CN108802708A - A kind of single photon counting heterodyne detection method based on sequence reconstruct - Google Patents
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Abstract
The invention discloses a kind of single photon counting heterodyne detection methods based on sequence reconstruct, belong to laser radar detection field, include the following steps：1. receiving photon with photon counting detector, photon pulse sequence, and recording impulse sequence time interval are generated；2. reconstructing photon pulse sequence based on pulse train time interval, reconstruction pulse sequence is obtained；3. the reconstruction pulse sequence of pair step 2 carries out Fourier transformation, after acquiring power spectrum, it is determined as heterodyne signal frequency with maximum value in signal frequency section, the present invention solves the problem of heterodyne signal waveform corresponding to the mismatch time interval interference photon interval that existing single photon heterodyne detection technology generates, attenuated signal oscillator intensity.
Description
Technical Field
The invention belongs to the field of laser radar detection, relates to the field of laser single photon technology heterodyne detection, and particularly relates to a single photon counting heterodyne detection method based on sequence reconstruction.
Background
Single photon detection techniques refer to a detector that outputs a pulse signal even when only one photon arrives at the detector. The principle of the single photon heterodyne detection technology is shown in fig. 2 and 3, and as shown in fig. 2, the pulse signal schematic diagram is shown, and when a trough of a heterodyne signal (in the form of a sine wave or a cosine wave) arrives, the distance between pulse signals output by a detector is maximum; and when the peak of the heterodyne signal arrives, the pitch of the pulse signal is minimum.
Because of extremely weak signals and single photon magnitude detection, the time of the photons reaching the detector has high randomness, and the Poisson distribution is satisfied. When the photon electric pulse signal is not output, photons may arrive to generate a pulse signal, such as a pulse shown by a dotted line in fig. 3; when the photon electric pulse signal is output, no photon may arrive to generate the electric pulse signal. Both of the above two cases will generate a "mismatch time interval", so as to interfere with the heterodyne signal waveform corresponding to the photon interval, and weaken the intensity of the signal amplitude in the frequency domain, as shown in fig. 3, which is a schematic diagram of the interference of the mismatch time interval to the signal waveform.
Disclosure of Invention
The invention aims to: the single photon counting heterodyne detection method based on sequence reconstruction is provided, and the problems that mismatch time intervals generated by the existing single photon heterodyne detection technology interfere heterodyne signal waveforms corresponding to photon intervals and the signal amplitude intensity is weakened are solved.
The technical scheme adopted by the invention is as follows:
a single photon counting heterodyne detection method based on sequence reconstruction comprises the following steps:
step 1: receiving photons, generating a photon pulse sequence, and recording the time interval of the pulse sequence;
step 2: reconstructing the photon pulse sequence based on the pulse sequence time interval to obtain a reconstructed pulse sequence;
and step 3: and (3) carrying out Fourier transform on the reconstructed pulse sequence in the step (2), and determining the maximum value in the signal frequency band as the heterodyne signal frequency after obtaining the power spectrum.
Further, the step 1 receives photons through a photon counting detector.
Further, the photon pulse sequence before reconstruction in step 1 is represented as:
wherein K is NS+NLOK is the total number of photons; δ (.) is a delta function; t is tkThe time of arrival of the kth photon.
Further, the reconstruction pulse sequence in step 2 is represented as:
wherein, taukFor the spacing between two adjacent delta functions, TuIs the detection time; tau ismaxIs the maximum of all intervals.
Further, the specific steps of step 3 are as follows:
step 3.1: performing Fourier transform on the reconstructed pulse sequence in the step 2 to obtain:
step 3.2: multiplying the formula of step 3.1 by its complex conjugate to obtain a power spectrum:
wherein, taulIs independent of taukOf (1);
step 3.3: the power spectrum is analyzed from a statistical point of view to obtain the mathematical expectation:
the term K ≠ l has K, and the term K ≠ l has K2-K;
step 3.4: from the mathematical expectation formula of step 3.3:
where p (τ) is the probability density distribution function for the time interval, | Fp(ω)|2Is the power of p (tau)(ii) spectral density;
step 3.5: substituting the formula in the step 3.4 into the power spectrum formula in the step 3.2 to obtain:
wherein,to average the number of photons, it follows from the above equation that the power spectral density characteristic of the reconstructed pulse sequence depends on the power spectral density | F of p (τ)p(ω)|2And | Fp(ω)|2The reconstruction pulse sequence contains frequency spectrum information of the heterodyne signals, so that the frequency characteristics of the heterodyne signals are still kept in the reconstruction pulse sequence.
In summary, due to the adoption of the technical scheme, the invention has the beneficial effects that:
1. a single photon counting heterodyne detection method based on sequence reconstruction is characterized in that a photon pulse sequence is reconstructed according to pulse sequence intervals, all sequences are compressed to the maximum time interval, the influence of mismatch time intervals on signal waveforms is effectively reduced, and therefore the signal intensity is increased.
2. The sequence reconstruction only needs the time interval of the photon pulse sequence, the short pulse signal splicing can be realized, when the pulse time is short, because the signal is weak, only a small number of photons exist in the pulse time, the power spectrum analysis of the short pulse signal is not meaningful, but the reconstruction method of the invention reconstructs the photon pulse time interval of a plurality of pulses into a longer sequence, and then the average accumulation of the power spectrum can be realized.
3. In the invention, all sequences are compressed into the maximum time interval, and the sequence time after reconstruction is reduced, so that the time of subsequent processing is reduced, the overall efficiency of photon counting is increased, and the processing of practical application is facilitated.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are required to be used in the embodiments will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present invention and therefore should not be considered as limiting the scope, and that for those skilled in the art, other relevant drawings can be obtained according to the drawings without inventive effort, wherein:
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic diagram of the pulse signal of the present invention;
FIG. 3 is a schematic diagram of the interference of the mismatch time interval on the signal waveform of the present invention;
FIG. 4 shows a pulse sequence distribution according to a first embodiment of the present invention;
FIG. 5 is a distribution of a reconstructed pulse sequence according to a first embodiment of the present invention;
FIG. 6 is a simulation diagram of a pulse sequence according to a first embodiment of the present invention;
FIG. 7 is a simulation diagram of a reconstructed pulse sequence according to a first embodiment of the present invention;
FIG. 8 is a power spectrum distribution of a pulse sequence according to a first embodiment of the present invention;
FIG. 9 is a power spectrum distribution of a reconstructed pulse sequence according to a first embodiment of the present invention;
fig. 10 is a schematic diagram of the present invention for splicing the segment pulses according to time intervals.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the detailed description and specific examples, while indicating the preferred embodiment of the invention, are intended for purposes of illustration only and are not intended to limit the scope of the invention. The components of embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations.
Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present invention without making any creative effort, shall fall within the protection scope of the present invention.
It is noted that relational terms such as "first" and "second," and the like, may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in a process, method, article, or apparatus that comprises the element.
A single photon counting heterodyne detection method based on sequence reconstruction solves the problems that mismatch time intervals generated by the existing single photon heterodyne detection technology interfere heterodyne signal waveforms corresponding to photon intervals and weaken signal amplitude intensity, and comprises the following steps as shown in figure 1:
step 1: receiving photons, generating a photon pulse sequence, and recording the time interval of the pulse sequence;
step 2: reconstructing the photon pulse sequence based on the pulse sequence time interval to obtain a reconstructed pulse sequence;
and step 3: and (3) carrying out Fourier transform on the reconstructed pulse sequence in the step (2), and after a power spectrum is obtained, regarding the maximum value in a signal frequency band as a heterodyne signal frequency relative to the frequency.
The invention reconstructs the photon pulse sequence according to the pulse sequence interval, compresses all the sequences to the maximum time interval, effectively reduces the influence of mismatch time interval on the signal waveform, thereby increasing the signal intensity.
Further, the step 1 receives photons through a photon counting detector.
Further, the photon pulse sequence in step 1 is represented as:
wherein K is NS+NLOK is the total number of photons; δ (.) is a delta function; t is tkThe time of arrival of the kth photon.
Further, the reconstruction pulse sequence in step 2 is represented as:
wherein, taukFor the spacing between two adjacent delta functions, TuIs the detection time; tau ismaxIs the maximum of all intervals.
Further, although reconstruction may reduce the impact of mismatch time intervals, reconstruction is meaningless if the reconstructed sequence does not contain signal frequency information. Thus, the following analysis illustrates that the sequence reconstruction will continue to preserve the frequency information of the heterodyne signal.
Further, the specific steps of step 3 are as follows:
step 3.1: performing Fourier transform on the reconstructed pulse sequence in the step 2 to obtain:
step 3.2: multiplying the formula of step 3.1 by its complex conjugate to obtain a power spectrum:
wherein, taulIs independent of taukOf (1);
step 3.3: the power spectrum is analyzed from a statistical point of view to obtain the mathematical expectation:
the term K ≠ l has K, and the term K ≠ l has K2-K;
step 3.4: from the mathematical expectation formula of step 3.3:
where p (τ) is the probability density distribution function for the time interval, | Fp(ω)|2Is the power spectral density of p (τ);
step 3.5: substituting the formula in the step 3.4 into the power spectrum formula in the step 3.2 to obtain:
wherein,to average the number of photons, it follows from the above equation that the power spectral density characteristic of the reconstructed pulse sequence depends on the power spectral density | F of p (τ)p(ω)|2And | Fp(ω)|2The reconstruction pulse sequence contains frequency spectrum information of the heterodyne signals, so that the frequency characteristics of the heterodyne signals are still kept in the reconstruction pulse sequence.
The features and properties of the present invention are described in further detail below with reference to examples.
Example one
The single photon counting heterodyne detection method based on sequence reconstruction provided by the preferred embodiment of the invention comprises the following steps:
step 1: receiving photons through a photon counting detector, generating a photon pulse sequence, and recording the time interval of the pulse sequence, as shown in the pulse sequence distribution situation shown in fig. 4, the pulse sequence simulation graph shown in fig. 6, and the pulse sequence power spectrum distribution shown in fig. 8, it can be seen from fig. 8 that heterodyne frequency signals are difficult to detect at present, and the photon pulse sequence is represented as:
wherein K is NS+NLOK is the total number of photons; δ (.) is a delta function; t is tkThe time of arrival of the kth photon;
step 2: reconstructing the photon pulse sequence based on the pulse sequence time interval to obtain a reconstructed pulse sequence, as shown in the reconstructed pulse sequence distribution situation shown in fig. 5, the reconstructed pulse sequence simulation graph shown in fig. 7, and the reconstructed pulse sequence power spectrum distribution shown in fig. 9, it can be seen from fig. 7 that the reconstructed pulse sequence is compressed in a very small time range, and as can be seen from fig. 9, the signal spectrum value of 40MHz is greatly improved, and at this time, the reconstructed pulse sequence is represented as:
wherein, taukFor the spacing between two adjacent delta functions, TuIs the detection time; tau ismaxIs the maximum of all intervals;
and step 3: fourier transform is carried out on the reconstructed pulse sequence in the step 2, after a power spectrum is obtained, the maximum value in a signal frequency band is determined as the heterodyne signal frequency;
step 3.1: performing Fourier transform on the reconstructed pulse sequence in the step 2 to obtain:
step 3.2: multiplying the formula of step 3.1 by its complex conjugate to obtain a power spectrum:
wherein, taulIs independent of taukOf (1);
step 3.3: the power spectrum is analyzed from a statistical point of view to obtain the mathematical expectation:
the term K ≠ l has K, and the term K ≠ l has K2-K;
step 3.4: from the mathematical expectation formula of step 3.3:
where p (τ) is the probability density distribution function for the time interval, | Fp(ω)|2Is the power spectral density of p (τ);
step 3.5: substituting the formula in the step 3.4 into the power spectrum formula in the step 3.2 to obtain:
wherein,to average the number of photons, it follows from the above equation that the power spectral density characteristic of the reconstructed pulse sequence depends on the power spectral density | F of p (τ)p(ω)|2According to the description of "statistical analysis of photon time intervals for photon counter laser heterodyne signal analysis" in "optical communication" published in 2012, | Fp(ω)|2The reconstruction method has the advantages that the reconstruction method contains frequency spectrum information of heterodyne signals, so that the reconstructed pulse sequence still keeps the frequency characteristics of the heterodyne signals, and further, the influence of mismatch time intervals on signal detection can be greatly reduced on the premise that the frequency characteristics of the signals are not influenced.
In the invention, the sequence reconstruction only needs the time interval of the photon pulse sequence to realize the splicing of short pulse signals, as shown in figure 10, when the pulse time is very short, because the signal is weak, only a small number of photons exist in the pulse time, and the power spectrum analysis of the signals is meaningless at the moment; all sequences are compressed into the maximum time interval, and the sequence time after reconstruction is reduced, so that the time of subsequent processing is reduced, the overall efficiency of photon counting is improved, and the processing of practical application is facilitated.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.
Claims (2)
1. A single photon counting heterodyne detection method based on sequence reconstruction is characterized by comprising the following steps:
step 1: receiving photons, generating a photon pulse sequence, and recording the time interval of the pulse sequence;
step 2: reconstructing the photon pulse sequence based on the pulse sequence time interval to obtain a reconstructed pulse sequence;
and step 3: and (3) carrying out Fourier transform on the reconstructed pulse sequence in the step (2), and determining the maximum value in the signal frequency band as the heterodyne signal frequency after obtaining the power spectrum.
2. The single photon counting heterodyne detection method based on sequence reconstruction as claimed in claim 1, wherein the step 1 receives photons through a photon counting detector.
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