e. the reference photon and the signal photon) are separated by a polarizing beam splitter (Polarization beam splitter, PBS) allowing passage of the wavelength of 810 nm;
step five: transmitting signal photons to a target to be imaged through a spatial channel, wherein reference photons are left locally;
step six: detecting signal photons transmitted by an object to be imaged by using the single photon detector 1, and detecting reference photons scanned by the DMD by using the single photon detector 2;
step seven: and carrying out coincidence measurement on the two paths of photons detected by the single photon detectors 1 and 2, and realizing imaging of a target according to a coincidence count value.
The seventh step comprises the following steps:
step seven (one): the single photon detector meets the count value C (x, y) at pixel (x, y) proportional to the second order correlation function at pixel (x, y):
wherein i is the total number of times of coincidence measurement, a is selected as a measurement matrix by using a random Bernoulli matrix i And n is the number of pixels of the target image, which is the measurement matrix used by the spatial light modulator on the reference light path when the i-th coincidence measurement is performed. The above formula can be expressed as a matrix form as follows:
C i ＝A i r (2)
wherein A is i And r is a column vector formed by the target image matrix.
Step seven (two): m coincidence count values C can be obtained after M coincidence measurements 1 ,…,C M Arrange it as a column vector c= (C 1 ,…,C M ) T Corresponding measurement matrix A 1 ,…,A M Arranged as a matrix a= [ a ] 1 ,…,A M ] T And C, A, r satisfy the relation:
C＝Ar (3)
step seven (three): for the compressive sensing reconstruction problem described in the above equation, the target image is required to be sparse, then it is subjected to sparse transform, r is transformed to the sparse domain using the wavelet transform matrix W, i.e., r=w -1 θ, where θ is the target imageSparse coefficients in the wavelet domain. In this case, the above formula is rewritten as:
C＝Ar＝AW -1 θ＝Pθ (4)
step seven (four): the sparsity coefficient θ of the target is reconstructed from a few measurements using the TVAL3 algorithm.
Step seven (five): from (4), it can be seen that r=w -1 θ, since the sparse coefficient θ and the wavelet transform matrix W are known, we can pass r=w -1 θ restores the target image.
Claims (1)
1. A low overhead quantum imaging method based on entangled light, characterized by comprising the steps of:
step one: generating pump light by using a semiconductor laser with a wavelength of 405 nm;
step two: a telescope system is formed by lenses with focal lengths of 300mm and 75mm respectively so as to shrink the generated pump light, so that the energy of the pump light is concentrated on periodically polarized potassium titanyl phosphate (Periodically poled KTiOPO, PPKTP) crystals, and stray light in the pump light is filtered by a high-pass filter with the wavelength of 810nm to obtain pure pump light;
step three: the pump light is incident into the PPKTP crystal, and photons in the light beam generate spontaneous parameter down-conversion (Spontaneous parametric down-conversion, SPDC) process with a certain probability, so as to obtain entangled two-photon pairs;
step four: reflecting the unconverted pump light via a high-pass total reflection mirror with a reflection wavelength of 405nm and separating two photons of the entangled photon pair, i.e. the reference photon and the signal photon, by means of a polarizing beam splitter (Polarization beam splitter, PBS) allowing passage of the wavelength of 810 nm;
step five: transmitting signal photons to a target to be imaged through a spatial channel, wherein reference photons are left locally;
step six: detecting signal photons transmitted by an object to be imaged by using the single photon detector 1, and detecting reference photons scanned by the DMD by using the single photon detector 2;
step seven: carrying out coincidence measurement on two paths of photons detected by the single photon detectors 1 and 2, and realizing imaging of a target according to coincidence count values;
the seventh step comprises the following steps:
step seven (one): the single photon detector meets the count value C (x, y) at pixel (x, y) proportional to the second order correlation function at pixel (x, y):
wherein i is the total number of times of coincidence measurement, a is selected as a measurement matrix by using a random Bernoulli matrix i For the measurement matrix used by the spatial light modulator on the reference light path in the ith coincidence measurement, n is the number of pixels of the target image; the above formula can be expressed as a matrix form as follows:
C i ＝A i r (2)
wherein A is i The row vector is composed of the ith measurement matrix, and r is a column vector composed of the target image matrix;
step seven (two): m coincidence count values C can be obtained after M coincidence measurements 1 ,…,C M Arrange it as a column vector c= (C 1 ,…,C M ) T Corresponding measurement matrix A 1 ,…,A M Arranged as a matrix a= [ a ] 1 ,…,A M ] T And C, A, r satisfy the relation:
C＝Ar (3)
step seven (three): for the compressive sensing reconstruction problem related to the above formula, the target image is required to be sparse, then the target image is subjected to sparse transformation, and r is transformed into a sparse domain by utilizing a wavelet transformation matrix W, namely r=w -1 θ, where θ is a sparse coefficient of the target image in the wavelet domain, and in this case, the above equation can be rewritten as:
C＝Ar＝AW -1 θ＝Pθ (4)
step seven (four): reconstructing a sparse coefficient theta of the target from a few measured values by utilizing a TVAL3 algorithm;
step seven (five): from (4), it can be seen that r=w -1 θ, since the sparse coefficient θ and the wavelet transform matrix W are known, we can pass r=w -1 θ restores the target image.
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| CN102495467A (en) * | 2011-11-11 | 2012-06-13 | 上海电机学院 | Method utilizing time correlation property of chaotic laser for imaging and device adopting same |
| CN103453993A (en) * | 2013-09-13 | 2013-12-18 | 中国科学院空间科学与应用研究中心 | Active hyperspectral imaging system and method based on sparse aperture compression calculation correlation |
| CN112904351A (en) * | 2021-01-20 | 2021-06-04 | 重庆邮电大学 | Single-source positioning method based on quantum entanglement light correlation characteristic |
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| US7847234B2 (en) * | 2003-08-06 | 2010-12-07 | The United States Of America As Represented By The Secretary Of The Army | Method and system for observing a subject at a first location based upon quantum properties measured at a second location |
| US9414887B2 (en) * | 2009-03-13 | 2016-08-16 | Robert R. Alfano | Method and apparatus for producing supercontinuum light for medical and biological applications |
| JP6394850B2 (en) * | 2013-09-20 | 2018-09-26 | 大学共同利用機関法人自然科学研究機構 | Compensating optical system and optical apparatus |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101846745A (en) * | 2010-05-07 | 2010-09-29 | 浙江大学 | Laser radar based on highly-correlated quantum imaging principle |
| CN102087411A (en) * | 2010-12-02 | 2011-06-08 | 上海电机学院 | Quantum imaging method and quantum imaging system |
| CN102495467A (en) * | 2011-11-11 | 2012-06-13 | 上海电机学院 | Method utilizing time correlation property of chaotic laser for imaging and device adopting same |
| CN103453993A (en) * | 2013-09-13 | 2013-12-18 | 中国科学院空间科学与应用研究中心 | Active hyperspectral imaging system and method based on sparse aperture compression calculation correlation |
| CN112904351A (en) * | 2021-01-20 | 2021-06-04 | 重庆邮电大学 | Single-source positioning method based on quantum entanglement light correlation characteristic |
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