Threshold value determination method, threshold value determination program, threshold value determination device, photon number identification system, photon number identification method, and photon number identification processing program
A threshold value determination method includes a step of calculating a probability distribution of a provisional value for each photon number of a target pixel based on an observation probability for each photoelectron number based on a probability distribution of the photon number and an observation probability for each photoelectron number based on a probability distribution of the photoelectron number accompanying reading noise of the target pixel and a step of calculating threshold value data for sorting the provisional value into a corresponding photon number based on the probability distribution for each photon number.
1 . A threshold value determination method of deriving threshold value data for sorting a provisional value of a photon number in a target pixel which is one of a plurality of pixels in a corresponding photon number in a photon number resolving system including the plurality of pixels of which each includes a photoelectric conversion element for converting input light to electric charges and an amplifier for amplifying the electric charges converted by the photoelectric conversion element and converting the electric charges to a voltage, an A/D converter configured to convert a voltage output from the amplifier of each of the plurality of pixels to a digital value, and a deriving unit configured to derive the provisional value of the photon number in each pixel of the plurality of pixels based on the digital value, the method comprising:
a step of calculating a first probability distribution of the provisional value with which the photon number in the target pixel is an integer n (where n is equal to or greater than 0) and a second probability distribution of the provision value with which the photon number in the target pixel is an integer m (where m is equal to or greater than 0 and is not equal to n) based on an observation probability for each photoelectron number based on a probability distribution of the photon number and an observation probability for each photoelectron number based on a probability distribution of the photoelectron number accompanying reading noise of the target pixel; and
a step of calculating threshold value data for sorting the provisional value into the integer n or the integer m based on the first probability distribution and the second probability distribution.
2 . The threshold value determination method according to claim 1 , wherein the integer m satisfies m=n+1.
3 . The threshold value determination method according to claim 1 , wherein the observation probability for each photoelectron number based on the probability distribution of the photon number is one of a poissonian distribution, a super-poissonian distribution, a sub-poissonian distribution, a photon number distribution in a multi-mode squeezed state, a Bose-Einstein distribution, a logarithmic normal distribution, a uniform distribution, and a mixed distribution.
4 . The threshold value determination method according to claim 1 , wherein the first probability distribution and the second probability distribution are derived based on a product of the observation probability for each photoelectron number based on the probability distribution of the photon number and the observation probability for each photoelectron number based on the probability distribution of the photoelectron number accompanying the reading noise of the target pixel.
5 . The threshold value determination method according to claim 1 , wherein the observation probability for each photoelectron number based on the probability distribution of the photon number is derived based on the digital value when the light is input to a reference pixel which is at least one pixel of the plurality of pixels.
6 . A non-transitory storage medium that stores a threshold value determination program, the program causing a computer to perform a process of deriving threshold value data for sorting a provisional value of a photon number in a target pixel which is one of a plurality of pixels in a corresponding photon number in a photon number resolving system including the plurality of pixels of which each includes a photoelectric conversion element for converting input light to electric charges and an amplifier for amplifying the electric charges converted by the photoelectric conversion element and converting the electric charges to a voltage, an A/D converter configured to convert a voltage output from the amplifier of each of the plurality of pixels to a digital value, and a deriving unit configured to derive the provisional value of the photon number in each pixel of the plurality of pixels based on the digital value, the process of deriving threshold value data comprising:
a process of calculating a first probability distribution of the provisional value with which the photon number in the target pixel is an integer n (where n is equal to or greater than 0) and a second probability distribution of the provision value with which the photon number in the target pixel is an integer m (where m is equal to or greater than 0 and is not equal to n) based on an observation probability for each photoelectron number based on a probability distribution of the photon number and an observation probability for each photoelectron number based on a probability distribution of the photoelectron number accompanying reading noise of the target pixel; and
a process of calculating threshold value data for sorting the provisional value into the integer n or the integer m based on the first probability distribution and the second probability distribution.
7 . The non-transitory storage medium according to claim 6 , wherein the integer m satisfies m=n+1.
8 . The non-transitory storage medium according to claim 6 , wherein the observation probability for each photoelectron number based on the probability distribution of the photon number is one of a poissonian distribution, a super-poissonian distribution, a sub-poissonian distribution, a photon number distribution in a multi-mode squeezed state, a Bose-Einstein distribution, a logarithmic normal distribution, a uniform distribution, and a mixed distribution.
9 . The non-transitory storage medium according to claim 6 , wherein the first probability distribution and the second probability distribution are derived based on a product of the observation probability for each photoelectron number based on the probability distribution of the photon number and the observation probability for each photoelectron number based on the probability distribution of the photoelectron number accompanying the reading noise of the target pixel.
10 . The non-transitory storage medium according to claim 6 , wherein the observation probability for each photoelectron number based on the probability distribution of the photon number is derived based on the digital value when the light is input to a reference pixel which is at least one pixel of the plurality of pixels.
11 . A threshold value determination device comprising:
a plurality of pixels of which each includes a photoelectric conversion element for converting input light to electric charges and an amplifier for amplifying the electric charges converted by the photoelectric conversion element and converting the electric charges to a voltage;
an A/D converter configured to convert a voltage output from the amplifier of each of the plurality of pixels to a digital value;
a first deriving unit configured to derive a provisional value of a photon number in each pixel of the plurality of pixels based on the digital value; and
a second deriving unit configured to derive threshold value data for sorting the provisional value of the photon number in a target pixel which is one of a plurality of pixels in a corresponding photon number,
wherein the second deriving unit includes:
a probability deriving unit configured to calculate a first probability distribution of the provisional value with which the photon number in the target pixel is an integer n (where n is equal to or greater than 0) and a second probability distribution of the provision value with which the photon number in the target pixel is an integer m (where m is equal to or greater than 0 and is not equal to n) based on an observation probability for each photoelectron number based on a probability distribution of the photon number and an observation probability for each photoelectron number based on a probability distribution of the photoelectron number accompanying reading noise of the target pixel; and
a threshold value determining unit configured to determine threshold value data for sorting the provisional value into the integer n and the integer m based on the first probability distribution and the second probability distribution.
12 . The threshold value determination device according to claim 11 , wherein the integer m satisfies m=n+1.
13 . The threshold value determination device according to claim 11 , wherein the observation probability for each photoelectron number based on the probability distribution of the photon number is one of a poissonian distribution, a super-poissonian distribution, a sub-poissonian distribution, a photon number distribution in a multi-mode squeezed state, a Bose-Einstein distribution, a logarithmic normal distribution, a uniform distribution, and a mixed distribution.
14 . The threshold value determination device according to claim 11 , wherein the first probability distribution and the second probability distribution are derived based on a product of the observation probability for each photoelectron number based on the probability distribution of the photon number and the observation probability for each photoelectron number based on the probability distribution of the photoelectron number accompanying the reading noise of the target pixel.
15 . The threshold value determination device according to claim 11 , wherein the observation probability for each photoelectron number based on the probability distribution of the photon number is derived based on the digital value when the light is input to a reference pixel which is at least one pixel of the plurality of pixels.
16 . A photon number resolving system comprising:
a plurality of pixels of which each includes a photoelectric conversion element for converting input light to electric charges and an amplifier for amplifying the electric charges converted by the photoelectric conversion element and converting the electric charges to a voltage;
an A/D converter configured to convert a voltage output from the amplifier of each of the plurality of pixels to a digital value;
a first deriving unit configured to derive a provisional value of a photon number in each pixel of the plurality of pixels based on the digital value; and
a second deriving unit configured to derive a photon number corresponding to the provisional value based on threshold value data for sorting the provisional value of the photon number in a target pixel which is one of a plurality of pixels in a corresponding photon number,
wherein the threshold value data is threshold value data for sorting the provisional value into an integer n (where n is equal to or greater than 0) or an integer m (where m is equal to or greater than 0 and is not equal to n) based on an observation probability for each photoelectron number based on a probability distribution of the photon number and an observation probability for each photoelectron number based on a probability distribution of the photoelectron number accompanying reading noise of the target pixel.
17 . A photon number resolving method comprising:
a step of deriving a provisional value of a photon number in each of a plurality of pixels based on digital values corresponding to the plurality of pixels output from a two-dimensional image sensor including the plurality of pixels; and
a step of deriving a photon number corresponding to the provisional value based on threshold value data for sorting the provisional value of the photon number in a target pixel which is one of a plurality of pixels in a corresponding photon number,
wherein the threshold value data is threshold value data for sorting the provisional value into an integer n (where n is equal to or greater than 0) or an integer m (where m is equal to or greater than 0 and is not equal to n) based on an observation probability for each photoelectron number based on a probability distribution of the photon number and an observation probability for each photoelectron number based on a probability distribution of the photoelectron number accompanying reading noise of the target pixel.
18 . A non-transitory storage medium that stores a photon number resolving processing program, the program causing a computer to perform a photon number resolving process based on digital values corresponding to a plurality of pixels output from a two-dimensional image sensor including the plurality of pixels, the program causing the computer to perform:
a process of deriving a provisional value of a photon number of each pixel of the plurality of pixels based on the digital values; and
a process of deriving a photon number corresponding to the provisional value based on threshold value data for sorting the provisional value of the photon number in a target pixel which is one of a plurality of pixels in a corresponding photon number,
wherein the threshold value data is threshold value data for sorting the provisional value into an integer n (where n is equal to or greater than 0) or an integer m (where m is equal to or greater than 0 and is not equal to n) based on an observation probability for each photoelectron number based on a probability distribution of the photon number and an observation probability for each photoelectron number based on a probability distribution of the photoelectron number accompanying reading noise of the target pixel.