A high-dynamic-range imaging method based on superconducting nanowire detectors

Abstract

The present invention discloses a high dynamic range imaging method based on a superconducting nanowire detector, including a flux estimation method based on SNSPD response counting under high flux and a flux estimation method based on PNR-SNSPD output energy under ultra-high flux. Under the high flux, the SNSPD operates in a linear mode, and the flux estimation method based on SNSPD response counting includes the equivalent of the detector efficiency recovery time and the establishment of a #imgabs0# flux estimation model. Under the ultra-high flux, the SNSPD operates in a quasi-linear model, and the flux estimation method based on PNR-SNSPD output energy includes the energy E T The correction of N and the establishment of the #imgabs1# flux estimation model are combined to obtain the high dynamic range of superconducting nanowire detectors. The method of the present invention can effectively achieve a light flux of 10 9 :1 and above high dynamic range imaging, through modeling and simulation, the dynamic range of superconducting nanowire imagers can be expanded.

Description

Technical Field

[0001] The present invention relates to the technical field of high dynamic range imaging, and in particular to a high dynamic range imaging method based on a superconducting nanowire detector, which improves the high dynamic range imaging capability of the detector. Background Art

[0002] In astronomical observation imaging applications such as coronagraphs, detectors with ultra-high dynamic range are required to estimate the scene luminous flux. The detectors must have the ability to detect single photons to achieve luminous flux estimation in weak light conditions. At the same time, they must also have a high counting rate to ensure that the detector is not saturated in strong light scenes, thereby achieving luminous flux estimation in strong light conditions.

[0003] The key concept behind traditional high-dynamic-range imaging using CMOS or CCD is similar to composite printing: capturing the same high-dynamic-range scene with different detector exposure times. Dark portions of the scene require longer exposure times to capture more light and mitigate the effects of noise, while bright portions require shorter exposure times to capture less light and avoid pixel saturation. Finally, the low-dynamic-range images captured with different exposure times are combined to create a high-dynamic-range image. This approach relies on the inherently small dynamic range of the detectors themselves and often requires complex hardware expansion or imaging algorithms to address ghosting issues during the image fusion process.

[0004] Count rate is the primary factor limiting high dynamic range. Superconducting nanowire single-photon detectors (SNSPDs) offer the advantages of a high dynamic range, with very low dark counts and high count rates. Currently reported single-pixel SNSPDs have an efficiency recovery time of less than 10 ns and a maximum count rate of 100 MHz, but they lack photon number resolution. To further improve the detector's dynamic range, SNSPDs with photon number resolution (PNR-SNSPDs) can be used to increase the maximum count rate of the SNSPD through time or spatial multiplexing. Summary of the Invention

[0005] In view of the above problems and shortcomings of the prior art, the present invention aims to provide a high dynamic range imaging method based on superconducting nanowire detectors, which can achieve 10 9 : Dynamic range luminous flux estimation for 1 and above.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] A high dynamic range imaging method based on a superconducting nanowire detector includes a flux estimation method based on SNSPD response counting at high flux and a flux estimation method based on PNR-SNSPD output energy at ultra-high flux. At high flux, the SNSPD operates in linear mode. The flux estimation method based on SNSPD response counting includes the equivalent and Establishment of flux estimation model. Under the ultra-high flux, SNSPD works in a quasi-linear model. The flux estimation method based on PNR-SNSPD output energy includes energy E T and the correction of N The flux estimation model is established. Combining the response methods under the two modes, the high dynamic range of the superconducting nanowire detector is obtained.

[0008] Furthermore, the equivalence of the detector efficiency recovery time includes the following steps: step 1, solving the recovery process of the bias current I with time t; step 2, solving the recovery process of the efficiency η with the bias current I; step 3, solving the recovery process of the efficiency η with time t.

[0009] Furthermore, in step 1, the recovery process of the bias current I over time t is fitted with two exponential functions:

[0010]

[0011] in, is the time constant for current recovery, usually tens of nanoseconds; is the time constant of the bias current decay, usually several hundred picoseconds; I b is the initial bias current value; I, I b The unit is μA.

[0012] In the second step, the recovery process of efficiency η with bias current I is fitted with Sigmoid function:

[0013]

[0014] where s = aI b , I b is the initially set bias current value, and a is a constant that needs to be determined based on device parameters.

[0015] In step 3, the recovery function of efficiency η over time t is obtained according to formula (1) and (2):

[0016]

[0017] The time it takes for η(t) to recover to 80% is equivalent to the efficiency recovery time τ η , after responding to the photon (0-τη ) time interval, the SNSPD cannot respond to the incident photons, and in >τ η After that, it can continue to respond to photons; let formula (3) = 80%, omit term (which contributes very little to Equation (3)), we get τ η The final expression of:

[0018]

[0019] Furthermore, the The flux estimation model is as follows:

[0020]

[0021] Among them, N is the count value output by the counter, Q s is the system efficiency (0<Q s <1), T is the total exposure time, τ η Recovery time for efficiency.

[0022] Furthermore, the efficiency recovery time τ η The dead time is much shorter than that of semiconductor single-photon detectors. SNSPD can still work in linear detection mode at high flux and estimate the light flux using the counting value.

[0023] Furthermore, under the ultra-high flux, the SNSPD operates in a quasi-linear mode, utilizing the photon number resolution capability of the PNR-SNSPD device to estimate the luminous flux based on the output energy.

[0024] Furthermore, the PNR-SNSPD device includes all superconducting nanowire detectors with photon number resolution capability.

[0025] Furthermore, the energy E T The process of correction with N is as follows:

[0026] The output voltage pulse function of a single pixel of PNR-SNSPD in response to a single photon is given by Equation (6). The energy of a single pulse is a fixed constant E0, which can be calculated by Equation (7).

[0027]

[0028]

[0029] Where A is the peak value of the voltage pulse, is the time constant of voltage drop, is the time constant of voltage rise;

[0030] The electrical pulse function output by the PNR-SNSPD can be expressed as the convolution of the random process of photon incidence and the device response;

[0031]

[0032] N(t,Φ) represents the random process of photon incidence within the exposure time [0,T], which is a Poisson process with parameter Φ and can be further expressed by the sampling function:

[0033]

[0034] Where n is the total number of PNR-SNSPD responses, t i is the time of the i-th response, M i is the number of pixels responding to the i-th time;

[0035] The total energy of the PNR-SNSPD output voltage pulse is:

[0036]

[0037] Get energy E T Relationship with N:

[0038]

[0039] Furthermore, using E T The relationship between N and the ultra-high flux mode is obtained. Flux estimation model:

[0040]

[0041] Compared with the prior art, the present invention has the following technical features and advantages:

[0042] 1. Unlike existing high dynamic range imaging technologies that require the fusion of multiple images with different exposure times, this method does not require multiple images with different exposure times. HDR images can be obtained through a single exposure, reducing the ghosting problem caused by the fusion of multiple images and ensuring the rapidity and real-time performance of HDR imaging.

[0043] 2. Compared with existing sensors, the equivalent efficiency recovery time proposed by this method is much shorter than the dead time of semiconductor detectors, achieving linear estimation under high flux.

[0044] 3. The photon number resolution capability of the PNR-SNSPD is utilized to improve the maximum counting rate, and the light flux is estimated based on the output voltage pulse energy, achieving quasi-linear estimation at ultra-high flux. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 It is a schematic diagram of the process of the present invention;

[0046] Figure 2is the efficiency recovery process curve over time;

[0047] Figure 3 Response curves for flux estimation based on count values;

[0048] Figure 4 This is the dynamic range curve of the two models;

[0049] Figure 5 This is a diagram showing the result of HDR imaging in an embodiment of the present invention. DETAILED DESCRIPTION

[0050] The present invention will be described in further detail below with reference to the accompanying drawings.

[0051] A high dynamic range imaging method based on a superconducting nanowire detector in this embodiment is as follows Figure 1 As shown in the flow chart, it includes a flux estimation method based on SNSPD response counting at high flux and a flux estimation method based on PNR-SNSPD output energy at ultra-high flux. At high flux, the SNSPD works in linear mode. The flux estimation method based on SNSPD response counting includes the equivalent and Establishment of flux estimation model. Under the ultra-high flux, SNSPD works in a quasi-linear model. The flux estimation method based on PNR-SNSPD output energy includes energy E T and the correction of N The flux estimation model is established. By combining the response methods under the two modes, the high dynamic range of the superconducting nanowire detector is obtained.

[0052] When the light intensity is not very strong, a single-pixel SNSPD can meet the requirements of luminous flux estimation, and the luminous flux can be estimated directly using the output count value.

[0053] The recovery process of the SNSPD's detection efficiency after responding to photons is relatively complex, so this process is simplified. The specific implementation process is divided into three steps.

[0054] Step 1: Calculate the recovery process of the bias current I over time t. The recovery process of the bias current I over time t is fitted with two exponential functions:

[0055]

[0056] in, is the time constant for current recovery, usually tens of nanoseconds; is the time constant of the bias current decay, usually several hundred picoseconds; I b is the initial bias current value. In order to facilitate the subsequent fitting process, I, I b The unit is μA.

[0057] Step 2: Calculate the recovery process of efficiency η with bias current I. The efficiency of a typical SNSPD changes in an S-shape with bias current, which can be fitted with a Sigmoid function:

[0058]

[0059] where s = aI b , I b is the initially set bias current value, and a is a constant that needs to be determined based on device parameters.

[0060] Step 3: Solve the recovery process of efficiency η with time t. According to formula (1) (2), the recovery function of efficiency η with time t is obtained:

[0061]

[0062] The time it takes for η(t) to recover to 80% is equivalent to the efficiency recovery time τ η , SNSPD works in free mode, after responding to photons (0-τ η ) time interval, the SNSPD cannot respond to the incident photons, and in >τ η After that, it can continue to respond to photons. Let equation (3) = 80%, calculate τ η expression.

[0063]

[0064]

[0065] The first term on the left side of the above formula The effect on the entire expression is very small and can be omitted, giving τ η The final expression of:

[0066]

[0067] Figure 2 In this embodiment, the parameter τ=5ns, I b =27uA,s=0.8I b The obtained η(t) curve is equivalent to τ η =9.53ns.

[0068] Substitute τ η get The flux estimation model is as follows:

[0069]

[0070] Among them, N is the count value output by the counter, Q s is the system efficiency (0<Qs <1), T is the total exposure time, τ η The parameters in this embodiment are set as T = 5ms, Q s =80%,τ η =9.53ns,

[0071] Figure 3 The N~Φ response curve is drawn for the case where the incident light flux exceeds 10 7 After a few photons, the mode changes from linear to nonlinear and tends to saturation.

[0072] Since τ η The dead time of the SNSPD is much shorter than that of the semiconductor detector (generally greater than 100 ns), and the flux estimation based on the output count value of the single-pixel SNSPD can achieve a larger dynamic range than that of the semiconductor detector.

[0073] In strong light scenes, in order to increase the maximum counting rate of the detector, a PNR-SNSPD device with photon number resolution capability is used. However, the output voltage pulse peaks are inconsistent and the waveforms overlap a lot. It is difficult to estimate the luminous flux using the counting value. Therefore, an energy-based method is used to estimate the luminous flux.

[0074] The output voltage pulse function of a single pixel of the PNR-SNSPD in response to a single photon is expressed as Equation (6). The energy of a single pulse is a fixed constant E0, which can be calculated by Equation (7).

[0075]

[0076]

[0077] Where A is the peak value of the voltage pulse, is the time constant of voltage drop, is the time constant of voltage rise.

[0078] The output electrical pulse function of the PNR-SNSPD can be expressed as the convolution of the random process of photon incidence and the device response, as shown in Equation (8).

[0079]

[0080] Where N(t,Φ) represents the random process of photon incidence within the exposure time [0,T], which is a Poisson process with parameter Φ and can be further expressed by the sampling function:

[0081]

[0082] Where n is the total number of PNR-SNSPD responses, t i is the time of the i-th response, M iis the number of pixels in the ith response.

[0083] The total energy of the PNR-SNSPD output voltage pulse is:

[0084]

[0085] According to the above process, the energy E is obtained T The relationship between N and (11):

[0086]

[0087] Substitute equation (11) into equation (5) and make corrections to obtain Flux estimation model:

[0088]

[0089] In this embodiment, a 6-pixel PNR-SNSPD is used to achieve the resolution of 6 photons. The incident photon process under different light fluxes is simulated and the two models are combined. Figure 4 The dynamic range of the response is given. The final 10 9 :1 dynamic range, Figure 5 The results of high dynamic imaging in this embodiment are shown.

[0090] In summary, the present invention proposes a high dynamic range imaging method based on superconducting nanowire detectors. Through the following improvements, the detector has the ability of high dynamic range imaging. (1) In high-throughput mode, based on Flux estimation model, which can achieve 10 7 :1 dynamic range; (2) in ultra-high throughput mode, based on Flux estimation model, which can increase the dynamic range to 10 9 :1 and above.

[0091] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principles of the present invention shall be included in the scope of protection of the present invention.

Claims

1. A high dynamic range imaging method based on superconducting nanowire detectors, characterized in that: include: Flux estimation methods based on SNSPD response counts at high flux and flux estimation methods based on PNR-SNSPD output energy at ultra-high flux; Under the high flux, the SNSPD works in linear mode, and the flux estimation method based on the SNSPD response count includes the equivalent and Establishment of flux estimation model; Under the ultra-high flux, SNSPD works in a quasi-linear model. The flux estimation method based on the PNR-SNSPD output energy includes energy E T and the correction of N Establishment of flux estimation model; Among them, using E T The relationship between N and the ultra-high flux mode is obtained. Flux estimation model: Where, E T is the total energy of the PNR-SNSPD output voltage pulse, E0 is the energy of a single pulse, Q s is the system efficiency, T is the total exposure time, N is the count value output by the counter, τ η is the efficiency recovery time, N(t,Φ) represents the random process of photon incidence within the exposure time [0,T], which is a Poisson process with parameter Φ, and V0(t) is the output voltage pulse of a single pixel of the PNR-SNSPD in response to one photon; By combining the response methods in the two modes, the high dynamic range that can be detected by superconducting nanowire detectors is obtained.

2. The high dynamic range imaging method based on superconducting nanowire detectors according to claim 1, characterized in that: The equivalence of the detector efficiency recovery time includes the following steps: step 1, solving the recovery process of the bias current I with time t; step 2, solving the recovery process of the efficiency η with the bias current I; step 3, solving the recovery process of the efficiency η with time t.

3. The high dynamic range imaging method based on superconducting nanowire detectors according to claim 2, characterized in that: In the first step, the recovery process of the bias current I over time t is fitted with two exponential functions: in, is the time constant for current recovery, usually tens of nanoseconds; is the time constant of the bias current decay, usually several hundred picoseconds; I b is the initial bias current value; I, I b The unit is μA; In the second step, the recovery process of efficiency η with bias current I is fitted with Sigmoid function: where s = aI b , I b is the initial bias current value, a is a constant that needs to be determined according to the device parameters; In step 3, the recovery function of efficiency η over time t is obtained according to formula (1) and (2): The time it takes for η(t) to recover to 80% is equivalent to the efficiency recovery time τ η , after responding to the photon (0-τ η ) time interval, the SNSPD cannot respond to the incident photons, and in >τ η After that, it can continue to respond to photons; let formula (3) = 80%, omit Term, we get τ η The final expression of:

4. The high dynamic range imaging method based on superconducting nanowire detectors according to claim 1, characterized in that: described The flux estimation model is as follows: Among them, N is the count value output by the counter, Q s is the system efficiency, 0<Q s <1, T is the total exposure time, τ η Recovery time for efficiency.

5. The high dynamic range imaging method based on superconducting nanowire detectors according to claim 4, characterized in that: The efficiency recovery time τ η The dead time is much shorter than that of semiconductor single-photon detectors. SNSPD can still work in linear detection mode at high flux and estimate the light flux using the counting value.

6. The high dynamic range imaging method based on superconducting nanowire detectors according to claim 1, characterized in that: Under the ultra-high flux, the SNSPD operates in a quasi-linear mode, utilizing the photon number resolution capability of the PNR-SNSPD device to estimate the luminous flux based on the output energy.

7. The high dynamic range imaging method based on superconducting nanowire detectors according to claim 6, characterized in that: The PNR-SNSPD device includes all superconducting nanowire detectors with photon number resolution capability.

8. The high dynamic range imaging method based on superconducting nanowire detectors according to claim 1, characterized in that: The energy E T The process of correction with N is as follows: The output voltage pulse function of a single pixel of PNR-SNSPD in response to a single photon is given by Equation (6). The energy of a single pulse is a fixed constant E0, which can be calculated by Equation (7). Where A is the peak value of the voltage pulse, is the time constant of voltage drop, is the time constant of voltage rise; The electrical pulse function output by the PNR-SNSPD can be expressed as the convolution of the random process of photon incidence and the device response; N(t,Φ) represents the random process of photon incidence within the exposure time [0,T], which is a Poisson process with parameter Φ and can be further expressed by the sampling function: Where n is the total number of PNR-SNSPD responses, t i is the time of the i-th response, M i is the number of pixels responding to the i-th time; The total energy of the PNR-SNSPD output voltage pulse is: Get energy E T Relationship with N:

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