Estimation method, estimation program, and estimation device

Abstract

An estimation device for estimating a conversion coefficient that is the ratio of the number of photoelectrons generated in a pixel when light enters the pixel and an electrical signal amount outputted according to the number of photoelectrons, the device comprising: an acquisition unit that acquires a plurality of data groups each including the electrical signal amount of each of a plurality of pixels when light enters the plurality of pixels; and a calculation unit that calculates the conversion coefficient for each of the pixels from the plurality of data groups, on the basis of a likelihood function that represents the likelihood of the conversion coefficient corresponding to the output electrical signal amount.

Description

[Technical Field]

[0001] This disclosure relates to estimation methods, estimation programs, and estimation apparatus. [Background technology]

[0002] For example, Patent Documents 1 and 2 describe a photon counting device using a CMOS (Complementary Metal Oxide Semiconductor) image sensor. In this device, when photons are input to a photoelectric conversion element, electrons generated according to the number of input photons are stored as electric charge. The electric charge stored in the photoelectric conversion element is converted into a voltage and amplified by an amplifier. The voltage output from the amplifier is converted into a digital value by an A / D converter. In the photon counting device, the number of photons in the pixels constituting the image sensor is determined based on the digital value output from the A / D converter.

[0003] Furthermore, Non-Patent Document 1 describes a technique for measuring gain in a CMOS image sensor. In this technique, a histogram of photon count values ​​is generated for each pixel, and the gain is calculated based on the peak interval of the histogram. [Prior art documents] [Patent Documents]

[0004] [Patent Document 1] International Publication No. 2019 / 102636 [Patent Document 2] International Publication No. 2019 / 102637 [Non-patent literature]

[0005] [Non-Patent Document 1] Starkey, Dakota A., and Eric R. Fossum. "Determining conversion gain and read noise using a photon-counting histogram method for deep sub-electron read noise image sensors." IEEE Journal of the Electron Devices Society 4.3 (2016): 129-135. [Overview of the Initiative] [Problems that the invention aims to solve]

[0006] When calculating gain (conversion coefficient) based on the peak interval of a histogram, it is necessary to be able to separate the peaks of the histogram. Therefore, to calculate the gain accurately, it is thought that data of, for example, 10,000 frames or more would be required.

[0007] One aspect of this disclosure is the provision of an estimation method that can reduce the amount of data required to estimate (calculate) the conversion coefficients. [Means for solving the problem]

[0008] One example of an estimation method is a method for estimating a conversion coefficient, which is the ratio of the number of photoelectrons generated in a pixel when light is input to the pixel to the amount of electrical signal output according to the number of photoelectrons, and comprises the steps of: acquiring multiple data sets containing the amount of electrical signal for each of the multiple pixels when light is input to each of the multiple pixels; and calculating the conversion coefficient for each of the multiple pixels from the multiple data sets based on a likelihood function that represents the likelihood of the conversion coefficient corresponding to the output electrical signal amount.

[0009] One example of an estimation program is a program that estimates a conversion coefficient, which is the ratio of the number of photoelectrons generated in a pixel when light is input to the pixel to the amount of electrical signal output according to the number of photoelectrons. The program causes a computer to perform an acquisition process that acquires multiple data sets containing the amount of electrical signal for each of the multiple pixels when light is input to each of the multiple pixels, and a calculation process that calculates the conversion coefficient for each of the multiple data sets from the multiple data sets based on a likelihood function that represents the likelihood of the conversion coefficient corresponding to the output electrical signal amount.

[0010] One example of an estimation device is an estimation device that estimates a conversion coefficient, which is the ratio of the number of photoelectrons generated in a pixel when light is input to the pixel to the amount of electrical signal output according to the number of photoelectrons, and comprises an acquisition unit that acquires multiple data sets containing the amount of electrical signal for each of the multiple pixels when light is input to each of the multiple pixels, and a calculation unit that calculates the conversion coefficient for each of the multiple pixels from the multiple data sets based on a likelihood function that represents the likelihood of the conversion coefficient corresponding to the output electrical signal amount.

[0011] In one example estimation method, estimation program, and estimation device, a likelihood function is used to estimate the conversion coefficients, thereby reducing the amount of data required for estimation. For example, if the data set consists of image data reflecting the electrical signal amount at each pixel, the number of frames required for estimation of the conversion coefficients can be reduced.

[0012] The likelihood function may be defined by referring to the probability density distribution of the electrical signal. The probability density distribution of the electrical signal may include a function that derives the electrical signal from the number of photoelectrons corresponding to the amount of light, with a conversion coefficient as a parameter.

[0013] The probability density distribution of electrical signal quantities may include a probability density distribution that takes into account readout noise at multiple pixels. Considering readout noise can improve the accuracy of the probability density distribution.

[0014] The probability density distribution of the electrical signal amount may include the probability distribution followed by the number of photoelectrons. In this configuration, the conversion coefficient can be accurately estimated whether the light with a constant average photon number is irradiated or the average photon number changes with time.

[0015] Let the probability distribution followed by the number of photoelectrons n be q (n), and when the conversion coefficient is α, let the function that determines the electrical signal amount x for the number of photoelectrons n be x = f(n; α). Let the electrical signal amount x in the i-th data group when the number of photoelectrons is n i follow the probability density distribution of r(x i ; n, α, [f]). When this is the case, the likelihood function L(α) is

Equation

[0016] When the average photon number is λ and the readout noise is σ, the likelihood function is

Equation

[0017] When the readout noise is σ, the likelihood function is

Equation

[0018] The probability density distribution r(x i ; n, α, [f]) has a degree of freedom ν as

Equation

Equation

Advantages of the Invention

[0019] According to one aspect of this disclosure, an estimation method can be provided that can reduce the amount of data required to estimate the conversion coefficients. [Brief explanation of the drawing]

[0020] [Figure 1] Figure 1 shows the configuration of an example photon counting device. [Figure 2] Figure 2 shows an example of how a photon counting device is used. [Figure 3] Figure 3 shows an example of how a photon counting device is used. [Figure 4] Figure 4 is a flowchart illustrating the estimation method. [Figure 5] Figure 5 shows a recording medium containing the program for an example of a photon counting device. [Figure 6] Figure 6 shows a histogram of the simulation results of digital values ​​derived by an example of a photon counting device. [Figure 7] Figure 7 shows a histogram of the simulation results of the number of photons derived by an example of a photon counting device. [Figure 8] Figure 8 shows a histogram of digital values ​​derived by an example of a photon counting device. [Figure 9] Figure 9 is a histogram showing the correction values ​​for digital values ​​derived by an example of a photon counting device. [Figure 10] Figure 10 shows a histogram of the simulation results of digital values ​​derived by another example of a photon counting device. [Modes for carrying out the invention]

[0021] The embodiments will be described in detail below with reference to the drawings. For convenience, substantially identical elements will be denoted by the same reference numerals, and their descriptions may be omitted. In the following description, a photon counting device will be described, but the estimation device of this disclosure may be a photon counting device, a part of a photon counting device, or a system including part or all of a photon counting device. In the following description, photon counting includes both counting the number of photoelectrons generated at each pixel of an image sensor, and counting the number of photons considering the quantum efficiency (QE) of the image sensor.

[0022] Figure 1 shows the configuration of an example photon counting device. As shown in Figure 1, an example photon counting device comprises a CMOS image sensor 10 as a two-dimensional image sensor and a computer (control device) 20 connected to the CMOS image sensor 10. The CMOS image sensor 10 includes a plurality of pixels 11 and an A / D converter 15. The plurality of pixels 11 are arranged in two dimensions; that is, the plurality of pixels 11 are arranged in the row direction and the column direction. Each pixel 11 has a photodiode (photoelectric conversion element) 12 and an amplifier 13. The photodiode 12 stores electrons (photoelectrons) generated by the input of photons as electric charge. The amplifier 13 converts the charge stored in the photodiode 12 into a voltage and amplifies the converted voltage. The amplified voltage is transferred to vertical signal lines 16 line by line (row by row) by switching a selection switch 14 of each pixel 11. A CDS (correlated double sampling) circuit 17 is arranged on each vertical signal line 16. The CDS circuit 17 removes noise that varies between pixels and temporarily stores the transferred voltage.

[0023] The A / D converter 15 converts the voltage output from each amplifier 13 in multiple pixels 11 into a digital value (pixel value). The A / D converter 15 may be provided in each pixel 11. In this embodiment, the A / D converter 15 converts the voltage stored in the CDS circuit 17 into a digital value. The converted digital values ​​are output to the computer 20. For example, the digital values ​​may be sent to a horizontal signal line (not shown) by switching column selection and output to the computer 20. In this way, when a photon is input to each pixel 11 of the CMOS image sensor 10, it outputs a digital value to the computer 20 corresponding to the number of input photons (number of photoelectrons generated). Note that when the voltage amplified by the amplifier 13 is read out, random noise called readout noise is generated within the amplifier 13.

[0024] The computer 20 is physically composed of a storage device such as RAM and ROM, a processor (arithmetic circuit) such as a CPU and GPU, and a communication interface. Examples of the computer 20 include a personal computer, a cloud server, a smart device (smartphone, tablet terminal, etc.), a microcomputer, and an FPGA (field-programmable gate array). The computer 20 functions as an estimation unit 21, a storage unit 22, a conversion unit 23, a data processing unit 24, and a control unit 25 by executing a program stored in the storage device using the computer system's processor. The computer 20 may be located inside the camera device, including the CMOS image sensor 10. The computer 20 may also be located outside the camera device.

[0025] A display device 26 and an input device 27 may be connected to the computer 20. The display device 26 is, for example, a display capable of displaying photon counting results obtained by the computer 20. The input device 27 may be a keyboard, mouse, etc., for the user to input measurement conditions. The display device 26 and the input device 27 may also be touchscreens. The display device 26 and the input device 27 may be included in the computer 20. Alternatively, the display device 26 and the input device 27 may be provided in a camera device including a CMOS image sensor 10.

[0026] The estimation unit 21 estimates the gain (conversion coefficient), which is the ratio of the number of photoelectrons generated at a pixel when a predetermined number of photons (light intensity) of light is input to the pixel, to the digital value (electrical signal amount) output according to the number of photoelectrons. The gain estimation by the estimation unit 21 may be performed, for example, in the manufacturing process of the photon counting device 1. Alternatively, the gain estimation by the estimation unit 21 may be performed, for example, at any time desired by the user of the photon counting device 1. Details of the processing by the estimation unit 21 will be described later.

[0027] The memory unit 22 stores data for converting digital values ​​output from the CMOS image sensor 10 into photoelectron counts. For example, the memory unit 22 stores the gain of each of the multiple pixels 11 as a lookup table. The gain may be a value estimated by the estimation unit 21. The memory unit 22 may also store the readout noise of each of the multiple pixels 11 as a lookup table.

[0028] The digital value [DN] output from the A / D converter 15 described above is given by the following equation when it is linear with respect to the number of photoelectrons.

number

[0029] As shown in this formula, in one example, the digital value is assumed not to include the offset value. When the digital value includes the offset value, the digital value is given by the following formula. Therefore, when the digital value includes the offset value, the value obtained by subtracting the offset value from the output digital value should be considered as the digital value in this specification.

number

[0030] The offset value [DN] is shown as a digital value output when no light is input. Therefore, the offset value is obtained by acquiring multiple digital values ​​from multiple dark images acquired by the CMOS image sensor 10 when no light is input, and averaging the acquired digital values ​​for each pixel 11. If the digital value includes the offset value, the storage unit 22 may store each of the offset values ​​for the multiple pixels 11 acquired as described above as a lookup table.

[0031] The conversion unit 23 refers to a table stored in the storage unit 22 and converts the digital values ​​for each of the multiple pixels 11 output from the A / D converter 15 into photoelectron counts. The conversion unit 23 may also derive the photoelectron count for each pixel 11 by dividing the digital value by the gain, as shown in the following formula. If the digital value includes an offset value, the photoelectron count may be derived by subtracting the offset value from the measured digital value and dividing the result by the gain.

number

[0032] The conversion unit 23 may obtain an integer number of photoelectrons by truncating the decimal part of the derived number of photoelectrons and rounding it. In this case, for example, the number of photoelectrons may be obtained as an integer by setting a predetermined threshold range for the number of photoelectrons derived by the above formula. For example, the threshold range corresponding to 5 photoelectrons is 4.5e or more and less than 5.5e. In one example, the conversion unit 23 can obtain the number of photons by dividing the number of photoelectrons by the quantum efficiency for each pixel 11. When the quantum efficiency is 100%, the number of photoelectrons and the number of photons will be the same. For convenience, the explanation will assume that the conversion unit 23 derives the number of photoelectrons, but the number of photoelectrons may be read as the number of photons.

[0033] The data processing unit 24 creates a two-dimensional image (photon count identification image) showing the number of photoelectrons in each pixel 11 based on the number of photoelectrons output from the conversion unit 23. For example, the two-dimensional image may be an image in which each pixel is drawn with brightness corresponding to the number of photoelectrons. The created two-dimensional image can be output to the display device 26. The data processing unit 24 may also create a histogram, which is a plot of the number of pixels against the number of photoelectrons. The control unit 25 can comprehensively control each function unit of the computer 20 and the CMOS image sensor 10.

[0034] The estimation unit 21 will now be described in detail. One example of the estimation unit 21 includes an acquisition unit 21a and a calculation unit 21b. The acquisition unit 21a performs an acquisition process to acquire multiple data sets, each containing a digital value for each of the multiple pixels 11 when light is input to each of the multiple pixels 11. The data sets may be acquired, for example, as image data (optical image) in which each pixel 11 is associated with a digital value. The acquisition unit 21a acquires multiple frames of such image data. The acquisition unit 21a also acquires multiple digital values ​​corresponding to each pixel 11 based on the image data of the multiple frames acquired.

[0035] Figures 2 and 3 illustrate an example of how a photon counting device can be used. For example, as shown in Figure 2, in the photon counting device 1, image data may be acquired when light output from the light source 30 is input to the CMOS image sensor 10. Alternatively, as shown in Figure 3, an object 40, such as an observation sample, may be placed in the optical path between the light source 30 and the CMOS image sensor 10. That is, the acquisition unit 21a may acquire image data of the object 40.

[0036] The calculation unit 21b performs a calculation process to calculate the gain for each of the multiple pixels 11 from multiple data sets based on a likelihood function for gain. The likelihood function for gain is a function that represents the likelihood of the gain corresponding to the multiple digital values ​​output for each pixel 11.

[0037] The likelihood function is defined by referring to the probability density distribution (probability model) of the digital value. The probability density distribution of the digital value may reflect the electrical characteristics of the CMOS image sensor 10. Furthermore, the probability density distribution of the digital value may reflect the characteristics of the light input to the CMOS image sensor 10. For example, let q(n) be the probability distribution followed by the number of photoelectrons n[e], and let x=f(n;α) be the function that determines the digital value x[DN] for the number of photoelectrons n when the gain is α[DN / e], and let the digital value x in the i-th data group when the number of photoelectrons is n be the digital value x i The probability density distribution that follows is r(x i Given n, α, and [f], the general likelihood function L(α) can be expressed by the following equation. [f] means that r is defined using the function f.

number

[0038] Furthermore, when the average number of photons in the irradiated light changes over time, the probability distribution that follows the number of photoelectrons n[e] is q. iWhen (n) is used, the gain α [DN / e] can be accurately estimated based on the likelihood function L(α) represented by the following formula. In the following formula, assuming that the probability distribution q i (n) that does not depend on i can be written as q(n), the likelihood function L(α) is represented by the above formula ([Equation 9]) when the average number of photons of the irradiated light is constant.

Equation

[0039] The probability density distribution of a digital value in one example may be the convolution (composite product) of the probability density distribution of the digital value considering the readout noise of the amplifier 13 in the pixel 11 when the number of photoelectrons is n and the probability distribution followed by the number of photoelectrons n. For example, assuming that the average number of photons is λ [photon], the probability distribution q(n) is the Poisson distribution with the average number of photons λ, the readout noise is σ [e-rms], the function f(n;α) is the linear function f(n;α)=αn, and the probability density distribution r(x i ;n,α,[f]) is the normal distribution with the mean f(n;α) and the standard deviation σ, the likelihood function L(α) is represented by the following formula.

Equation

[0040] The calculation unit 21b calculates the most probable gain α from the likelihood function by so-called maximum likelihood estimation. In one example, the gain α that maximizes the log-likelihood function derived from the likelihood function is calculated. A log-likelihood function in one example is shown below.

Equation

[0041] The readout noise σ may be obtained using a known method. Readout noise can be defined as gain fluctuations. Therefore, the standard deviation of the digital value may be obtained for each pixel 11 in multiple (e.g., 100 or more frames) dark images, and the obtained standard deviation may be used as the readout noise σ. Note that the readout noise σ does not need to be known with high precision.

[0042] If the average photon number λ is a known value, that value may be used. Similar to the readout noise σ, the average photon number λ does not need to be known with high precision. Therefore, if the average photon number λ is unknown, the calculation unit 21b may determine the average photon number λ using, for example, an approximate value α' of the gain α. For example, for N pixels in a predetermined range, the average photon number λ can be calculated as an approximate value based on the following formula. Note that the N pixels may be all pixels. Also, the following formula does not take into account the nonlinearity of the digital value.

number

[0043] Furthermore, if the average number of photons λ is unknown, the average number of photons may be defined by the following formula.

number

[0044] In this case, the calculation unit 21b may calculate the gain α that maximizes the log-likelihood function expressed by the following equation.

number

[0045] For example, when obtaining an approximate value α' of the gain α, the mean value and variance of the digital value of the target pixel may be calculated for each frame with the same average number of photons, the mean value may be plotted on the x-axis and the variance on the y-axis, and the reciprocal of the slope of the approximating line may be used as the approximate value α'. If the measurement is performed without changing the amount of light, the value obtained by dividing the variance of the digital value by the mean value of the digital value may be used as the approximate value α'. The approximate gain values ​​α' of each pixel 11 obtained in this way may be stored in the storage unit 22.

[0046] When estimating the gain α based on the log-likelihood function, the log-likelihood function with respect to α should be maximized. If an approximate value α' of α has been determined, the calculation unit 21b may use α' as the initial value and maximize the log-likelihood function using a gradient method such as Newton's method. When the likelihood function has a local optimum and an approximate value α' of α has not been determined, the gradient method cannot be used. In this case, it is necessary to exhaustively search for the α that maximizes the log-likelihood function within a predetermined range. The calculation unit 21b may estimate the gain α for all pixels by performing such processing for each pixel 11. The estimated gain α for each pixel 11 is associated with each pixel 11 and stored in the storage unit 22. The conversion unit 23 then performs the estimation of the number of photoelectrons by referencing the gain α thus estimated.

[0047] If the above process for estimating the gain α is performed for, for example, several thousand by several thousand pixels, the computational load can become enormous. In one example, the calculation unit 21b processes the estimation of the gain α at high speed by performing parallel computation. For example, when searching for 10 search points for 10 pixels, high-speed processing is possible by evaluating the j-th search point of the i-th pixel in the (i + j × 10)th thread.

[0048] Note that the likelihood function described above is just one example. Other likelihood functions may be used in the gain α estimation process in the estimation unit 21. For example, the likelihood function may be expressed by the following equation, assuming that the probability distribution q(n) followed by the number of photoelectrons is constant.

number

[0049] Also, the probability density distribution r(x i If n, α, [f]) ​​is given by equation [Equation 18] using a t-distribution with degrees of freedom ν given by equation [Equation 17], the likelihood function may also be given by equation [Equation 19], where the probability distribution q(n) is a Poisson distribution with mean photon number λ, and the function f(n;α) is a linear function αn.

number

number

number

[0050] Figure 4 is a flowchart showing an example of the process by which the estimation unit 21 estimates the gain α. As shown in Figure 4, the estimation unit 21 acquires digital values ​​(step S1). That is, the estimation unit 21 acquires multiple data sets containing the digital values ​​for each of the multiple pixels 11 when light is input to the multiple pixels 11. In one example, the estimation unit 21 acquires multiple image data showing the light intensity distribution associated with each pixel 11 and its digital value, while light is irradiated from the light source 30. For example, the number of image data acquired by the estimation unit 21 may be around 100 to 1000 frames. The light intensity distribution formed by the light source 30 may or may not be uniform in space and time.

[0051] Next, the estimation unit 21 estimates the gain α, which is a conversion coefficient (step S2). That is, the estimation unit 21 calculates the gain α for each of the multiple pixels 11 from the digital values ​​of the multiple image data based on the likelihood function that represents the likelihood of the gain α corresponding to the output digital value. If the light emitted from the light source 30 can be controlled, the average number of photons λ may be specified based on information about the controlled light. The estimation unit 21 stores the estimated gain for each of the pixels in the storage unit 22.

[0052] Figure 5 is a block diagram showing a recording medium 100 containing a processing program P1 (estimation program) that causes a computer to perform a photon counting process, including the gain α estimation process described above. The processing program P1 stored in the recording medium 100 comprises an acquisition processing module P21a, a calculation processing module P21b, a storage processing module P22, a conversion processing module P23, a data processing module P24, and a control module P25. The functions realized by executing the acquisition processing module P21a, calculation processing module P21b, storage processing module P22, conversion processing module P23, data processing module P24, and control module P25 are the same as the functions of the acquisition unit 21a, calculation unit 21b, storage unit 22, conversion unit 23, data processing unit 24, and control unit 25 described above.

[0053] The processing program P1 is recorded in the program recording area of ​​a computer-readable recording medium 100. The recording medium 100 may be a non-temporary recording medium. The recording medium 100 is composed of recording media such as CD-ROM, DVD, ROM, or semiconductor memory. The processing program P1 may be provided via a communication network as a computer data signal superimposed on a carrier wave.

[0054] Figure 6 shows a histogram of the simulation results of digital values ​​derived by an example photon counting device. The horizontal axis represents the digital value, and the vertical axis represents the count. In Figure 6, the average number of photons λ is 80. The average gain α is assumed to be 7 [DN / e]. The standard deviation of the gain α is assumed to be 0.02. The readout noise σ is 1.8 [DN]. This readout noise value corresponds to approximately 0.26 [e-rms] in terms of the number of photoelectrons. The number of pixels is 32 × 32. The number of frames in the acquired image data (data set) is 1000. As shown in Figure 6, in the histogram of digital values, the separation of peaks (peaks and valleys) becomes less clear as the digital value increases.

[0055] Figure 7 shows the effectiveness of the gain estimated based on the digital values ​​in the example in Figure 6. In Figure 7, the digital values ​​are converted to the number of photons based on the gain estimated using the method described above, and a histogram of the converted number of photons is shown. The horizontal axis represents the number of photons, and the vertical axis represents the count. It can be seen that the separation of peaks is clearer in the histogram of the number of photons shown in Figure 7 compared to the histogram of digital values ​​shown in Figure 6. The likelihood function used to estimate the gain in the example in Figure 7 is given by the following equation.

number

[0056] Figure 8 shows a histogram of measured digital values ​​derived from an example of a photon counting device. The horizontal axis represents the digital value, and the vertical axis represents the count. Figure 8 shows three patterns with average photon numbers λ of 14, 39, and 84. The pixel count is 1630 × 1630. The number of frames in the acquired image data (data set) is 1000. In the histogram of digital values ​​shown in Figure 8, the separation of peaks becomes less clear as the digital value increases. Furthermore, the greater the average photon number λ, the less clear the separation of peaks becomes.

[0057] Figure 9 shows the effectiveness of the gain estimated based on the digital values ​​in the example in Figure 8. In Figure 9, the digital values ​​are converted to photoelectron counts based on the gain α estimated by the method described above, and the converted photoelectron counts are converted back to digital values ​​using the average value of gain α. Figure 9 shows the histogram of the reconverted digital values. The horizontal axis is the reconverted digital values, and the vertical axis is the count. Gain α was estimated by the method described above based on image data acquired when the average number of photons λ was 84. This gain α was used to reconvert the three histograms with average number of photons λ of 14, 39, and 84. It can be seen that the peak separation is clearer in the histogram of the reconverted digital values ​​shown in Figure 9 compared to the histogram of digital values ​​shown in Figure 8.

[0058] Figure 10 shows the histogram of the simulation results of the digital values ​​derived by the photon counting device (before estimation) and the histogram of the re-converted digital values ​​(after estimation). The re-converted digital values ​​are obtained by converting the original digital values ​​to the number of photoelectrons based on the gain α estimated by the method described above, and then converting the converted number of photoelectrons back into digital values ​​using the average value of the gain α. The horizontal axis is the digital value, and the vertical axis is the count. The average number of photons λ is 100. The average gain α is assumed to be 7 [DN / e]. The standard deviation of the gain α is assumed to be 0.05. The readout noise σ is 0.25 × gain. That is, when the average gain α is 7 [DN / e], the average readout noise σ is 1.75 [DN]. The number of pixels is 32 × 32. The number of frames in the acquired image data (data set) is 500. The likelihood function used to estimate the gain in the example in Figure 10 is given by the following equation.

number

[0059] As shown in Figure 10, the re-transformed histogram shows clearer peak separation compared to the original digital histogram. Thus, the likelihood function used in the estimation method can be defined by referencing various models, as long as it is based on the probability model of the output digital values.

[0060] As described above, the photon counting device 1, as an example of an estimation device, comprises an acquisition unit 21a that acquires multiple digital values ​​of the pixel 11 when light is input to the pixel 11, and a calculation unit 21b that calculates the gain of the pixel from the multiple data based on a likelihood function that represents the likelihood of the gain corresponding to the output digital value.

[0061] In such a photon counting device 1, the amount of data required for gain estimation can be reduced by using a likelihood function for gain estimation. For example, if the data is image data reflecting the digital value of each pixel, the number of frames required for gain estimation can be reduced.

[0062] The likelihood function may be defined by referring to the probability density distribution of the digital value. The probability density distribution of the digital value is the probability distribution q(n) followed by the number of photoelectrons n and the probability density distribution r(x) followed by the digital value when the number of photoelectrons is n. i It may include n, α, [f]). In such a likelihood function, the probability distribution of the number of photoelectrons and the probability density distribution of the digital value when the number of photoelectrons is determined are referenced, so the gain can be estimated with high accuracy.

[0063] The probability density distribution of the digital values ​​may include a probability density distribution that takes into account the readout noise of the amplifier 13 at multiple pixels 11. Considering the readout noise can improve the accuracy of the probability density distribution.

[0064] The probability distribution q(n) that follows the number of photoelectrons n may be constant. In this case, even if there are fluctuations in the amount of light during measurement, the influence of these fluctuations on the gain estimation can be mitigated.

[0065] Although the embodiments have been described in detail above with reference to the drawings, the specific configuration is not limited to these embodiments.

[0066] As illustrated by the examples of several probability density distributions for digital values, probability density distributions do not need to be truly accurate. For example, a symmetrical distribution may be adopted when the distribution is inherently asymmetric, an approximate distribution different from the distribution of the actual physical phenomenon may be adopted, or distributions that cannot be strictly omitted may be omitted.

[0067] As an example of a likelihood function, we showed an example where the function f(n;α) is a linear function f(n;α) = αn. However, if the digital value [DN] is nonlinear with respect to the number of photoelectrons, the function f(n;α) becomes f(n;α) = α0n + α1n 2It can be a quadratic function like this, or a function of degree three or higher. In this way, when the digital value [DN] is nonlinear with respect to the number of photoelectrons, the inverse function n=f(n;α) of the function x=f(n;α) that determines the digital value x[DN] for the number of photoelectrons n when the gain is α[DN / e] is n=f -1 The number of photoelectrons n can be determined from (x;α). In this case, the average number of photons λ can be determined from the following formula.

number

[0068] In the above embodiment, the dark count is not considered. However, if the dark count is too large to ignore, the average number of photons may be the sum of the true average number of photons and the average number of dark counts. [Explanation of Symbols]

[0069] 1...Photon counting device, 11...Pixel, 21...Estimation unit, 21a...Acquisition unit, 21b...Calculation unit.

Claims

1. An estimation method for estimating a conversion coefficient which is the ratio of the number of photoelectrons generated in a pixel when light is input to the pixel to the amount of electrical signal output according to the number of photoelectrons, The steps include acquiring multiple data sets, each containing the amount of electrical signal for each of the multiple pixels when the light is input to each of the multiple pixels, The process includes the step of calculating the conversion coefficient for each of the multiple pixels from a plurality of data sets based on a likelihood function that represents the likelihood of the conversion coefficient corresponding to the output electrical signal amount, Let q i(n) be the probability distribution followed by the number of photoelectrons n, let x = f(n; α) be the function that determines the electrical signal amount x for the number of photoelectrons n when the conversion coefficient is α, and let r(x i; n, α, [f]) ​​be the probability density distribution followed by the electrical signal amount x i in the i-th data group when the number of photoelectrons is n, then the likelihood function L(α) is, [Math 1] An estimation method represented by the following:

2. The estimation method according to claim 1, wherein the likelihood function is defined with reference to the probability density distribution of the electrical signal quantity.

3. The estimation method according to claim 2, wherein the probability density distribution of the electrical signal quantity includes a probability density distribution that takes into account the readout noise in the plurality of pixels.

4. The estimation method according to claim 2, wherein the probability density distribution of the electrical signal quantity includes the probability distribution followed by the number of photoelectrons.

5. The likelihood function described above is given by, where λ is the average number of photons and σ is the readout noise, [Math 2] The estimation method according to any one of claims 1 to 4, as represented by the following:

6. The likelihood function mentioned above, when the readout noise is σ, [Math 3] The estimation method according to any one of claims 1 to 4, as represented by the following:

7. The probability density distribution shown above is r(x ｉ n, α, [f]) ​​has degrees of freedom ν [Math 4] It is defined using the t-distribution of the aforementioned degrees of freedom ν, The aforementioned likelihood function is, [Math 5] The estimation method according to any one of claims 1 to 4, as represented by the following:

8. An estimation program for estimating a conversion coefficient which is the ratio of the number of photoelectrons generated in a pixel when light is input to the pixel to the amount of electrical signal output according to the number of photoelectrons, An acquisition process that acquires multiple data sets, each containing the amount of electrical signal for each of the multiple pixels when the light is input to each of the multiple pixels, The computer is made to perform a calculation process that calculates the conversion coefficient for each of the multiple pixels from a plurality of data sets based on a likelihood function that represents the likelihood of the conversion coefficient corresponding to the output electrical signal amount. Let q i(n) be the probability distribution followed by the number of photoelectrons n, let x = f(n; α) be the function that determines the electrical signal amount x for the number of photoelectrons n when the conversion coefficient is α, and let r(x i; n, α, [f]) ​​be the probability density distribution followed by the electrical signal amount x i in the i-th data group when the number of photoelectrons is n, then the likelihood function L(α) is, [Math 6] An estimation program represented by [this].

9. The estimation program according to claim 8, wherein the likelihood function is defined with reference to the probability density distribution of the electrical signal quantity.

10. The estimation program according to claim 9, wherein the probability density distribution of the electrical signal quantity includes a probability density distribution that takes into account readout noise in the plurality of pixels.

11. The estimation program according to claim 9, wherein the probability density distribution of the electrical signal quantity includes the probability distribution followed by the number of photoelectrons.

12. The likelihood function described above is given by, where λ is the average number of photons and σ is the readout noise, 【Number 7】 An estimation program according to any one of claims 8 to 11, as represented by the above.

13. The likelihood function described above is given by, where λ is the average number of photons and σ is the readout noise, [Number 8] An estimation program according to any one of claims 8 to 11, as represented by the above.

14. The likelihood function mentioned above, when the readout noise is σ, [Number 9] An estimation program according to any one of claims 8 to 11, as represented by the above.

15. The probability density distribution shown above is r(x ｉ n, α, [f]) ​​has degrees of freedom ν [Number 10] It is defined using the t-distribution of the aforementioned degrees of freedom ν, The aforementioned likelihood function is, [Math 11] An estimation program according to any one of claims 8 to 11, as represented by the above.

16. An estimation device for estimating a conversion coefficient which is the ratio of the number of photoelectrons generated in a pixel when light is input to the pixel to the amount of electrical signal output according to the number of photoelectrons, An acquisition unit that acquires multiple data sets, each containing the amount of electrical signal for each of the multiple pixels when the light is input to each of the multiple pixels, The system includes a calculation unit that calculates the conversion coefficient for each of the multiple pixels from a plurality of data sets based on a likelihood function that represents the likelihood of the conversion coefficient corresponding to the output electrical signal amount, Let q i(n) be the probability distribution followed by the number of photoelectrons n, let x = f(n; α) be the function that determines the electrical signal amount x for the number of photoelectrons n when the conversion coefficient is α, and let r(x i; n, α, [f]) ​​be the probability density distribution followed by the electrical signal amount x i in the i-th data group when the number of photoelectrons is n, then the likelihood function L(α) is, [Math 12] An estimation device represented by [the symbol].

17. The estimation apparatus according to claim 16, wherein the likelihood function is defined with reference to the probability density distribution of the electrical signal quantity.

18. The estimation apparatus according to claim 17, wherein the probability density distribution of the electrical signal quantity includes a probability density distribution that takes into account the readout noise in the plurality of pixels.

19. The estimation apparatus according to claim 17, wherein the probability density distribution of the electrical signal quantity includes the probability distribution followed by the number of photoelectrons.

20. The likelihood function described above is given by, where λ is the average number of photons and σ is the readout noise, [Number 13] An estimation device according to any one of claims 16 to 19, as represented by the following:

21. The likelihood function described above is given by, where λ is the average number of photons and σ is the readout noise, [Number 14] An estimation device according to any one of claims 16 to 19, as represented by the following:

22. The likelihood function mentioned above, when the readout noise is σ, [Number 15] An estimation device according to any one of claims 16 to 19, as represented by the following:

23. The probability density distribution shown above is r(x ｉ n, α, [f]) ​​has degrees of freedom ν [Number 16] It is defined using the t-distribution of the aforementioned degrees of freedom ν, The aforementioned likelihood function is, [Number 17] An estimation device according to any one of claims 16 to 19, as represented by the following:

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