Ground-based measurement method and system for the transmission function of the x-ray modulation telescope collimator based on square wave approximation

Abstract

The application discloses a kind of ground measurement method and system of X-ray modulation telescope sub-collimator transmittance function based on square wave approximation.The method and system of the present application give the transformation relationship between the transmittance function under the ground beam experiment condition and the transmittance function of the sub-collimator under parallel light by square wave approximation of the transmittance function of the grating, so that the complete sub-collimator transmittance function of the telescope under parallel light can be quickly obtained through the ground beam experiment.Compared with the previous method of measuring part of the transmittance function and calibrating in orbit by searching for cosmic X-ray source, the working time can be effectively compressed under the condition of ensuring the measurement accuracy, the experimental efficiency and the experimental coverage are greatly improved, the completeness of the modulation function obtained and the efficiency of the ground measurement are greatly improved, and it has considerable value in practical application.

Description

Technical Field

[0001] This invention belongs to the field of X-ray imaging telescope technology, specifically relating to the ground measurement of the photon transmittance function of a dual-grating modulated X-ray imaging telescope. Background Technology

[0002] The Hard X-ray Imaging Telescope (HXI) aboard China's Advanced Space-Based Solar Observatory (Kuafu-1) employs space modulation imaging technology and carries 91 sub-collimators. Each sub-collimator consists of a double-layer grating, which restricts the direction of incident light. By combining sub-collimators with different grating pitches and placement angles, the collimators can capture different wavenumber-angle points in frequency space, thus covering a two-dimensional frequency space. This physically performs a Fourier transform on the incident light, and the detection unit behind the sub-collimator records the number of incident photons as the measurement result. The measurement results are then inversely transformed to reconstruct the image, thereby achieving X-ray imaging observation. An important method for performing the inverse transform is to solve for the image by performing maximum likelihood estimation inversion on the transmittance functions of all sub-collimators; this is called the counting-based inversion method. In this method, the image needs to be based on accurate sub-collimator transmittance functions. If the function used is not accurate enough, it can lead to degraded image quality, deviation from the true image, or even failure to reconstruct the image. Because X-ray telescopes operate under parallel light conditions in space, while the X-ray beams obtained by X-ray optical engines on the ground are mostly not very parallel, the time required to fully measure the modulation function of the sub-collimators on the ground is too long. For large array collimators, only sub-collimators at some positions in the array can be measured, and rough calibration is performed after launch using X-ray sources in space. This has an adverse effect on both imaging quality and telescope calibration time. Summary of the Invention

[0003] In view of this, the present invention provides a ground measurement method and system for the transmittance function of a subcollimator of an X-ray modulated telescope based on the square wave approximation, which can rapidly measure the transmittance function of the subcollimator under the condition of non-parallel light of the ground X-ray beam.

[0004] To achieve the above-mentioned technical objectives, the technical solution provided by the present invention is as follows:

[0005] A ground-based method for measuring the transmittance function of an X-ray modulated telescope subcollimator based on the square wave approximation, characterized by comprising:

[0006] Step 1: Approximate the transmittance function of each single-layer grating of the sub-collimator as a square wave form. The transmittance function of the single-layer grating is the transmittance function when the incident photon energy is below 30keV.

[0007] Step 2: Perform Fourier series expansion on the transmittance function of each single-layer grating in the square wave form of the sub-collimator to obtain the transmittance function T(x, θ) in the Fourier series form;

[0008] Step 3: Perform convolution integration on the transmittance function T(x, θ) of each single-layer grating of the sub-collimator in Fourier series form to obtain the transmittance function of the sub-collimator. After determining and ignoring the negligible terms of the transmittance function of the sub-collimator under spatial parallel light conditions, the transmittance function P(θ) of the sub-collimator under the processing precision of the hard X-ray imaging telescope is obtained:

[0009]

[0010] In the formula, t t (θ) and t b (θ) represents the duty cycle of the transmitted portion of the front and rear gratings of the subcollimator at an incident angle of θ, n is the Fourier summation order, the summation range is from 1 to infinity, p is the grating pitch, L is the distance between the front and rear gratings of the subcollimator, and θ0 is the phase difference between the front and rear gratings.

[0011] Step four: Set the parameters for the ground-based beam experiment, controlling the aperture radius R > 25p. Then, use the transmittance functions T(x, θ) of the two single-layer gratings before and after the sub-collimator in Fourier series form to represent the aperture region x of the X-ray beam. 2 +y 2 ≤R 2 and light source area Integrate to obtain the integral value T′(θ) for each single-layer grating, and then use the following formula to calculate t. t (θ) and t b (θ):

[0012] T′(θ)=t(θ)(10);

[0013] The obtained t t (θ) and t b Substituting (θ) into formula (5), we obtain the transmittance function value of the target subcollimator under spatial parallel light conditions.

[0014] Based on the above solutions, further improvements or preferred solutions include:

[0015] Furthermore, in step one, the method for approximating the transmittance function of a single-layer grating as a square wave is as follows:

[0016] The origin of the monolithic grating coordinate system is defined as being located at the center of the monolithic grating, and the origin is located at the center of the grating slit. The square wave expansion formula of the monolithic grating is as follows:

[0017]

[0018] Where, x l (θ) and x r (θ) represents the left and right truncation positions of the square wave when the photon is incident at an angle of θ.

[0019] Furthermore, in step two, the transmittance function T(x, θ) in Fourier series form is:

[0020]

[0021] Furthermore, in step three:

[0022] By convolving and integrating the transmittance functions T(x, θ) of the two single-layer gratings before and after the sub-collimator in Fourier series form, the transmittance function of the sub-collimator is obtained as follows:

[0023]

[0024] In this context, a parameter or function with the subscript t indicates that it is a parameter or function of the front grating, and a parameter or function with the subscript b indicates that it is a parameter or function of the rear grating.

[0025] Based on the manufacturing precision of hard X-ray imaging telescopes The item it belongs to The term is determined to be negligible, and after ignoring it, we obtain formula (5).

[0026] Furthermore, in step four:

[0027] The parameters of an X-ray beam in ground-based measurements are defined as follows: beam length is l, and the radius of the light source is r. s The radius of the aperture is R, (x s y s () represents the coordinates of the plane containing the light source, with the origin of the coordinate system located at the center of the light source;

[0028] The integral yields T′(x, θ) as follows:

[0029]

[0030] x-axis of front and rear gratings under ground measurement conditions l (θ) and x r The change of (θ) within the integration interval is small enough that formula (6) can be approximated as:

[0031]

[0032] Based on ground-based beam experiments, as the aperture radius increases, the term...

[0033] In the case where the aperture radius R of the X-ray beam is controlled to be greater than 25p in the ground beam experiment, this term is ignored in formula (8), that is:

[0034] T′(x, θ)=t(θ)(10).

[0035] Furthermore, the method of the present invention includes an error verification process, comprising:

[0036] In step four, formula (5) is used to calculate the transmittance function P(θ) of the sub-collimator to be calculated relative to the aperture region x of the X-ray beam. 2 +y 2 ≤R 2 and light source area Integrating, we get:

[0037]

[0038] x-axis of front and rear gratings under ground measurement conditions l (θ) and x r The change of (θ) within the integration interval is small enough that formula (7) can be approximated as:

[0039]

[0040] in, J1 is a first-order Bessel-J function;

[0041] Given that L is sufficiently large under engineering conditions for a hard X-ray imaging telescope, we can ignore higher-order terms that are close to zero. and After retaining only the DC and first-order terms in formula (9), we get:

[0042]

[0043] Step 5: Using ground-based beam experiments, obtain the term t in formula (11). t (θ)t b (θ) and terms The measured values ​​are compared with the term t in the target sub-collimator transmittance function value. t (θ)t b (θ) and terms By comparing the calculated values, error data is obtained.

[0044] Furthermore, in step five, the measurement methods for the two measurements are as follows:

[0045] Adjust the aperture size so that the term in equation (11) Measure P′(θ) of the sub-collimator, at this time Get t t (θ)tb The measured value of the (θ) term;

[0046] Adjust the aperture size to make Find the local maximum value, measure P′(θ) over some intervals and subtract t. t (θ)t b (θ) term and After the item was obtained The measured value of the item.

[0047] A ground-based measurement system for the transmittance function of an X-ray modulation telescope subcollimator based on the square wave approximation, characterized by comprising the following components:

[0048] The square wave form conversion module is used to approximate the transmittance function of each single-layer grating in the sub-collimator into a square wave form, wherein the transmittance function of the single-layer grating is the transmittance function when the incident photon energy is below 30keV.

[0049] The Fourier series expansion module is used to perform Fourier series expansion on the transmittance function in the form of a single-layer grating square wave, so as to obtain the transmittance function T(x, θ) in the form of Fourier series.

[0050] The sub-collimator transmittance function construction module integrates the transmittance functions T(x, θ) in Fourier series form of the two single-layer gratings before and after the sub-collimator to obtain the transmittance function of the sub-collimator. After determining and ignoring the negligible terms of the transmittance function of the sub-collimator under the processing accuracy of the hard X-ray imaging telescope, the transmittance function P(θ) to be calculated is obtained.

[0051]

[0052] In the formula, t t (θ) and t b (θ) represents the duty cycle of the transmitted portion of the front and rear gratings of the subcollimator relative to the pitch at the incident angle θ, n is the Fourier summation order, the summation range is from 1 to infinity, p is the pitch of the grating, L is the distance between the front and rear gratings of the subcollimator, and θ0 is the phase difference between the front and rear gratings.

[0053] The transmittance function value calculation module is used for:

[0054] Using parameters from ground-based beam experiments, the transmittance function T(x, θ) in Fourier series form of each single-layer grating of the sub-collimator was applied to the aperture region x of the X-ray beam. 2 +y 2 ≤R 2 and light source area Integrate to obtain the integral value T′(θ) corresponding to each single-layer grating, where the radius of the aperture R > 25p;

[0055] Then, t is obtained using the following formula. t (θ) and t b (θ):

[0056] T′(θ)=t(θ)(10);

[0057] Then calculate t t (θ) and t b Substituting (θ) into formula (5), we obtain the transmittance function of the target subcollimator under spatial parallel light conditions.

[0058] The beneficial effects of this invention are:

[0059] This invention approximates the transmittance function of a grating using a square wave, providing a transformation relationship between the transmittance function under measurable ground-based beam experimental conditions and the transmittance function of a sub-collimator under parallel light. This allows for the rapid acquisition of the complete sub-collimator transmittance function of a telescope under parallel light through ground-based beam experiments. In existing methods, measuring the modulation capability of a sub-collimator requires significant time for meticulous measurement of its modulation curve. For large array collimators, unless months of experimental time are dedicated, it is impossible to obtain the complete transmittance function of all sub-collimators; typically, only a local transmittance function of the sub-collimators within the array is obtained. Using the method of this invention, the modulation function of the sub-collimator under parallel light can be rapidly obtained simply by measuring the DC component of a single grating under ground-based experimental conditions. Due to the nature of the grating's DC component, a large amount of measurement work can be replaced by linear interpolation. With almost no loss of accuracy, the work that previously took months can be compressed into a few days, greatly improving experimental efficiency and coverage. Attached Figure Description

[0060] Figure 1 This is a flowchart of the square wave approximation calculation of the transmittance function of the X-ray modulation telescope sub-collimator in this invention;

[0061] Figure 2 This is a diagram defining a Cartesian coordinate system based on a monolithic grating and the photon incident angle.

[0062] Figure 3 This is a schematic diagram showing the relationship between the coordinate systems of the front and rear gratings and the coordinate system of the sub-collimator;

[0063] Figure 4 The t is the value measured in a ground-based beam experiment for the gratings before and after the sub-collimator with a pitch of 76 micrometers. t (θ) and t b (θ) value;

[0064] Figure 5 The DC component t of the subcollimator with a pitch of 76 micrometers t (θ)t b (θ) Comparison of calculated and measured values;

[0065] Figure 6 The positions of the center points of the five selected regions on the DC component curve were determined to verify the modulation terms of the subcollimator with a pitch of 76 micrometers. Detailed Implementation

[0066] Example 1:

[0067] This invention's ground-based measurement method approximates the transmittance function of a telescope's sub-collimator at lower energies using a square wave, and then performs a Fourier expansion on this approximation. This reveals a specific relationship between the DC component and the higher-order Fourier modulation term in the transmittance function of the modulated telescope's sub-collimator. Based on this, the approximated square wave is integrated over a ground-based X-ray optical machine beam. Through analysis and adjustment, the conversion relationship between the transmittance function under X-ray beam and the transmittance function under parallel spatial light can be obtained. This allows for rapid and complete measurement of the transmittance function of an X-ray modulated telescope's sub-collimator under parallel light conditions via ground-based beam experiments. Simultaneously, in ground-based measurements, by measuring the DC component and the first-order Fourier modulation term of the transmittance function under X-ray machine conditions, the transmittance function under parallel spatial light can be derived, thus enabling error verification.

[0068] The following detailed description, in conjunction with specific embodiments, provides a thorough explanation of the derivation and implementation process of the ground measurement method for the transmittance function of the X-ray modulation telescope subcollimator based on the square wave approximation of this invention.

[0069] The derivation and implementation process of the ground measurement method for the transmittance function of the X-ray modulation telescope subcollimator based on the square wave approximation in this invention are as follows:

[0070] Step 1: Approximate the transmittance function of each single-layer grating of the sub-collimator as a square wave.

[0071] For solar X-rays, most incident photons have energies below 30 keV (kiloelectron volts), meaning they are approximately completely absorbed by the tungsten filament array. Therefore, the method of this invention approximates the transmittance function T(x, θ) of the telescope's sub-collimator at lower energies using a square wave, where lower energies refer to those not exceeding 30 keV.

[0072] The coordinate system of a single-layer grating is defined as a three-axis rectangular coordinate system with its origin located at the center of the grating. It is assumed that the origin of this coordinate system is also exactly at the center of the grating slit. Its xy plane is parallel to the principal plane of the grating, the x-axis is parallel to the arrangement direction of the tungsten filament array in the grating, the y-axis is parallel to the direction of extension of the individual tungsten filaments, and the z-axis is perpendicular to the xy plane and points towards the sun. The angle θ of the incident photon is the angle between its projection onto the xz plane and the positive direction of the z-axis, with clockwise as the positive direction. Figure 2 If the transmittance function T(x, θ) of a single-layer grating is expressed as a square wave, then the expansion formula of T(x, θ) in square wave form is:

[0073]

[0074] Where, x l (θ) and x r (θ) represents the left and right cutoff positions of the square wave when the photon is at an incident angle of θ, p is the pitch of the grating, and x is the horizontal coordinate variable.

[0075] The collimator of this invention comprises two parallel single-layer gratings. The coordinate system of the front grating is xyz, and the coordinate system of the rear grating is x'-y'-z'. The xy and x'-y' planes of the front and rear gratings are parallel, and the x-axis, x'-y'-y'-z'-y'-z'-z'-z'-z'-z'-y'-y'-z ... The distance. The sub-collimator coordinate system is defined as a three-axis rectangular coordinate system xy-z0 with its origin located between the front and rear gratings. The xy plane of the sub-collimator coordinate system is parallel to the xy plane of the front grating coordinate system. The x and y axes of both coordinate systems point in the same direction, and the z0 axis is collinear with the z axis. Figure 3 That is: the x-coordinate and y-coordinate of any point in space are the same in both the sub-collimator coordinate system and the front grating coordinate system; the x-coordinate x′ of any point in space in the rear grating coordinate system has the following transformation relationship with its x-coordinate x in the sub-collimator coordinate system:

[0076]

[0077] Using this transformation relationship, the square wave form of the transmittance function of the front and rear gratings, unified in the sub-collimator coordinate system, can be obtained.

[0078] Step 2: Perform Fourier series expansion on the transmittance function T(x, θ) of each single-layer grating in the sub-collimator in square wave form. Based on formula (1), the expansion formula is as follows:

[0079]

[0080] Where t(θ) is the duty cycle of the transmitted portion of the single-layer grating with respect to the pitch at an incident angle of θ, and it is also the DC component of the Fourier transform term. n is the Fourier series order, ranging from 1 to infinity (the same applies below). Step 3: Integrate the transmittance functions of the two monolithic gratings before and after the sub-collimator in the form of a Fourier series to obtain the transmittance function P(θ) of the sub-collimator, as follows:

[0081] For a sub-collimator composed of two layers of gratings, based on the Fourier expansion of formula (2), the transmittance functions of the front and rear gratings of the sub-collimator are respectively denoted as:

[0082]

[0083]

[0084] Among them, T t (x, θ), T b (x′, θ) represent the transmittance functions of the front and rear gratings, respectively, where t t (θ), t b (θ) represents the duty cycle of the transmitted portion of the front and rear gratings relative to their pitch at an incident angle of θ, respectively. lt (θ) and x rt (θ), x lb (θ) and x rb (θ) represents the left and right cutoff positions of the square wave of the front and rear gratings when the photon is at an incident angle of θ, respectively. That is, the parameter with the subscript t represents the parameter of the front grating, and the parameter with the subscript b represents the parameter of the rear grating, and so on.

[0085] Since the two layers of gratings in the sub-collimator are installed in parallel, the xy planes of the coordinate systems of the front and rear gratings and the overall coordinate system of the sub-collimator are parallel and the z-axis points in the same direction. The transmittance function P(θ) of the sub-collimator is obtained by convolution integration of the two layers of gratings as follows:

[0086]

[0087] Where L is the distance between the front and rear gratings, and θ0 is the phase difference between the front and rear gratings.

[0088] Meanwhile, as a special case of step three, considering the manufacturing precision of hard X-ray imaging telescopes, the following always applies:

[0089] when When, its effect in equation (4) can be ignored.

[0090] Since the manufacturing precision of the hard X-ray imaging telescope meets this special case, equation (4) can be written as follows under parallel light conditions:

[0091]

[0092] Step four: The X-ray beam used in the ground-based beam experiment is an isotropic, uniformly distributed, non-parallel beam stream generated by a circular extended light source constrained by a circular aperture. The beam length of this non-parallel beam stream is defined as l, and the radius of the light source is r. s The radius of the aperture is R, (x s y s Let θ be the coordinates of the plane containing the light source, with its origin at the center of the light source. The transmittance function T(x, θ) of the single-layer grating and the transmittance function P(θ) of the sub-collimator are respectively mapped to the beam stop region x. 2 +y 2 ≤R 2 and light source area Integral, we have:

[0093]

[0094]

[0095] In formulas (6) and (7), if x lt (θ), x rt (θ), x lb (θ), x rb (θ) does not change much within the integration interval, i.e., x lt (θ), x rt (θ), x lb (θ), x rb When the change of (θ) within the interval is equal to 1 / 10 or less of the change of θ within the interval, equations (6) and (7) can be approximated as:

[0096]

[0097]

[0098] in, J1 is a first-order Bessel-J function.

[0099] Under experimental testing conditions, the approximate conditions of equations (6) and (7) are generally satisfied.

[0100] When the aperture radius R is very large (R > 25p), in equation (8), the term

[0101]

[0102] If it can be ignored, then:

[0103] T′(x, θ)=t(θ) (10)

[0104] Meanwhile, under engineering conditions, the sub-collimator L of the hard X-ray imaging telescope is large enough to enable... and Since the higher-order terms are almost zero, only the DC and first-order terms are left in equation (9), therefore:

[0105]

[0106] For the X-ray machine, a larger aperture is used to ensure that R > 25p. Then, T′(x, θ) corresponding to the front and rear gratings are measured respectively. Substituting the T′(x, θ) obtained from the ground into equation (10) yields the t values ​​of the front and rear gratings. t (θ) and t b (θ), then t t (θ) and t b Substituting (θ) into equation (5), the target transmittance function value under spatial parallel light conditions can be calculated.

[0107] Error verification:

[0108] The method of this invention can verify the accuracy of the sub-collimator transmittance function value calculated in step four by using formula (11) and ground beam experiments. This is mainly achieved by comparing the measured and calculated values ​​of the DC component term and the first-order Fourier modulation term of the transmittance function.

[0109] The methods for obtaining the test items and their measured values ​​are as follows:

[0110] 1) By adjusting the size of the X-ray machine aperture, the term in equation (11) is made easier. Measure P′(θ) of the sub-collimator. Item t t (θ)t b (θ) is the DC component term in equation (5);

[0111] 2) By adjusting the size of the X-ray machine aperture, Find the local maximum value, measure P′(θ) over some intervals and subtract the term t in equation (11). t (θ)t b (θ) and terms Later, the item was obtained This term is the first term in the Fourier expansion of equation (5).

[0112] The experimental conditions for a specific ground-based beam experiment are as follows:

[0113] X-ray beam parameters: source radius is 0.2675 mm, beam length l is 18.5 m, and angle θ is -0.3° to 0.37°;

[0114] Subcollimator parameters: pitch p is 76 micrometers, distance L between the front and rear gratings is 1190 millimeters;

[0115] For this sub-collimator, to satisfy R > 25p = 1.9 mm, an aperture with a radius R of 1.915 mm is used. The transmittance functions T′(x, θ) of the front and rear gratings of the sub-collimator are measured at points under the X-ray beam. The transmittance values ​​of the front and rear gratings at these points are obtained, and t is obtained through linear interpolation. t (θ) and t b The complete function curve of (θ) (see) Figure 4 ):

[0116] t t (θ)=0.246θ+0.329,-0.3°<θ<0.37° (1′)

[0117]

[0118] In the above formula, θ is in radians; at this time, the interpolated t t (θ) and t b Substituting the curve (θ) into equation (5), the numerical form of the transmittance function P(θ) of the sub-collimator under parallel light is obtained as follows:

[0119]

[0120] The following tests were then performed:

[0121] Project 1: By selecting an aperture radius R of 1.915 mm, thus... To measure its DC component t t (θ)t b (θ), the DC component t will be measured t (θ)t b The comparison results are as follows: (θ) is compared with P(θ) calculated by equation (3′). Figure 5 As shown, the two remain consistent within the allowable error range (not greater than 0.02).

[0122] Project Two: By selecting an aperture radius R of 1.585 mm, thus... The maximum value of 0.0645 was obtained locally. The value is then 0.768; based on the DC component t t (θ)t b The shape of (θ) selects five intervals for measuring its modulation capability (see...). Figure 6 ), after deducting t t (θ)t b (θ) term and The term is followed by the Fourier first-order modulation term. Here we give the amplitude of this modulation term. The fitting results of the measured values ​​at these five points are compared with the calculated values. The two are basically consistent within the allowable error range (including the local error of the points, which is generally no greater than 0.2).

[0123] -0.197 0.143 0.143 0.001 0.172 0.176 0.148 0.182 0.178 0.222 0.188 0.162 0.295 0.194 0.184

[0124] By measuring and comparing the DC component with the first-order Fourier modulation term, it can be determined that the transmittance function P(θ) of the sub-collimator obtained in the above steps is accurate enough and can be used as a calibration reference.

[0125] This invention provides, for the first time, a method for rapidly and completely measuring the transmittance function of a subcollimator of an X-ray modulation telescope using a ground-based X-ray machine. The complete parallel light modulation function of the telescope can be obtained on the ground. Compared with the previous method of measuring part of the transmittance function and calibrating by searching for cosmic X-ray sources in orbit, this method has significantly improved the completeness of the obtained modulation function and the efficiency of ground measurement, and has considerable value in practical applications.

[0126] Example 2:

[0127] A ground-based method system for measuring the transmittance function of an X-ray modulated telescope subcollimator based on the square wave approximation includes the following components:

[0128] The square wave form conversion module is used to approximate the transmittance function of each single-layer grating in the sub-collimator into a square wave form, wherein the transmittance function of the single-layer grating is the transmittance function when the incident photon energy is below 30keV.

[0129] The Fourier series expansion module is used to perform Fourier series expansion on the transmittance function in the form of a single-layer grating square wave, so as to obtain the transmittance function T(x, θ) in the form of Fourier series.

[0130] The sub-collimator transmittance function construction module integrates the transmittance functions T(x, θ) in Fourier series form of the two single-layer gratings before and after the sub-collimator to obtain the transmittance function of the sub-collimator. After determining and ignoring the negligible terms of the transmittance function of the sub-collimator under the processing accuracy of the hard X-ray imaging telescope, the transmittance function P(θ) to be calculated is obtained.

[0131]

[0132] In the formula, t t (θ) and t b (θ) represents the duty cycle of the transmitted portion of the front and rear gratings of the subcollimator relative to the pitch at the incident angle θ, n is the Fourier summation order, the summation range is from 1 to infinity, p is the pitch of the grating, L is the distance between the front and rear gratings of the subcollimator, and θ0 is the phase difference between the front and rear gratings.

[0133] The transmittance function value calculation module is used for:

[0134] Using parameters from ground-based beam experiments, the transmittance function T(x, θ) in Fourier series form of each single-layer grating of the sub-collimator was applied to the aperture region x of the X-ray beam. 2 +y 2 ≤R 2 and light source area Integrate to obtain the integral value T′(θ) corresponding to each single-layer grating, where the radius of the aperture R > 25p;

[0135] Then, t is obtained using the following formula. t (θ) and t b (θ):

[0136] T′(θ)=t(θ)(10);

[0137] Then calculate t t (θ) and t b Substituting (θ) into formula (5), we obtain the transmittance function of the target subcollimator under spatial parallel light conditions.

[0138] This embodiment and Embodiment 1 are two designs under the same overall inventive concept, and the derivation process of the algorithm used is the same as that in Embodiment 1. Those skilled in the art will recognize that the algorithm steps described in Embodiment 1 can be implemented using electronic hardware or a combination of computer software and electronic hardware. For those skilled in the art, any improvements and modifications made without departing from the principles of this invention should be considered within the scope of protection of this invention.

[0139] The above are merely preferred embodiments of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions that fall within the scope of the present invention are within the scope of protection of the present invention.

Claims

1. A ground-based method for measuring the transmittance function of an X-ray modulated telescope subcollimator based on the square wave approximation, characterized in that, include: Step 1: Approximate the transmittance function of each single-layer grating of the sub-collimator as a square wave form. The transmittance function of the single-layer grating is the transmittance function when the incident photon energy is below 30keV. Step two: Perform a Fourier series expansion on the transmittance function of each single-layer grating in the sub-collimator in square wave form to obtain the transmittance function in Fourier series form. ; Step 3: Transmittance function of each single-layer grating of the collimator in Fourier series form. By performing convolution integration, the transmittance function of the sub-collimator is obtained. After determining and ignoring the negligible terms of the sub-collimator's transmittance function under the processing precision of the hard X-ray imaging telescope, the transmittance function of the sub-collimator under spatial parallel light conditions is obtained. : In the formula, and The front and rear gratings of the sub-collimator are respectively located at... The duty cycle of the transmitted portion relative to the pitch at the incident angle. To find the Fourier summation order, the summation range is from 1 to infinity. The pitch of the grating. L The distance between the front and rear gratings of the sub-collimator. The phase difference between the front and rear gratings; Specifically: Transmittance functions of the two single-layer gratings before and after the collimator in Fourier series form Performing convolution integration yields the following transmittance function for the sub-collimator: In this context, a parameter or function with the subscript t indicates that it is a parameter or function of the front grating, and a parameter or function with the subscript b indicates that it is a parameter or function of the rear grating. Based on the manufacturing precision of hard X-ray imaging telescopes, , and the item it belongs to After determining that the term is negligible, we obtain formula (5) by ignoring the term. Step four: Set the parameters for the ground-based beam experiment and control the aperture radius. The transmittance functions of the two single-layer gratings before and after the sub-collimator in Fourier series form The aperture regions of the X-ray beam were respectively... and light source area Integrate to obtain the integral value corresponding to each single-layer grating. Then, the following formula is used to obtain... and : The obtained and Substituting into formula (5), we obtain the transmittance function value of the target subcollimator under spatial parallel light conditions.

2. The ground measurement method for the transmittance function of an X-ray modulation telescope subcollimator based on the square wave approximation according to claim 1, characterized in that, In step one, the method for approximating the transmittance function of a single-layer grating as a square wave is as follows: The origin of the monolithic grating coordinate system is defined as being located at the center of the monolithic grating, and the origin is located at the center of the grating slit. The square wave expansion formula of the monolithic grating is: in, and For square waves in photons The left and right truncation positions at the angle of incidence.

3. The ground measurement method for the transmittance function of an X-ray modulation telescope subcollimator based on the square wave approximation according to claim 2, characterized in that, In step two, the transmittance function in Fourier series form for: 。 4. The ground measurement method for the transmittance function of an X-ray modulation telescope subcollimator based on the square wave approximation according to claim 1, characterized in that, In step four: The parameters of an X-ray beam in ground measurements are defined as follows: beam length is... The radius of the light source is The radius of the aperture is , The coordinates of the plane containing the light source are given, with the origin of the coordinate system located at the center of the light source. The result after integration for: Based on front and rear gratings under ground measurement conditions and The change within the integration interval is small enough that formula (6) can be approximated as: Based on ground-based beam experiments, as the aperture radius increases, the term... In the case of controlling the aperture radius of the X-ray beam in ground-based beam experiments Then, this term is ignored in formula (8), that is: 。 5. The ground measurement method for the transmittance function of an X-ray modulation telescope subcollimator based on the square wave approximation according to claim 4, characterized in that, An error verification process is established, including: In step four, the transmittance function of the sub-collimator to be calculated is obtained using formula (5). Aperture region of X-ray beam and light source area Integrating, we get: Based on front and rear gratings under ground measurement conditions and The change within the integration interval is small enough that formula (7) can be approximated as: in, , , It is a first-order Bessel-J function; Based on the engineering conditions of hard X-ray imaging telescopes L Large enough to ignore higher-order terms that are close to 0. and After retaining only the DC and first-order terms in formula (9), we get: Step 5: Obtain the formula using ground-based beam experiments. In and The measured values ​​are compared with the term in the target sub-collimator transmittance function value. and By comparing the calculated values, error data is obtained.

6. The ground measurement method for the transmittance function of an X-ray modulation telescope subcollimator based on the square wave approximation according to claim 5, characterized in that, In step five, the measurement methods for the two measurements are as follows: Adjust the aperture size so that the term in equation (11) Measuring sub-collimator ,at this time ,get The measured value of the item; Adjust the aperture size to make Find the local maximum value and measure over some intervals. And deduct Item and After the item was obtained The measured value of the item.

7. A ground-based measurement system for the transmittance function of an X-ray modulated telescope subcollimator based on the square wave approximation, characterized in that, It includes the following components: The square wave form conversion module is used to approximate the transmittance function of each single-layer grating in the sub-collimator into a square wave form, wherein the transmittance function of the single-layer grating is the transmittance function when the incident photon energy is below 30keV. The Fourier series expansion module is used to perform Fourier series expansion on the transmittance function in the form of a single-layer grating square wave, obtaining the transmittance function in Fourier series form. ; The sub-collimator transmittance function construction module constructs the transmittance functions of the two single-layer gratings before and after the sub-collimator in Fourier series form. By integrating, the transmittance function of the sub-collimator is obtained. After determining and ignoring the negligible terms of the transmittance function of the sub-collimator under the processing precision of the hard X-ray imaging telescope, the transmittance function of the sub-collimator to be calculated is obtained. : In the formula, and The front and rear gratings of the sub-collimator are respectively located at the incident angle. The duty cycle of the lower light-transmitting section relative to the pitch. To find the Fourier summation order, the summation range is from 1 to infinity. The pitch of the grating. L The distance between the front and rear gratings of the sub-collimator. The phase difference between the front and rear gratings; Specifically: Transmittance functions of the two single-layer gratings before and after the collimator in Fourier series form Performing convolution integration yields the following transmittance function for the sub-collimator: In this context, a parameter or function with the subscript t indicates that it is a parameter or function of the front grating, and a parameter or function with the subscript b indicates that it is a parameter or function of the rear grating. Based on the manufacturing precision of hard X-ray imaging telescopes, , and the item it belongs to After determining that the term is negligible, we obtain formula (5) by ignoring the term. The transmittance function value calculation module is used for: Using parameters from ground-based beam experiments, the transmittance function in Fourier series form of each monolayer grating of the sub-collimator is expressed. The aperture regions of the X-ray beam were respectively... and light source area Integrate to obtain the integral value corresponding to each single-layer grating. The radius of the aperture ; Then, the following formula is used to obtain... and : Then obtain and Substituting into formula (5), we obtain the transmittance function of the target subcollimator under the condition of spatial parallel light.

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